http://2012.igem.org/wiki/index.php?title=Special:Contributions&feed=atom&limit=500&target=Lbwang&year=&month=2012.igem.org - User contributions [en]2021-04-11T20:04:11ZFrom 2012.igem.orgMediaWiki 1.16.0http://2012.igem.org/Team:NTU-Taida/sandboxTeam:NTU-Taida/sandbox2013-05-08T11:09:32Z<p>Lbwang: /* Passion */</p>
<hr />
<div><h1>Whoa! This is a sandbox</h1><br />
<html><br />
<script type="text/javascript"<br />
src="http://cdn.mathjax.org/mathjax/latest/MathJax.js?config=TeX-AMS-MML_HTMLorMML"><br />
</script><br />
</html><br />
What should we do now?<br />
<br />
<ul><br />
<li><br />
'snoozing'<br /><br />
''snoozing''<br /><br />
'''snoozing'''<br /><br />
'''''snoozing'''''<br/><br />
"snoozing"<br />
</li><br />
<li><br />
sleeping<br />
</li><br />
<li><br />
wiki-ing<br />
</li><br />
</ul><br />
<br />
==Intonation==<br />
The way we talk is always full of different combinations of '''intonation''', thus making our speech or chat attractive. A speech without appropriate intonation may easily make listeners bored. Although intonation is somehow different among languages, the basic concept remains the same: putting your emotions into your words, making the words fill with power, and being confident to yourself. <br />
<br />
==Talking speed==<br />
This is also an important part when delivering a speech. With an appropriate speed, you can overwhelm listeners with your charm. An average talking speed is about 150 words per minute in English.<br />
<br />
==Eye contact==<br />
This is self-evident, so there's no need to explain it. Be calm, act naturally, get ready to dominate the floor!!<br />
<br />
==Passion==<br />
According to Dr. Chenistine, the formula for passion is: <br />
<br />
$$ Passion=\frac{(love-hatred) \times willingness}{Tiredness} $$<br />
<br />
===Mind===<br />
This is totally absurd~{{:Team:NTU-Taida/template:hahaha}}<br />
<br />
{{:Team:NTU-Taida/template/CSStime|challenge=TEMPLATE}}<br />
<p id="te"><br />
[http://ntumed96.wikidot.com/faq:how-to 語法教學3]<br />
</p><br />
<br />
==Picture==<br />
<br />
1.'''Wiki style'''<br />
[[File:single picture.jpg|300px|thumb|center|igem2012 asia jamboree]]<br />
[[File:try.jpg|300px|thumb|center|try]]<br />
<br />
2.'''Wiki style with field'''<br />
{|align='center'<br />
|[[File:left picture.jpg|250px|thumb|center|2012]]<br />
|[[File:right picture.jpg|250px|thumb|center|2013]]<br />
|}<br />
<br />
3.'''Html template'''<br />
{{:Team:NTU-Taida/template/picture|file=html.jpg |width=350px |describe=Landscape in Hualien}}<br />
<br />
==Table==<br />
1.'''Example'''<br />
<html><br />
<style><br />
<br />
table {<br />
background-color: white;<br />
color: blue;<br />
margin-bottom: 0.5em;<br />
padding: 0.25em;<br />
text-align: center;<br />
border-width: 3px;<br />
border-left-width: 3px;<br />
border-right-width: 3px;<br />
border-color: red;<br />
margin-bottom: 7px;<br />
}<br />
</style><br />
<table class='table table-bordered'><br />
<thead><br />
<tr><br />
<th>1</th><br />
<th>2</th><br />
<th>3</th><br />
</tr><br />
</thead><br />
<tbody><br />
<tr><br />
<td>4</td><br />
<td>5</td><br />
<td>6</td><br />
</tr> <br />
<tr><br />
<td>7</td><br />
<td>8</td><br />
<td>9</td> <br />
</tr><br />
<tr><br />
<td>10</td><br />
<td>11</td><br />
<td>12</td><br />
<br />
</tr><br />
</tbody><br />
</table><br />
</html><br />
<br />
2.'''Example2'''<br />
{| border="1" cellpadding="5" cellspacing="0" |-<br />
| 列1 || 列2 || 列3<br />
|-<br />
| rowspan="2" | A<br />
| colspan="2" style="text-align: center;" | B<br />
|-<br />
| C<br />
| D<br />
|-<br />
| E<br />
| rowspan="2" colspan="2" style="text-align: center;" | F<br />
|-<br />
| G<br />
|-<br />
| colspan="3" style="text-align: center;" | H<br />
|}<br />
<br />
===Reference===<br />
<ol><br />
<li>Sam Tsai, ''et al.'' (2013) The tutorial of wiki writing. ''Let's practice in sandbox.'' AOP, published online 8 May 2013, 1-1000.</li><br />
<ol><br />
<br />
<br />
<br />
[http://2012.igem.org/wiki/index.php?title=Team:NTU-Taida/sandbox&action=submit EDIT SANDBOX]</div>Lbwanghttp://2012.igem.org/Team:NTU-Taida/Modeling/2D-3D-CombinedTeam:NTU-Taida/Modeling/2D-3D-Combined2013-01-03T14:34:25Z<p>Lbwang: /* X_fadR */</p>
<hr />
<div>{{:Team:NTU-Taida/Templates/Header}}{{:Team:NTU-Taida/Templates/Navbar}}{{:Team:NTU-Taida/Templates/Sidebar|Title=2D &amp; 3D Combined Model}}{{:Team:NTU-Taida/Templates/ContentStart}}<br />
{{:Team:NTU-Taida/Templates/BSHero|Title=2D &amp; 3D Combined Model|Content=<p></p>}}<br />
<br />
== Overview ==<br />
<p style="text-indent: 2em;"><br />
With the single cell model, fatty acid reaction-absorption model, and system analysis, we have verified the '''filter function''' of our circuit, simulated the '''real physiological fatty acid level at intestinal wall''', and '''adjust our filter threshold to fit to the real condition'''. Next, we want to combine them together and see what would happen when we put cells in the intestine after a fatty meal.<br />
</p><br />
<p style="text-indent: 2em;"><br />
The combined model is composed of three different sections. 2D combined model simulates the GLP1 response of Pepdex E-coli cells after the food intake in the x-y cross-sectional plane. 2D Cell population response model further considers the possible uneven concentration of fatty acid along the z-axis due to non-uniform distribution of lipase and simulates how the quorum sensing system assists our system to overcame this possible limitation and enhance the response. Finally, '''3D Cell population response model incorporates all the consideration to generate a full model to visualize the dynamic behavior of our system.'''<br />
</p><br />
<br />
==2D Combined Model==<br />
So far, we have the spatial-temporal concentration of fatty acid, and cells with suitable threshold. In this model, we want to see what would happen when we put cells in the intestine after a meal. <br />
<br />
[[File:NTU-Taida-Model-Combined-fig1.png|600px|center|thumb|Figure 1]]<br />
<br />
We achieve this by further coupling the single cell ODEs (with parameters adjusted by system analysis) locally to the fatty acid reaction-absorption model at the intestinal wall, as shown in Figure 2.<br />
<br />
[[File:NTU-Taida-Model-Combined-fig2.png|600px|center|thumb|Figure 2]]<br />
<br />
Besides to see the cell response when combined with the environmental input, we also want to simulate the prolonged effect of the quorum sensing module with physiological input. Therefore, we simulate system with and without quorum sensing modules and compare their results.<br />
<br />
===Spatial-temporal Model Equations ===<br />
The equations used in our 2D combined model mainly come from the reaction-absorption model and the single cell model. The following three equations are the same as those in the reaction-absorption model, which simulates the change in fatty acid concentration in time and space. <br />
<br />
{{:Team:NTU-Taida/Templates/Eq|num=1|eq=<br />
\frac{d fat}{d t} = -\frac{k_{cat}[E]_t\cdot[S]}{K_m + [S]} <br />
}}<br />
<br />
{{:Team:NTU-Taida/Templates/Eq|num=2|eq=<br />
\frac{d FA}{d t} = 3 \cdot \frac{k_{cat}[E]_t\cdot[S]}{K_m + [S]} <br />
}}<br />
<br />
{{:Team:NTU-Taida/Templates/Eq|num=3|eq=<br />
J=(C_1 - C_2)(D_{FA}/d) <br />
}}<br />
<br />
Other equations in the model are almost the same as those derived in our single cell model, with slightly difference in those for AHL, which will be discussed thoroughly in the 2D Cell population response model. The equations are shown as below.<br />
<br />
{{:Team:NTU-Taida/Templates/Eq|num=4|eq=<br />
\frac{d FadR}{d t} = \alpha_{FadR} - \gamma_{FadR} \cdot FadR <br />
}}<br />
<br />
$$X_{FadR} = \frac{FadR \cdot \beta_{FA}^{n2}}{FA^{n2} + \beta_{FA}^{n2}}$$<br />
{{:Team:NTU-Taida/Templates/Eq|num=5|eq=<br />
}}<br />
<br />
$$\frac{dTetR_1}{dt} = \frac{\alpha_{TetR_1} \cdot {\beta_{FadR}^{n1}}}{\beta_{FadR}^{n1} + X_{FadR}^{n1}} - \gamma_{TetR_1} \cdot TetR_1 $$<br />
{{:Team:NTU-Taida/Templates/Eq|num=6|eq=<br />
}}<br />
<br />
$$\frac{d TetR_2}{d t} = \frac{\alpha_{TetR_2} \cdot R^{n3}}{\beta_R^{n3} + R^{n3}} - \gamma_{TetR_2} \cdot TetR_2$$<br />
{{:Team:NTU-Taida/Templates/Eq|num=7|eq=<br />
}}<br />
<br />
$$\frac{d LuxI}{d t} = \frac{\alpha_{LuxI} \cdot \beta_{FadR}^{n1}}{\beta_{FadR}^{n1} + X_{FadR}^{n1}} - \gamma_{LuxI} \cdot LuxI$$<br />
{{:Team:NTU-Taida/Templates/Eq|num=8|eq=<br />
}}<br />
<br />
$$\frac{\partial^2 AHL}{\partial x^2} + \frac{\partial^2 AHL}{y^2} - \frac{1}{D_{AHL}}\cdot \frac{\partial AHL}{\partial t} = 0$$<br />
{{:Team:NTU-Taida/Templates/Eq|num=9|eq=<br />
}}<br />
<br />
$$R(AHL) = - \gamma_{AHL_{ext}} \cdot AHL + cd(k_{s1}LuxI - k_{s0}AHL)$$<br />
{{:Team:NTU-Taida/Templates/Eq|num=10|eq=<br />
}}<br />
<br />
$$\frac{d R}{d t} = \rho (LuxR)^2(AHL_i)^2 - \gamma_R \cdot R$$<br />
{{:Team:NTU-Taida/Templates/Eq|num=11|eq=<br />
}}<br />
<br />
$$\frac{d LacI}{d t} = \frac{\alpha_{LacI}}{1 + (\frac{TetR_1 + TetR_2}{\beta_{TetR}})^{n5}} - \gamma_{LacI} \cdot LacI$$<br />
{{:Team:NTU-Taida/Templates/Eq|num=12|eq=<br />
}}<br />
<br />
$$\frac{d GLP1}{d t} = \frac{\alpha_{GLP1}}{1 + (\frac{LacI}{\beta_{LacI}})^{n6}} - \gamma_{GLP1} \cdot GLP1$$<br />
{{:Team:NTU-Taida/Templates/Eq|num=13|eq=<br />
}}<br />
<br />
<br />
For the control group without the quorum sensing module, we simply discard the terms related to quorum sensing system in the ODE set.<br />
<br />
===Results===<br />
<br />
{| align='center'<br />
| {{:Team:NTU-Taida/Templates/Vid|num=1.1 Fatty acid concentration|width=350px|name=NTU-Taida-Model-Combined-Image5.gif}}<br />
| {{:Team:NTU-Taida/Templates/Vid|num=1.2 Closer look of fatty acid concentration|width=350px|name=NTU-Taida-Model-Combined-Image8.gif}}<br />
|}<br />
{| align='center'<br />
| {{:Team:NTU-Taida/Templates/Vid|num=2.1 GLP-1 expression in system without quorum sensing|width=350px|name=NTU-Taida-Model-Combined-Image4.gif}}<br />
| {{:Team:NTU-Taida/Templates/Vid|num=2.2 Closer look ofGLP-1 expression in system without quorum sensing|width=350px|name=NTU-Taida-Model-Combined-Image7.gif}}<br />
|}<br />
{| align='center'<br />
| {{:Team:NTU-Taida/Templates/Vid|num=3.1 GLP-1 expression in system with quorum sensing|width=350px|name=NTU-Taida-Model-Combined-Image3.gif}}<br />
| {{:Team:NTU-Taida/Templates/Vid|num=3.2 Closer look at GLP-1 expression in system with quorum sensing|width=350px|name=NTU-Taida-Model-Combined-Image6.gif}} <br />
|}<br />
<br />
Video 1 shows the spatial temporal concentration change of fatty acid. Video 2 and three show the corresponding spatial temporal response of GLP-1 expression in system without and with quorum sensing module, respectively.<br />
<br />
We can see from the videos that the fatty acid concentration at the intestinal wall first increases rapidly, turning on the circuits in the cells and resulting in GLP-1 expression at the intestinal wall. Then due to the absorption of fatty acid, the concentration gradually falls and the GLP-1 concentration started to decrease. Notice that the GLP1 expression in the system with Quorum sensing, shown in Video 3, lasts longer than that of the system without quorum sensing, shown in Video 2. Consistent to the single cell model, the system with QS has more prolonged response compared to the one without it.<br />
<br />
==Cell Population Response Model==<br />
<br />
We have assumed that fat distributes uniformly along the z-axis in the lumen after a meal in the previous models. However, in real situation in human body, lipase only exists in certain segments of the intestine. Therefore, fat hydrolysis will only take place in those segments and there will be no fatty acid produced outside these segments, as shown in Figure 3. Cells residing in the segments without lipase activity can only sense the fatty acid diffused from the source segments. Because AHL diffuses faster than fatty acid, we incorporate the quorum sensing system to enable faster recruitment of more bacteria to express GLP-1 in regions without lipase.<br />
<br />
Quorum sensing module enables cells to communicate with each other, as the uneven distribution of fatty acid in the intestines may cause gaps in individual detection. Cells with the quorum sensing module can respond to food intake event as long as their neighboring cells have detected fatty acid, enhancing the overall response to the food intake (Figure 4). However, the communication between cells via AHL can’t be seen when only viewing a single cell. Therefore, we construct spatial temporal models with COMSOL Multiphysics in order to gain insights into the influence of cell-cell communication mediated via the quorum sensing module on the overall GLP1 expression.<br />
<br />
[[File:NTU-Taida-Model-Combined-fig3.png|600px|center|thumb|Figure 3]]<br />
[[File:NTU-Taida-Model-Combined-fig4.png|600px|center|thumb|Figure 4]]<br />
<br />
==2D Cell Population Response Model==<br />
We start our effort with a 2D spatial temporal model. When E.coli cells colonize the intestine, they tend to attach onto the intestinal walls instead of distributing evenly throughout the intestine lumen. Therefore, we first view our system as a two dimensional system, with the modeling plane in the x-z (or either y-z) dimension.<br />
<br />
===Geometry Design===<br />
[[File:NTU-Taida-Model-Combined-fig5.png|600px|center|thumb|Figure 5]]<br />
<br />
With this in mind, we construct a plane in 2D geometry and couple the ODEs derived in our single cell model to simulate the presence of cells.<br />
<br />
To model the effect of quorum sensing, we establish an uneven distribution of fatty acid by giving a constant concentration source of fatty acid in the middle of our modeled plane, as shown in Figure 6. There are no cells within the circular fatty acid source. As time goes on, fatty acids diffuse from the source and establish a concentric gradient. To see the effect of quorum sensing mechanism on overall GLP1 expression in a cell population with uneven distributed fatty acid input, we model cells with and without quorum sensing and compare their spatial –temporal GLP1 expression.<br />
[[File:NTU-Taida-Model-Combined-fig6.png|600px|center|thumb|Figure 6]]<br />
<br />
===Spatial-temporal Model Equations===<br />
The first equation used in our model describes the free diffusion of fatty acids from the central source.<br />
<br />
$$\frac{\partial^2 FA}{\partial x^2} + \frac{\partial^2 FA}{\partial z^2} - \frac{1}{D_{FA}} \frac{\partial FA}{\partial t} = 0$$<br />
{{:Team:NTU-Taida/Templates/Eq|num=14|eq=<br />
}}<br />
<br />
Other equations in the model are almost the same as those derived in our single cell model, except for the ones for AHL. For AHL, we have to set up a partial differential equation describing both the diffusion and the reaction event of AHL. We assume that AHL diffusion into and out of cells is fast and do not model this diffusion process explicitly. Therefore, in contrast to the single-cell model, we only use one species called AHL instead of an internal AHL concentration AHLi and an external AHL concentration AHLe. <br />
<br />
For the reaction term of AHL, we first discard the terms describing the diffusion into and out of the cell membrane in the ODEs of AHLi and AHLe in the single cell model. <br />
As previously mentioned, we assume that the diffusion AHL diffusion into and out of cells is fast. Therefore, we simply account for the diffusion of AHL across cell membrane by multiplying the intracellular AHLi terms by the relative cell density, which will be described in the next section. With these considerations, we combine the two equations of AHLi and AHLe (Eq. 15 and Eq. 16) into one reaction equation (Eq. 17 ).<br />
<br />
{{:Team:NTU-Taida/Templates/Eq|num=15|eq=\frac{d AHL_i}{d t} = ks1 \cdot LuxI - ks0 \cdot AHL_i - \eta (AHL_i - AHL_e)<br />
}}<br />
<br />
{{:Team:NTU-Taida/Templates/Eq|num=16|eq=\frac{d AHL_e}{d t} = - kse \cdot AHL_e + \eta_{Ext} (AHL_i - AHL_e)<br />
}}<br />
<br />
$$R (AHL) = - \gamma_{AHL_{ext}} \cdot AHL + cd (k_{s1} \cdot LuxI - k_{s0} \cdot AHL)$$<br />
{{:Team:NTU-Taida/Templates/Eq|num=17|eq=<br />
}}<br />
<br />
With the help of COMSOL Multiphysics, we can consider both the diffusion and reaction terms of AHL by giving the diffusion (Eq. 14) and reaction (Eq. 17) equations above, without the need to solve the explicit PDE of AHL.<br />
<br />
The diffusion of AHL is modeled by a free diffusion equation.<br />
<br />
$$ \frac{\partial^2 AHL}{\partial x^2} + \frac{\partial^2 AHL}{\partial z^2} - \frac{1}{D_{AHL}} \frac{\partial AHL}{\partial t} = 0$$<br />
{{:Team:NTU-Taida/Templates/Eq|num=18|eq=<br />
}}<br />
<br />
Other equations in the model are the same as those derived in our single cell model.<br />
For the control group without the quorum sensing module, we discard the terms related to quorum sensing system in the ODE set.<br />
<br />
==Relative Cell density==<br />
The relative cell density is defined as the ratio of the total area E.coli cells occupy to the area of the intestinal wall. By multiplying the intracellular AHL synthesis and degradation terms by the relative cell density, we assume that as a cell synthesizes or degrades AHL, the addition or reduction of AHL molecules is dispersed evenly through the neighboring area. (Mind that the diffusion of these AHL molecules on global scale is still governed by the free diffusion equation.)<br />
<br />
We calculated the relative cell density by assuming there are 1014 bacteria cells residing in the intestine, which has a total surface area of 200 m2. Thus, the average cell density is 5*1011 cells/m2. We can measure the surface area of each individual cell by multiplying their length by their width, giving a surface area of 10-12 m2 per cell. Multiplying the surface area per cell and the average cell density gives the area density of total cells as 0.5. <br />
Since 99% of the gut flora consists of 30-40 species of bacteria, we can assume that each of the common types contribute to approximately 1% of the total surface area of the intestine. Considering the clustering effect of cells, we assume that some regions would have much higher cell densities than others, such that the uneven distribution may result in a tenfold fluctuation in cell density. We hypothesize that the relative cell density in our model could be as high as 0.1.<br />
<br />
Cell density has dramatic effect on the overall effect of quorum sensing system, as supported by a recent study investigating the synchronization of repressilators by quorum sensing mechanisms [1]. Therefore, we also model our system with different cell densities, as can be seen in the results.<br />
<br />
===Results===<br />
To see the effect of quorum sensing mechanism on overall GLP1 expression in a cell population with uneven distributed fatty acid input, we model cells with and without quorum sensing and compare their spatial - temporal GLP1 expression, with relative cell density of 0.1<br />
The results show that species which are not regulated by the quorum sensing module, such as FA, X_FadR, and TetR1, show no difference in the spatial temporal expression pattern between system with and without the quorum sensing system. <br />
<br />
However, species affected by the quorum sensing module, such as LacI and GLP1, show striking difference in their spatial temporal concentration pattern. Within the given time span, systems with a quorum sensing module produces GLP1 over a broader spatial region, resulting in more total GLP1. <br />
<br />
===Species unregulated by the quorum sensing module===<br />
<br />
====FA====<br />
<br />
{| align='center'<br />
| {{:Team:NTU-Taida/Templates/Vid|num=4.1 |width=350px|name=NTU-Taida-Model-Combined-video4-1.gif}}<br />
| {{:Team:NTU-Taida/Templates/Vid|num=4.2 |width=350px|name=NTU-Taida-Model-Combined-video4-2.gif}}<br />
|}<br />
<br />
====X_fadR====<br />
{| align='center'<br />
| {{:Team:NTU-Taida/Templates/Vid|num=5.1 |width=350px|name=NTU-Taida-Model-Combined-video5-1.gif}}<br />
| {{:Team:NTU-Taida/Templates/Vid|num=5.2 |width=350px|name=NTU-Taida-Model-Combined-video5-2.gif}}<br />
|}<br />
====TetR1====<br />
{| align='center'<br />
| {{:Team:NTU-Taida/Templates/Vid|num=6.1 |width=350px|name=NTU-Taida-Model-Combined-video6-1.gif}}<br />
| {{:Team:NTU-Taida/Templates/Vid|num=6.2 |width=350px|name=NTU-Taida-Model-Combined-video6-2.gif}}<br />
|}<br />
<br />
===Species regulated by the quorum sensing module===<br />
====LacI====<br />
<br />
{|align="center"<br />
| {{:Team:NTU-Taida/Templates/Vid|num=7-1 |width=350px|name=NTU-Taida-Model-Combined-video7-1.gif}}<br />
| {{:Team:NTU-Taida/Templates/Vid|num=7-2 |width=350px|name=NTU-Taida-Model-Combined-video7-2.gif}}<br />
|}<br />
<br />
The expression of LacI is inhibited by TetR proteins, and therefore is regulated by the quorum sensing module. Although the concentration of TetR1 is the same in systems with and without quorum sensing, cells with quorum sensing produce TetR2 as the output of the quorum sensing module and therefore result in overall more total TetR proteins. Thus, the repression of LacI is more significant in systems with the quorum sensing module.<br />
<br />
====GLP1====<br />
{|align="center"<br />
| {{:Team:NTU-Taida/Templates/Vid|num=8-1 |width=350px|name=NTU-Taida-Model-Combined-video8-1.gif}}<br />
| {{:Team:NTU-Taida/Templates/Vid|num=8-2 |width=350px|name=NTU-Taida-Model-Combined-video8-2.gif}}<br />
|}<br />
<br />
As the expression of GLP1 is repressed by LacI proteins, GLP1 also displays different spatial-temporal concentration pattern between the two systems. With quorum sensing module, the system produces more GLP1 overall.<br />
<br />
===Effect of cell density===<br />
<br />
Relative cell density plays a critical role in determining whether we can see a significant difference between systems with and without quorum sensing. We simulated the spatial-temporal response of GLP1 of four systems, all of them with the quorum sensing module but with relative cell densities of 0.2, 0.1, and 0.01, respectively. <br />
<br />
Then we compare their response to that of system without quorum sensing to determine if there exists a threshold of cell density, below which the effect of quorum sensing module is unperceivable. <br />
<br />
{|align="center"<br />
| {{:Team:NTU-Taida/Templates/Vid|num=9-1 cd = 0.2 |width=280px|name=NTU-Taida-Model-Combined-video9-1.gif}}<br />
| {{:Team:NTU-Taida/Templates/Vid|num=9-2 cd = 0.1 |width=280px|name=NTU-Taida-Model-Combined-video9-2.gif}}<br />
| {{:Team:NTU-Taida/Templates/Vid|num=9-3 cd = 0.05 |width=280px|name=NTU-Taida-Model-Combined-video9-3.gif}}<br />
|}<br />
<br />
{|align="center"<br />
| {{:Team:NTU-Taida/Templates/Vid|num=9-4 cd = 0.01 |width=280px|name=NTU-Taida-Model-Combined-video9-4.gif}}<br />
| {{:Team:NTU-Taida/Templates/Vid|num=9-5 without quorum sensing module |width=280px|name=NTU-Taida-Model-Combined-video9-5.gif}}<br />
|}<br />
<br />
<br />
<br />
We can see from Video 9 that the system with a relative cell density of 0.2 differs most with the system without the quorum sensing module. The system with a relative cell density of 0.1 shows moderate difference. The system with a relative cell density of 0.05 displays very subtle difference. There is no difference between the system with a relative cell density of 0.01 and the system with no quorum sensing module. Therefore, the threshold of relative cell density may lie between 0.05 and 0.01.<br />
<br />
==3D Cell population response model==<br />
<br />
Finally, we construct a full 3D model, combing the consideration on the x-y plane and the x-z plane. Our goal is to simulate the effect of non-uniform production of fatty acid due to the spatially limited lipase activity. We modeled the intestine by a cylindrical tube, with a fat source limited to the z=0 plane, to simulate the situations similar to that shown in Figure 7, and examine the effect of Quorum sensing. <br />
<br />
[[File:NTU-Taida-Model-Combined-fig7.png|600px|center|thumb|Figure 7]]<br />
<br />
The equations used are the same as those in the 2D cell population response model, but with the equations governing diffusions changing from the two-dimension form to their three-dimension counterparts.<br />
<br />
{|align="center"<br />
| {{:Team:NTU-Taida/Templates/Vid|num=10 Full Thumbnails |width=400px|name=image24.gif}}<br />
| {{:Team:NTU-Taida/Templates/Vid|num=10 Enlargement |width=400px|name=image26.gif}}<br />
|}<br />
<br />
{|align="center"<br />
| {{:Team:NTU-Taida/Templates/Vid|num=11 Full Thumbnails |width=400px|name=image25.gif}}<br />
| {{:Team:NTU-Taida/Templates/Vid|num=11 Enlargement |width=400px|name=image27.gif}}<br />
|}<br />
<br />
<br />
<br />
Video 10 shows the result of system without quorum sensing module while Video 11 shows the result of system with quorum sensing module. From Video 10 and 11, we can see that GLP-1 starts to be expressed at similar time point at the intestinal wall on the z=0 plane. However, the GLP-1 expression spreads faster along the z-axis in system with quorum sensing.<br />
<br />
==Reference==<br />
<ol id='Ref'><br />
<li>Jordi Garcia-Ojalvo , Michael B. Elowitz, and Steven H. Strogatz , Modeling a synthetic multicellular clock: Repressilators coupled by quorum sensing, pnas,2004</li><br />
</ol><br />
<!--EOF--><br />
{{:Team:NTU-Taida/Templates/ContentEnd}}{{:Team:NTU-Taida/Templates/Footer|ActiveNavbar=Modeling, #nav-Modeling-Combined}}</div>Lbwanghttp://2012.igem.org/Team:NTU-Taida/Modeling/2D-3D-CombinedTeam:NTU-Taida/Modeling/2D-3D-Combined2013-01-03T14:32:51Z<p>Lbwang: /* Species regulated by the quorum sensing module */</p>
<hr />
<div>{{:Team:NTU-Taida/Templates/Header}}{{:Team:NTU-Taida/Templates/Navbar}}{{:Team:NTU-Taida/Templates/Sidebar|Title=2D &amp; 3D Combined Model}}{{:Team:NTU-Taida/Templates/ContentStart}}<br />
{{:Team:NTU-Taida/Templates/BSHero|Title=2D &amp; 3D Combined Model|Content=<p></p>}}<br />
<br />
== Overview ==<br />
<p style="text-indent: 2em;"><br />
With the single cell model, fatty acid reaction-absorption model, and system analysis, we have verified the '''filter function''' of our circuit, simulated the '''real physiological fatty acid level at intestinal wall''', and '''adjust our filter threshold to fit to the real condition'''. Next, we want to combine them together and see what would happen when we put cells in the intestine after a fatty meal.<br />
</p><br />
<p style="text-indent: 2em;"><br />
The combined model is composed of three different sections. 2D combined model simulates the GLP1 response of Pepdex E-coli cells after the food intake in the x-y cross-sectional plane. 2D Cell population response model further considers the possible uneven concentration of fatty acid along the z-axis due to non-uniform distribution of lipase and simulates how the quorum sensing system assists our system to overcame this possible limitation and enhance the response. Finally, '''3D Cell population response model incorporates all the consideration to generate a full model to visualize the dynamic behavior of our system.'''<br />
</p><br />
<br />
==2D Combined Model==<br />
So far, we have the spatial-temporal concentration of fatty acid, and cells with suitable threshold. In this model, we want to see what would happen when we put cells in the intestine after a meal. <br />
<br />
[[File:NTU-Taida-Model-Combined-fig1.png|600px|center|thumb|Figure 1]]<br />
<br />
We achieve this by further coupling the single cell ODEs (with parameters adjusted by system analysis) locally to the fatty acid reaction-absorption model at the intestinal wall, as shown in Figure 2.<br />
<br />
[[File:NTU-Taida-Model-Combined-fig2.png|600px|center|thumb|Figure 2]]<br />
<br />
Besides to see the cell response when combined with the environmental input, we also want to simulate the prolonged effect of the quorum sensing module with physiological input. Therefore, we simulate system with and without quorum sensing modules and compare their results.<br />
<br />
===Spatial-temporal Model Equations ===<br />
The equations used in our 2D combined model mainly come from the reaction-absorption model and the single cell model. The following three equations are the same as those in the reaction-absorption model, which simulates the change in fatty acid concentration in time and space. <br />
<br />
{{:Team:NTU-Taida/Templates/Eq|num=1|eq=<br />
\frac{d fat}{d t} = -\frac{k_{cat}[E]_t\cdot[S]}{K_m + [S]} <br />
}}<br />
<br />
{{:Team:NTU-Taida/Templates/Eq|num=2|eq=<br />
\frac{d FA}{d t} = 3 \cdot \frac{k_{cat}[E]_t\cdot[S]}{K_m + [S]} <br />
}}<br />
<br />
{{:Team:NTU-Taida/Templates/Eq|num=3|eq=<br />
J=(C_1 - C_2)(D_{FA}/d) <br />
}}<br />
<br />
Other equations in the model are almost the same as those derived in our single cell model, with slightly difference in those for AHL, which will be discussed thoroughly in the 2D Cell population response model. The equations are shown as below.<br />
<br />
{{:Team:NTU-Taida/Templates/Eq|num=4|eq=<br />
\frac{d FadR}{d t} = \alpha_{FadR} - \gamma_{FadR} \cdot FadR <br />
}}<br />
<br />
$$X_{FadR} = \frac{FadR \cdot \beta_{FA}^{n2}}{FA^{n2} + \beta_{FA}^{n2}}$$<br />
{{:Team:NTU-Taida/Templates/Eq|num=5|eq=<br />
}}<br />
<br />
$$\frac{dTetR_1}{dt} = \frac{\alpha_{TetR_1} \cdot {\beta_{FadR}^{n1}}}{\beta_{FadR}^{n1} + X_{FadR}^{n1}} - \gamma_{TetR_1} \cdot TetR_1 $$<br />
{{:Team:NTU-Taida/Templates/Eq|num=6|eq=<br />
}}<br />
<br />
$$\frac{d TetR_2}{d t} = \frac{\alpha_{TetR_2} \cdot R^{n3}}{\beta_R^{n3} + R^{n3}} - \gamma_{TetR_2} \cdot TetR_2$$<br />
{{:Team:NTU-Taida/Templates/Eq|num=7|eq=<br />
}}<br />
<br />
$$\frac{d LuxI}{d t} = \frac{\alpha_{LuxI} \cdot \beta_{FadR}^{n1}}{\beta_{FadR}^{n1} + X_{FadR}^{n1}} - \gamma_{LuxI} \cdot LuxI$$<br />
{{:Team:NTU-Taida/Templates/Eq|num=8|eq=<br />
}}<br />
<br />
$$\frac{\partial^2 AHL}{\partial x^2} + \frac{\partial^2 AHL}{y^2} - \frac{1}{D_{AHL}}\cdot \frac{\partial AHL}{\partial t} = 0$$<br />
{{:Team:NTU-Taida/Templates/Eq|num=9|eq=<br />
}}<br />
<br />
$$R(AHL) = - \gamma_{AHL_{ext}} \cdot AHL + cd(k_{s1}LuxI - k_{s0}AHL)$$<br />
{{:Team:NTU-Taida/Templates/Eq|num=10|eq=<br />
}}<br />
<br />
$$\frac{d R}{d t} = \rho (LuxR)^2(AHL_i)^2 - \gamma_R \cdot R$$<br />
{{:Team:NTU-Taida/Templates/Eq|num=11|eq=<br />
}}<br />
<br />
$$\frac{d LacI}{d t} = \frac{\alpha_{LacI}}{1 + (\frac{TetR_1 + TetR_2}{\beta_{TetR}})^{n5}} - \gamma_{LacI} \cdot LacI$$<br />
{{:Team:NTU-Taida/Templates/Eq|num=12|eq=<br />
}}<br />
<br />
$$\frac{d GLP1}{d t} = \frac{\alpha_{GLP1}}{1 + (\frac{LacI}{\beta_{LacI}})^{n6}} - \gamma_{GLP1} \cdot GLP1$$<br />
{{:Team:NTU-Taida/Templates/Eq|num=13|eq=<br />
}}<br />
<br />
<br />
For the control group without the quorum sensing module, we simply discard the terms related to quorum sensing system in the ODE set.<br />
<br />
===Results===<br />
<br />
{| align='center'<br />
| {{:Team:NTU-Taida/Templates/Vid|num=1.1 Fatty acid concentration|width=350px|name=NTU-Taida-Model-Combined-Image5.gif}}<br />
| {{:Team:NTU-Taida/Templates/Vid|num=1.2 Closer look of fatty acid concentration|width=350px|name=NTU-Taida-Model-Combined-Image8.gif}}<br />
|}<br />
{| align='center'<br />
| {{:Team:NTU-Taida/Templates/Vid|num=2.1 GLP-1 expression in system without quorum sensing|width=350px|name=NTU-Taida-Model-Combined-Image4.gif}}<br />
| {{:Team:NTU-Taida/Templates/Vid|num=2.2 Closer look ofGLP-1 expression in system without quorum sensing|width=350px|name=NTU-Taida-Model-Combined-Image7.gif}}<br />
|}<br />
{| align='center'<br />
| {{:Team:NTU-Taida/Templates/Vid|num=3.1 GLP-1 expression in system with quorum sensing|width=350px|name=NTU-Taida-Model-Combined-Image3.gif}}<br />
| {{:Team:NTU-Taida/Templates/Vid|num=3.2 Closer look at GLP-1 expression in system with quorum sensing|width=350px|name=NTU-Taida-Model-Combined-Image6.gif}} <br />
|}<br />
<br />
Video 1 shows the spatial temporal concentration change of fatty acid. Video 2 and three show the corresponding spatial temporal response of GLP-1 expression in system without and with quorum sensing module, respectively.<br />
<br />
We can see from the videos that the fatty acid concentration at the intestinal wall first increases rapidly, turning on the circuits in the cells and resulting in GLP-1 expression at the intestinal wall. Then due to the absorption of fatty acid, the concentration gradually falls and the GLP-1 concentration started to decrease. Notice that the GLP1 expression in the system with Quorum sensing, shown in Video 3, lasts longer than that of the system without quorum sensing, shown in Video 2. Consistent to the single cell model, the system with QS has more prolonged response compared to the one without it.<br />
<br />
==Cell Population Response Model==<br />
<br />
We have assumed that fat distributes uniformly along the z-axis in the lumen after a meal in the previous models. However, in real situation in human body, lipase only exists in certain segments of the intestine. Therefore, fat hydrolysis will only take place in those segments and there will be no fatty acid produced outside these segments, as shown in Figure 3. Cells residing in the segments without lipase activity can only sense the fatty acid diffused from the source segments. Because AHL diffuses faster than fatty acid, we incorporate the quorum sensing system to enable faster recruitment of more bacteria to express GLP-1 in regions without lipase.<br />
<br />
Quorum sensing module enables cells to communicate with each other, as the uneven distribution of fatty acid in the intestines may cause gaps in individual detection. Cells with the quorum sensing module can respond to food intake event as long as their neighboring cells have detected fatty acid, enhancing the overall response to the food intake (Figure 4). However, the communication between cells via AHL can’t be seen when only viewing a single cell. Therefore, we construct spatial temporal models with COMSOL Multiphysics in order to gain insights into the influence of cell-cell communication mediated via the quorum sensing module on the overall GLP1 expression.<br />
<br />
[[File:NTU-Taida-Model-Combined-fig3.png|600px|center|thumb|Figure 3]]<br />
[[File:NTU-Taida-Model-Combined-fig4.png|600px|center|thumb|Figure 4]]<br />
<br />
==2D Cell Population Response Model==<br />
We start our effort with a 2D spatial temporal model. When E.coli cells colonize the intestine, they tend to attach onto the intestinal walls instead of distributing evenly throughout the intestine lumen. Therefore, we first view our system as a two dimensional system, with the modeling plane in the x-z (or either y-z) dimension.<br />
<br />
===Geometry Design===<br />
[[File:NTU-Taida-Model-Combined-fig5.png|600px|center|thumb|Figure 5]]<br />
<br />
With this in mind, we construct a plane in 2D geometry and couple the ODEs derived in our single cell model to simulate the presence of cells.<br />
<br />
To model the effect of quorum sensing, we establish an uneven distribution of fatty acid by giving a constant concentration source of fatty acid in the middle of our modeled plane, as shown in Figure 6. There are no cells within the circular fatty acid source. As time goes on, fatty acids diffuse from the source and establish a concentric gradient. To see the effect of quorum sensing mechanism on overall GLP1 expression in a cell population with uneven distributed fatty acid input, we model cells with and without quorum sensing and compare their spatial –temporal GLP1 expression.<br />
[[File:NTU-Taida-Model-Combined-fig6.png|600px|center|thumb|Figure 6]]<br />
<br />
===Spatial-temporal Model Equations===<br />
The first equation used in our model describes the free diffusion of fatty acids from the central source.<br />
<br />
$$\frac{\partial^2 FA}{\partial x^2} + \frac{\partial^2 FA}{\partial z^2} - \frac{1}{D_{FA}} \frac{\partial FA}{\partial t} = 0$$<br />
{{:Team:NTU-Taida/Templates/Eq|num=14|eq=<br />
}}<br />
<br />
Other equations in the model are almost the same as those derived in our single cell model, except for the ones for AHL. For AHL, we have to set up a partial differential equation describing both the diffusion and the reaction event of AHL. We assume that AHL diffusion into and out of cells is fast and do not model this diffusion process explicitly. Therefore, in contrast to the single-cell model, we only use one species called AHL instead of an internal AHL concentration AHLi and an external AHL concentration AHLe. <br />
<br />
For the reaction term of AHL, we first discard the terms describing the diffusion into and out of the cell membrane in the ODEs of AHLi and AHLe in the single cell model. <br />
As previously mentioned, we assume that the diffusion AHL diffusion into and out of cells is fast. Therefore, we simply account for the diffusion of AHL across cell membrane by multiplying the intracellular AHLi terms by the relative cell density, which will be described in the next section. With these considerations, we combine the two equations of AHLi and AHLe (Eq. 15 and Eq. 16) into one reaction equation (Eq. 17 ).<br />
<br />
{{:Team:NTU-Taida/Templates/Eq|num=15|eq=\frac{d AHL_i}{d t} = ks1 \cdot LuxI - ks0 \cdot AHL_i - \eta (AHL_i - AHL_e)<br />
}}<br />
<br />
{{:Team:NTU-Taida/Templates/Eq|num=16|eq=\frac{d AHL_e}{d t} = - kse \cdot AHL_e + \eta_{Ext} (AHL_i - AHL_e)<br />
}}<br />
<br />
$$R (AHL) = - \gamma_{AHL_{ext}} \cdot AHL + cd (k_{s1} \cdot LuxI - k_{s0} \cdot AHL)$$<br />
{{:Team:NTU-Taida/Templates/Eq|num=17|eq=<br />
}}<br />
<br />
With the help of COMSOL Multiphysics, we can consider both the diffusion and reaction terms of AHL by giving the diffusion (Eq. 14) and reaction (Eq. 17) equations above, without the need to solve the explicit PDE of AHL.<br />
<br />
The diffusion of AHL is modeled by a free diffusion equation.<br />
<br />
$$ \frac{\partial^2 AHL}{\partial x^2} + \frac{\partial^2 AHL}{\partial z^2} - \frac{1}{D_{AHL}} \frac{\partial AHL}{\partial t} = 0$$<br />
{{:Team:NTU-Taida/Templates/Eq|num=18|eq=<br />
}}<br />
<br />
Other equations in the model are the same as those derived in our single cell model.<br />
For the control group without the quorum sensing module, we discard the terms related to quorum sensing system in the ODE set.<br />
<br />
==Relative Cell density==<br />
The relative cell density is defined as the ratio of the total area E.coli cells occupy to the area of the intestinal wall. By multiplying the intracellular AHL synthesis and degradation terms by the relative cell density, we assume that as a cell synthesizes or degrades AHL, the addition or reduction of AHL molecules is dispersed evenly through the neighboring area. (Mind that the diffusion of these AHL molecules on global scale is still governed by the free diffusion equation.)<br />
<br />
We calculated the relative cell density by assuming there are 1014 bacteria cells residing in the intestine, which has a total surface area of 200 m2. Thus, the average cell density is 5*1011 cells/m2. We can measure the surface area of each individual cell by multiplying their length by their width, giving a surface area of 10-12 m2 per cell. Multiplying the surface area per cell and the average cell density gives the area density of total cells as 0.5. <br />
Since 99% of the gut flora consists of 30-40 species of bacteria, we can assume that each of the common types contribute to approximately 1% of the total surface area of the intestine. Considering the clustering effect of cells, we assume that some regions would have much higher cell densities than others, such that the uneven distribution may result in a tenfold fluctuation in cell density. We hypothesize that the relative cell density in our model could be as high as 0.1.<br />
<br />
Cell density has dramatic effect on the overall effect of quorum sensing system, as supported by a recent study investigating the synchronization of repressilators by quorum sensing mechanisms [1]. Therefore, we also model our system with different cell densities, as can be seen in the results.<br />
<br />
===Results===<br />
To see the effect of quorum sensing mechanism on overall GLP1 expression in a cell population with uneven distributed fatty acid input, we model cells with and without quorum sensing and compare their spatial - temporal GLP1 expression, with relative cell density of 0.1<br />
The results show that species which are not regulated by the quorum sensing module, such as FA, X_FadR, and TetR1, show no difference in the spatial temporal expression pattern between system with and without the quorum sensing system. <br />
<br />
However, species affected by the quorum sensing module, such as LacI and GLP1, show striking difference in their spatial temporal concentration pattern. Within the given time span, systems with a quorum sensing module produces GLP1 over a broader spatial region, resulting in more total GLP1. <br />
<br />
===Species unregulated by the quorum sensing module===<br />
<br />
====FA====<br />
<br />
{| align='center'<br />
| {{:Team:NTU-Taida/Templates/Vid|num=4.1 |width=350px|name=NTU-Taida-Model-Combined-video4-1.gif}}<br />
| {{:Team:NTU-Taida/Templates/Vid|num=4.2 |width=350px|name=NTU-Taida-Model-Combined-video4-2.gif}}<br />
|}<br />
<br />
====X_fadR====<br />
{| align='center'<br />
| {{:Team:NTU-Taida/Templates/Vid|num=5.1 |width=350px|name=NTU-Taida-Model-Combined-video5-1.gif}}<br />
| {{:Team:NTU-Taida/Templates/Vid|num=5.2 |width=350px|name=NTU-Taida-Model-Combined-video5-2.gif}}<br />
|}<br />
{| align='center'<br />
| {{:Team:NTU-Taida/Templates/Vid|num=6.1 |width=350px|name=NTU-Taida-Model-Combined-video6-1.gif}}<br />
| {{:Team:NTU-Taida/Templates/Vid|num=6.2 |width=350px|name=NTU-Taida-Model-Combined-video6-2.gif}}<br />
|}<br />
<br />
===Species regulated by the quorum sensing module===<br />
====LacI====<br />
<br />
{|align="center"<br />
| {{:Team:NTU-Taida/Templates/Vid|num=7-1 |width=350px|name=NTU-Taida-Model-Combined-video7-1.gif}}<br />
| {{:Team:NTU-Taida/Templates/Vid|num=7-2 |width=350px|name=NTU-Taida-Model-Combined-video7-2.gif}}<br />
|}<br />
<br />
The expression of LacI is inhibited by TetR proteins, and therefore is regulated by the quorum sensing module. Although the concentration of TetR1 is the same in systems with and without quorum sensing, cells with quorum sensing produce TetR2 as the output of the quorum sensing module and therefore result in overall more total TetR proteins. Thus, the repression of LacI is more significant in systems with the quorum sensing module.<br />
<br />
====GLP1====<br />
{|align="center"<br />
| {{:Team:NTU-Taida/Templates/Vid|num=8-1 |width=350px|name=NTU-Taida-Model-Combined-video8-1.gif}}<br />
| {{:Team:NTU-Taida/Templates/Vid|num=8-2 |width=350px|name=NTU-Taida-Model-Combined-video8-2.gif}}<br />
|}<br />
<br />
As the expression of GLP1 is repressed by LacI proteins, GLP1 also displays different spatial-temporal concentration pattern between the two systems. With quorum sensing module, the system produces more GLP1 overall.<br />
<br />
===Effect of cell density===<br />
<br />
Relative cell density plays a critical role in determining whether we can see a significant difference between systems with and without quorum sensing. We simulated the spatial-temporal response of GLP1 of four systems, all of them with the quorum sensing module but with relative cell densities of 0.2, 0.1, and 0.01, respectively. <br />
<br />
Then we compare their response to that of system without quorum sensing to determine if there exists a threshold of cell density, below which the effect of quorum sensing module is unperceivable. <br />
<br />
{|align="center"<br />
| {{:Team:NTU-Taida/Templates/Vid|num=9-1 cd = 0.2 |width=280px|name=NTU-Taida-Model-Combined-video9-1.gif}}<br />
| {{:Team:NTU-Taida/Templates/Vid|num=9-2 cd = 0.1 |width=280px|name=NTU-Taida-Model-Combined-video9-2.gif}}<br />
| {{:Team:NTU-Taida/Templates/Vid|num=9-3 cd = 0.05 |width=280px|name=NTU-Taida-Model-Combined-video9-3.gif}}<br />
|}<br />
<br />
{|align="center"<br />
| {{:Team:NTU-Taida/Templates/Vid|num=9-4 cd = 0.01 |width=280px|name=NTU-Taida-Model-Combined-video9-4.gif}}<br />
| {{:Team:NTU-Taida/Templates/Vid|num=9-5 without quorum sensing module |width=280px|name=NTU-Taida-Model-Combined-video9-5.gif}}<br />
|}<br />
<br />
<br />
<br />
We can see from Video 9 that the system with a relative cell density of 0.2 differs most with the system without the quorum sensing module. The system with a relative cell density of 0.1 shows moderate difference. The system with a relative cell density of 0.05 displays very subtle difference. There is no difference between the system with a relative cell density of 0.01 and the system with no quorum sensing module. Therefore, the threshold of relative cell density may lie between 0.05 and 0.01.<br />
<br />
==3D Cell population response model==<br />
<br />
Finally, we construct a full 3D model, combing the consideration on the x-y plane and the x-z plane. Our goal is to simulate the effect of non-uniform production of fatty acid due to the spatially limited lipase activity. We modeled the intestine by a cylindrical tube, with a fat source limited to the z=0 plane, to simulate the situations similar to that shown in Figure 7, and examine the effect of Quorum sensing. <br />
<br />
[[File:NTU-Taida-Model-Combined-fig7.png|600px|center|thumb|Figure 7]]<br />
<br />
The equations used are the same as those in the 2D cell population response model, but with the equations governing diffusions changing from the two-dimension form to their three-dimension counterparts.<br />
<br />
{|align="center"<br />
| {{:Team:NTU-Taida/Templates/Vid|num=10 Full Thumbnails |width=400px|name=image24.gif}}<br />
| {{:Team:NTU-Taida/Templates/Vid|num=10 Enlargement |width=400px|name=image26.gif}}<br />
|}<br />
<br />
{|align="center"<br />
| {{:Team:NTU-Taida/Templates/Vid|num=11 Full Thumbnails |width=400px|name=image25.gif}}<br />
| {{:Team:NTU-Taida/Templates/Vid|num=11 Enlargement |width=400px|name=image27.gif}}<br />
|}<br />
<br />
<br />
<br />
Video 10 shows the result of system without quorum sensing module while Video 11 shows the result of system with quorum sensing module. From Video 10 and 11, we can see that GLP-1 starts to be expressed at similar time point at the intestinal wall on the z=0 plane. However, the GLP-1 expression spreads faster along the z-axis in system with quorum sensing.<br />
<br />
==Reference==<br />
<ol id='Ref'><br />
<li>Jordi Garcia-Ojalvo , Michael B. Elowitz, and Steven H. Strogatz , Modeling a synthetic multicellular clock: Repressilators coupled by quorum sensing, pnas,2004</li><br />
</ol><br />
<!--EOF--><br />
{{:Team:NTU-Taida/Templates/ContentEnd}}{{:Team:NTU-Taida/Templates/Footer|ActiveNavbar=Modeling, #nav-Modeling-Combined}}</div>Lbwanghttp://2012.igem.org/Team:NTU-Taida/Modeling/2D-3D-CombinedTeam:NTU-Taida/Modeling/2D-3D-Combined2013-01-03T14:31:45Z<p>Lbwang: /* Species regulated by the quorum sensing module */</p>
<hr />
<div>{{:Team:NTU-Taida/Templates/Header}}{{:Team:NTU-Taida/Templates/Navbar}}{{:Team:NTU-Taida/Templates/Sidebar|Title=2D &amp; 3D Combined Model}}{{:Team:NTU-Taida/Templates/ContentStart}}<br />
{{:Team:NTU-Taida/Templates/BSHero|Title=2D &amp; 3D Combined Model|Content=<p></p>}}<br />
<br />
== Overview ==<br />
<p style="text-indent: 2em;"><br />
With the single cell model, fatty acid reaction-absorption model, and system analysis, we have verified the '''filter function''' of our circuit, simulated the '''real physiological fatty acid level at intestinal wall''', and '''adjust our filter threshold to fit to the real condition'''. Next, we want to combine them together and see what would happen when we put cells in the intestine after a fatty meal.<br />
</p><br />
<p style="text-indent: 2em;"><br />
The combined model is composed of three different sections. 2D combined model simulates the GLP1 response of Pepdex E-coli cells after the food intake in the x-y cross-sectional plane. 2D Cell population response model further considers the possible uneven concentration of fatty acid along the z-axis due to non-uniform distribution of lipase and simulates how the quorum sensing system assists our system to overcame this possible limitation and enhance the response. Finally, '''3D Cell population response model incorporates all the consideration to generate a full model to visualize the dynamic behavior of our system.'''<br />
</p><br />
<br />
==2D Combined Model==<br />
So far, we have the spatial-temporal concentration of fatty acid, and cells with suitable threshold. In this model, we want to see what would happen when we put cells in the intestine after a meal. <br />
<br />
[[File:NTU-Taida-Model-Combined-fig1.png|600px|center|thumb|Figure 1]]<br />
<br />
We achieve this by further coupling the single cell ODEs (with parameters adjusted by system analysis) locally to the fatty acid reaction-absorption model at the intestinal wall, as shown in Figure 2.<br />
<br />
[[File:NTU-Taida-Model-Combined-fig2.png|600px|center|thumb|Figure 2]]<br />
<br />
Besides to see the cell response when combined with the environmental input, we also want to simulate the prolonged effect of the quorum sensing module with physiological input. Therefore, we simulate system with and without quorum sensing modules and compare their results.<br />
<br />
===Spatial-temporal Model Equations ===<br />
The equations used in our 2D combined model mainly come from the reaction-absorption model and the single cell model. The following three equations are the same as those in the reaction-absorption model, which simulates the change in fatty acid concentration in time and space. <br />
<br />
{{:Team:NTU-Taida/Templates/Eq|num=1|eq=<br />
\frac{d fat}{d t} = -\frac{k_{cat}[E]_t\cdot[S]}{K_m + [S]} <br />
}}<br />
<br />
{{:Team:NTU-Taida/Templates/Eq|num=2|eq=<br />
\frac{d FA}{d t} = 3 \cdot \frac{k_{cat}[E]_t\cdot[S]}{K_m + [S]} <br />
}}<br />
<br />
{{:Team:NTU-Taida/Templates/Eq|num=3|eq=<br />
J=(C_1 - C_2)(D_{FA}/d) <br />
}}<br />
<br />
Other equations in the model are almost the same as those derived in our single cell model, with slightly difference in those for AHL, which will be discussed thoroughly in the 2D Cell population response model. The equations are shown as below.<br />
<br />
{{:Team:NTU-Taida/Templates/Eq|num=4|eq=<br />
\frac{d FadR}{d t} = \alpha_{FadR} - \gamma_{FadR} \cdot FadR <br />
}}<br />
<br />
$$X_{FadR} = \frac{FadR \cdot \beta_{FA}^{n2}}{FA^{n2} + \beta_{FA}^{n2}}$$<br />
{{:Team:NTU-Taida/Templates/Eq|num=5|eq=<br />
}}<br />
<br />
$$\frac{dTetR_1}{dt} = \frac{\alpha_{TetR_1} \cdot {\beta_{FadR}^{n1}}}{\beta_{FadR}^{n1} + X_{FadR}^{n1}} - \gamma_{TetR_1} \cdot TetR_1 $$<br />
{{:Team:NTU-Taida/Templates/Eq|num=6|eq=<br />
}}<br />
<br />
$$\frac{d TetR_2}{d t} = \frac{\alpha_{TetR_2} \cdot R^{n3}}{\beta_R^{n3} + R^{n3}} - \gamma_{TetR_2} \cdot TetR_2$$<br />
{{:Team:NTU-Taida/Templates/Eq|num=7|eq=<br />
}}<br />
<br />
$$\frac{d LuxI}{d t} = \frac{\alpha_{LuxI} \cdot \beta_{FadR}^{n1}}{\beta_{FadR}^{n1} + X_{FadR}^{n1}} - \gamma_{LuxI} \cdot LuxI$$<br />
{{:Team:NTU-Taida/Templates/Eq|num=8|eq=<br />
}}<br />
<br />
$$\frac{\partial^2 AHL}{\partial x^2} + \frac{\partial^2 AHL}{y^2} - \frac{1}{D_{AHL}}\cdot \frac{\partial AHL}{\partial t} = 0$$<br />
{{:Team:NTU-Taida/Templates/Eq|num=9|eq=<br />
}}<br />
<br />
$$R(AHL) = - \gamma_{AHL_{ext}} \cdot AHL + cd(k_{s1}LuxI - k_{s0}AHL)$$<br />
{{:Team:NTU-Taida/Templates/Eq|num=10|eq=<br />
}}<br />
<br />
$$\frac{d R}{d t} = \rho (LuxR)^2(AHL_i)^2 - \gamma_R \cdot R$$<br />
{{:Team:NTU-Taida/Templates/Eq|num=11|eq=<br />
}}<br />
<br />
$$\frac{d LacI}{d t} = \frac{\alpha_{LacI}}{1 + (\frac{TetR_1 + TetR_2}{\beta_{TetR}})^{n5}} - \gamma_{LacI} \cdot LacI$$<br />
{{:Team:NTU-Taida/Templates/Eq|num=12|eq=<br />
}}<br />
<br />
$$\frac{d GLP1}{d t} = \frac{\alpha_{GLP1}}{1 + (\frac{LacI}{\beta_{LacI}})^{n6}} - \gamma_{GLP1} \cdot GLP1$$<br />
{{:Team:NTU-Taida/Templates/Eq|num=13|eq=<br />
}}<br />
<br />
<br />
For the control group without the quorum sensing module, we simply discard the terms related to quorum sensing system in the ODE set.<br />
<br />
===Results===<br />
<br />
{| align='center'<br />
| {{:Team:NTU-Taida/Templates/Vid|num=1.1 Fatty acid concentration|width=350px|name=NTU-Taida-Model-Combined-Image5.gif}}<br />
| {{:Team:NTU-Taida/Templates/Vid|num=1.2 Closer look of fatty acid concentration|width=350px|name=NTU-Taida-Model-Combined-Image8.gif}}<br />
|}<br />
{| align='center'<br />
| {{:Team:NTU-Taida/Templates/Vid|num=2.1 GLP-1 expression in system without quorum sensing|width=350px|name=NTU-Taida-Model-Combined-Image4.gif}}<br />
| {{:Team:NTU-Taida/Templates/Vid|num=2.2 Closer look ofGLP-1 expression in system without quorum sensing|width=350px|name=NTU-Taida-Model-Combined-Image7.gif}}<br />
|}<br />
{| align='center'<br />
| {{:Team:NTU-Taida/Templates/Vid|num=3.1 GLP-1 expression in system with quorum sensing|width=350px|name=NTU-Taida-Model-Combined-Image3.gif}}<br />
| {{:Team:NTU-Taida/Templates/Vid|num=3.2 Closer look at GLP-1 expression in system with quorum sensing|width=350px|name=NTU-Taida-Model-Combined-Image6.gif}} <br />
|}<br />
<br />
Video 1 shows the spatial temporal concentration change of fatty acid. Video 2 and three show the corresponding spatial temporal response of GLP-1 expression in system without and with quorum sensing module, respectively.<br />
<br />
We can see from the videos that the fatty acid concentration at the intestinal wall first increases rapidly, turning on the circuits in the cells and resulting in GLP-1 expression at the intestinal wall. Then due to the absorption of fatty acid, the concentration gradually falls and the GLP-1 concentration started to decrease. Notice that the GLP1 expression in the system with Quorum sensing, shown in Video 3, lasts longer than that of the system without quorum sensing, shown in Video 2. Consistent to the single cell model, the system with QS has more prolonged response compared to the one without it.<br />
<br />
==Cell Population Response Model==<br />
<br />
We have assumed that fat distributes uniformly along the z-axis in the lumen after a meal in the previous models. However, in real situation in human body, lipase only exists in certain segments of the intestine. Therefore, fat hydrolysis will only take place in those segments and there will be no fatty acid produced outside these segments, as shown in Figure 3. Cells residing in the segments without lipase activity can only sense the fatty acid diffused from the source segments. Because AHL diffuses faster than fatty acid, we incorporate the quorum sensing system to enable faster recruitment of more bacteria to express GLP-1 in regions without lipase.<br />
<br />
Quorum sensing module enables cells to communicate with each other, as the uneven distribution of fatty acid in the intestines may cause gaps in individual detection. Cells with the quorum sensing module can respond to food intake event as long as their neighboring cells have detected fatty acid, enhancing the overall response to the food intake (Figure 4). However, the communication between cells via AHL can’t be seen when only viewing a single cell. Therefore, we construct spatial temporal models with COMSOL Multiphysics in order to gain insights into the influence of cell-cell communication mediated via the quorum sensing module on the overall GLP1 expression.<br />
<br />
[[File:NTU-Taida-Model-Combined-fig3.png|600px|center|thumb|Figure 3]]<br />
[[File:NTU-Taida-Model-Combined-fig4.png|600px|center|thumb|Figure 4]]<br />
<br />
==2D Cell Population Response Model==<br />
We start our effort with a 2D spatial temporal model. When E.coli cells colonize the intestine, they tend to attach onto the intestinal walls instead of distributing evenly throughout the intestine lumen. Therefore, we first view our system as a two dimensional system, with the modeling plane in the x-z (or either y-z) dimension.<br />
<br />
===Geometry Design===<br />
[[File:NTU-Taida-Model-Combined-fig5.png|600px|center|thumb|Figure 5]]<br />
<br />
With this in mind, we construct a plane in 2D geometry and couple the ODEs derived in our single cell model to simulate the presence of cells.<br />
<br />
To model the effect of quorum sensing, we establish an uneven distribution of fatty acid by giving a constant concentration source of fatty acid in the middle of our modeled plane, as shown in Figure 6. There are no cells within the circular fatty acid source. As time goes on, fatty acids diffuse from the source and establish a concentric gradient. To see the effect of quorum sensing mechanism on overall GLP1 expression in a cell population with uneven distributed fatty acid input, we model cells with and without quorum sensing and compare their spatial –temporal GLP1 expression.<br />
[[File:NTU-Taida-Model-Combined-fig6.png|600px|center|thumb|Figure 6]]<br />
<br />
===Spatial-temporal Model Equations===<br />
The first equation used in our model describes the free diffusion of fatty acids from the central source.<br />
<br />
$$\frac{\partial^2 FA}{\partial x^2} + \frac{\partial^2 FA}{\partial z^2} - \frac{1}{D_{FA}} \frac{\partial FA}{\partial t} = 0$$<br />
{{:Team:NTU-Taida/Templates/Eq|num=14|eq=<br />
}}<br />
<br />
Other equations in the model are almost the same as those derived in our single cell model, except for the ones for AHL. For AHL, we have to set up a partial differential equation describing both the diffusion and the reaction event of AHL. We assume that AHL diffusion into and out of cells is fast and do not model this diffusion process explicitly. Therefore, in contrast to the single-cell model, we only use one species called AHL instead of an internal AHL concentration AHLi and an external AHL concentration AHLe. <br />
<br />
For the reaction term of AHL, we first discard the terms describing the diffusion into and out of the cell membrane in the ODEs of AHLi and AHLe in the single cell model. <br />
As previously mentioned, we assume that the diffusion AHL diffusion into and out of cells is fast. Therefore, we simply account for the diffusion of AHL across cell membrane by multiplying the intracellular AHLi terms by the relative cell density, which will be described in the next section. With these considerations, we combine the two equations of AHLi and AHLe (Eq. 15 and Eq. 16) into one reaction equation (Eq. 17 ).<br />
<br />
{{:Team:NTU-Taida/Templates/Eq|num=15|eq=\frac{d AHL_i}{d t} = ks1 \cdot LuxI - ks0 \cdot AHL_i - \eta (AHL_i - AHL_e)<br />
}}<br />
<br />
{{:Team:NTU-Taida/Templates/Eq|num=16|eq=\frac{d AHL_e}{d t} = - kse \cdot AHL_e + \eta_{Ext} (AHL_i - AHL_e)<br />
}}<br />
<br />
$$R (AHL) = - \gamma_{AHL_{ext}} \cdot AHL + cd (k_{s1} \cdot LuxI - k_{s0} \cdot AHL)$$<br />
{{:Team:NTU-Taida/Templates/Eq|num=17|eq=<br />
}}<br />
<br />
With the help of COMSOL Multiphysics, we can consider both the diffusion and reaction terms of AHL by giving the diffusion (Eq. 14) and reaction (Eq. 17) equations above, without the need to solve the explicit PDE of AHL.<br />
<br />
The diffusion of AHL is modeled by a free diffusion equation.<br />
<br />
$$ \frac{\partial^2 AHL}{\partial x^2} + \frac{\partial^2 AHL}{\partial z^2} - \frac{1}{D_{AHL}} \frac{\partial AHL}{\partial t} = 0$$<br />
{{:Team:NTU-Taida/Templates/Eq|num=18|eq=<br />
}}<br />
<br />
Other equations in the model are the same as those derived in our single cell model.<br />
For the control group without the quorum sensing module, we discard the terms related to quorum sensing system in the ODE set.<br />
<br />
==Relative Cell density==<br />
The relative cell density is defined as the ratio of the total area E.coli cells occupy to the area of the intestinal wall. By multiplying the intracellular AHL synthesis and degradation terms by the relative cell density, we assume that as a cell synthesizes or degrades AHL, the addition or reduction of AHL molecules is dispersed evenly through the neighboring area. (Mind that the diffusion of these AHL molecules on global scale is still governed by the free diffusion equation.)<br />
<br />
We calculated the relative cell density by assuming there are 1014 bacteria cells residing in the intestine, which has a total surface area of 200 m2. Thus, the average cell density is 5*1011 cells/m2. We can measure the surface area of each individual cell by multiplying their length by their width, giving a surface area of 10-12 m2 per cell. Multiplying the surface area per cell and the average cell density gives the area density of total cells as 0.5. <br />
Since 99% of the gut flora consists of 30-40 species of bacteria, we can assume that each of the common types contribute to approximately 1% of the total surface area of the intestine. Considering the clustering effect of cells, we assume that some regions would have much higher cell densities than others, such that the uneven distribution may result in a tenfold fluctuation in cell density. We hypothesize that the relative cell density in our model could be as high as 0.1.<br />
<br />
Cell density has dramatic effect on the overall effect of quorum sensing system, as supported by a recent study investigating the synchronization of repressilators by quorum sensing mechanisms [1]. Therefore, we also model our system with different cell densities, as can be seen in the results.<br />
<br />
===Results===<br />
To see the effect of quorum sensing mechanism on overall GLP1 expression in a cell population with uneven distributed fatty acid input, we model cells with and without quorum sensing and compare their spatial - temporal GLP1 expression, with relative cell density of 0.1<br />
The results show that species which are not regulated by the quorum sensing module, such as FA, X_FadR, and TetR1, show no difference in the spatial temporal expression pattern between system with and without the quorum sensing system. <br />
<br />
However, species affected by the quorum sensing module, such as LacI and GLP1, show striking difference in their spatial temporal concentration pattern. Within the given time span, systems with a quorum sensing module produces GLP1 over a broader spatial region, resulting in more total GLP1. <br />
<br />
===Species unregulated by the quorum sensing module===<br />
<br />
====FA====<br />
<br />
{| align='center'<br />
| {{:Team:NTU-Taida/Templates/Vid|num=4.1 |width=350px|name=NTU-Taida-Model-Combined-video4-1.gif}}<br />
| {{:Team:NTU-Taida/Templates/Vid|num=4.2 |width=350px|name=NTU-Taida-Model-Combined-video4-2.gif}}<br />
|}<br />
<br />
====X_fadR====<br />
{| align='center'<br />
| {{:Team:NTU-Taida/Templates/Vid|num=5.1 |width=350px|name=NTU-Taida-Model-Combined-video5-1.gif}}<br />
| {{:Team:NTU-Taida/Templates/Vid|num=5.2 |width=350px|name=NTU-Taida-Model-Combined-video5-2.gif}}<br />
|}<br />
{| align='center'<br />
| {{:Team:NTU-Taida/Templates/Vid|num=6.1 |width=350px|name=NTU-Taida-Model-Combined-video6-1.gif}}<br />
| {{:Team:NTU-Taida/Templates/Vid|num=6.2 |width=350px|name=NTU-Taida-Model-Combined-video6-2.gif}}<br />
|}<br />
<br />
===Species regulated by the quorum sensing module===<br />
====LacI====<br />
<br />
{|align="center"<br />
| {{:Team:NTU-Taida/Templates/Vid|num=7-1 |width=350px|name=NTU-Taida-Model-Combined-video7-1}}<br />
| {{:Team:NTU-Taida/Templates/Vid|num=7-2 |width=350px|name=NTU-Taida-Model-Combined-video7-2}}<br />
|}<br />
<br />
The expression of LacI is inhibited by TetR proteins, and therefore is regulated by the quorum sensing module. Although the concentration of TetR1 is the same in systems with and without quorum sensing, cells with quorum sensing produce TetR2 as the output of the quorum sensing module and therefore result in overall more total TetR proteins. Thus, the repression of LacI is more significant in systems with the quorum sensing module.<br />
<br />
====GLP1====<br />
{|align="center"<br />
| {{:Team:NTU-Taida/Templates/Vid|num=8-1 |width=350px|name=NTU-Taida-Model-Combined-video8-1}}<br />
| {{:Team:NTU-Taida/Templates/Vid|num=8-2 |width=350px|name=NTU-Taida-Model-Combined-video8-2}}<br />
|}<br />
<br />
As the expression of GLP1 is repressed by LacI proteins, GLP1 also displays different spatial-temporal concentration pattern between the two systems. With quorum sensing module, the system produces more GLP1 overall.<br />
<br />
===Effect of cell density===<br />
<br />
Relative cell density plays a critical role in determining whether we can see a significant difference between systems with and without quorum sensing. We simulated the spatial-temporal response of GLP1 of four systems, all of them with the quorum sensing module but with relative cell densities of 0.2, 0.1, and 0.01, respectively. <br />
<br />
Then we compare their response to that of system without quorum sensing to determine if there exists a threshold of cell density, below which the effect of quorum sensing module is unperceivable. <br />
<br />
{|align="center"<br />
| {{:Team:NTU-Taida/Templates/Vid|num=9-1 cd = 0.2 |width=280px|name=NTU-Taida-Model-Combined-video9-1.gif}}<br />
| {{:Team:NTU-Taida/Templates/Vid|num=9-2 cd = 0.1 |width=280px|name=NTU-Taida-Model-Combined-video9-2.gif}}<br />
| {{:Team:NTU-Taida/Templates/Vid|num=9-3 cd = 0.05 |width=280px|name=NTU-Taida-Model-Combined-video9-3.gif}}<br />
|}<br />
<br />
{|align="center"<br />
| {{:Team:NTU-Taida/Templates/Vid|num=9-4 cd = 0.01 |width=280px|name=NTU-Taida-Model-Combined-video9-4.gif}}<br />
| {{:Team:NTU-Taida/Templates/Vid|num=9-5 without quorum sensing module |width=280px|name=NTU-Taida-Model-Combined-video9-5.gif}}<br />
|}<br />
<br />
<br />
<br />
We can see from Video 9 that the system with a relative cell density of 0.2 differs most with the system without the quorum sensing module. The system with a relative cell density of 0.1 shows moderate difference. The system with a relative cell density of 0.05 displays very subtle difference. There is no difference between the system with a relative cell density of 0.01 and the system with no quorum sensing module. Therefore, the threshold of relative cell density may lie between 0.05 and 0.01.<br />
<br />
==3D Cell population response model==<br />
<br />
Finally, we construct a full 3D model, combing the consideration on the x-y plane and the x-z plane. Our goal is to simulate the effect of non-uniform production of fatty acid due to the spatially limited lipase activity. We modeled the intestine by a cylindrical tube, with a fat source limited to the z=0 plane, to simulate the situations similar to that shown in Figure 7, and examine the effect of Quorum sensing. <br />
<br />
[[File:NTU-Taida-Model-Combined-fig7.png|600px|center|thumb|Figure 7]]<br />
<br />
The equations used are the same as those in the 2D cell population response model, but with the equations governing diffusions changing from the two-dimension form to their three-dimension counterparts.<br />
<br />
{|align="center"<br />
| {{:Team:NTU-Taida/Templates/Vid|num=10 Full Thumbnails |width=400px|name=image24.gif}}<br />
| {{:Team:NTU-Taida/Templates/Vid|num=10 Enlargement |width=400px|name=image26.gif}}<br />
|}<br />
<br />
{|align="center"<br />
| {{:Team:NTU-Taida/Templates/Vid|num=11 Full Thumbnails |width=400px|name=image25.gif}}<br />
| {{:Team:NTU-Taida/Templates/Vid|num=11 Enlargement |width=400px|name=image27.gif}}<br />
|}<br />
<br />
<br />
<br />
Video 10 shows the result of system without quorum sensing module while Video 11 shows the result of system with quorum sensing module. From Video 10 and 11, we can see that GLP-1 starts to be expressed at similar time point at the intestinal wall on the z=0 plane. However, the GLP-1 expression spreads faster along the z-axis in system with quorum sensing.<br />
<br />
==Reference==<br />
<ol id='Ref'><br />
<li>Jordi Garcia-Ojalvo , Michael B. Elowitz, and Steven H. Strogatz , Modeling a synthetic multicellular clock: Repressilators coupled by quorum sensing, pnas,2004</li><br />
</ol><br />
<!--EOF--><br />
{{:Team:NTU-Taida/Templates/ContentEnd}}{{:Team:NTU-Taida/Templates/Footer|ActiveNavbar=Modeling, #nav-Modeling-Combined}}</div>Lbwanghttp://2012.igem.org/File:NTU-Taida-Model-Combined-video8-2.gifFile:NTU-Taida-Model-Combined-video8-2.gif2013-01-03T14:31:14Z<p>Lbwang: </p>
<hr />
<div></div>Lbwanghttp://2012.igem.org/Team:NTU-Taida/Modeling/2D-3D-CombinedTeam:NTU-Taida/Modeling/2D-3D-Combined2013-01-03T14:31:02Z<p>Lbwang: /* X_fadR */</p>
<hr />
<div>{{:Team:NTU-Taida/Templates/Header}}{{:Team:NTU-Taida/Templates/Navbar}}{{:Team:NTU-Taida/Templates/Sidebar|Title=2D &amp; 3D Combined Model}}{{:Team:NTU-Taida/Templates/ContentStart}}<br />
{{:Team:NTU-Taida/Templates/BSHero|Title=2D &amp; 3D Combined Model|Content=<p></p>}}<br />
<br />
== Overview ==<br />
<p style="text-indent: 2em;"><br />
With the single cell model, fatty acid reaction-absorption model, and system analysis, we have verified the '''filter function''' of our circuit, simulated the '''real physiological fatty acid level at intestinal wall''', and '''adjust our filter threshold to fit to the real condition'''. Next, we want to combine them together and see what would happen when we put cells in the intestine after a fatty meal.<br />
</p><br />
<p style="text-indent: 2em;"><br />
The combined model is composed of three different sections. 2D combined model simulates the GLP1 response of Pepdex E-coli cells after the food intake in the x-y cross-sectional plane. 2D Cell population response model further considers the possible uneven concentration of fatty acid along the z-axis due to non-uniform distribution of lipase and simulates how the quorum sensing system assists our system to overcame this possible limitation and enhance the response. Finally, '''3D Cell population response model incorporates all the consideration to generate a full model to visualize the dynamic behavior of our system.'''<br />
</p><br />
<br />
==2D Combined Model==<br />
So far, we have the spatial-temporal concentration of fatty acid, and cells with suitable threshold. In this model, we want to see what would happen when we put cells in the intestine after a meal. <br />
<br />
[[File:NTU-Taida-Model-Combined-fig1.png|600px|center|thumb|Figure 1]]<br />
<br />
We achieve this by further coupling the single cell ODEs (with parameters adjusted by system analysis) locally to the fatty acid reaction-absorption model at the intestinal wall, as shown in Figure 2.<br />
<br />
[[File:NTU-Taida-Model-Combined-fig2.png|600px|center|thumb|Figure 2]]<br />
<br />
Besides to see the cell response when combined with the environmental input, we also want to simulate the prolonged effect of the quorum sensing module with physiological input. Therefore, we simulate system with and without quorum sensing modules and compare their results.<br />
<br />
===Spatial-temporal Model Equations ===<br />
The equations used in our 2D combined model mainly come from the reaction-absorption model and the single cell model. The following three equations are the same as those in the reaction-absorption model, which simulates the change in fatty acid concentration in time and space. <br />
<br />
{{:Team:NTU-Taida/Templates/Eq|num=1|eq=<br />
\frac{d fat}{d t} = -\frac{k_{cat}[E]_t\cdot[S]}{K_m + [S]} <br />
}}<br />
<br />
{{:Team:NTU-Taida/Templates/Eq|num=2|eq=<br />
\frac{d FA}{d t} = 3 \cdot \frac{k_{cat}[E]_t\cdot[S]}{K_m + [S]} <br />
}}<br />
<br />
{{:Team:NTU-Taida/Templates/Eq|num=3|eq=<br />
J=(C_1 - C_2)(D_{FA}/d) <br />
}}<br />
<br />
Other equations in the model are almost the same as those derived in our single cell model, with slightly difference in those for AHL, which will be discussed thoroughly in the 2D Cell population response model. The equations are shown as below.<br />
<br />
{{:Team:NTU-Taida/Templates/Eq|num=4|eq=<br />
\frac{d FadR}{d t} = \alpha_{FadR} - \gamma_{FadR} \cdot FadR <br />
}}<br />
<br />
$$X_{FadR} = \frac{FadR \cdot \beta_{FA}^{n2}}{FA^{n2} + \beta_{FA}^{n2}}$$<br />
{{:Team:NTU-Taida/Templates/Eq|num=5|eq=<br />
}}<br />
<br />
$$\frac{dTetR_1}{dt} = \frac{\alpha_{TetR_1} \cdot {\beta_{FadR}^{n1}}}{\beta_{FadR}^{n1} + X_{FadR}^{n1}} - \gamma_{TetR_1} \cdot TetR_1 $$<br />
{{:Team:NTU-Taida/Templates/Eq|num=6|eq=<br />
}}<br />
<br />
$$\frac{d TetR_2}{d t} = \frac{\alpha_{TetR_2} \cdot R^{n3}}{\beta_R^{n3} + R^{n3}} - \gamma_{TetR_2} \cdot TetR_2$$<br />
{{:Team:NTU-Taida/Templates/Eq|num=7|eq=<br />
}}<br />
<br />
$$\frac{d LuxI}{d t} = \frac{\alpha_{LuxI} \cdot \beta_{FadR}^{n1}}{\beta_{FadR}^{n1} + X_{FadR}^{n1}} - \gamma_{LuxI} \cdot LuxI$$<br />
{{:Team:NTU-Taida/Templates/Eq|num=8|eq=<br />
}}<br />
<br />
$$\frac{\partial^2 AHL}{\partial x^2} + \frac{\partial^2 AHL}{y^2} - \frac{1}{D_{AHL}}\cdot \frac{\partial AHL}{\partial t} = 0$$<br />
{{:Team:NTU-Taida/Templates/Eq|num=9|eq=<br />
}}<br />
<br />
$$R(AHL) = - \gamma_{AHL_{ext}} \cdot AHL + cd(k_{s1}LuxI - k_{s0}AHL)$$<br />
{{:Team:NTU-Taida/Templates/Eq|num=10|eq=<br />
}}<br />
<br />
$$\frac{d R}{d t} = \rho (LuxR)^2(AHL_i)^2 - \gamma_R \cdot R$$<br />
{{:Team:NTU-Taida/Templates/Eq|num=11|eq=<br />
}}<br />
<br />
$$\frac{d LacI}{d t} = \frac{\alpha_{LacI}}{1 + (\frac{TetR_1 + TetR_2}{\beta_{TetR}})^{n5}} - \gamma_{LacI} \cdot LacI$$<br />
{{:Team:NTU-Taida/Templates/Eq|num=12|eq=<br />
}}<br />
<br />
$$\frac{d GLP1}{d t} = \frac{\alpha_{GLP1}}{1 + (\frac{LacI}{\beta_{LacI}})^{n6}} - \gamma_{GLP1} \cdot GLP1$$<br />
{{:Team:NTU-Taida/Templates/Eq|num=13|eq=<br />
}}<br />
<br />
<br />
For the control group without the quorum sensing module, we simply discard the terms related to quorum sensing system in the ODE set.<br />
<br />
===Results===<br />
<br />
{| align='center'<br />
| {{:Team:NTU-Taida/Templates/Vid|num=1.1 Fatty acid concentration|width=350px|name=NTU-Taida-Model-Combined-Image5.gif}}<br />
| {{:Team:NTU-Taida/Templates/Vid|num=1.2 Closer look of fatty acid concentration|width=350px|name=NTU-Taida-Model-Combined-Image8.gif}}<br />
|}<br />
{| align='center'<br />
| {{:Team:NTU-Taida/Templates/Vid|num=2.1 GLP-1 expression in system without quorum sensing|width=350px|name=NTU-Taida-Model-Combined-Image4.gif}}<br />
| {{:Team:NTU-Taida/Templates/Vid|num=2.2 Closer look ofGLP-1 expression in system without quorum sensing|width=350px|name=NTU-Taida-Model-Combined-Image7.gif}}<br />
|}<br />
{| align='center'<br />
| {{:Team:NTU-Taida/Templates/Vid|num=3.1 GLP-1 expression in system with quorum sensing|width=350px|name=NTU-Taida-Model-Combined-Image3.gif}}<br />
| {{:Team:NTU-Taida/Templates/Vid|num=3.2 Closer look at GLP-1 expression in system with quorum sensing|width=350px|name=NTU-Taida-Model-Combined-Image6.gif}} <br />
|}<br />
<br />
Video 1 shows the spatial temporal concentration change of fatty acid. Video 2 and three show the corresponding spatial temporal response of GLP-1 expression in system without and with quorum sensing module, respectively.<br />
<br />
We can see from the videos that the fatty acid concentration at the intestinal wall first increases rapidly, turning on the circuits in the cells and resulting in GLP-1 expression at the intestinal wall. Then due to the absorption of fatty acid, the concentration gradually falls and the GLP-1 concentration started to decrease. Notice that the GLP1 expression in the system with Quorum sensing, shown in Video 3, lasts longer than that of the system without quorum sensing, shown in Video 2. Consistent to the single cell model, the system with QS has more prolonged response compared to the one without it.<br />
<br />
==Cell Population Response Model==<br />
<br />
We have assumed that fat distributes uniformly along the z-axis in the lumen after a meal in the previous models. However, in real situation in human body, lipase only exists in certain segments of the intestine. Therefore, fat hydrolysis will only take place in those segments and there will be no fatty acid produced outside these segments, as shown in Figure 3. Cells residing in the segments without lipase activity can only sense the fatty acid diffused from the source segments. Because AHL diffuses faster than fatty acid, we incorporate the quorum sensing system to enable faster recruitment of more bacteria to express GLP-1 in regions without lipase.<br />
<br />
Quorum sensing module enables cells to communicate with each other, as the uneven distribution of fatty acid in the intestines may cause gaps in individual detection. Cells with the quorum sensing module can respond to food intake event as long as their neighboring cells have detected fatty acid, enhancing the overall response to the food intake (Figure 4). However, the communication between cells via AHL can’t be seen when only viewing a single cell. Therefore, we construct spatial temporal models with COMSOL Multiphysics in order to gain insights into the influence of cell-cell communication mediated via the quorum sensing module on the overall GLP1 expression.<br />
<br />
[[File:NTU-Taida-Model-Combined-fig3.png|600px|center|thumb|Figure 3]]<br />
[[File:NTU-Taida-Model-Combined-fig4.png|600px|center|thumb|Figure 4]]<br />
<br />
==2D Cell Population Response Model==<br />
We start our effort with a 2D spatial temporal model. When E.coli cells colonize the intestine, they tend to attach onto the intestinal walls instead of distributing evenly throughout the intestine lumen. Therefore, we first view our system as a two dimensional system, with the modeling plane in the x-z (or either y-z) dimension.<br />
<br />
===Geometry Design===<br />
[[File:NTU-Taida-Model-Combined-fig5.png|600px|center|thumb|Figure 5]]<br />
<br />
With this in mind, we construct a plane in 2D geometry and couple the ODEs derived in our single cell model to simulate the presence of cells.<br />
<br />
To model the effect of quorum sensing, we establish an uneven distribution of fatty acid by giving a constant concentration source of fatty acid in the middle of our modeled plane, as shown in Figure 6. There are no cells within the circular fatty acid source. As time goes on, fatty acids diffuse from the source and establish a concentric gradient. To see the effect of quorum sensing mechanism on overall GLP1 expression in a cell population with uneven distributed fatty acid input, we model cells with and without quorum sensing and compare their spatial –temporal GLP1 expression.<br />
[[File:NTU-Taida-Model-Combined-fig6.png|600px|center|thumb|Figure 6]]<br />
<br />
===Spatial-temporal Model Equations===<br />
The first equation used in our model describes the free diffusion of fatty acids from the central source.<br />
<br />
$$\frac{\partial^2 FA}{\partial x^2} + \frac{\partial^2 FA}{\partial z^2} - \frac{1}{D_{FA}} \frac{\partial FA}{\partial t} = 0$$<br />
{{:Team:NTU-Taida/Templates/Eq|num=14|eq=<br />
}}<br />
<br />
Other equations in the model are almost the same as those derived in our single cell model, except for the ones for AHL. For AHL, we have to set up a partial differential equation describing both the diffusion and the reaction event of AHL. We assume that AHL diffusion into and out of cells is fast and do not model this diffusion process explicitly. Therefore, in contrast to the single-cell model, we only use one species called AHL instead of an internal AHL concentration AHLi and an external AHL concentration AHLe. <br />
<br />
For the reaction term of AHL, we first discard the terms describing the diffusion into and out of the cell membrane in the ODEs of AHLi and AHLe in the single cell model. <br />
As previously mentioned, we assume that the diffusion AHL diffusion into and out of cells is fast. Therefore, we simply account for the diffusion of AHL across cell membrane by multiplying the intracellular AHLi terms by the relative cell density, which will be described in the next section. With these considerations, we combine the two equations of AHLi and AHLe (Eq. 15 and Eq. 16) into one reaction equation (Eq. 17 ).<br />
<br />
{{:Team:NTU-Taida/Templates/Eq|num=15|eq=\frac{d AHL_i}{d t} = ks1 \cdot LuxI - ks0 \cdot AHL_i - \eta (AHL_i - AHL_e)<br />
}}<br />
<br />
{{:Team:NTU-Taida/Templates/Eq|num=16|eq=\frac{d AHL_e}{d t} = - kse \cdot AHL_e + \eta_{Ext} (AHL_i - AHL_e)<br />
}}<br />
<br />
$$R (AHL) = - \gamma_{AHL_{ext}} \cdot AHL + cd (k_{s1} \cdot LuxI - k_{s0} \cdot AHL)$$<br />
{{:Team:NTU-Taida/Templates/Eq|num=17|eq=<br />
}}<br />
<br />
With the help of COMSOL Multiphysics, we can consider both the diffusion and reaction terms of AHL by giving the diffusion (Eq. 14) and reaction (Eq. 17) equations above, without the need to solve the explicit PDE of AHL.<br />
<br />
The diffusion of AHL is modeled by a free diffusion equation.<br />
<br />
$$ \frac{\partial^2 AHL}{\partial x^2} + \frac{\partial^2 AHL}{\partial z^2} - \frac{1}{D_{AHL}} \frac{\partial AHL}{\partial t} = 0$$<br />
{{:Team:NTU-Taida/Templates/Eq|num=18|eq=<br />
}}<br />
<br />
Other equations in the model are the same as those derived in our single cell model.<br />
For the control group without the quorum sensing module, we discard the terms related to quorum sensing system in the ODE set.<br />
<br />
==Relative Cell density==<br />
The relative cell density is defined as the ratio of the total area E.coli cells occupy to the area of the intestinal wall. By multiplying the intracellular AHL synthesis and degradation terms by the relative cell density, we assume that as a cell synthesizes or degrades AHL, the addition or reduction of AHL molecules is dispersed evenly through the neighboring area. (Mind that the diffusion of these AHL molecules on global scale is still governed by the free diffusion equation.)<br />
<br />
We calculated the relative cell density by assuming there are 1014 bacteria cells residing in the intestine, which has a total surface area of 200 m2. Thus, the average cell density is 5*1011 cells/m2. We can measure the surface area of each individual cell by multiplying their length by their width, giving a surface area of 10-12 m2 per cell. Multiplying the surface area per cell and the average cell density gives the area density of total cells as 0.5. <br />
Since 99% of the gut flora consists of 30-40 species of bacteria, we can assume that each of the common types contribute to approximately 1% of the total surface area of the intestine. Considering the clustering effect of cells, we assume that some regions would have much higher cell densities than others, such that the uneven distribution may result in a tenfold fluctuation in cell density. We hypothesize that the relative cell density in our model could be as high as 0.1.<br />
<br />
Cell density has dramatic effect on the overall effect of quorum sensing system, as supported by a recent study investigating the synchronization of repressilators by quorum sensing mechanisms [1]. Therefore, we also model our system with different cell densities, as can be seen in the results.<br />
<br />
===Results===<br />
To see the effect of quorum sensing mechanism on overall GLP1 expression in a cell population with uneven distributed fatty acid input, we model cells with and without quorum sensing and compare their spatial - temporal GLP1 expression, with relative cell density of 0.1<br />
The results show that species which are not regulated by the quorum sensing module, such as FA, X_FadR, and TetR1, show no difference in the spatial temporal expression pattern between system with and without the quorum sensing system. <br />
<br />
However, species affected by the quorum sensing module, such as LacI and GLP1, show striking difference in their spatial temporal concentration pattern. Within the given time span, systems with a quorum sensing module produces GLP1 over a broader spatial region, resulting in more total GLP1. <br />
<br />
===Species unregulated by the quorum sensing module===<br />
<br />
====FA====<br />
<br />
{| align='center'<br />
| {{:Team:NTU-Taida/Templates/Vid|num=4.1 |width=350px|name=NTU-Taida-Model-Combined-video4-1.gif}}<br />
| {{:Team:NTU-Taida/Templates/Vid|num=4.2 |width=350px|name=NTU-Taida-Model-Combined-video4-2.gif}}<br />
|}<br />
<br />
====X_fadR====<br />
{| align='center'<br />
| {{:Team:NTU-Taida/Templates/Vid|num=5.1 |width=350px|name=NTU-Taida-Model-Combined-video5-1.gif}}<br />
| {{:Team:NTU-Taida/Templates/Vid|num=5.2 |width=350px|name=NTU-Taida-Model-Combined-video5-2.gif}}<br />
|}<br />
{| align='center'<br />
| {{:Team:NTU-Taida/Templates/Vid|num=6.1 |width=350px|name=NTU-Taida-Model-Combined-video6-1.gif}}<br />
| {{:Team:NTU-Taida/Templates/Vid|num=6.2 |width=350px|name=NTU-Taida-Model-Combined-video6-2.gif}}<br />
|}<br />
<br />
===Species regulated by the quorum sensing module===<br />
====LacI====<br />
<br />
{|align="center"<br />
| {{:Team:NTU-Taida/Templates/Vid|num=7-1 |width=350px|name=image15.gif}}<br />
| {{:Team:NTU-Taida/Templates/Vid|num=7-2 |width=350px|name=image16.gif}}<br />
|}<br />
<br />
The expression of LacI is inhibited by TetR proteins, and therefore is regulated by the quorum sensing module. Although the concentration of TetR1 is the same in systems with and without quorum sensing, cells with quorum sensing produce TetR2 as the output of the quorum sensing module and therefore result in overall more total TetR proteins. Thus, the repression of LacI is more significant in systems with the quorum sensing module.<br />
<br />
====GLP1====<br />
{|align="center"<br />
| {{:Team:NTU-Taida/Templates/Vid|num=8-1 |width=350px|name=image17.gif}}<br />
| {{:Team:NTU-Taida/Templates/Vid|num=8-2 |width=350px|name=image18.gif}}<br />
|}<br />
<br />
As the expression of GLP1 is repressed by LacI proteins, GLP1 also displays different spatial-temporal concentration pattern between the two systems. With quorum sensing module, the system produces more GLP1 overall.<br />
<br />
===Effect of cell density===<br />
<br />
Relative cell density plays a critical role in determining whether we can see a significant difference between systems with and without quorum sensing. We simulated the spatial-temporal response of GLP1 of four systems, all of them with the quorum sensing module but with relative cell densities of 0.2, 0.1, and 0.01, respectively. <br />
<br />
Then we compare their response to that of system without quorum sensing to determine if there exists a threshold of cell density, below which the effect of quorum sensing module is unperceivable. <br />
<br />
{|align="center"<br />
| {{:Team:NTU-Taida/Templates/Vid|num=9-1 cd = 0.2 |width=280px|name=NTU-Taida-Model-Combined-video9-1.gif}}<br />
| {{:Team:NTU-Taida/Templates/Vid|num=9-2 cd = 0.1 |width=280px|name=NTU-Taida-Model-Combined-video9-2.gif}}<br />
| {{:Team:NTU-Taida/Templates/Vid|num=9-3 cd = 0.05 |width=280px|name=NTU-Taida-Model-Combined-video9-3.gif}}<br />
|}<br />
<br />
{|align="center"<br />
| {{:Team:NTU-Taida/Templates/Vid|num=9-4 cd = 0.01 |width=280px|name=NTU-Taida-Model-Combined-video9-4.gif}}<br />
| {{:Team:NTU-Taida/Templates/Vid|num=9-5 without quorum sensing module |width=280px|name=NTU-Taida-Model-Combined-video9-5.gif}}<br />
|}<br />
<br />
<br />
<br />
We can see from Video 9 that the system with a relative cell density of 0.2 differs most with the system without the quorum sensing module. The system with a relative cell density of 0.1 shows moderate difference. The system with a relative cell density of 0.05 displays very subtle difference. There is no difference between the system with a relative cell density of 0.01 and the system with no quorum sensing module. Therefore, the threshold of relative cell density may lie between 0.05 and 0.01.<br />
<br />
==3D Cell population response model==<br />
<br />
Finally, we construct a full 3D model, combing the consideration on the x-y plane and the x-z plane. Our goal is to simulate the effect of non-uniform production of fatty acid due to the spatially limited lipase activity. We modeled the intestine by a cylindrical tube, with a fat source limited to the z=0 plane, to simulate the situations similar to that shown in Figure 7, and examine the effect of Quorum sensing. <br />
<br />
[[File:NTU-Taida-Model-Combined-fig7.png|600px|center|thumb|Figure 7]]<br />
<br />
The equations used are the same as those in the 2D cell population response model, but with the equations governing diffusions changing from the two-dimension form to their three-dimension counterparts.<br />
<br />
{|align="center"<br />
| {{:Team:NTU-Taida/Templates/Vid|num=10 Full Thumbnails |width=400px|name=image24.gif}}<br />
| {{:Team:NTU-Taida/Templates/Vid|num=10 Enlargement |width=400px|name=image26.gif}}<br />
|}<br />
<br />
{|align="center"<br />
| {{:Team:NTU-Taida/Templates/Vid|num=11 Full Thumbnails |width=400px|name=image25.gif}}<br />
| {{:Team:NTU-Taida/Templates/Vid|num=11 Enlargement |width=400px|name=image27.gif}}<br />
|}<br />
<br />
<br />
<br />
Video 10 shows the result of system without quorum sensing module while Video 11 shows the result of system with quorum sensing module. From Video 10 and 11, we can see that GLP-1 starts to be expressed at similar time point at the intestinal wall on the z=0 plane. However, the GLP-1 expression spreads faster along the z-axis in system with quorum sensing.<br />
<br />
==Reference==<br />
<ol id='Ref'><br />
<li>Jordi Garcia-Ojalvo , Michael B. Elowitz, and Steven H. Strogatz , Modeling a synthetic multicellular clock: Repressilators coupled by quorum sensing, pnas,2004</li><br />
</ol><br />
<!--EOF--><br />
{{:Team:NTU-Taida/Templates/ContentEnd}}{{:Team:NTU-Taida/Templates/Footer|ActiveNavbar=Modeling, #nav-Modeling-Combined}}</div>Lbwanghttp://2012.igem.org/File:NTU-Taida-Model-Combined-video8-1.gifFile:NTU-Taida-Model-Combined-video8-1.gif2013-01-03T14:30:10Z<p>Lbwang: </p>
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<div></div>Lbwanghttp://2012.igem.org/File:NTU-Taida-Model-Combined-video7-2.gifFile:NTU-Taida-Model-Combined-video7-2.gif2013-01-03T14:29:54Z<p>Lbwang: </p>
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<div></div>Lbwanghttp://2012.igem.org/File:NTU-Taida-Model-Combined-video7-1.gifFile:NTU-Taida-Model-Combined-video7-1.gif2013-01-03T14:29:38Z<p>Lbwang: </p>
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<div></div>Lbwanghttp://2012.igem.org/File:NTU-Taida-Model-Combined-video6-2.gifFile:NTU-Taida-Model-Combined-video6-2.gif2013-01-03T14:29:17Z<p>Lbwang: uploaded a new version of &quot;File:NTU-Taida-Model-Combined-video6-2.gif&quot;</p>
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<div></div>Lbwanghttp://2012.igem.org/File:NTU-Taida-Model-Combined-video6-2.gifFile:NTU-Taida-Model-Combined-video6-2.gif2013-01-03T14:28:32Z<p>Lbwang: uploaded a new version of &quot;File:NTU-Taida-Model-Combined-video6-2.gif&quot;</p>
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<div></div>Lbwanghttp://2012.igem.org/File:NTU-Taida-Model-Combined-video6-2.gifFile:NTU-Taida-Model-Combined-video6-2.gif2013-01-03T14:28:01Z<p>Lbwang: </p>
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<div></div>Lbwanghttp://2012.igem.org/File:NTU-Taida-Model-Combined-video6-1.gifFile:NTU-Taida-Model-Combined-video6-1.gif2013-01-03T14:27:48Z<p>Lbwang: </p>
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<div></div>Lbwanghttp://2012.igem.org/File:NTU-Taida-Model-Combined-video5-2.gifFile:NTU-Taida-Model-Combined-video5-2.gif2013-01-03T14:27:32Z<p>Lbwang: </p>
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<div></div>Lbwanghttp://2012.igem.org/File:NTU-Taida-Model-Combined-video5-1.gifFile:NTU-Taida-Model-Combined-video5-1.gif2013-01-03T14:27:13Z<p>Lbwang: </p>
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<div></div>Lbwanghttp://2012.igem.org/File:NTU-Taida-Model-Combined-video4-2.gifFile:NTU-Taida-Model-Combined-video4-2.gif2013-01-03T14:26:58Z<p>Lbwang: </p>
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<div></div>Lbwanghttp://2012.igem.org/File:NTU-Taida-Model-Combined-video4-1.gifFile:NTU-Taida-Model-Combined-video4-1.gif2013-01-03T14:26:42Z<p>Lbwang: </p>
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<div></div>Lbwanghttp://2012.igem.org/Team:NTU-Taida/Modeling/2D-3D-CombinedTeam:NTU-Taida/Modeling/2D-3D-Combined2013-01-03T14:26:19Z<p>Lbwang: /* FA */</p>
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<div>{{:Team:NTU-Taida/Templates/Header}}{{:Team:NTU-Taida/Templates/Navbar}}{{:Team:NTU-Taida/Templates/Sidebar|Title=2D &amp; 3D Combined Model}}{{:Team:NTU-Taida/Templates/ContentStart}}<br />
{{:Team:NTU-Taida/Templates/BSHero|Title=2D &amp; 3D Combined Model|Content=<p></p>}}<br />
<br />
== Overview ==<br />
<p style="text-indent: 2em;"><br />
With the single cell model, fatty acid reaction-absorption model, and system analysis, we have verified the '''filter function''' of our circuit, simulated the '''real physiological fatty acid level at intestinal wall''', and '''adjust our filter threshold to fit to the real condition'''. Next, we want to combine them together and see what would happen when we put cells in the intestine after a fatty meal.<br />
</p><br />
<p style="text-indent: 2em;"><br />
The combined model is composed of three different sections. 2D combined model simulates the GLP1 response of Pepdex E-coli cells after the food intake in the x-y cross-sectional plane. 2D Cell population response model further considers the possible uneven concentration of fatty acid along the z-axis due to non-uniform distribution of lipase and simulates how the quorum sensing system assists our system to overcame this possible limitation and enhance the response. Finally, '''3D Cell population response model incorporates all the consideration to generate a full model to visualize the dynamic behavior of our system.'''<br />
</p><br />
<br />
==2D Combined Model==<br />
So far, we have the spatial-temporal concentration of fatty acid, and cells with suitable threshold. In this model, we want to see what would happen when we put cells in the intestine after a meal. <br />
<br />
[[File:NTU-Taida-Model-Combined-fig1.png|600px|center|thumb|Figure 1]]<br />
<br />
We achieve this by further coupling the single cell ODEs (with parameters adjusted by system analysis) locally to the fatty acid reaction-absorption model at the intestinal wall, as shown in Figure 2.<br />
<br />
[[File:NTU-Taida-Model-Combined-fig2.png|600px|center|thumb|Figure 2]]<br />
<br />
Besides to see the cell response when combined with the environmental input, we also want to simulate the prolonged effect of the quorum sensing module with physiological input. Therefore, we simulate system with and without quorum sensing modules and compare their results.<br />
<br />
===Spatial-temporal Model Equations ===<br />
The equations used in our 2D combined model mainly come from the reaction-absorption model and the single cell model. The following three equations are the same as those in the reaction-absorption model, which simulates the change in fatty acid concentration in time and space. <br />
<br />
{{:Team:NTU-Taida/Templates/Eq|num=1|eq=<br />
\frac{d fat}{d t} = -\frac{k_{cat}[E]_t\cdot[S]}{K_m + [S]} <br />
}}<br />
<br />
{{:Team:NTU-Taida/Templates/Eq|num=2|eq=<br />
\frac{d FA}{d t} = 3 \cdot \frac{k_{cat}[E]_t\cdot[S]}{K_m + [S]} <br />
}}<br />
<br />
{{:Team:NTU-Taida/Templates/Eq|num=3|eq=<br />
J=(C_1 - C_2)(D_{FA}/d) <br />
}}<br />
<br />
Other equations in the model are almost the same as those derived in our single cell model, with slightly difference in those for AHL, which will be discussed thoroughly in the 2D Cell population response model. The equations are shown as below.<br />
<br />
{{:Team:NTU-Taida/Templates/Eq|num=4|eq=<br />
\frac{d FadR}{d t} = \alpha_{FadR} - \gamma_{FadR} \cdot FadR <br />
}}<br />
<br />
$$X_{FadR} = \frac{FadR \cdot \beta_{FA}^{n2}}{FA^{n2} + \beta_{FA}^{n2}}$$<br />
{{:Team:NTU-Taida/Templates/Eq|num=5|eq=<br />
}}<br />
<br />
$$\frac{dTetR_1}{dt} = \frac{\alpha_{TetR_1} \cdot {\beta_{FadR}^{n1}}}{\beta_{FadR}^{n1} + X_{FadR}^{n1}} - \gamma_{TetR_1} \cdot TetR_1 $$<br />
{{:Team:NTU-Taida/Templates/Eq|num=6|eq=<br />
}}<br />
<br />
$$\frac{d TetR_2}{d t} = \frac{\alpha_{TetR_2} \cdot R^{n3}}{\beta_R^{n3} + R^{n3}} - \gamma_{TetR_2} \cdot TetR_2$$<br />
{{:Team:NTU-Taida/Templates/Eq|num=7|eq=<br />
}}<br />
<br />
$$\frac{d LuxI}{d t} = \frac{\alpha_{LuxI} \cdot \beta_{FadR}^{n1}}{\beta_{FadR}^{n1} + X_{FadR}^{n1}} - \gamma_{LuxI} \cdot LuxI$$<br />
{{:Team:NTU-Taida/Templates/Eq|num=8|eq=<br />
}}<br />
<br />
$$\frac{\partial^2 AHL}{\partial x^2} + \frac{\partial^2 AHL}{y^2} - \frac{1}{D_{AHL}}\cdot \frac{\partial AHL}{\partial t} = 0$$<br />
{{:Team:NTU-Taida/Templates/Eq|num=9|eq=<br />
}}<br />
<br />
$$R(AHL) = - \gamma_{AHL_{ext}} \cdot AHL + cd(k_{s1}LuxI - k_{s0}AHL)$$<br />
{{:Team:NTU-Taida/Templates/Eq|num=10|eq=<br />
}}<br />
<br />
$$\frac{d R}{d t} = \rho (LuxR)^2(AHL_i)^2 - \gamma_R \cdot R$$<br />
{{:Team:NTU-Taida/Templates/Eq|num=11|eq=<br />
}}<br />
<br />
$$\frac{d LacI}{d t} = \frac{\alpha_{LacI}}{1 + (\frac{TetR_1 + TetR_2}{\beta_{TetR}})^{n5}} - \gamma_{LacI} \cdot LacI$$<br />
{{:Team:NTU-Taida/Templates/Eq|num=12|eq=<br />
}}<br />
<br />
$$\frac{d GLP1}{d t} = \frac{\alpha_{GLP1}}{1 + (\frac{LacI}{\beta_{LacI}})^{n6}} - \gamma_{GLP1} \cdot GLP1$$<br />
{{:Team:NTU-Taida/Templates/Eq|num=13|eq=<br />
}}<br />
<br />
<br />
For the control group without the quorum sensing module, we simply discard the terms related to quorum sensing system in the ODE set.<br />
<br />
===Results===<br />
<br />
{| align='center'<br />
| {{:Team:NTU-Taida/Templates/Vid|num=1.1 Fatty acid concentration|width=350px|name=NTU-Taida-Model-Combined-Image5.gif}}<br />
| {{:Team:NTU-Taida/Templates/Vid|num=1.2 Closer look of fatty acid concentration|width=350px|name=NTU-Taida-Model-Combined-Image8.gif}}<br />
|}<br />
{| align='center'<br />
| {{:Team:NTU-Taida/Templates/Vid|num=2.1 GLP-1 expression in system without quorum sensing|width=350px|name=NTU-Taida-Model-Combined-Image4.gif}}<br />
| {{:Team:NTU-Taida/Templates/Vid|num=2.2 Closer look ofGLP-1 expression in system without quorum sensing|width=350px|name=NTU-Taida-Model-Combined-Image7.gif}}<br />
|}<br />
{| align='center'<br />
| {{:Team:NTU-Taida/Templates/Vid|num=3.1 GLP-1 expression in system with quorum sensing|width=350px|name=NTU-Taida-Model-Combined-Image3.gif}}<br />
| {{:Team:NTU-Taida/Templates/Vid|num=3.2 Closer look at GLP-1 expression in system with quorum sensing|width=350px|name=NTU-Taida-Model-Combined-Image6.gif}} <br />
|}<br />
<br />
Video 1 shows the spatial temporal concentration change of fatty acid. Video 2 and three show the corresponding spatial temporal response of GLP-1 expression in system without and with quorum sensing module, respectively.<br />
<br />
We can see from the videos that the fatty acid concentration at the intestinal wall first increases rapidly, turning on the circuits in the cells and resulting in GLP-1 expression at the intestinal wall. Then due to the absorption of fatty acid, the concentration gradually falls and the GLP-1 concentration started to decrease. Notice that the GLP1 expression in the system with Quorum sensing, shown in Video 3, lasts longer than that of the system without quorum sensing, shown in Video 2. Consistent to the single cell model, the system with QS has more prolonged response compared to the one without it.<br />
<br />
==Cell Population Response Model==<br />
<br />
We have assumed that fat distributes uniformly along the z-axis in the lumen after a meal in the previous models. However, in real situation in human body, lipase only exists in certain segments of the intestine. Therefore, fat hydrolysis will only take place in those segments and there will be no fatty acid produced outside these segments, as shown in Figure 3. Cells residing in the segments without lipase activity can only sense the fatty acid diffused from the source segments. Because AHL diffuses faster than fatty acid, we incorporate the quorum sensing system to enable faster recruitment of more bacteria to express GLP-1 in regions without lipase.<br />
<br />
Quorum sensing module enables cells to communicate with each other, as the uneven distribution of fatty acid in the intestines may cause gaps in individual detection. Cells with the quorum sensing module can respond to food intake event as long as their neighboring cells have detected fatty acid, enhancing the overall response to the food intake (Figure 4). However, the communication between cells via AHL can’t be seen when only viewing a single cell. Therefore, we construct spatial temporal models with COMSOL Multiphysics in order to gain insights into the influence of cell-cell communication mediated via the quorum sensing module on the overall GLP1 expression.<br />
<br />
[[File:NTU-Taida-Model-Combined-fig3.png|600px|center|thumb|Figure 3]]<br />
[[File:NTU-Taida-Model-Combined-fig4.png|600px|center|thumb|Figure 4]]<br />
<br />
==2D Cell Population Response Model==<br />
We start our effort with a 2D spatial temporal model. When E.coli cells colonize the intestine, they tend to attach onto the intestinal walls instead of distributing evenly throughout the intestine lumen. Therefore, we first view our system as a two dimensional system, with the modeling plane in the x-z (or either y-z) dimension.<br />
<br />
===Geometry Design===<br />
[[File:NTU-Taida-Model-Combined-fig5.png|600px|center|thumb|Figure 5]]<br />
<br />
With this in mind, we construct a plane in 2D geometry and couple the ODEs derived in our single cell model to simulate the presence of cells.<br />
<br />
To model the effect of quorum sensing, we establish an uneven distribution of fatty acid by giving a constant concentration source of fatty acid in the middle of our modeled plane, as shown in Figure 6. There are no cells within the circular fatty acid source. As time goes on, fatty acids diffuse from the source and establish a concentric gradient. To see the effect of quorum sensing mechanism on overall GLP1 expression in a cell population with uneven distributed fatty acid input, we model cells with and without quorum sensing and compare their spatial –temporal GLP1 expression.<br />
[[File:NTU-Taida-Model-Combined-fig6.png|600px|center|thumb|Figure 6]]<br />
<br />
===Spatial-temporal Model Equations===<br />
The first equation used in our model describes the free diffusion of fatty acids from the central source.<br />
<br />
$$\frac{\partial^2 FA}{\partial x^2} + \frac{\partial^2 FA}{\partial z^2} - \frac{1}{D_{FA}} \frac{\partial FA}{\partial t} = 0$$<br />
{{:Team:NTU-Taida/Templates/Eq|num=14|eq=<br />
}}<br />
<br />
Other equations in the model are almost the same as those derived in our single cell model, except for the ones for AHL. For AHL, we have to set up a partial differential equation describing both the diffusion and the reaction event of AHL. We assume that AHL diffusion into and out of cells is fast and do not model this diffusion process explicitly. Therefore, in contrast to the single-cell model, we only use one species called AHL instead of an internal AHL concentration AHLi and an external AHL concentration AHLe. <br />
<br />
For the reaction term of AHL, we first discard the terms describing the diffusion into and out of the cell membrane in the ODEs of AHLi and AHLe in the single cell model. <br />
As previously mentioned, we assume that the diffusion AHL diffusion into and out of cells is fast. Therefore, we simply account for the diffusion of AHL across cell membrane by multiplying the intracellular AHLi terms by the relative cell density, which will be described in the next section. With these considerations, we combine the two equations of AHLi and AHLe (Eq. 15 and Eq. 16) into one reaction equation (Eq. 17 ).<br />
<br />
{{:Team:NTU-Taida/Templates/Eq|num=15|eq=\frac{d AHL_i}{d t} = ks1 \cdot LuxI - ks0 \cdot AHL_i - \eta (AHL_i - AHL_e)<br />
}}<br />
<br />
{{:Team:NTU-Taida/Templates/Eq|num=16|eq=\frac{d AHL_e}{d t} = - kse \cdot AHL_e + \eta_{Ext} (AHL_i - AHL_e)<br />
}}<br />
<br />
$$R (AHL) = - \gamma_{AHL_{ext}} \cdot AHL + cd (k_{s1} \cdot LuxI - k_{s0} \cdot AHL)$$<br />
{{:Team:NTU-Taida/Templates/Eq|num=17|eq=<br />
}}<br />
<br />
With the help of COMSOL Multiphysics, we can consider both the diffusion and reaction terms of AHL by giving the diffusion (Eq. 14) and reaction (Eq. 17) equations above, without the need to solve the explicit PDE of AHL.<br />
<br />
The diffusion of AHL is modeled by a free diffusion equation.<br />
<br />
$$ \frac{\partial^2 AHL}{\partial x^2} + \frac{\partial^2 AHL}{\partial z^2} - \frac{1}{D_{AHL}} \frac{\partial AHL}{\partial t} = 0$$<br />
{{:Team:NTU-Taida/Templates/Eq|num=18|eq=<br />
}}<br />
<br />
Other equations in the model are the same as those derived in our single cell model.<br />
For the control group without the quorum sensing module, we discard the terms related to quorum sensing system in the ODE set.<br />
<br />
==Relative Cell density==<br />
The relative cell density is defined as the ratio of the total area E.coli cells occupy to the area of the intestinal wall. By multiplying the intracellular AHL synthesis and degradation terms by the relative cell density, we assume that as a cell synthesizes or degrades AHL, the addition or reduction of AHL molecules is dispersed evenly through the neighboring area. (Mind that the diffusion of these AHL molecules on global scale is still governed by the free diffusion equation.)<br />
<br />
We calculated the relative cell density by assuming there are 1014 bacteria cells residing in the intestine, which has a total surface area of 200 m2. Thus, the average cell density is 5*1011 cells/m2. We can measure the surface area of each individual cell by multiplying their length by their width, giving a surface area of 10-12 m2 per cell. Multiplying the surface area per cell and the average cell density gives the area density of total cells as 0.5. <br />
Since 99% of the gut flora consists of 30-40 species of bacteria, we can assume that each of the common types contribute to approximately 1% of the total surface area of the intestine. Considering the clustering effect of cells, we assume that some regions would have much higher cell densities than others, such that the uneven distribution may result in a tenfold fluctuation in cell density. We hypothesize that the relative cell density in our model could be as high as 0.1.<br />
<br />
Cell density has dramatic effect on the overall effect of quorum sensing system, as supported by a recent study investigating the synchronization of repressilators by quorum sensing mechanisms [1]. Therefore, we also model our system with different cell densities, as can be seen in the results.<br />
<br />
===Results===<br />
To see the effect of quorum sensing mechanism on overall GLP1 expression in a cell population with uneven distributed fatty acid input, we model cells with and without quorum sensing and compare their spatial - temporal GLP1 expression, with relative cell density of 0.1<br />
The results show that species which are not regulated by the quorum sensing module, such as FA, X_FadR, and TetR1, show no difference in the spatial temporal expression pattern between system with and without the quorum sensing system. <br />
<br />
However, species affected by the quorum sensing module, such as LacI and GLP1, show striking difference in their spatial temporal concentration pattern. Within the given time span, systems with a quorum sensing module produces GLP1 over a broader spatial region, resulting in more total GLP1. <br />
<br />
===Species unregulated by the quorum sensing module===<br />
<br />
====FA====<br />
<br />
{| align='center'<br />
| {{:Team:NTU-Taida/Templates/Vid|num=4.1 |width=350px|name=NTU-Taida-Model-Combined-video4-1.gif}}<br />
| {{:Team:NTU-Taida/Templates/Vid|num=4.2 |width=350px|name=NTU-Taida-Model-Combined-video4-2.gif}}<br />
|}<br />
<br />
====X_fadR====<br />
{| align='center'<br />
| {{:Team:NTU-Taida/Templates/Vid|num=5.1 |width=350px|name=NTU-Taida-Model-Combined-Image13.gif}}<br />
| {{:Team:NTU-Taida/Templates/Vid|num=5.2 |width=350px|name=NTU-Taida-Model-Combined-Image14.gif}}<br />
|}<br />
{| align='center'<br />
| {{:Team:NTU-Taida/Templates/Vid|num=6.1 |width=350px|name=NTU-Taida-Model-Combined-Image15.gif}}<br />
| {{:Team:NTU-Taida/Templates/Vid|num=6.2 |width=350px|name=NTU-Taida-Model-Combined-Image16.gif}}<br />
|}<br />
<br />
===Species regulated by the quorum sensing module===<br />
====LacI====<br />
<br />
{|align="center"<br />
| {{:Team:NTU-Taida/Templates/Vid|num=7-1 |width=350px|name=image15.gif}}<br />
| {{:Team:NTU-Taida/Templates/Vid|num=7-2 |width=350px|name=image16.gif}}<br />
|}<br />
<br />
The expression of LacI is inhibited by TetR proteins, and therefore is regulated by the quorum sensing module. Although the concentration of TetR1 is the same in systems with and without quorum sensing, cells with quorum sensing produce TetR2 as the output of the quorum sensing module and therefore result in overall more total TetR proteins. Thus, the repression of LacI is more significant in systems with the quorum sensing module.<br />
<br />
====GLP1====<br />
{|align="center"<br />
| {{:Team:NTU-Taida/Templates/Vid|num=8-1 |width=350px|name=image17.gif}}<br />
| {{:Team:NTU-Taida/Templates/Vid|num=8-2 |width=350px|name=image18.gif}}<br />
|}<br />
<br />
As the expression of GLP1 is repressed by LacI proteins, GLP1 also displays different spatial-temporal concentration pattern between the two systems. With quorum sensing module, the system produces more GLP1 overall.<br />
<br />
===Effect of cell density===<br />
<br />
Relative cell density plays a critical role in determining whether we can see a significant difference between systems with and without quorum sensing. We simulated the spatial-temporal response of GLP1 of four systems, all of them with the quorum sensing module but with relative cell densities of 0.2, 0.1, and 0.01, respectively. <br />
<br />
Then we compare their response to that of system without quorum sensing to determine if there exists a threshold of cell density, below which the effect of quorum sensing module is unperceivable. <br />
<br />
{|align="center"<br />
| {{:Team:NTU-Taida/Templates/Vid|num=9-1 cd = 0.2 |width=280px|name=NTU-Taida-Model-Combined-video9-1.gif}}<br />
| {{:Team:NTU-Taida/Templates/Vid|num=9-2 cd = 0.1 |width=280px|name=NTU-Taida-Model-Combined-video9-2.gif}}<br />
| {{:Team:NTU-Taida/Templates/Vid|num=9-3 cd = 0.05 |width=280px|name=NTU-Taida-Model-Combined-video9-3.gif}}<br />
|}<br />
<br />
{|align="center"<br />
| {{:Team:NTU-Taida/Templates/Vid|num=9-4 cd = 0.01 |width=280px|name=NTU-Taida-Model-Combined-video9-4.gif}}<br />
| {{:Team:NTU-Taida/Templates/Vid|num=9-5 without quorum sensing module |width=280px|name=NTU-Taida-Model-Combined-video9-5.gif}}<br />
|}<br />
<br />
<br />
<br />
We can see from Video 9 that the system with a relative cell density of 0.2 differs most with the system without the quorum sensing module. The system with a relative cell density of 0.1 shows moderate difference. The system with a relative cell density of 0.05 displays very subtle difference. There is no difference between the system with a relative cell density of 0.01 and the system with no quorum sensing module. Therefore, the threshold of relative cell density may lie between 0.05 and 0.01.<br />
<br />
==3D Cell population response model==<br />
<br />
Finally, we construct a full 3D model, combing the consideration on the x-y plane and the x-z plane. Our goal is to simulate the effect of non-uniform production of fatty acid due to the spatially limited lipase activity. We modeled the intestine by a cylindrical tube, with a fat source limited to the z=0 plane, to simulate the situations similar to that shown in Figure 7, and examine the effect of Quorum sensing. <br />
<br />
[[File:NTU-Taida-Model-Combined-fig7.png|600px|center|thumb|Figure 7]]<br />
<br />
The equations used are the same as those in the 2D cell population response model, but with the equations governing diffusions changing from the two-dimension form to their three-dimension counterparts.<br />
<br />
{|align="center"<br />
| {{:Team:NTU-Taida/Templates/Vid|num=10 Full Thumbnails |width=400px|name=image24.gif}}<br />
| {{:Team:NTU-Taida/Templates/Vid|num=10 Enlargement |width=400px|name=image26.gif}}<br />
|}<br />
<br />
{|align="center"<br />
| {{:Team:NTU-Taida/Templates/Vid|num=11 Full Thumbnails |width=400px|name=image25.gif}}<br />
| {{:Team:NTU-Taida/Templates/Vid|num=11 Enlargement |width=400px|name=image27.gif}}<br />
|}<br />
<br />
<br />
<br />
Video 10 shows the result of system without quorum sensing module while Video 11 shows the result of system with quorum sensing module. From Video 10 and 11, we can see that GLP-1 starts to be expressed at similar time point at the intestinal wall on the z=0 plane. However, the GLP-1 expression spreads faster along the z-axis in system with quorum sensing.<br />
<br />
==Reference==<br />
<ol id='Ref'><br />
<li>Jordi Garcia-Ojalvo , Michael B. Elowitz, and Steven H. Strogatz , Modeling a synthetic multicellular clock: Repressilators coupled by quorum sensing, pnas,2004</li><br />
</ol><br />
<!--EOF--><br />
{{:Team:NTU-Taida/Templates/ContentEnd}}{{:Team:NTU-Taida/Templates/Footer|ActiveNavbar=Modeling, #nav-Modeling-Combined}}</div>Lbwanghttp://2012.igem.org/File:NTU-Taida-Model-Combined-Image16.gifFile:NTU-Taida-Model-Combined-Image16.gif2013-01-03T14:22:07Z<p>Lbwang: uploaded a new version of &quot;File:NTU-Taida-Model-Combined-Image16.gif&quot;</p>
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<div></div>Lbwanghttp://2012.igem.org/Team:NTU-Taida/Modeling/2D-3D-CombinedTeam:NTU-Taida/Modeling/2D-3D-Combined2013-01-03T13:41:24Z<p>Lbwang: </p>
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<div>{{:Team:NTU-Taida/Templates/Header}}{{:Team:NTU-Taida/Templates/Navbar}}{{:Team:NTU-Taida/Templates/Sidebar|Title=2D &amp; 3D Combined Model}}{{:Team:NTU-Taida/Templates/ContentStart}}<br />
{{:Team:NTU-Taida/Templates/BSHero|Title=2D &amp; 3D Combined Model|Content=<p></p>}}<br />
<br />
== Overview ==<br />
<p style="text-indent: 2em;"><br />
With the single cell model, fatty acid reaction-absorption model, and system analysis, we have verified the '''filter function''' of our circuit, simulated the '''real physiological fatty acid level at intestinal wall''', and '''adjust our filter threshold to fit to the real condition'''. Next, we want to combine them together and see what would happen when we put cells in the intestine after a fatty meal.<br />
</p><br />
<p style="text-indent: 2em;"><br />
The combined model is composed of three different sections. 2D combined model simulates the GLP1 response of Pepdex E-coli cells after the food intake in the x-y cross-sectional plane. 2D Cell population response model further considers the possible uneven concentration of fatty acid along the z-axis due to non-uniform distribution of lipase and simulates how the quorum sensing system assists our system to overcame this possible limitation and enhance the response. Finally, '''3D Cell population response model incorporates all the consideration to generate a full model to visualize the dynamic behavior of our system.'''<br />
</p><br />
<br />
==2D Combined Model==<br />
So far, we have the spatial-temporal concentration of fatty acid, and cells with suitable threshold. In this model, we want to see what would happen when we put cells in the intestine after a meal. <br />
<br />
[[File:NTU-Taida-Model-Combined-fig1.png|600px|center|thumb|Figure 1]]<br />
<br />
We achieve this by further coupling the single cell ODEs (with parameters adjusted by system analysis) locally to the fatty acid reaction-absorption model at the intestinal wall, as shown in Figure 2.<br />
<br />
[[File:NTU-Taida-Model-Combined-fig2.png|600px|center|thumb|Figure 2]]<br />
<br />
Besides to see the cell response when combined with the environmental input, we also want to simulate the prolonged effect of the quorum sensing module with physiological input. Therefore, we simulate system with and without quorum sensing modules and compare their results.<br />
<br />
===Spatial-temporal Model Equations ===<br />
The equations used in our 2D combined model mainly come from the reaction-absorption model and the single cell model. The following three equations are the same as those in the reaction-absorption model, which simulates the change in fatty acid concentration in time and space. <br />
<br />
{{:Team:NTU-Taida/Templates/Eq|num=1|eq=<br />
\frac{d fat}{d t} = -\frac{k_{cat}[E]_t\cdot[S]}{K_m + [S]} <br />
}}<br />
<br />
{{:Team:NTU-Taida/Templates/Eq|num=2|eq=<br />
\frac{d FA}{d t} = 3 \cdot \frac{k_{cat}[E]_t\cdot[S]}{K_m + [S]} <br />
}}<br />
<br />
{{:Team:NTU-Taida/Templates/Eq|num=3|eq=<br />
J=(C_1 - C_2)(D_{FA}/d) <br />
}}<br />
<br />
Other equations in the model are almost the same as those derived in our single cell model, with slightly difference in those for AHL, which will be discussed thoroughly in the 2D Cell population response model. The equations are shown as below.<br />
<br />
{{:Team:NTU-Taida/Templates/Eq|num=4|eq=<br />
\frac{d FadR}{d t} = \alpha_{FadR} - \gamma_{FadR} \cdot FadR <br />
}}<br />
<br />
$$X_{FadR} = \frac{FadR \cdot \beta_{FA}^{n2}}{FA^{n2} + \beta_{FA}^{n2}}$$<br />
{{:Team:NTU-Taida/Templates/Eq|num=5|eq=<br />
}}<br />
<br />
$$\frac{dTetR_1}{dt} = \frac{\alpha_{TetR_1} \cdot {\beta_{FadR}^{n1}}}{\beta_{FadR}^{n1} + X_{FadR}^{n1}} - \gamma_{TetR_1} \cdot TetR_1 $$<br />
{{:Team:NTU-Taida/Templates/Eq|num=6|eq=<br />
}}<br />
<br />
$$\frac{d TetR_2}{d t} = \frac{\alpha_{TetR_2} \cdot R^{n3}}{\beta_R^{n3} + R^{n3}} - \gamma_{TetR_2} \cdot TetR_2$$<br />
{{:Team:NTU-Taida/Templates/Eq|num=7|eq=<br />
}}<br />
<br />
$$\frac{d LuxI}{d t} = \frac{\alpha_{LuxI} \cdot \beta_{FadR}^{n1}}{\beta_{FadR}^{n1} + X_{FadR}^{n1}} - \gamma_{LuxI} \cdot LuxI$$<br />
{{:Team:NTU-Taida/Templates/Eq|num=8|eq=<br />
}}<br />
<br />
$$\frac{\partial^2 AHL}{\partial x^2} + \frac{\partial^2 AHL}{y^2} - \frac{1}{D_{AHL}}\cdot \frac{\partial AHL}{\partial t} = 0$$<br />
{{:Team:NTU-Taida/Templates/Eq|num=9|eq=<br />
}}<br />
<br />
$$R(AHL) = - \gamma_{AHL_{ext}} \cdot AHL + cd(k_{s1}LuxI - k_{s0}AHL)$$<br />
{{:Team:NTU-Taida/Templates/Eq|num=10|eq=<br />
}}<br />
<br />
$$\frac{d R}{d t} = \rho (LuxR)^2(AHL_i)^2 - \gamma_R \cdot R$$<br />
{{:Team:NTU-Taida/Templates/Eq|num=11|eq=<br />
}}<br />
<br />
$$\frac{d LacI}{d t} = \frac{\alpha_{LacI}}{1 + (\frac{TetR_1 + TetR_2}{\beta_{TetR}})^{n5}} - \gamma_{LacI} \cdot LacI$$<br />
{{:Team:NTU-Taida/Templates/Eq|num=12|eq=<br />
}}<br />
<br />
$$\frac{d GLP1}{d t} = \frac{\alpha_{GLP1}}{1 + (\frac{LacI}{\beta_{LacI}})^{n6}} - \gamma_{GLP1} \cdot GLP1$$<br />
{{:Team:NTU-Taida/Templates/Eq|num=13|eq=<br />
}}<br />
<br />
<br />
For the control group without the quorum sensing module, we simply discard the terms related to quorum sensing system in the ODE set.<br />
<br />
===Results===<br />
<br />
{| align='center'<br />
| {{:Team:NTU-Taida/Templates/Vid|num=1.1 Fatty acid concentration|width=350px|name=NTU-Taida-Model-Combined-Image5.gif}}<br />
| {{:Team:NTU-Taida/Templates/Vid|num=1.2 Closer look of fatty acid concentration|width=350px|name=NTU-Taida-Model-Combined-Image8.gif}}<br />
|}<br />
{| align='center'<br />
| {{:Team:NTU-Taida/Templates/Vid|num=2.1 GLP-1 expression in system without quorum sensing|width=350px|name=NTU-Taida-Model-Combined-Image4.gif}}<br />
| {{:Team:NTU-Taida/Templates/Vid|num=2.2 Closer look ofGLP-1 expression in system without quorum sensing|width=350px|name=NTU-Taida-Model-Combined-Image7.gif}}<br />
|}<br />
{| align='center'<br />
| {{:Team:NTU-Taida/Templates/Vid|num=3.1 GLP-1 expression in system with quorum sensing|width=350px|name=NTU-Taida-Model-Combined-Image3.gif}}<br />
| {{:Team:NTU-Taida/Templates/Vid|num=3.2 Closer look at GLP-1 expression in system with quorum sensing|width=350px|name=NTU-Taida-Model-Combined-Image6.gif}} <br />
|}<br />
<br />
Video 1 shows the spatial temporal concentration change of fatty acid. Video 2 and three show the corresponding spatial temporal response of GLP-1 expression in system without and with quorum sensing module, respectively.<br />
<br />
We can see from the videos that the fatty acid concentration at the intestinal wall first increases rapidly, turning on the circuits in the cells and resulting in GLP-1 expression at the intestinal wall. Then due to the absorption of fatty acid, the concentration gradually falls and the GLP-1 concentration started to decrease. Notice that the GLP1 expression in the system with Quorum sensing, shown in Video 3, lasts longer than that of the system without quorum sensing, shown in Video 2. Consistent to the single cell model, the system with QS has more prolonged response compared to the one without it.<br />
<br />
==Cell Population Response Model==<br />
<br />
We have assumed that fat distributes uniformly along the z-axis in the lumen after a meal in the previous models. However, in real situation in human body, lipase only exists in certain segments of the intestine. Therefore, fat hydrolysis will only take place in those segments and there will be no fatty acid produced outside these segments, as shown in Figure 3. Cells residing in the segments without lipase activity can only sense the fatty acid diffused from the source segments. Because AHL diffuses faster than fatty acid, we incorporate the quorum sensing system to enable faster recruitment of more bacteria to express GLP-1 in regions without lipase.<br />
<br />
Quorum sensing module enables cells to communicate with each other, as the uneven distribution of fatty acid in the intestines may cause gaps in individual detection. Cells with the quorum sensing module can respond to food intake event as long as their neighboring cells have detected fatty acid, enhancing the overall response to the food intake (Figure 4). However, the communication between cells via AHL can’t be seen when only viewing a single cell. Therefore, we construct spatial temporal models with COMSOL Multiphysics in order to gain insights into the influence of cell-cell communication mediated via the quorum sensing module on the overall GLP1 expression.<br />
<br />
[[File:NTU-Taida-Model-Combined-fig3.png|600px|center|thumb|Figure 3]]<br />
[[File:NTU-Taida-Model-Combined-fig4.png|600px|center|thumb|Figure 4]]<br />
<br />
==2D Cell Population Response Model==<br />
We start our effort with a 2D spatial temporal model. When E.coli cells colonize the intestine, they tend to attach onto the intestinal walls instead of distributing evenly throughout the intestine lumen. Therefore, we first view our system as a two dimensional system, with the modeling plane in the x-z (or either y-z) dimension.<br />
<br />
===Geometry Design===<br />
[[File:NTU-Taida-Model-Combined-fig5.png|600px|center|thumb|Figure 5]]<br />
<br />
With this in mind, we construct a plane in 2D geometry and couple the ODEs derived in our single cell model to simulate the presence of cells.<br />
<br />
To model the effect of quorum sensing, we establish an uneven distribution of fatty acid by giving a constant concentration source of fatty acid in the middle of our modeled plane, as shown in Figure 6. There are no cells within the circular fatty acid source. As time goes on, fatty acids diffuse from the source and establish a concentric gradient. To see the effect of quorum sensing mechanism on overall GLP1 expression in a cell population with uneven distributed fatty acid input, we model cells with and without quorum sensing and compare their spatial –temporal GLP1 expression.<br />
[[File:NTU-Taida-Model-Combined-fig6.png|600px|center|thumb|Figure 6]]<br />
<br />
===Spatial-temporal Model Equations===<br />
The first equation used in our model describes the free diffusion of fatty acids from the central source.<br />
<br />
$$\frac{\partial^2 FA}{\partial x^2} + \frac{\partial^2 FA}{\partial z^2} - \frac{1}{D_{FA}} \frac{\partial FA}{\partial t} = 0$$<br />
{{:Team:NTU-Taida/Templates/Eq|num=14|eq=<br />
}}<br />
<br />
Other equations in the model are almost the same as those derived in our single cell model, except for the ones for AHL. For AHL, we have to set up a partial differential equation describing both the diffusion and the reaction event of AHL. We assume that AHL diffusion into and out of cells is fast and do not model this diffusion process explicitly. Therefore, in contrast to the single-cell model, we only use one species called AHL instead of an internal AHL concentration AHLi and an external AHL concentration AHLe. <br />
<br />
For the reaction term of AHL, we first discard the terms describing the diffusion into and out of the cell membrane in the ODEs of AHLi and AHLe in the single cell model. <br />
As previously mentioned, we assume that the diffusion AHL diffusion into and out of cells is fast. Therefore, we simply account for the diffusion of AHL across cell membrane by multiplying the intracellular AHLi terms by the relative cell density, which will be described in the next section. With these considerations, we combine the two equations of AHLi and AHLe (Eq. 15 and Eq. 16) into one reaction equation (Eq. 17 ).<br />
<br />
{{:Team:NTU-Taida/Templates/Eq|num=15|eq=\frac{d AHL_i}{d t} = ks1 \cdot LuxI - ks0 \cdot AHL_i - \eta (AHL_i - AHL_e)<br />
}}<br />
<br />
{{:Team:NTU-Taida/Templates/Eq|num=16|eq=\frac{d AHL_e}{d t} = - kse \cdot AHL_e + \eta_{Ext} (AHL_i - AHL_e)<br />
}}<br />
<br />
$$R (AHL) = - \gamma_{AHL_{ext}} \cdot AHL + cd (k_{s1} \cdot LuxI - k_{s0} \cdot AHL)$$<br />
{{:Team:NTU-Taida/Templates/Eq|num=17|eq=<br />
}}<br />
<br />
With the help of COMSOL Multiphysics, we can consider both the diffusion and reaction terms of AHL by giving the diffusion (Eq. 14) and reaction (Eq. 17) equations above, without the need to solve the explicit PDE of AHL.<br />
<br />
The diffusion of AHL is modeled by a free diffusion equation.<br />
<br />
$$ \frac{\partial^2 AHL}{\partial x^2} + \frac{\partial^2 AHL}{\partial z^2} - \frac{1}{D_{AHL}} \frac{\partial AHL}{\partial t} = 0$$<br />
{{:Team:NTU-Taida/Templates/Eq|num=18|eq=<br />
}}<br />
<br />
Other equations in the model are the same as those derived in our single cell model.<br />
For the control group without the quorum sensing module, we discard the terms related to quorum sensing system in the ODE set.<br />
<br />
==Relative Cell density==<br />
The relative cell density is defined as the ratio of the total area E.coli cells occupy to the area of the intestinal wall. By multiplying the intracellular AHL synthesis and degradation terms by the relative cell density, we assume that as a cell synthesizes or degrades AHL, the addition or reduction of AHL molecules is dispersed evenly through the neighboring area. (Mind that the diffusion of these AHL molecules on global scale is still governed by the free diffusion equation.)<br />
<br />
We calculated the relative cell density by assuming there are 1014 bacteria cells residing in the intestine, which has a total surface area of 200 m2. Thus, the average cell density is 5*1011 cells/m2. We can measure the surface area of each individual cell by multiplying their length by their width, giving a surface area of 10-12 m2 per cell. Multiplying the surface area per cell and the average cell density gives the area density of total cells as 0.5. <br />
Since 99% of the gut flora consists of 30-40 species of bacteria, we can assume that each of the common types contribute to approximately 1% of the total surface area of the intestine. Considering the clustering effect of cells, we assume that some regions would have much higher cell densities than others, such that the uneven distribution may result in a tenfold fluctuation in cell density. We hypothesize that the relative cell density in our model could be as high as 0.1.<br />
<br />
Cell density has dramatic effect on the overall effect of quorum sensing system, as supported by a recent study investigating the synchronization of repressilators by quorum sensing mechanisms [1]. Therefore, we also model our system with different cell densities, as can be seen in the results.<br />
<br />
===Results===<br />
To see the effect of quorum sensing mechanism on overall GLP1 expression in a cell population with uneven distributed fatty acid input, we model cells with and without quorum sensing and compare their spatial - temporal GLP1 expression, with relative cell density of 0.1<br />
The results show that species which are not regulated by the quorum sensing module, such as FA, X_FadR, and TetR1, show no difference in the spatial temporal expression pattern between system with and without the quorum sensing system. <br />
<br />
However, species affected by the quorum sensing module, such as LacI and GLP1, show striking difference in their spatial temporal concentration pattern. Within the given time span, systems with a quorum sensing module produces GLP1 over a broader spatial region, resulting in more total GLP1. <br />
<br />
===Species unregulated by the quorum sensing module===<br />
<br />
====FA====<br />
<br />
{| align='center'<br />
| {{:Team:NTU-Taida/Templates/Vid|num=4.1 |width=350px|name=NTU-Taida-Model-Combined-Image11.gif}}<br />
| {{:Team:NTU-Taida/Templates/Vid|num=4.2 |width=350px|name=NTU-Taida-Model-Combined-Image12.gif}}<br />
|}<br />
<br />
====X_fadR====<br />
{| align='center'<br />
| {{:Team:NTU-Taida/Templates/Vid|num=5.1 |width=350px|name=NTU-Taida-Model-Combined-Image13.gif}}<br />
| {{:Team:NTU-Taida/Templates/Vid|num=5.2 |width=350px|name=NTU-Taida-Model-Combined-Image14.gif}}<br />
|}<br />
{| align='center'<br />
| {{:Team:NTU-Taida/Templates/Vid|num=6.1 |width=350px|name=NTU-Taida-Model-Combined-Image15.gif}}<br />
| {{:Team:NTU-Taida/Templates/Vid|num=6.2 |width=350px|name=NTU-Taida-Model-Combined-Image16.gif}}<br />
|}<br />
<br />
===Species regulated by the quorum sensing module===<br />
====LacI====<br />
<br />
{|align="center"<br />
| {{:Team:NTU-Taida/Templates/Vid|num=7-1 |width=350px|name=image15.gif}}<br />
| {{:Team:NTU-Taida/Templates/Vid|num=7-2 |width=350px|name=image16.gif}}<br />
|}<br />
<br />
The expression of LacI is inhibited by TetR proteins, and therefore is regulated by the quorum sensing module. Although the concentration of TetR1 is the same in systems with and without quorum sensing, cells with quorum sensing produce TetR2 as the output of the quorum sensing module and therefore result in overall more total TetR proteins. Thus, the repression of LacI is more significant in systems with the quorum sensing module.<br />
<br />
====GLP1====<br />
{|align="center"<br />
| {{:Team:NTU-Taida/Templates/Vid|num=8-1 |width=350px|name=image17.gif}}<br />
| {{:Team:NTU-Taida/Templates/Vid|num=8-2 |width=350px|name=image18.gif}}<br />
|}<br />
<br />
As the expression of GLP1 is repressed by LacI proteins, GLP1 also displays different spatial-temporal concentration pattern between the two systems. With quorum sensing module, the system produces more GLP1 overall.<br />
<br />
===Effect of cell density===<br />
<br />
Relative cell density plays a critical role in determining whether we can see a significant difference between systems with and without quorum sensing. We simulated the spatial-temporal response of GLP1 of four systems, all of them with the quorum sensing module but with relative cell densities of 0.2, 0.1, and 0.01, respectively. <br />
<br />
Then we compare their response to that of system without quorum sensing to determine if there exists a threshold of cell density, below which the effect of quorum sensing module is unperceivable. <br />
<br />
{|align="center"<br />
| {{:Team:NTU-Taida/Templates/Vid|num=9-1 cd = 0.2 |width=280px|name=NTU-Taida-Model-Combined-video9-1.gif}}<br />
| {{:Team:NTU-Taida/Templates/Vid|num=9-2 cd = 0.1 |width=280px|name=NTU-Taida-Model-Combined-video9-2.gif}}<br />
| {{:Team:NTU-Taida/Templates/Vid|num=9-3 cd = 0.05 |width=280px|name=NTU-Taida-Model-Combined-video9-3.gif}}<br />
|}<br />
<br />
{|align="center"<br />
| {{:Team:NTU-Taida/Templates/Vid|num=9-4 cd = 0.01 |width=280px|name=NTU-Taida-Model-Combined-video9-4.gif}}<br />
| {{:Team:NTU-Taida/Templates/Vid|num=9-5 without quorum sensing module |width=280px|name=NTU-Taida-Model-Combined-video9-5.gif}}<br />
|}<br />
<br />
<br />
<br />
We can see from Video 9 that the system with a relative cell density of 0.2 differs most with the system without the quorum sensing module. The system with a relative cell density of 0.1 shows moderate difference. The system with a relative cell density of 0.05 displays very subtle difference. There is no difference between the system with a relative cell density of 0.01 and the system with no quorum sensing module. Therefore, the threshold of relative cell density may lie between 0.05 and 0.01.<br />
<br />
==3D Cell population response model==<br />
<br />
Finally, we construct a full 3D model, combing the consideration on the x-y plane and the x-z plane. Our goal is to simulate the effect of non-uniform production of fatty acid due to the spatially limited lipase activity. We modeled the intestine by a cylindrical tube, with a fat source limited to the z=0 plane, to simulate the situations similar to that shown in Figure 7, and examine the effect of Quorum sensing. <br />
<br />
[[File:NTU-Taida-Model-Combined-fig7.png|600px|center|thumb|Figure 7]]<br />
<br />
The equations used are the same as those in the 2D cell population response model, but with the equations governing diffusions changing from the two-dimension form to their three-dimension counterparts.<br />
<br />
{|align="center"<br />
| {{:Team:NTU-Taida/Templates/Vid|num=10 Full Thumbnails |width=400px|name=image24.gif}}<br />
| {{:Team:NTU-Taida/Templates/Vid|num=10 Enlargement |width=400px|name=image26.gif}}<br />
|}<br />
<br />
{|align="center"<br />
| {{:Team:NTU-Taida/Templates/Vid|num=11 Full Thumbnails |width=400px|name=image25.gif}}<br />
| {{:Team:NTU-Taida/Templates/Vid|num=11 Enlargement |width=400px|name=image27.gif}}<br />
|}<br />
<br />
<br />
<br />
Video 10 shows the result of system without quorum sensing module while Video 11 shows the result of system with quorum sensing module. From Video 10 and 11, we can see that GLP-1 starts to be expressed at similar time point at the intestinal wall on the z=0 plane. However, the GLP-1 expression spreads faster along the z-axis in system with quorum sensing.<br />
<br />
==Reference==<br />
<ol id='Ref'><br />
<li>Jordi Garcia-Ojalvo , Michael B. Elowitz, and Steven H. Strogatz , Modeling a synthetic multicellular clock: Repressilators coupled by quorum sensing, pnas,2004</li><br />
</ol><br />
<!--EOF--><br />
{{:Team:NTU-Taida/Templates/ContentEnd}}{{:Team:NTU-Taida/Templates/Footer|ActiveNavbar=Modeling, #nav-Modeling-Combined}}</div>Lbwanghttp://2012.igem.org/File:NTU-Taida-Model-Combined-video9-1.gifFile:NTU-Taida-Model-Combined-video9-1.gif2013-01-03T13:40:29Z<p>Lbwang: </p>
<hr />
<div></div>Lbwanghttp://2012.igem.org/Team:NTU-Taida/Modeling/FATeam:NTU-Taida/Modeling/FA2013-01-03T13:29:51Z<p>Lbwang: /* Animations showing the spatial temporal change in concentration of fat and fatty acid */</p>
<hr />
<div>{{:Team:NTU-Taida/Templates/Header}}{{:Team:NTU-Taida/Templates/Navbar}}{{:Team:NTU-Taida/Templates/Sidebar|Title=Fatty Acid Reaction Absorption Model}}{{:Team:NTU-Taida/Templates/ContentStart}}<br />
{{:Team:NTU-Taida/Templates/BSHero|Title=Fatty Acid Reaction Absorption Model|Content=}}<br />
<br />
==Overview==<br />
<p style="text-indent: 2em;">With the single cell model, we are able to simulate the response time of our system after the concentration of fatty acid exceeds our filtering threshold. However, the overall response time is also determined by the time needed for the eaten fat to be hydrolyzed and produce a fatty acid concentration higher than the threshold.</p><br />
<p style="text-indent: 2em;">Since E.coli cells reside mainly on the intestinal walls instead of in the lumen, we have to determine the actual concentration of fatty acid around the intestinal wall, which is different from that in the lumen space. Therefore, we first performed a simulation to model the '''hydrolysis of fat by lipase''' into glycerol and fatty acids. In parallel, we investigated the mechanism of long chain fatty acid absorption and constructed a two dimensional spatial-temporal model with COMSOL Multiphysics. Finally, we incorporate the reaction of fat hydrolysis into our spatial-temporal model describing fatty acid absorption and therefore result in a combined model simulating the '''reaction''' and '''absorption''' of fatty acid around the intestinal wall.</p><br />
<br />
==The Reaction Model==<br />
===Background===<br />
<p style="text-indent: 2em;">We start our effort for simulating the hydrolysis of fat by determining the rate of fat hydrolysis when catalyzed by lipase.</p><br />
<p style="text-indent: 2em;">Lipase catalysed reaction take place at the interface between the aqueous phase containing the enzyme and the oil phase, therefore the rate of hydrolysis by lipase will depend on the total specific interfacial area.[1] When considering systems in which the total specific interfacial area changes with changes in operating condition, the rate of fat hydrolysis can be given by</p><br />
<br />
$$v=\frac{k^*_{cat}[E]_t\cdot[S]}{K_e[\frac{k_d}{k_pa^2_t}+l]+[S]}$$<br />
<br />
<html><dl class="dl-horizontal"><br />
<dt>a<sub>t</sub></dt><dd>Total specific interfacial area [m<sup>-1</sup>]</dd><br />
<dt>k<sup>*</sup><sub>cat</sub></dt><dd>Catalytic rate constant [min<sup>-1</sup>]</dd><br />
<dt>[E]<sub>t</sub></dt><dd>Total active enzyme concentration [kLU m<sup>-3</sup>]</dd><br />
<dt>k<sub>d</sub></dt><dd>Desorption rate constant [min<sup>-1</sup>]</dd><br />
<dt>k<sub>p</sub></dt><dd>Adsorption rate constant [m<sup>2</sup> min<sup>-1</sup>]</dd><br />
<dt>K<sub>e</sub></dt><dd>Equilibrium constant of ES [mol m<sup>-3</sup>]</dd><br />
<dt>[S]</dt><dd>Substrate concentration [mol m<sup>-3</sup>]</dd><br />
<dt>v</dt><dd>Reaction rate [mol m<sup>-3</sup> min<sup>-1</sup>]</dd><br />
</dl></html><br />
<br />
<p style="text-indent: 2em;">When considering a stable system aided by emulsification reagent, the total free interfacial area will be nearly constant and therefore can result in a more simple equation, which is actually in the form of the Michaelis-Menten kinetic equation[[#Ref2|[2]]].</p><br />
<br />
$$v=\frac{k^*_{cat}[E]_t\cdot[S]}{K_m+[S]}$$<br />
<br />
<p style="text-indent: 2em;">Considering the effect of bile acids as emulsification reagents, we used the latter form in our model, with parameters derived from literature[[#Ref1|[1]]][[#Ref2|[2]]][[#Ref3|[3]]].</p><br />
<br />
===Equations===<br />
<p style="text-indent: 2em;">Since one molecule of fat will produce three molecules of fatty acids when hydrolyzed, we have the relationship between the rate of reduction of fats and the rate of production of fatty acids, and are able to derive the ODEs describing the change in concentration of fat and fatty acid over time.</p><br />
<br />
$${\frac{dfat}{dt}}=-{\frac{k^*_{cat}[E]_t\cdot[S]}{K_m+[S]}}$$<br />
$${\frac{dFA}{dt}}=3\cdot{\frac{k^*_{cat}[E]_t\cdot[S]}{K_m+[S]}}$$<br />
<br />
===Results===<br />
<p style="text-indent: 2em;">We solved the ODEs above by the Matlab solver with initial concentration of fat as 20 mM, and obtain the following result.</p><br />
<br />
[[FIle:NTU-Taida-Model-FA-fig1.png|thumb|500px|center|Fig 1]]<br />
<br />
<p style="text-indent: 2em;">Figure 1 shows the dynamic change of concentration of fat and FA over time when lipase catalyzes the hydrolysis of fat. Since our sensing threshold is only about 0.8 mol/m3, it takes very little time for fatty acid to reach our threshold level.</p><br />
<br />
<p style="text-indent: 2em;">Without considering the absorption of fatty acid, the rising of the concentration of fatty acid is quite fast, and therefore the response time would not be limited by the process of fat hydrolysis but by the process of GLP1 synthesis, which is described in single cell model. We further consider the effect of fatty acid absorption.</p><br />
<br />
==The Combined Reaction-absorption Model==<br />
<br />
<p style="text-indent: 2em;">Fatty acid absorption takes place on the intestinal walls. This absorption process may generate a concentration gradient near the walls where E.coli cells mainly reside. To more accurately simulate the actual fatty acid concentration in the microenvironment of our E.coli cells, we consider the effect of the absorption process and construct a two-dimensional reaction-absorption model in COMSOL.</p><br />
<p style="text-indent: 2em;">The intestinal absorption rate of fatty acid is mainly determined by how fast fatty acid can diffuse through the unstirred water layer and the lipid cell membrane. It has been shown that the rate limiting process in the absorption of short- and medium- chain fatty acid is the diffusion across lipid cell membrane, while the absorption rate of long- chain fatty acid is limited by the diffusion across the unstirred water layer.[[#Ref4|[4]]] </p> <br />
<br />
<p style="text-indent: 2em;">Since oleic acid is a long-chain fatty acid, we simulate its absorption by considering the diffusion process across the unstirred water layer, which can be governed by the following equation:</p><br />
<br />
$$J=(C_1-C_2)(D_{FA}/d)$$<br />
<br />
<p style="text-indent: 2em;">where C<sub>1</sub> and C<sub>2</sub> are the concentrations of the acid in the bulk phase and at the aqueous-lipid interface, respectively. D is the free diffusion coefficient and d represents the thickness of the unstirred water layer.</p><br />
<br />
===Spatial-temporal Model Equations ===<br />
<br />
<p style="text-indent: 2em;">The followings are the equations used in our reaction-absorption model.</p><br />
<br />
$${\frac{dfat}{dt}}=-{\frac{k_{cat}[E]_t\cdot[S]}{K_m+[S]}}$$<br />
$${\frac{dFA}{dt}}=3\cdot{\frac{k_{cat}[E]_t\cdot[S]}{K_m+[S]}}$$<br />
$$J=(C_1-C_2)(D_{FA}/d)$$<br />
<br />
===Model Design===<br />
<br />
<p style="text-indent: 2em;">We consider intestinal environment as a cylindrical tube, with cells residing on the walls of the tube, as shown in Figure 2.</p><br />
<br />
[[FIle:NTU-Taida-Model-FA-fig2.png|thumb|400px|center|Fig 2]]<br />
<br />
We assume that the fat distribution in the lumen is uniform and the absorption occurs uniformly along the cylindrical wall. In this way, the distribution of fat or fatty acid would be independent of the z axis (the non-uniform distribution of fatty acid along the z-axis will be discussed in the "Cell Population Response Model" section of the "2D & 3D Combined Model"). Therefore, we simplified the three dimensional model into a two dimensional one, represented by the cut plane shown in Figure 3.<br />
<br />
[[FIle:NTU-Taida-Model-FA-fig3.png|thumb|400px|center|300px|Fig 3]]<br />
<br />
<p style="text-indent: 2em;">The geometry design of our model is shown in figure 4.</p><br />
<br />
<p style="text-indent: 2em;">We coupled the ODEs of the reaction model locally at the lumen space, but not in the extra-intestinal space as the fat would only be hydrolyzed in the lumen. On the boundary of the lumen, we incorporate the equation accounting for the diffusion of fatty acid through the unstirred water layer. Initially, there is no fatty acid in either the lumen space or the extra-intestinal space, and the lumen is uniformly filled with fat of 20 mM. As the reaction proceeds, we expect to see the concentration of fat start to decline uniformly regardless of proximity to the perimeter. In contrast, while the concentration of fatty acid starts to rise, the rate of increase is not uniform because of the diffusion through the unstirred water layer.</p><br />
<br />
[[FIle:NTU-Taida-Model-FA-fig4.png|thumb|600px|center|Fig 4]]<br />
<br />
==Results==<br />
===Animations showing the spatial temporal change in concentration of fat and fatty acid===<br />
<p style="text-indent: 2em;">We simulated the concentration of fat and fatty acid for 4\(\times\)10<sup>4</sup> seconds with initial conditions described in the Model design section.</p><br />
<p style="text-indent: 2em;">The results are shown in video 1 and 2 for the concentration of fat and fatty acid, respectively. As we expected, the concentration of fat declines uniformly in the lumen and the concentration of fatty acid rises but with the presence of non-uniform distribution near the unstirred water layer barrier.</p><br />
<br />
{| align="center"<br />
|{{:Team:NTU-Taida/Templates/Vid|num=1|width=400px|name=Image6.gif}}<br />
|{{:Team:NTU-Taida/Templates/Vid|num=2|width=400px|name=NTU-Taida-Model-FA-vid1.gif}}<br />
|}<br />
<br />
<p style="text-indent: 2em;">To gain further insights into our simulation results, we plot the concentration of fat and fatty acid along the diameter of the circle. Figure 5 and 6 shows the resulting line graph for fat and fatty acid concentration over a simulation time of 10000 sec, with time steps of 1000 sec. Curves with different colors represent the concentration along the cut line at different time, with the numbers in the legend showing the time in seconds. The water layer barriers locate at y-coordinate of -1 and 1, respectively.</p><br />
<p style="text-indent: 2em;">From the two figures, we can see that the concentration of fat falls uniformly within the y-coordinates of -1 and 1, and remains at zero outside of the lumen space, which means that fat is continuously hydrolyzed during the first 10000 sec and therefore the concentration of fatty acid will keep increasing during this time.</p><br />
<p style="text-indent: 2em;">In Figure 6, we can see that as the time goes on, the overall concentration of fatty acids increase dramatically, but with the central plateau becoming thinner and thinner due to absorption at the unstirred water layer.</p><br />
<p style="text-indent: 2em;">During the first 10000 sec of simulation, the concentration of fatty acid near the water layer barrier remains much lower than that of the central part, confirming that the concentration of fatty acid near the intestinal walls is quite different from that of the lumen space.</p><br />
<br />
{| align="center"<br />
| [[FIle:NTU-Taida-Model-FA-fig5.png|thumb|400px|center|Fig 5]]<br />
| [[FIle:NTU-Taida-Model-FA-fig6.png|thumb|400px|center|Fig 6]]<br />
|}<br />
<br />
<p style="text-indent: 2em;">Figure 7 and 8 shows the resulting line graph for fat and fatty acid concentration over a simulation time of 43200 sec, with time steps of 3600 sec, which is an hour. From the two figures we can see that fat is hydrolyzed completely around 5 to 6 hours and therefore the concentration of fatty acid reaches its maximum level around 5 hour and starts to fall afterwards.</p><br />
<br />
{| align="center"<br />
| [[FIle:NTU-Taida-Model-FA-fig7.png|thumb|400px|center|Fig 7]]<br />
| [[FIle:NTU-Taida-Model-FA-fig8.png|thumb|400px|center|Fig 8]]<br />
|}<br />
<br />
<p style="text-indent: 2em;">With these line graphs, we visualize the concentration distribution along the diameter of the intestinal lumen. To understand the concentration change around the intestinal wall, we zoom in to see the line graph around y-coordinate of -1 or 1. From the line graphs of fatty acid concentration near the intestinal wall, we quantify the time needed for fatty acid to exceed the circuit threshold and the time when fatty acid level again falls below the threshold, as described next.</p><br />
<br />
===Quantifying the rising time and falling time of fatty acid concentration===<br />
<h4>Rising time</h4><br />
<p style="text-indent: 2em;">The rising time of fatty acid concentration is defined as the time needed for fatty acid to rise to the threshold of our circuit, which is about 0.8 mM, after giving an input of fat. Here, we quantify the fatty acid rising time for a fat input of 20 mM from the zoomed in line graph with simulation time from 0 to 3000 sec and time intervals between the recorded curves as 100 sec.</p><br />
<br />
<h4>Simulation time 0~3000, step 100</h4><br />
<p style="text-indent: 2em;">Figure 9 shows the zoomed in line graph, with curves in different colors representing the fatty acid concentration at different time points. The time is shown in the legend with unit in seconds. We only show the curves within y-coordinate of -1 to 1 to more clearly see the concentration change around y= -1. The yellow horizontal line highlights the threshold value, 0.8 mM. We find the time when the concentration achieves the threshold by looking for the first curve whose level is higher than the yellow horizontal line at y=-1, as highlighted in the red line in the figure. The corresponding time point for the red line is 900 seconds. This means that fatty acid concentration around intestinal wall will rise above the threshold in 900 sec after a fat input of 20 mM, enabling our system to sense the fat intake event rapidly and start our circuit in time.</p><br />
<br />
[[FIle:NTU-Taida-Model-FA-fig9.png|thumb|700px|center|Fig 9]]<br />
<br />
<h4>Falling time</h4><br />
<p style="text-indent: 2em;">Similarly, we seek to find the falling time of fatty acid concentration, which is defined as the time needed for fatty acid to first reach the maximum level and again fall below the threshold of our circuit. Here, we quantify the fatty acid falling time for a fat input of 20 mM from the zoomed in line graph with simulation time from 0 to 43200 sec and time intervals between the recorded curves as 3600 sec.</p><br />
<br />
<h4>Simulation time 0~43200, step 3600</h4><br />
<p style="text-indent: 2em;">Figure 10 shows the zoomed in line graph, with curves in different colors representing the fatty acid concentration at different time points. The yellow horizontal line highlights the threshold value, 0.8 mM. We find the time when the concentration falls below the threshold by looking for the first curve whose level falls below the yellow horizontal line at y=-1, as highlighted in the red line in the figure. The corresponding time point for the red line is 21600 seconds, which is 6 hr. This means that fatty acid concentration around intestinal wall will again fall below the threshold and begin to turn off our system in 6 hr after a fat input of 20 mM, which is in a physiological reasonable time scale.</p><br />
<br />
[[FIle:NTU-Taida-Model-FA-fig10.png|thumb|700px|center|Fig 10]]<br />
<br />
<p style="text-indent: 2em;">After quantifying the rising time and falling time of fatty acid concentration, we verify that our system will start quickly in about 15 min after a fat input of 20 mM, and start to shut off after about 6 hours, in a physiological time scale. Now, we want to see if our system will adapt to different fat input level and gives different response accordingly.</p><br />
<br />
===Dosage response===<br />
<p style="text-indent: 2em;">By following the way to quantify the rising time and falling time of fatty acid concentration described in the previous section, we find the rising time and falling time for fat input of 20, 22, 24, 26, 28, 30, 35, and 40 mM, and plot the dosage response curve of the rising time and falling time, as shown below.</p><br />
<br />
<h4>Time needed for fatty acid to exceed the threshold</h4><br />
<br />
[[FIle:NTU-Taida-Model-FA-fig11.png|thumb|600px|center|Fig 11]]<br />
<br />
<h4>Time needed for fatty acid to fall below the threshold</h4><br />
<br />
[[FIle:NTU-Taida-Model-FA-fig12.png|thumb|600px|center|Fig 12]]<br />
<br />
<p style="text-indent: 2em;">From these figures, we can see that our system will start in shorter time but shut down after longer time when the input fat level is higher, resulting in a longer GLP-1 response when the food intake contains more fat, thereby providing an adaptable response.</p><br />
<br />
<br />
<br />
==Reference==<br />
<br />
<html><ol><br />
<li id='Ref1'> Ho-Shing Wu, Ming-Ju Tsai, ''Kinetics of tributyrin hydrolysis by lipase'', Enzyme and Microbial Technology, Volume 35, Issues 6–7, 2004</li><br />
<li id='Ref2'> Ho-Shing Wu, Ming-Ju Tsai, ''Kinetics of tributyrin hydrolysis by lipase'', Enzyme and Microbial Technology, Volume 35, Issues 6–7, 2004</li><br />
<li id='Ref3'>Bengt Borgstrom, ''Luminal Digestion of Fats'', Handbook of Physiology, The Gastrointestinal System, Intestinal Absorption and Secretion, 1991</li><br />
<li id='Ref4'>Sallee VL, Dietschy JM., ''Determinants of intestinal mucosal uptake of short- and medium-chain fatty acids and alcohols'', Journal of Lipid Research, 1973</li><br />
</ol></html><br />
<br />
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<li><a href='' id='nav-edit'>Edit</a></li><br />
<li><a href='' id='nav-history'>History</a></li><br />
<li><a href='/Special:Upload' id='nav-upload'>Upload</a></li> <br />
<li class="divider"></li><br />
<li><a href='' id='nav-logout'>Logout</a></li><br />
</ul><br />
</li> <!-- dropdown --><br />
<br />
</ul> <!-- nav --><br />
</div><br />
</div> <!-- container --><br />
</div> <!-- nav-inner --><br />
</div> <!-- navbar --><br />
</html></div>Lbwanghttp://2012.igem.org/Team:NTU-Taida/Templates/NavbarTeam:NTU-Taida/Templates/Navbar2012-10-26T23:28:50Z<p>Lbwang: </p>
<hr />
<div><html><br />
<!-- Navbar================================================== --><br />
<div class="navbar navbar-fixed-top"> <!-- navbar-inverse --><br />
<div class="navbar-inner"><br />
<div class="container"><br />
<br />
<!-- .btn-navbar to toggle for --><br />
<a class="btn btn-navbar" data-toggle="collapse" data-target=".nav-collapse"><br />
<span class="icon-bar"></span><br />
<span class="icon-bar"></span><br />
<span class="icon-bar"></span><br />
<span class="icon-bar"></span><br />
<span class="icon-bar"></span><br />
</a><br />
<br />
<!-- Be sure to leave the brand out there if you want it shown --><br />
<a class="brand" href="/Team:NTU-Taida">NTU-Taida</a><br />
<br />
<div class='nav-collapse'><br />
<ul class="nav" id='wiki-navbar'><br />
<li id='nav-Home'><a href='/Team:NTU-Taida'>Home</a></li><br />
<!-- Dropdown Project--><br />
<li class="dropdown" id="nav-Project"><br />
<a class="dropdown-toggle" data-toggle="dropdown" href="#">Project<b class="caret"></b></a><br />
<ul class="dropdown-menu" id='nav-projectmenu'><br />
<li id='nav-Project-Intro'><a href='/Team:NTU-Taida/Project/Introduction'>Introduction</a></li> <br />
<li id='nav-Project-Background'><a href='/Team:NTU-Taida/Project/Background'>Background</a></li> <br />
<li class="divider"></li> <br />
<li id='nav-Project-Overview'><a href='/Team:NTU-Taida/Project/Overview'>Project Overview</a></li> <br />
<li id='nav-Project-Effector' style="margin-left: 10px;"><a href='/Team:NTU-Taida/Project/Effector'>Effector</a></li><br />
<li id='nav-Project-Sensor' style="margin-left: 10px;"><a href='/Team:NTU-Taida/Project/Sensor'>Sensor</a></li><br />
<li id='nav-Project-Circuit' style="margin-left: 10px;"><a href='/Team:NTU-Taida/Project/Circuit'>Circuit</a></li><br />
<li id='nav-Project-Stability' style="margin-left: 10px;"><a href='/Team:NTU-Taida/Project/Stability'>Stability</a></li><br />
<li id='nav-Project-Safety' style="margin-left: 10px;"><a href='/Team:NTU-Taida/Project/Safety'>Safety</a></li><br />
<li class="divider"></li><br />
<li id='nav-Project-Future'><a href='/Team:NTU-Taida/Project/Future-Plan'>Future Plan</a></li><br />
<br />
<!--<li class="nav-header" style='border: none'>Circuit</li>--> <br />
<!--<li class="nav-header" style='border: none'>Deprecated</li>--><br />
<!--<li id='nav-Project-Fat'><a href='/Team:NTU-Taida/Project/Fat-Extinguisher'>Fat Extinguisher</a></li>--><br />
<!--<li id='nav-Project-Thermal'><a href='/Team:NTU-Taida/Project/Thermal-Avenger'>Thermal Avenger</a></li>--><br />
</ul><br />
</li> <!-- dropdown --><br />
<br />
<br />
<!--<li id='nav-Result'><a href='/Team:NTU-Taida/Result'>Result</a></li>--><br />
<!-- Dropdown Result--><br />
<li class="dropdown" id="nav-Result"><br />
<a class="dropdown-toggle" data-toggle="dropdown" href="#">Result<b class="caret"></b></a><br />
<ul class="dropdown-menu" id='nav-resultmenu'><br />
<!--<li id='nav-Result-Overview'><a href='/Team:NTU-Taida/Result'>Overview</a></li>--><br />
<li id='nav-Result-pFadBA'><a href='/Team:NTU-Taida/Result/pFadBA'>pFadBA Promoter</a></li><br />
<li id='nav-Result-Thermal'><a href='/Team:NTU-Taida/Result/Thermal-Promoter'>Thermal Promoter</a></li><br />
<li id='nav-Result-clPromoter'><a href='/Team:NTU-Taida/Result/Modified-cI-promoter'>Modified cI promoter</a></li> <br />
<li id='nav-Result-Secetion-CPP'><a href='/Team:NTU-Taida/Result/Secretion-CPP'>Secretion: CPP</a></li><br />
<li id='nav-Result-Secetion-GLP1'><a href='/Team:NTU-Taida/Result/Secretion-GLP1'>Secretion: GLP-1</a></li><br />
<li id='nav-Result-Penetration'><a href='/Team:NTU-Taida/Result/Penetration'>Penetration</a></li><br />
<li id='nav-Result-Stability'><a href='/Team:NTU-Taida/Result/Stability'>Stability</a></li><br />
</ul><br />
</li> <!-- dropdown --><br />
<br />
<!-- Dropdown Model--><br />
<li class="dropdown" id="nav-Modeling"><br />
<a class="dropdown-toggle" id="nav-model-overview" data-toggle="dropdown" href="#">Modeling<b class="caret"></b></a><br />
<ul class="dropdown-menu" id='nav-modelmenu'><br />
<li id='nav-Modeling-Overview'><a href='/Team:NTU-Taida/Modeling'>Overview</a></li><br />
<li class="divider"></li><br />
<li id='nav-Modeling-Single'><a href='/Team:NTU-Taida/Modeling/Single-Cell'>Single Cell Model</a></li><br />
<li id='nav-Modeling-FA'><a href='/Team:NTU-Taida/Modeling/FA'>Fatty Acid Reaction-Absorption Model</a></li><br />
<li id='nav-Modeling-System'><a href='/Team:NTU-Taida/Modeling/System-Analysis'>System Analysis</a></li> <br />
<li id='nav-Modeling-Stochastic'><a href='/Team:NTU-Taida/Modeling/Stochastic-Analysis'>Stochastic Analysis</a></li> <br />
<!--<li id='nav-Modeling-Combined'><a href='/Team:NTU-Taida/Modeling/2D-3D-Combined'>2D &amp; 3D Combined Model</a></li>--><br />
<li class="dropdown" id="nav-Modeling-Combined"><br />
<a class="dropdown-toggle" id="nav-model-overview" data-toggle="dropdown" href="/Team:NTU-Taida/Modeling/2D-3D-Combined">2D &amp; 3D Combined Model<i class="icon-chevron-right"></i></a><br />
<ul class='dropdown-menu'><br />
<li><a href='1'>1</a></li><br />
<li><a href='2'>2</a></li><br />
</ul><br />
</li><!--dropdown--><br />
<li id='nav-Modeling-Plasmid'><a href='/Team:NTU-Taida/Modeling/Plasmid-Stability'>Plasmid Stability Model</a></li><br />
<li class="divider"></li><br />
<li id='nav-Modeling-Parameters'><a href='/Team:NTU-Taida/Modeling/Parameters'>Parameters</a></li><br />
<br />
<!--<li id='nav-Modeling-Cell-Population'><a href='/Team:NTU-Taida/Modeling/Cell-Population-Response'>Cell Population Response Model</a></li>--><br />
</ul><br />
</li> <!-- dropdown --><br />
<br />
<li id='nav-Parts'><a href='/Team:NTU-Taida/Parts'>Parts</a></li><br />
<li id='nav-Safety'><a href='/Team:NTU-Taida/Safety'>Safety</a></li><br />
<li id='nav-Team'><a href='/Team:NTU-Taida/Team'>Team</a></li><br />
<br />
<!-- Dropdown Human Practice --><br />
<li class="dropdown" id="nav-HumanPractice"><br />
<a class="dropdown-toggle" data-toggle="dropdown" href="#">Human Practice<b class="caret"></b></a><br />
<ul class="dropdown-menu" id='nav-humanpractice-menu'><br />
<li id='nav-HumanPractice-Overview'><a href='/Team:NTU-Taida/Human Practice/Overview'>Overview</a></li><br />
<li class="divider"></li> <br />
<li id='nav-HumanPractice-Symposium'><a href='/Team:NTU-Taida/Human Practice/Symposium'>Symposium with High School Students</a></li><br />
<li id='nav-HumanPractice-Questionnaire'><a href='/Team:NTU-Taida/Human Practice/Questionnaire'>Questionnaire Analysis</a></li><br />
<li id='nav-HumanPractice-SafetyiniGEM'><a href='/Team:NTU-Taida/Human Practice/Safety-in-iGEM'>Safety in iGEM</a></li><br />
<li id='nav-HumanPractice-DoctorInterview'><a href='/Team:NTU-Taida/Human Practice/Doctor-Interview'>Doctor Interview</a></li><br />
<li id='nav-HumanPractice-Collaboration'><a href='/Team:NTU-Taida/Human Practice/Collaboration'>Collaboration and Other Activities</a></li><br />
<li id='nav-HumanPractice-InformationPlatform'><a href='/Team:NTU-Taida/Human Practice/Information-Platform'>Information Platform</a></li><br />
</ul><br />
<!--<li id='nav-HumanPractice'><a href='/Team:NTU-Taida/Human Practice' >Human Practice</a></li>--><br />
<br />
<!-- Dropdown User--><br />
<li class="dropdown" id="nav-user"><br />
<a class="dropdown-toggle" id="nav-login" role="button" data-toggle="dropdown" data-target="#" href=''><br />
Login<br />
</a><br />
<ul class="dropdown-menu" id='nav-usermenu' role="menu" aria-labelledby="nav-login"><br />
<li><a href='' id='nav-edit'>Edit</a></li><br />
<li><a href='' id='nav-history'>History</a></li><br />
<li><a href='/Special:Upload' id='nav-upload'>Upload</a></li> <br />
<li class="divider"></li><br />
<li><a href='' id='nav-logout'>Logout</a></li><br />
</ul><br />
</li> <!-- dropdown --><br />
<br />
</ul> <!-- nav --><br />
</div><br />
</div> <!-- container --><br />
</div> <!-- nav-inner --><br />
</div> <!-- navbar --><br />
</html></div>Lbwanghttp://2012.igem.org/Team:NTU-TaidaTeam:NTU-Taida2012-10-26T23:28:34Z<p>Lbwang: Replaced content with "{{:Team:NTU-Taida/Templates/Header}}{{:Team:NTU-Taida/Templates/Navbar}}<html>
<!--跨頁========================================= -->
<div style='
width: 100%;
'>
<div cla..."</p>
<hr />
<div>{{:Team:NTU-Taida/Templates/Header}}{{:Team:NTU-Taida/Templates/Navbar}}<html><br />
<!--跨頁========================================= --><br />
<div style='<br />
width: 100%;<br />
'><br />
<div class="container"><br />
<div class='row'><br />
<img src='http://2012.igem.org/wiki/images/5/53/NTU-Taida-Home-2012.jpg' width='100%'><br />
</div><br />
</div> <!-- /container --><br />
</div><br />
<br />
</html>{{:Team:NTU-Taida/Templates/Footer|ActiveNavbar=Home}}</div>Lbwanghttp://2012.igem.org/Team:NTU-TaidaTeam:NTU-Taida2012-10-26T23:26:01Z<p>Lbwang: </p>
<hr />
<div><html><br />
<!-- Navbar================================================== --><br />
<div class="navbar navbar-fixed-top"> <!-- navbar-inverse --><br />
<div class="navbar-inner"><br />
<div class="container"><br />
<br />
<!-- .btn-navbar to toggle for --><br />
<a class="btn btn-navbar" data-toggle="collapse" data-target=".nav-collapse"><br />
<span class="icon-bar"></span><br />
<span class="icon-bar"></span><br />
<span class="icon-bar"></span><br />
<span class="icon-bar"></span><br />
<span class="icon-bar"></span><br />
</a><br />
<br />
<!-- Be sure to leave the brand out there if you want it shown --><br />
<a class="brand" href="/Team:NTU-Taida">NTU-Taida</a><br />
<br />
<div class='nav-collapse'><br />
<ul class="nav" id='wiki-navbar'><br />
<li id='nav-Home'><a href='/Team:NTU-Taida'>Home</a></li><br />
<!-- Dropdown Project--><br />
<li class="dropdown" id="nav-Project"><br />
<a class="dropdown-toggle" data-toggle="dropdown" href="#">Project<b class="caret"></b></a><br />
<ul class="dropdown-menu" id='nav-projectmenu'><br />
<li id='nav-Project-Intro'><a href='/Team:NTU-Taida/Project/Introduction'>Introduction</a></li> <br />
<li id='nav-Project-Background'><a href='/Team:NTU-Taida/Project/Background'>Background</a></li> <br />
<li class="divider"></li> <br />
<li id='nav-Project-Overview'><a href='/Team:NTU-Taida/Project/Overview'>Project Overview</a></li> <br />
<li id='nav-Project-Effector' style="margin-left: 10px;"><a href='/Team:NTU-Taida/Project/Effector'>Effector</a></li><br />
<li id='nav-Project-Sensor' style="margin-left: 10px;"><a href='/Team:NTU-Taida/Project/Sensor'>Sensor</a></li><br />
<li id='nav-Project-Circuit' style="margin-left: 10px;"><a href='/Team:NTU-Taida/Project/Circuit'>Circuit</a></li><br />
<li id='nav-Project-Stability' style="margin-left: 10px;"><a href='/Team:NTU-Taida/Project/Stability'>Stability</a></li><br />
<li id='nav-Project-Safety' style="margin-left: 10px;"><a href='/Team:NTU-Taida/Project/Safety'>Safety</a></li><br />
<li class="divider"></li><br />
<li id='nav-Project-Future'><a href='/Team:NTU-Taida/Project/Future-Plan'>Future Plan</a></li><br />
<br />
<!--<li class="nav-header" style='border: none'>Circuit</li>--> <br />
<!--<li class="nav-header" style='border: none'>Deprecated</li>--><br />
<!--<li id='nav-Project-Fat'><a href='/Team:NTU-Taida/Project/Fat-Extinguisher'>Fat Extinguisher</a></li>--><br />
<!--<li id='nav-Project-Thermal'><a href='/Team:NTU-Taida/Project/Thermal-Avenger'>Thermal Avenger</a></li>--><br />
</ul><br />
</li> <!-- dropdown --><br />
<br />
<br />
<!--<li id='nav-Result'><a href='/Team:NTU-Taida/Result'>Result</a></li>--><br />
<!-- Dropdown Result--><br />
<li class="dropdown" id="nav-Result"><br />
<a class="dropdown-toggle" data-toggle="dropdown" href="#">Result<b class="caret"></b></a><br />
<ul class="dropdown-menu" id='nav-resultmenu'><br />
<!--<li id='nav-Result-Overview'><a href='/Team:NTU-Taida/Result'>Overview</a></li>--><br />
<li id='nav-Result-pFadBA'><a href='/Team:NTU-Taida/Result/pFadBA'>pFadBA Promoter</a></li><br />
<li id='nav-Result-Thermal'><a href='/Team:NTU-Taida/Result/Thermal-Promoter'>Thermal Promoter</a></li><br />
<li id='nav-Result-clPromoter'><a href='/Team:NTU-Taida/Result/Modified-cI-promoter'>Modified cI promoter</a></li> <br />
<li id='nav-Result-Secetion-CPP'><a href='/Team:NTU-Taida/Result/Secretion-CPP'>Secretion: CPP</a></li><br />
<li id='nav-Result-Secetion-GLP1'><a href='/Team:NTU-Taida/Result/Secretion-GLP1'>Secretion: GLP-1</a></li><br />
<li id='nav-Result-Penetration'><a href='/Team:NTU-Taida/Result/Penetration'>Penetration</a></li><br />
<li id='nav-Result-Stability'><a href='/Team:NTU-Taida/Result/Stability'>Stability</a></li><br />
</ul><br />
</li> <!-- dropdown --><br />
<br />
<!-- Dropdown Model--><br />
<li class="dropdown" id="nav-Modeling"><br />
<a class="dropdown-toggle" id="nav-model-overview" data-toggle="dropdown" href="#">Modeling<b class="caret"></b></a><br />
<ul class="dropdown-menu" id='nav-modelmenu'><br />
<li id='nav-Modeling-Overview'><a href='/Team:NTU-Taida/Modeling'>Overview</a></li><br />
<li class="divider"></li><br />
<li id='nav-Modeling-Single'><a href='/Team:NTU-Taida/Modeling/Single-Cell'>Single Cell Model</a></li><br />
<li id='nav-Modeling-FA'><a href='/Team:NTU-Taida/Modeling/FA'>Fatty Acid Reaction-Absorption Model</a></li><br />
<li id='nav-Modeling-System'><a href='/Team:NTU-Taida/Modeling/System-Analysis'>System Analysis</a></li> <br />
<li id='nav-Modeling-Stochastic'><a href='/Team:NTU-Taida/Modeling/Stochastic-Analysis'>Stochastic Analysis</a></li> <br />
<!--<li id='nav-Modeling-Combined'><a href='/Team:NTU-Taida/Modeling/2D-3D-Combined'>2D &amp; 3D Combined Model</a></li>--><br />
<li class="dropdown" id="nav-Modeling-Combined"><br />
<a class="dropdown-toggle" id="nav-model-overview" data-toggle="dropdown" href="/Team:NTU-Taida/Modeling/2D-3D-Combined">2D &amp; 3D Combined Model<i class="icon-chevron-right"></i></a><br />
<ul class='dropdown-menu'><br />
<li><a href='1'>1</a></li><br />
<li><a href='2'>2</a></li><br />
</ul><br />
</li><!--dropdown--><br />
<li id='nav-Modeling-Plasmid'><a href='/Team:NTU-Taida/Modeling/Plasmid-Stability'>Plasmid Stability Model</a></li><br />
<li class="divider"></li><br />
<li id='nav-Modeling-Parameters'><a href='/Team:NTU-Taida/Modeling/Parameters'>Parameters</a></li><br />
<br />
<!--<li id='nav-Modeling-Cell-Population'><a href='/Team:NTU-Taida/Modeling/Cell-Population-Response'>Cell Population Response Model</a></li>--><br />
</ul><br />
</li> <!-- dropdown --><br />
<br />
<li id='nav-Parts'><a href='/Team:NTU-Taida/Parts'>Parts</a></li><br />
<li id='nav-Safety'><a href='/Team:NTU-Taida/Safety'>Safety</a></li><br />
<li id='nav-Team'><a href='/Team:NTU-Taida/Team'>Team</a></li><br />
<br />
<!-- Dropdown Human Practice --><br />
<li class="dropdown" id="nav-HumanPractice"><br />
<a class="dropdown-toggle" data-toggle="dropdown" href="#">Human Practice<b class="caret"></b></a><br />
<ul class="dropdown-menu" id='nav-humanpractice-menu'><br />
<li id='nav-HumanPractice-Overview'><a href='/Team:NTU-Taida/Human Practice/Overview'>Overview</a></li><br />
<li class="divider"></li> <br />
<li id='nav-HumanPractice-Symposium'><a href='/Team:NTU-Taida/Human Practice/Symposium'>Symposium with High School Students</a></li><br />
<li id='nav-HumanPractice-Questionnaire'><a href='/Team:NTU-Taida/Human Practice/Questionnaire'>Questionnaire Analysis</a></li><br />
<li id='nav-HumanPractice-SafetyiniGEM'><a href='/Team:NTU-Taida/Human Practice/Safety-in-iGEM'>Safety in iGEM</a></li><br />
<li id='nav-HumanPractice-DoctorInterview'><a href='/Team:NTU-Taida/Human Practice/Doctor-Interview'>Doctor Interview</a></li><br />
<li id='nav-HumanPractice-Collaboration'><a href='/Team:NTU-Taida/Human Practice/Collaboration'>Collaboration and Other Activities</a></li><br />
<li id='nav-HumanPractice-InformationPlatform'><a href='/Team:NTU-Taida/Human Practice/Information-Platform'>Information Platform</a></li><br />
</ul><br />
<!--<li id='nav-HumanPractice'><a href='/Team:NTU-Taida/Human Practice' >Human Practice</a></li>--><br />
<br />
<!-- Dropdown User--><br />
<li class="dropdown" id="nav-user"><br />
<a class="dropdown-toggle" id="nav-login" role="button" data-toggle="dropdown" data-target="#" href=''><br />
Login<br />
</a><br />
<ul class="dropdown-menu" id='nav-usermenu' role="menu" aria-labelledby="nav-login"><br />
<li><a href='' id='nav-edit'>Edit</a></li><br />
<li><a href='' id='nav-history'>History</a></li><br />
<li><a href='/Special:Upload' id='nav-upload'>Upload</a></li> <br />
<li class="divider"></li><br />
<li><a href='' id='nav-logout'>Logout</a></li><br />
</ul><br />
</li> <!-- dropdown --><br />
<br />
</ul> <!-- nav --><br />
</div><br />
</div> <!-- container --><br />
</div> <!-- nav-inner --><br />
</div> <!-- navbar --><br />
</html></div>Lbwanghttp://2012.igem.org/Team:NTU-TaidaTeam:NTU-Taida2012-10-26T23:24:59Z<p>Lbwang: </p>
<hr />
<div><html><br />
<!-- Navbar================================================== --><br />
<div class="navbar navbar-fixed-top"> <!-- navbar-inverse --><br />
<div class="navbar-inner"><br />
<div class="container"><br />
<br />
<!-- .btn-navbar to toggle for --><br />
<a class="btn btn-navbar" data-toggle="collapse" data-target=".nav-collapse"><br />
<span class="icon-bar"></span><br />
<span class="icon-bar"></span><br />
<span class="icon-bar"></span><br />
<span class="icon-bar"></span><br />
<span class="icon-bar"></span><br />
</a><br />
<br />
<!-- Be sure to leave the brand out there if you want it shown --><br />
<a class="brand" href="/Team:NTU-Taida">NTU-Taida</a><br />
<br />
<div class='nav-collapse'><br />
<ul class="nav" id='wiki-navbar'><br />
<li id='nav-Home'><a href='/Team:NTU-Taida'>Home</a></li><br />
<!-- Dropdown Project--><br />
<li class="dropdown" id="nav-Project"><br />
<a class="dropdown-toggle" data-toggle="dropdown" href="#">Project<b class="caret"></b></a><br />
<ul class="dropdown-menu" id='nav-projectmenu'><br />
<li id='nav-Project-Intro'><a href='/Team:NTU-Taida/Project/Introduction'>Introduction</a></li> <br />
<li id='nav-Project-Background'><a href='/Team:NTU-Taida/Project/Background'>Background</a></li> <br />
<li class="divider"></li> <br />
<li id='nav-Project-Overview'><a href='/Team:NTU-Taida/Project/Overview'>Project Overview</a></li> <br />
<li id='nav-Project-Effector' style="margin-left: 10px;"><a href='/Team:NTU-Taida/Project/Effector'>Effector</a></li><br />
<li id='nav-Project-Sensor' style="margin-left: 10px;"><a href='/Team:NTU-Taida/Project/Sensor'>Sensor</a></li><br />
<li id='nav-Project-Circuit' style="margin-left: 10px;"><a href='/Team:NTU-Taida/Project/Circuit'>Circuit</a></li><br />
<li id='nav-Project-Stability' style="margin-left: 10px;"><a href='/Team:NTU-Taida/Project/Stability'>Stability</a></li><br />
<li id='nav-Project-Safety' style="margin-left: 10px;"><a href='/Team:NTU-Taida/Project/Safety'>Safety</a></li><br />
<li class="divider"></li><br />
<li id='nav-Project-Future'><a href='/Team:NTU-Taida/Project/Future-Plan'>Future Plan</a></li><br />
<br />
<!--<li class="nav-header" style='border: none'>Circuit</li>--> <br />
<!--<li class="nav-header" style='border: none'>Deprecated</li>--><br />
<!--<li id='nav-Project-Fat'><a href='/Team:NTU-Taida/Project/Fat-Extinguisher'>Fat Extinguisher</a></li>--><br />
<!--<li id='nav-Project-Thermal'><a href='/Team:NTU-Taida/Project/Thermal-Avenger'>Thermal Avenger</a></li>--><br />
</ul><br />
</li> <!-- dropdown --><br />
<br />
<br />
<!--<li id='nav-Result'><a href='/Team:NTU-Taida/Result'>Result</a></li>--><br />
<!-- Dropdown Result--><br />
<li class="dropdown" id="nav-Result"><br />
<a class="dropdown-toggle" data-toggle="dropdown" href="#">Result<b class="caret"></b></a><br />
<ul class="dropdown-menu" id='nav-resultmenu'><br />
<!--<li id='nav-Result-Overview'><a href='/Team:NTU-Taida/Result'>Overview</a></li>--><br />
<li id='nav-Result-pFadBA'><a href='/Team:NTU-Taida/Result/pFadBA'>pFadBA Promoter</a></li><br />
<li id='nav-Result-Thermal'><a href='/Team:NTU-Taida/Result/Thermal-Promoter'>Thermal Promoter</a></li><br />
<li id='nav-Result-clPromoter'><a href='/Team:NTU-Taida/Result/Modified-cI-promoter'>Modified cI promoter</a></li> <br />
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</html></div>Lbwanghttp://2012.igem.org/Team:NTU-Taida/Templates/FigTeam:NTU-Taida/Templates/Fig2012-10-26T23:19:23Z<p>Lbwang: </p>
<hr />
<div><html><div class="center"><br />
<div class="thumb tnone"><br />
<div class="thumbinner" style="width:</html>{{{width}}}<html>"><br />
<a href="</html>{{filepath:{{{name}}}|nowiki}}<html>" class="image"><br />
<img src="</html>{{filepath:{{{name}}}|nowiki}}<html>" style="width:</html>{{{width}}}<html>"><br />
</a><br />
<div class="thumbcaption"><br />
<div class="magnify"><br />
<a href="</html>{{filepath:{{{name}}}|nowiki}}<html>" class="internal" title="Enlarge"><br />
<img src="/wiki/skins/common/images/magnify-clip.png" width="15" height="11" alt=""></a></div>Figure </html>{{{num}}}<html></div><br />
</div><br />
</div><br />
</div><br />
</html></div>Lbwanghttp://2012.igem.org/Team:NTU-Taida/Templates/VidTeam:NTU-Taida/Templates/Vid2012-10-26T23:19:13Z<p>Lbwang: </p>
<hr />
<div><html><div class="center"><br />
<div class="thumb tnone"><br />
<div class="thumbinner" style="width:</html>{{{width}}}<html>"><br />
<a href="</html>{{filepath:{{{name}}}|nowiki}}<html>" class="image"><br />
<img src="</html>{{filepath:{{{name}}}|nowiki}}<html>" style="width:</html>{{{width}}}<html>"><br />
</a><br />
<div class="thumbcaption"><br />
<div class="magnify"><br />
<a href="</html>{{filepath:{{{name}}}|nowiki}}<html>" class="internal" title="Enlarge"><br />
<img src="/wiki/skins/common/images/magnify-clip.png" width="15" height="11" alt=""></a></div>Video </html>{{{num}}}<html></div><br />
</div><br />
</div><br />
</div><br />
</html></div>Lbwanghttp://2012.igem.org/Team:NTU-Taida/Templates/FigTeam:NTU-Taida/Templates/Fig2012-10-26T23:18:52Z<p>Lbwang: </p>
<hr />
<div><html><div class="center"><br />
<div class="thumb tnone"><br />
<div class="thumbinner" style="width:</html>{{{width}}}<html>"><br />
<a href="</html>{{filepath:{{{name}}}|nowiki}}<html>" class="image"><br />
<img src="</html>{{filepath:{{{name}}}|nowiki}}<html>" style="width:</html>{{{width}}}<html>"><br />
</a><br />
<div class="thumbcaption"><br />
<div class="magnify"><br />
<a href="</html>{{filepath:{{{name}}}|nowiki}}}<html>" class="internal" title="Enlarge"><br />
<img src="/wiki/skins/common/images/magnify-clip.png" width="15" height="11" alt=""></a></div>Figure </html>{{{num}}}<html></div><br />
</div><br />
</div><br />
</div><br />
</html></div>Lbwanghttp://2012.igem.org/Team:NTU-Taida/Templates/VidTeam:NTU-Taida/Templates/Vid2012-10-26T23:18:30Z<p>Lbwang: </p>
<hr />
<div><html><div class="center"><br />
<div class="thumb tnone"><br />
<div class="thumbinner" style="width:</html>{{{width}}}<html>"><br />
<a href="</html>{{filepath:{{{name}}}|nowiki}}<html>" class="image"><br />
<img src="</html>{{filepath:{{{name}}}|nowiki}}<html>" style="width:</html>{{{width}}}<html>"><br />
</a><br />
<div class="thumbcaption"><br />
<div class="magnify"><br />
<a href="</html>{{filepath:{{{name}}}|nowiki}}}<html>" class="internal" title="Enlarge"><br />
<img src="/wiki/skins/common/images/magnify-clip.png" width="15" height="11" alt=""></a></div>Video </html>{{{num}}}<html></div><br />
</div><br />
</div><br />
</div><br />
</html></div>Lbwanghttp://2012.igem.org/Team:NTU-Taida/SafetyTeam:NTU-Taida/Safety2012-10-26T23:16:51Z<p>Lbwang: /* Testing Function */</p>
<hr />
<div>{{:Team:NTU-Taida/Templates/Header}}{{:Team:NTU-Taida/Templates/Navbar}}{{:Team:NTU-Taida/Templates/Sidebar}}{{:Team:NTU-Taida/Templates/ContentStart}}<br />
{{:Team:NTU-Taida/Templates/BSHero|Title=Safety|Content=<p>Use this page to answer the questions on the <a href='/Safety'>safety page</a>.</p>}}<br />
<br />
==Question 1 ==<br />
'''Would any of your project ideas raise safety issues in terms of:'''<br />
*'''researcher safety,'''<br />
*'''public safety, or'''<br />
*'''environmental safety?'''<br />
The biosafety concerns can be simplified to an equation, Risk= probabilityX Hazard. <br />
In our project, the questions we deal with are basically human disease-oriented. We try to prevent any concern regarding potential harms to human. <br />
<br />
As for the researchers, our research is conducted in a safely regulated laboratory, and the ideas of our project do not require etiologic agents, hosts or vectors for experiment. Also no toxic reagent or high risk chemical compound is used. In all, our project hasn’t yet raised researcher safety issues thus far. <br />
For we do not apply any virulent genes or etiologic agents, there seems no additional threats on public safety. Furthermore, the non-pathogenic E. coli we try to deliver into human body can be easily eliminated by antibiotic use if infection arises and is the main concern of patient's safety. <br />
<br />
However, the antibiotics resistance plasmid used in our project may harbor the threats of horizontal gene transfer, which will enhance the virulence of other Escherichia coli in the environment. Though a self-destruction mechanism is designed in our project, we are still aware of the risk on environmental safety. The rules and regulations of concern will be under close supervision of Environmental Protection and Occupational Safety and Hygiene Unit of NTUCM.<br />
<br />
==Question 2 ==<br />
'''Do any of the new BioBrick parts (or devices) that you made this year raise any safety issues? If yes,'''<br />
* '''Did you document these issues in the Registry?'''<br />
* '''How did you manage to handle the safety issue?'''<br />
* '''How could other teams learn from your experience?'''<br />
<br />
The most common question people would have judged us is how we make sure that it is safe to deliver this bug into human intestine. As we noted, the output we would like to deliver, GLP-1, is innate and has no significant harms to the human body. Cell penetrating peptides, which is another peptide we are going to deliver into gastroenterological tract, do no harm as well, since it has a pretty short half life (<15 mins) inside GI tract. <br />
<br />
What’s more, intestine is an organ with an abundance of normal flora, mainly consisting of Streptococcus and Lactobacillus in the middle intestine. In ileum and section close to ileo-cecal valve, bacteroides and coliform bacteria are dominant. First, for the E. coli itself, it’s very hard to colonize in the GI tract as it would face a bunch of competitors over nutrients and space. Second, the bugs we are going to deliver inside human body is pretty fragile, which can be easily eliminated by some antibiotics, 2nd generation cephalosporin, high ampicillin plus sulbactam, or erythromycin, which is ideal of usage in our cases, since it not only provided anti-microbial effects, but also increases the motility of intestine. Above all, the design we are going to bring to synthetic biology community has little safety concerns, and can be easily circumvented or adjusted.<br />
<br />
==Question 3 ==<br />
'''Is there a local biosafety group, committee, or review board at your institution?<br />
*'''If yes, what does your local biosafety group think about your project?'''<br />
*'''If no, which specific biosafety rules or guidelines do you have to consider in your country?'''<br />
<br />
In National Taiwan University, College of Medicine, where the experiments of our project are conducted, Environmental Protection and Occupational Safety and Hygiene Unit of NTUCM takes charge of promoting and supervising safety and health issues.<br />
Before beginning of our project, our team members and advisors have attended the safety education series and training courses held by this unit. All of us were qualified by passing the tests at the end of the training to be sure that all the rules of concern are well understood. The application of our project was also verified and qualified. All experiments are conducted under the biosafety rules of Environmental Protection and Occupational Safety and Hygiene Unit of NTUCM, of which all of our experimental procedures, equipments, facilities were under close supervision.<br />
http://www.mc.ntu.edu.tw/department/safety/index.htm<br />
<br />
==Question 4 ==<br />
'''Do you have any other ideas how to deal with safety issues that could be useful for future iGEM competitions? How could parts, devices and systems be made even safer through biosafety engineering?'''<br />
<br />
As our opinion, we think that for every iGEM teams' circuit design, a mechanism to turn off is necessary. In order to improve the iGEM competition safety concern, we would like to suggest a turn-off mechanism as requirement. Also, the microorganisms should be kept dependent on controlled conditions in the lab to prohibit the unwanted spreading and multiplication outside the lab. Moreover, a suicide switch for all BioBricks or dependence on special nutrients lack in nature for organisms should be engineered in case organisms escape and cause safety concern. The most important thing is that every team and the advisor should know their potential danger and the ways to assess the risk. This aim could be approached by emphasizing the safety rules. Creating a page on the registry for the teams to explain their event tree analysis and fault tree analysis would be an easiest method to increase safety when working with BioBrick parts.<br />
<br />
For our PepdEx system, we proposed two layers of safety regulations: (1) temperature inducible suicide system to prevent gene recombination/pollution, and (2) RNA interaction/competitive inhibition to prevent horizontal gene transfer. Detailed descriptions can be found in our "Project" section.<br />
<br />
== Testing Function ==<br />
<br />
{{:Team:NTU-Taida/Templates/Eq|num=1|eq=a_x+c}}<br />
<br />
When \(a \ne 0\), there are two solutions to \(ax^2 + bx + c = 0\) and they are<br />
$$x = {-b \pm \sqrt{b^2-4ac} \over 2a}.$$<br />
<br />
<html><iframe width="420" height="315" src="http://www.youtube.com/embed/04854XqcfCY" frameborder="0" allowfullscreen></iframe></html><br />
<br />
<br />
{{:Team:NTU-Taida/Templates/Vid|num=3 I can also put in words|width=600px|name=NTU-Taida-Model-Combined-vedio1-1.gif}}<br />
<br />
<br />
<!--EOF --><br />
{{:Team:NTU-Taida/Templates/ContentEnd}}{{:Team:NTU-Taida/Templates/Footer|ActiveNavbar=Safety}}</div>Lbwanghttp://2012.igem.org/Team:NTU-Taida/SafetyTeam:NTU-Taida/Safety2012-10-26T23:16:39Z<p>Lbwang: /* Testing Function */</p>
<hr />
<div>{{:Team:NTU-Taida/Templates/Header}}{{:Team:NTU-Taida/Templates/Navbar}}{{:Team:NTU-Taida/Templates/Sidebar}}{{:Team:NTU-Taida/Templates/ContentStart}}<br />
{{:Team:NTU-Taida/Templates/BSHero|Title=Safety|Content=<p>Use this page to answer the questions on the <a href='/Safety'>safety page</a>.</p>}}<br />
<br />
==Question 1 ==<br />
'''Would any of your project ideas raise safety issues in terms of:'''<br />
*'''researcher safety,'''<br />
*'''public safety, or'''<br />
*'''environmental safety?'''<br />
The biosafety concerns can be simplified to an equation, Risk= probabilityX Hazard. <br />
In our project, the questions we deal with are basically human disease-oriented. We try to prevent any concern regarding potential harms to human. <br />
<br />
As for the researchers, our research is conducted in a safely regulated laboratory, and the ideas of our project do not require etiologic agents, hosts or vectors for experiment. Also no toxic reagent or high risk chemical compound is used. In all, our project hasn’t yet raised researcher safety issues thus far. <br />
For we do not apply any virulent genes or etiologic agents, there seems no additional threats on public safety. Furthermore, the non-pathogenic E. coli we try to deliver into human body can be easily eliminated by antibiotic use if infection arises and is the main concern of patient's safety. <br />
<br />
However, the antibiotics resistance plasmid used in our project may harbor the threats of horizontal gene transfer, which will enhance the virulence of other Escherichia coli in the environment. Though a self-destruction mechanism is designed in our project, we are still aware of the risk on environmental safety. The rules and regulations of concern will be under close supervision of Environmental Protection and Occupational Safety and Hygiene Unit of NTUCM.<br />
<br />
==Question 2 ==<br />
'''Do any of the new BioBrick parts (or devices) that you made this year raise any safety issues? If yes,'''<br />
* '''Did you document these issues in the Registry?'''<br />
* '''How did you manage to handle the safety issue?'''<br />
* '''How could other teams learn from your experience?'''<br />
<br />
The most common question people would have judged us is how we make sure that it is safe to deliver this bug into human intestine. As we noted, the output we would like to deliver, GLP-1, is innate and has no significant harms to the human body. Cell penetrating peptides, which is another peptide we are going to deliver into gastroenterological tract, do no harm as well, since it has a pretty short half life (<15 mins) inside GI tract. <br />
<br />
What’s more, intestine is an organ with an abundance of normal flora, mainly consisting of Streptococcus and Lactobacillus in the middle intestine. In ileum and section close to ileo-cecal valve, bacteroides and coliform bacteria are dominant. First, for the E. coli itself, it’s very hard to colonize in the GI tract as it would face a bunch of competitors over nutrients and space. Second, the bugs we are going to deliver inside human body is pretty fragile, which can be easily eliminated by some antibiotics, 2nd generation cephalosporin, high ampicillin plus sulbactam, or erythromycin, which is ideal of usage in our cases, since it not only provided anti-microbial effects, but also increases the motility of intestine. Above all, the design we are going to bring to synthetic biology community has little safety concerns, and can be easily circumvented or adjusted.<br />
<br />
==Question 3 ==<br />
'''Is there a local biosafety group, committee, or review board at your institution?<br />
*'''If yes, what does your local biosafety group think about your project?'''<br />
*'''If no, which specific biosafety rules or guidelines do you have to consider in your country?'''<br />
<br />
In National Taiwan University, College of Medicine, where the experiments of our project are conducted, Environmental Protection and Occupational Safety and Hygiene Unit of NTUCM takes charge of promoting and supervising safety and health issues.<br />
Before beginning of our project, our team members and advisors have attended the safety education series and training courses held by this unit. All of us were qualified by passing the tests at the end of the training to be sure that all the rules of concern are well understood. The application of our project was also verified and qualified. All experiments are conducted under the biosafety rules of Environmental Protection and Occupational Safety and Hygiene Unit of NTUCM, of which all of our experimental procedures, equipments, facilities were under close supervision.<br />
http://www.mc.ntu.edu.tw/department/safety/index.htm<br />
<br />
==Question 4 ==<br />
'''Do you have any other ideas how to deal with safety issues that could be useful for future iGEM competitions? How could parts, devices and systems be made even safer through biosafety engineering?'''<br />
<br />
As our opinion, we think that for every iGEM teams' circuit design, a mechanism to turn off is necessary. In order to improve the iGEM competition safety concern, we would like to suggest a turn-off mechanism as requirement. Also, the microorganisms should be kept dependent on controlled conditions in the lab to prohibit the unwanted spreading and multiplication outside the lab. Moreover, a suicide switch for all BioBricks or dependence on special nutrients lack in nature for organisms should be engineered in case organisms escape and cause safety concern. The most important thing is that every team and the advisor should know their potential danger and the ways to assess the risk. This aim could be approached by emphasizing the safety rules. Creating a page on the registry for the teams to explain their event tree analysis and fault tree analysis would be an easiest method to increase safety when working with BioBrick parts.<br />
<br />
For our PepdEx system, we proposed two layers of safety regulations: (1) temperature inducible suicide system to prevent gene recombination/pollution, and (2) RNA interaction/competitive inhibition to prevent horizontal gene transfer. Detailed descriptions can be found in our "Project" section.<br />
<br />
== Testing Function ==<br />
<br />
{{:Team:NTU-Taida/Templates/Eq|num=1|eq=a_x+c}}<br />
<br />
When \(a \ne 0\), there are two solutions to \(ax^2 + bx + c = 0\) and they are<br />
$$x = {-b \pm \sqrt{b^2-4ac} \over 2a}.$$<br />
<br />
<html><iframe width="420" height="315" src="http://www.youtube.com/embed/04854XqcfCY" frameborder="0" allowfullscreen></iframe></html><br />
<br />
<br />
{{:Team:NTU-Taida/Templates/Fig|num=3 I can also put in words|width=600px|name=NTU-Taida-Model-Combined-vedio1-1.gif}}<br />
<br />
<br />
<!--EOF --><br />
{{:Team:NTU-Taida/Templates/ContentEnd}}{{:Team:NTU-Taida/Templates/Footer|ActiveNavbar=Safety}}</div>Lbwanghttp://2012.igem.org/Team:NTU-Taida/Modeling/2D-3D-CombinedTeam:NTU-Taida/Modeling/2D-3D-Combined2012-10-26T23:02:51Z<p>Lbwang: /* Spatial-temporal Model Equations */</p>
<hr />
<div>{{:Team:NTU-Taida/Templates/Header}}{{:Team:NTU-Taida/Templates/Navbar}}{{:Team:NTU-Taida/Templates/Sidebar|Title=2D &amp; 3D Combined Model}}{{:Team:NTU-Taida/Templates/ContentStart}}<br />
{{:Team:NTU-Taida/Templates/BSHero|Title=2D &amp; 3D Combined Model|Content=<p></p>}}<br />
<br />
== Overview ==<br />
<p style="text-indent: 2em;"><br />
With the single cell model, fatty acid reaction-absorption model, and system analysis, we have verified the filter function of our circuit, simulated the real physiological fatty acid level at intestinal wall, and adjust our filter threshold to fit to the real condition. Next, we want to combine them together and see what would happen when we put cells in the intestine after a fatty meal.<br />
</p><br />
<p style="text-indent: 2em;"><br />
The combined model is composed of three different sections. 2D combined model simulates the GLP1 response of Pepdex E-coli cells after the food intake in the x-y cross-sectional plane. 2D Cell population response model further considers the possible uneven concentration of fatty acid along the z-axis due to non-uniform distribution of lipase and simulates how the quorum sensing system assists our system to overcame this possible limitation and enhance the response. Finally, 3D Cell population response model incorporates all the consideration to generate a full model to visualize the dynamic behavior of our system.<br />
</p><br />
<br />
<br />
==2D Combined Model==<br />
So far, we have the spatial-temporal concentration of fatty acid, and cells with suitable threshold. In this model, we want to see what would happen when we put cells in the intestine after a meal. <br />
<br />
[[File:NTU-Taida-Model-Combined-fig1.png|600px|center|thumb|Figure 1]]<br />
<br />
We achieve this by further coupling the single cell ODEs (with parameters adjusted by system analysis) locally to the fatty acid reaction-absorption model at the intestinal wall, as shown in Figure 2.<br />
<br />
[[File:NTU-Taida-Model-Combined-fig2.png|600px|center|thumb|Figure 2]]<br />
<br />
Besides to see the cell response when combined with the environmental input, we also want to simulate the prolonged effect of the quorum sensing module with physiological input. Therefore, we simulate system with and without quorum sensing modules and compare their results.<br />
<br />
===Spatial-temporal Model Equations ===<br />
The equations used in our 2D combined model mainly come from the reaction-absorption model and the single cell model. The following three equations are the same as those in the reaction-absorption model, which simulates the change in fatty acid concentration in time and space. <br />
<br />
{{:Team:NTU-Taida/Templates/Eq|num=1|eq=<br />
\frac{d fat}{d t} = -\frac{k_{cat}[E]_t\cdot[S]}{K_m + [S]} <br />
}}<br />
<br />
{{:Team:NTU-Taida/Templates/Eq|num=2|eq=<br />
\frac{d FA}{d t} = 3 \cdot \frac{k_{cat}[E]_t\cdot[S]}{K_m + [S]} <br />
}}<br />
<br />
{{:Team:NTU-Taida/Templates/Eq|num=3|eq=<br />
J=(C_1 - C_2)(D_{FA}/d) <br />
}}<br />
<br />
Other equations in the model are almost the same as those derived in our single cell model, with slightly difference in those for AHL, which will be discussed thoroughly in the 2D Cell population response model. The equations are shown as below.<br />
<br />
{{:Team:NTU-Taida/Templates/Eq|num=4|eq=<br />
\frac{d FadR}{d t} = \alpha_{FadR} - \gamma_{FadR} \cdot FadR <br />
}}<br />
<br />
$$X_{FadR} = \frac{FadR \cdot \beta_{FA}^{n2}}{FA^{n2} + \beta_{FA}^{n2}}$$<br />
{{:Team:NTU-Taida/Templates/Eq|num=5|eq=<br />
}}<br />
<br />
$$\frac{dTetR_1}{dt} = \frac{\alpha_{TetR_1} \cdot {\beta_{FadR}^{n1}}}{\beta_{FadR}^{n1} + X_{FadR}^{n1}} - \gamma_{TetR_1} \cdot TetR_1 $$<br />
{{:Team:NTU-Taida/Templates/Eq|num=6|eq=<br />
}}<br />
<br />
$$\frac{d TetR_2}{d t} = \frac{\alpha_{TetR_2} \cdot R^{n3}}{\beta_R^{n3} + R^{n3}} - \gamma_{TetR_2} \cdot TetR_2$$<br />
{{:Team:NTU-Taida/Templates/Eq|num=7|eq=<br />
}}<br />
<br />
$$\frac{d LuxI}{d t} = \frac{\alpha_{LuxI} \cdot \beta_{FadR}^{n1}}{\beta_{FadR}^{n1} + X_{FadR}^{n1}} - \gamma_{LuxI} \cdot LuxI$$<br />
{{:Team:NTU-Taida/Templates/Eq|num=8|eq=<br />
}}<br />
<br />
$$\frac{\partial^2 AHL}{\partial x^2} + \frac{\partial^2 AHL}{y^2} - \frac{1}{D_{AHL}}\cdot \frac{\partial AHL}{\partial t} = 0$$<br />
{{:Team:NTU-Taida/Templates/Eq|num=9|eq=<br />
}}<br />
<br />
$$R(AHL) = - \gamma_{AHL_{ext}} \cdot AHL + cd(k_{s1}LuxI - k_{s0}AHL)$$<br />
{{:Team:NTU-Taida/Templates/Eq|num=10|eq=<br />
}}<br />
<br />
$$\frac{d R}{d t} = \rho (LuxR)^2(AHL_i)^2 - \gamma_R \cdot R$$<br />
{{:Team:NTU-Taida/Templates/Eq|num=11|eq=<br />
}}<br />
<br />
$$\frac{d LacI}{d t} = \frac{\alpha_{LacI}}{1 + (\frac{TetR_1 + TetR_2}{\beta_{TetR}})^{n5}} - \gamma_{LacI} \cdot LacI$$<br />
{{:Team:NTU-Taida/Templates/Eq|num=12|eq=<br />
}}<br />
<br />
$$\frac{d GLP1}{d t} = \frac{\alpha_{GLP1}}{1 + (\frac{LacI}{\beta_{LacI}})^{n6}} - \gamma_{GLP1} \cdot GLP1$$<br />
{{:Team:NTU-Taida/Templates/Eq|num=13|eq=<br />
}}<br />
<br />
<br />
For the control group without the quorum sensing module, we simply discard the terms related to quorum sensing system in the ODE set.<br />
<br />
===Results===<br />
<br />
{{:Team:NTU-Taida/Templates/Vid|num=1-3|width=600px|name=NTU-Taida-Model-Combined-video1-3.gif}}<br />
<br />
[[FIle:NTU-Taida-Model-2D3D-vedio1-3.gif|450px|thumb|center|video1-3]]<br />
<br />
<br />
Video 1 shows the spatial temporal concentration change of fatty acid. Video 2 and three show the corresponding spatial temporal response of GLP-1 expression in system without and with quorum sensing module, respectively.<br />
<br />
We can see from the videos that the fatty acid concentration at the intestinal wall first increases rapidly, turning on the circuits in the cells and resulting in GLP-1 expression at the intestinal wall. Then due to the absorption of fatty acid, the concentration gradually falls and the GLP-1 concentration started to decrease. Notice that the GLP1 expression in the system with Quorum sensing, shown in Video 3, lasts longer than that of the system without quorum sensing, shown in Video 2. Consistent to the single cell model, the system with QS has more prolonged response compared to the one without it.<br />
<br />
==Cell Population Response Model==<br />
<br />
We have assumed that fat distributes uniformly along the z-axis in the lumen after a meal in the previous models. However, in real situation in human body, lipase only exists in certain segments of the intestine. Therefore, fat hydrolysis will only take place in those segments and there will be no fatty acid produced outside these segments, as shown in Figure 3. Cells residing in the segments without lipase activity can only sense the fatty acid diffused from the source segments. Because AHL diffuses faster than fatty acid, we incorporate the quorum sensing system to enable faster recruitment of more bacteria to express GLP-1 in regions without lipase.<br />
<br />
Quorum sensing module enables cells to communicate with each other, as the uneven distribution of fatty acid in the intestines may cause gaps in individual detection. Cells with the quorum sensing module can respond to food intake event as long as their neighboring cells have detected fatty acid, enhancing the overall response to the food intake (Figure 4). However, the communication between cells via AHL can’t be seen when only viewing a single cell. Therefore, we construct spatial temporal models with COMSOL Multiphysics in order to gain insights into the influence of cell-cell communication mediated via the quorum sensing module on the overall GLP1 expression.<br />
<br />
[[File:NTU-Taida-Model-Combined-fig3.png|600px|center|thumb|Figure 3]]<br />
[[File:NTU-Taida-Model-Combined-fig4.png|600px|center|thumb|Figure 4]]<br />
<br />
==2D Cell Population Response Model==<br />
We start our effort with a 2D spatial temporal model. When E.coli cells colonize the intestine, they tend to attach onto the intestinal walls instead of distributing evenly throughout the intestine lumen. Therefore, we first view our system as a two dimensional system, with the modeling plane in the x-z (or either y-z) dimension.<br />
<br />
===Geometry Design===<br />
[[File:NTU-Taida-Model-Combined-fig5.png|600px|center|thumb|Figure 5]]<br />
<br />
With this in mind, we construct a plane in 2D geometry and couple the ODEs derived in our single cell model to simulate the presence of cells.<br />
<br />
To model the effect of quorum sensing, we establish an uneven distribution of fatty acid by giving a constant concentration source of fatty acid in the middle of our modeled plane, as shown in Figure 6. There are no cells within the circular fatty acid source. As time goes on, fatty acids diffuse from the source and establish a concentric gradient. To see the effect of quorum sensing mechanism on overall GLP1 expression in a cell population with uneven distributed fatty acid input, we model cells with and without quorum sensing and compare their spatial –temporal GLP1 expression.<br />
[[File:NTU-Taida-Model-Combined-fig6.png|600px|center|thumb|Figure 6]]<br />
<br />
===Spatial-temporal Model Equations===<br />
The first equation used in our model describes the free diffusion of fatty acids from the central source.<br />
<br />
$$\frac{\partial^2 FA}{\partial x^2} + \frac{\partial^2 FA}{\partial z^2} - \frac{1}{D_{FA}} \frac{\partial FA}{\partial t} = 0$$<br />
{{:Team:NTU-Taida/Templates/Eq|num=1|eq=<br />
}}<br />
<br />
Other equations in the model are almost the same as those derived in our single cell model, except for the ones for AHL. For AHL, we have to set up a partial differential equation describing both the diffusion and the reaction event of AHL. We assume that AHL diffusion into and out of cells is fast and do not model this diffusion process explicitly. Therefore, in contrast to the single-cell model, we only use one species called AHL instead of an internal AHL concentration AHLi and an external AHL concentration AHLe. <br />
<br />
For the reaction term of AHL, we first discard the terms describing the diffusion into and out of the cell membrane in the ODEs of AHLi and AHLe in the single cell model. <br />
As previously mentioned, we assume that the diffusion AHL diffusion into and out of cells is fast. Therefore, we simply account for the diffusion of AHL across cell membrane by multiplying the intracellular AHLi terms by the relative cell density, which will be described in the next section. With these considerations, we combine the two equations of AHLi and AHLe (Eq . and Eq. )into one reaction equation (Eq. ).<br />
<br />
{{:Team:NTU-Taida/Templates/Eq|num=3|eq=xxxxxyyyyyzzzz<br />
}}<br />
<br />
{{:Team:NTU-Taida/Templates/Eq|num=4|eq=xxxxxyyyyyzzzz<br />
}}<br />
<br />
{{:Team:NTU-Taida/Templates/Eq|num=5|eq=xxxxxyyyyyzzzz<br />
}}<br />
<br />
With the help of COMSOL Multiphysics, we can consider both the diffusion and reaction terms of AHL by giving the diffusion (Eq. 2) and reaction (Eq. 5) equations above, without the need to solve the explicit PDE of AHL.<br />
<br />
The diffusion of AHL is modeled by a free diffusion equation.<br />
{{:Team:NTU-Taida/Templates/Eq|num=2|eq=xxxxxyyyyyzzzz<br />
}}<br />
<br />
Other equations in the model are the same as those derived in our single cell model.<br />
For the control group without the quorum sensing module, we discard the terms related to quorum sensing system in the ODE set.<br />
<br />
==Relative Cell density==<br />
The relative cell density is defined as the ratio of the total area E.coli cells occupy to the area of the intestinal wall. By multiplying the intracellular AHL synthesis and degradation terms by the relative cell density, we assume that as a cell synthesizes or degrades AHL, the addition or reduction of AHL molecules is dispersed evenly through the neighboring area. (Mind that the diffusion of these AHL molecules on global scale is still governed by the free diffusion equation.)<br />
<br />
We calculated the relative cell density by assuming there are 1014 bacteria cells residing in the intestine, which has a total surface area of 200 m2. Thus, the average cell density is 5*1011 cells/m2. We can measure the surface area of each individual cell by multiplying their length by their width, giving a surface area of 10-12 m2 per cell. Multiplying the surface area per cell and the average cell density gives the area density of total cells as 0.5. <br />
Since 99% of the gut flora consists of 30-40 species of bacteria, we can assume that each of the common types contribute to approximately 1% of the total surface area of the intestine. Considering the clustering effect of cells, we assume that some regions would have much higher cell densities than others, such that the uneven distribution may result in a tenfold fluctuation in cell density. We hypothesize that the relative cell density in our model could be as high as 0.1.<br />
<br />
Cell density has dramatic effect on the overall effect of quorum sensing system, as supported by a recent study investigating the synchronization of repressilators by quorum sensing mechanisms [1]. Therefore, we also model our system with different cell densities, as can be seen in the results.<br />
<br />
===Results===<br />
To see the effect of quorum sensing mechanism on overall GLP1 expression in a cell population with uneven distributed fatty acid input, we model cells with and without quorum sensing and compare their spatial - temporal GLP1 expression, with relative cell density of 0.1<br />
The results show that species which are not regulated by the quorum sensing module, such as FA, X_FadR, and TetR1, show no difference in the spatial temporal expression pattern between system with and without the quorum sensing system. <br />
<br />
However, species affected by the quorum sensing module, such as LacI and GLP1, show striking difference in their spatial temporal concentration pattern. Within the given time span, systems with a quorum sensing module produces GLP1 over a broader spatial region, resulting in more total GLP1. <br />
<br />
===Species unregulated by the quorum sensing module===<br />
<br />
====FA====<br />
<br />
{{:Team:NTU-Taida/Templates/Vid|num=4|width=600px|name=NTU-Taida-Model-Combined-video4.gif}}<br />
<br />
====X_fadR====<br />
{{:Team:NTU-Taida/Templates/Vid|num=5|width=600px|name=NTU-Taida-Model-Combined-video5.gif}}<br />
{{:Team:NTU-Taida/Templates/Vid|num=6|width=600px|name=NTU-Taida-Model-Combined-video6.gif}}<br />
<br />
===Species regulated by the quorum sensing module===<br />
====LacI====<br />
{{:Team:NTU-Taida/Templates/Vid|num=7|width=450px|name=NTU-Taida-Model-Combined-video7.gif}}<br />
The expression of LacI is inhibited by TetR proteins, and therefore is regulated by the quorum sensing module. Although the concentration of TetR1 is the same in systems with and without quorum sensing, cells with quorum sensing produce TetR2 as the output of the quorum sensing module and therefore result in overall more total TetR proteins. Thus, the repression of LacI is more significant in systems with the quorum sensing module. <br />
<br />
====GLP1====<br />
{{:Team:NTU-Taida/Templates/Vid|num=8|width=600px|name=NTU-Taida-Model-Combined-video8.gif}}<br />
As the expression of GLP1 is repressed by LacI proteins, GLP1 also displays different spatial-temporal concentration pattern between the two systems. With quorum sensing module, the system produces more GLP1 overall.<br />
<br />
===Effect of cell density===<br />
<br />
Relative cell density plays a critical role in determining whether we can see a significant difference between systems with and without quorum sensing. We simulated the spatial-temporal response of GLP1 of four systems, all of them with the quorum sensing module but with relative cell densities of 0.2, 0.1, and 0.01, respectively. <br />
<br />
Then we compare their response to that of system without quorum sensing to determine if there exists a threshold of cell density, below which the effect of quorum sensing module is unperceivable. <br />
<br />
{{:Team:NTU-Taida/Templates/Vid|num=9|width=600px|name=NTU-Taida-Model-Combined-video9.gif}}<br />
<br />
We can see from Video 9 that the system with a relative cell density of 0.2 differs most with the system without the quorum sensing module. The system with a relative cell density of 0.1 shows moderate difference. The system with a relative cell density of 0.05 displays very subtle difference. There is no difference between the system with a relative cell density of 0.01 and the system with no quorum sensing module. Therefore, the threshold of relative cell density may lie between 0.05 and 0.01.<br />
<br />
<br />
==3D Cell population response model==<br />
<br />
Finally, we construct a full 3D model, combing the consideration on the x-y plane and the x-z plane. Our goal is to simulate the effect of non-uniform production of fatty acid due to the spatially limited lipase activity. We modeled the intestine by a cylindrical tube, with a fat source limited to the z=0 plane, to simulate the situations similar to that shown in Figure 7, and examine the effect of Quorum sensing. <br />
<br />
[[File:NTU-Taida-Model-Combined-fig7.png|600px|center|thumb|Figure 7]]<br />
<br />
The equations used are the same as those in the 2D cell population response model, but with the equations governing diffusions changing from the two-dimension form to their three-dimension counterparts.<br />
<br />
{{:Team:NTU-Taida/Templates/Vid|num=10-11|width=600px|name=NTU-Taida-Model-Combined-video10-11.gif}}<br />
<br />
Video 10 shows the result of system without quorum sensing module while Video 11 shows the result of system with quorum sensing module. From Video 10 and 11, we can see that GLP-1 starts to be expressed at similar time point at the intestinal wall on the z=0 plane. However, the GLP-1 expression spreads faster along the z-axis in system with quorum sensing.<br />
<br />
==Reference==<br />
<ol id='Ref'><br />
<li>Jordi Garcia-Ojalvo , Michael B. Elowitz, and Steven H. Strogatz , Modeling a synthetic multicellular clock: Repressilators coupled by quorum sensing, pnas,2004</li><br />
</ol><br />
<!--EOF--><br />
{{:Team:NTU-Taida/Templates/ContentEnd}}{{:Team:NTU-Taida/Templates/Footer|ActiveNavbar=Modeling, #nav-Modeling-Combined}}</div>Lbwanghttp://2012.igem.org/Team:NTU-Taida/Modeling/2D-3D-CombinedTeam:NTU-Taida/Modeling/2D-3D-Combined2012-10-26T23:01:53Z<p>Lbwang: /* Spatial-temporal Model Equations */</p>
<hr />
<div>{{:Team:NTU-Taida/Templates/Header}}{{:Team:NTU-Taida/Templates/Navbar}}{{:Team:NTU-Taida/Templates/Sidebar|Title=2D &amp; 3D Combined Model}}{{:Team:NTU-Taida/Templates/ContentStart}}<br />
{{:Team:NTU-Taida/Templates/BSHero|Title=2D &amp; 3D Combined Model|Content=<p></p>}}<br />
<br />
== Overview ==<br />
<p style="text-indent: 2em;"><br />
With the single cell model, fatty acid reaction-absorption model, and system analysis, we have verified the filter function of our circuit, simulated the real physiological fatty acid level at intestinal wall, and adjust our filter threshold to fit to the real condition. Next, we want to combine them together and see what would happen when we put cells in the intestine after a fatty meal.<br />
</p><br />
<p style="text-indent: 2em;"><br />
The combined model is composed of three different sections. 2D combined model simulates the GLP1 response of Pepdex E-coli cells after the food intake in the x-y cross-sectional plane. 2D Cell population response model further considers the possible uneven concentration of fatty acid along the z-axis due to non-uniform distribution of lipase and simulates how the quorum sensing system assists our system to overcame this possible limitation and enhance the response. Finally, 3D Cell population response model incorporates all the consideration to generate a full model to visualize the dynamic behavior of our system.<br />
</p><br />
<br />
<br />
==2D Combined Model==<br />
So far, we have the spatial-temporal concentration of fatty acid, and cells with suitable threshold. In this model, we want to see what would happen when we put cells in the intestine after a meal. <br />
<br />
[[File:NTU-Taida-Model-Combined-fig1.png|600px|center|thumb|Figure 1]]<br />
<br />
We achieve this by further coupling the single cell ODEs (with parameters adjusted by system analysis) locally to the fatty acid reaction-absorption model at the intestinal wall, as shown in Figure 2.<br />
<br />
[[File:NTU-Taida-Model-Combined-fig2.png|600px|center|thumb|Figure 2]]<br />
<br />
Besides to see the cell response when combined with the environmental input, we also want to simulate the prolonged effect of the quorum sensing module with physiological input. Therefore, we simulate system with and without quorum sensing modules and compare their results.<br />
<br />
===Spatial-temporal Model Equations ===<br />
The equations used in our 2D combined model mainly come from the reaction-absorption model and the single cell model. The following three equations are the same as those in the reaction-absorption model, which simulates the change in fatty acid concentration in time and space. <br />
<br />
{{:Team:NTU-Taida/Templates/Eq|num=1|eq=<br />
\frac{d fat}{d t} = -\frac{k_{cat}[E]_t\cdot[S]}{K_m + [S]} <br />
}}<br />
<br />
{{:Team:NTU-Taida/Templates/Eq|num=2|eq=<br />
\frac{d FA}{d t} = 3 \cdot \frac{k_{cat}[E]_t\cdot[S]}{K_m + [S]} <br />
}}<br />
<br />
{{:Team:NTU-Taida/Templates/Eq|num=3|eq=<br />
J=(C_1 - C_2)(D_{FA}/d) <br />
}}<br />
<br />
Other equations in the model are almost the same as those derived in our single cell model, with slightly difference in those for AHL, which will be discussed thoroughly in the 2D Cell population response model. The equations are shown as below.<br />
<br />
{{:Team:NTU-Taida/Templates/Eq|num=4|eq=<br />
\frac{d FadR}{d t} = \alpha_{FadR} - \gamma_{FadR} \cdot FadR <br />
}}<br />
<br />
$$X_{FadR} = \frac{FadR \cdot \beta_{FA}^{n2}}{FA^{n2} + \beta_{FA}^{n2}}$$<br />
{{:Team:NTU-Taida/Templates/Eq|num=5|eq=<br />
}}<br />
<br />
$$\frac{dTetR_1}{dt} = \frac{\alpha_{TetR_1} \cdot {\beta_{FadR}^{n1}}}{\beta_{FadR}^{n1} + X_{FadR}^{n1}} - \gamma_{TetR_1} \cdot TetR_1 $$<br />
{{:Team:NTU-Taida/Templates/Eq|num=6|eq=<br />
}}<br />
<br />
$$\frac{d TetR_2}{d t} = \frac{\alpha_{TetR_2} \cdot R^{n3}}{\beta_R^{n3} + R^{n3}} - \gamma_{TetR_2} \cdot TetR_2$$<br />
{{:Team:NTU-Taida/Templates/Eq|num=7|eq=<br />
}}<br />
<br />
$$\frac{d LuxI}{d t} = \frac{\alpha_{LuxI} \cdot \beta_{FadR}^{n1}}{\beta_{FadR}^{n1} + X_{FadR}^{n1}} - \gamma_{LuxI} \cdot LuxI$$<br />
{{:Team:NTU-Taida/Templates/Eq|num=8|eq=<br />
}}<br />
<br />
{{:Team:NTU-Taida/Templates/Eq|num=9|eq=<br />
\frac{\partial^2 AHL}{\partial x^2} + \frac{\partial^2 AHL}{y^2} - \frac{1}{D_{AHL}}\cdot \frac{\partial AHL}{\partial t} = 0<br />
}}<br />
<br />
$$R(AHL) = - \gamma_{AHL_{ext}} \cdot AHL + cd(k_{s1}LuxI - k_{s0}AHL)$$<br />
{{:Team:NTU-Taida/Templates/Eq|num=10|eq=<br />
}}<br />
<br />
$$\frac{d R}{d t} = \rho (LuxR)^2(AHL_i)^2 - \gamma_R \cdot R$$<br />
{{:Team:NTU-Taida/Templates/Eq|num=11|eq=<br />
}}<br />
<br />
$$\frac{d LacI}{d t} = \frac{\alpha_{LacI}}{1 + (\frac{TetR_1 + TetR_2}{\beta_{TetR}})^{n5}} - \gamma_{LacI} \cdot LacI$$<br />
{{:Team:NTU-Taida/Templates/Eq|num=12|eq=<br />
}}<br />
<br />
$$\frac{d GLP1}{d t} = \frac{\alpha_{GLP1}}{1 + (\frac{LacI}{\beta_{LacI}})^{n6}} - \gamma_{GLP1} \cdot GLP1$$<br />
{{:Team:NTU-Taida/Templates/Eq|num=13|eq=<br />
}}<br />
<br />
<br />
For the control group without the quorum sensing module, we simply discard the terms related to quorum sensing system in the ODE set.<br />
<br />
===Results===<br />
<br />
{{:Team:NTU-Taida/Templates/Vid|num=1-3|width=600px|name=NTU-Taida-Model-Combined-video1-3.gif}}<br />
<br />
[[FIle:NTU-Taida-Model-2D3D-vedio1-3.gif|450px|thumb|center|video1-3]]<br />
<br />
<br />
Video 1 shows the spatial temporal concentration change of fatty acid. Video 2 and three show the corresponding spatial temporal response of GLP-1 expression in system without and with quorum sensing module, respectively.<br />
<br />
We can see from the videos that the fatty acid concentration at the intestinal wall first increases rapidly, turning on the circuits in the cells and resulting in GLP-1 expression at the intestinal wall. Then due to the absorption of fatty acid, the concentration gradually falls and the GLP-1 concentration started to decrease. Notice that the GLP1 expression in the system with Quorum sensing, shown in Video 3, lasts longer than that of the system without quorum sensing, shown in Video 2. Consistent to the single cell model, the system with QS has more prolonged response compared to the one without it.<br />
<br />
==Cell Population Response Model==<br />
<br />
We have assumed that fat distributes uniformly along the z-axis in the lumen after a meal in the previous models. However, in real situation in human body, lipase only exists in certain segments of the intestine. Therefore, fat hydrolysis will only take place in those segments and there will be no fatty acid produced outside these segments, as shown in Figure 3. Cells residing in the segments without lipase activity can only sense the fatty acid diffused from the source segments. Because AHL diffuses faster than fatty acid, we incorporate the quorum sensing system to enable faster recruitment of more bacteria to express GLP-1 in regions without lipase.<br />
<br />
Quorum sensing module enables cells to communicate with each other, as the uneven distribution of fatty acid in the intestines may cause gaps in individual detection. Cells with the quorum sensing module can respond to food intake event as long as their neighboring cells have detected fatty acid, enhancing the overall response to the food intake (Figure 4). However, the communication between cells via AHL can’t be seen when only viewing a single cell. Therefore, we construct spatial temporal models with COMSOL Multiphysics in order to gain insights into the influence of cell-cell communication mediated via the quorum sensing module on the overall GLP1 expression.<br />
<br />
[[File:NTU-Taida-Model-Combined-fig3.png|600px|center|thumb|Figure 3]]<br />
[[File:NTU-Taida-Model-Combined-fig4.png|600px|center|thumb|Figure 4]]<br />
<br />
==2D Cell Population Response Model==<br />
We start our effort with a 2D spatial temporal model. When E.coli cells colonize the intestine, they tend to attach onto the intestinal walls instead of distributing evenly throughout the intestine lumen. Therefore, we first view our system as a two dimensional system, with the modeling plane in the x-z (or either y-z) dimension.<br />
<br />
===Geometry Design===<br />
[[File:NTU-Taida-Model-Combined-fig5.png|600px|center|thumb|Figure 5]]<br />
<br />
With this in mind, we construct a plane in 2D geometry and couple the ODEs derived in our single cell model to simulate the presence of cells.<br />
<br />
To model the effect of quorum sensing, we establish an uneven distribution of fatty acid by giving a constant concentration source of fatty acid in the middle of our modeled plane, as shown in Figure 6. There are no cells within the circular fatty acid source. As time goes on, fatty acids diffuse from the source and establish a concentric gradient. To see the effect of quorum sensing mechanism on overall GLP1 expression in a cell population with uneven distributed fatty acid input, we model cells with and without quorum sensing and compare their spatial –temporal GLP1 expression.<br />
[[File:NTU-Taida-Model-Combined-fig6.png|600px|center|thumb|Figure 6]]<br />
<br />
===Spatial-temporal Model Equations===<br />
The first equation used in our model describes the free diffusion of fatty acids from the central source.<br />
<br />
$$\frac{\partial^2 FA}{\partial x^2} + \frac{\partial^2 FA}{\partial z^2} - \frac{1}{D_{FA}} \frac{\partial FA}{\partial t} = 0$$<br />
{{:Team:NTU-Taida/Templates/Eq|num=1|eq=<br />
}}<br />
<br />
Other equations in the model are almost the same as those derived in our single cell model, except for the ones for AHL. For AHL, we have to set up a partial differential equation describing both the diffusion and the reaction event of AHL. We assume that AHL diffusion into and out of cells is fast and do not model this diffusion process explicitly. Therefore, in contrast to the single-cell model, we only use one species called AHL instead of an internal AHL concentration AHLi and an external AHL concentration AHLe. <br />
<br />
For the reaction term of AHL, we first discard the terms describing the diffusion into and out of the cell membrane in the ODEs of AHLi and AHLe in the single cell model. <br />
As previously mentioned, we assume that the diffusion AHL diffusion into and out of cells is fast. Therefore, we simply account for the diffusion of AHL across cell membrane by multiplying the intracellular AHLi terms by the relative cell density, which will be described in the next section. With these considerations, we combine the two equations of AHLi and AHLe (Eq . and Eq. )into one reaction equation (Eq. ).<br />
<br />
{{:Team:NTU-Taida/Templates/Eq|num=3|eq=xxxxxyyyyyzzzz<br />
}}<br />
<br />
{{:Team:NTU-Taida/Templates/Eq|num=4|eq=xxxxxyyyyyzzzz<br />
}}<br />
<br />
{{:Team:NTU-Taida/Templates/Eq|num=5|eq=xxxxxyyyyyzzzz<br />
}}<br />
<br />
With the help of COMSOL Multiphysics, we can consider both the diffusion and reaction terms of AHL by giving the diffusion (Eq. 2) and reaction (Eq. 5) equations above, without the need to solve the explicit PDE of AHL.<br />
<br />
The diffusion of AHL is modeled by a free diffusion equation.<br />
{{:Team:NTU-Taida/Templates/Eq|num=2|eq=xxxxxyyyyyzzzz<br />
}}<br />
<br />
Other equations in the model are the same as those derived in our single cell model.<br />
For the control group without the quorum sensing module, we discard the terms related to quorum sensing system in the ODE set.<br />
<br />
==Relative Cell density==<br />
The relative cell density is defined as the ratio of the total area E.coli cells occupy to the area of the intestinal wall. By multiplying the intracellular AHL synthesis and degradation terms by the relative cell density, we assume that as a cell synthesizes or degrades AHL, the addition or reduction of AHL molecules is dispersed evenly through the neighboring area. (Mind that the diffusion of these AHL molecules on global scale is still governed by the free diffusion equation.)<br />
<br />
We calculated the relative cell density by assuming there are 1014 bacteria cells residing in the intestine, which has a total surface area of 200 m2. Thus, the average cell density is 5*1011 cells/m2. We can measure the surface area of each individual cell by multiplying their length by their width, giving a surface area of 10-12 m2 per cell. Multiplying the surface area per cell and the average cell density gives the area density of total cells as 0.5. <br />
Since 99% of the gut flora consists of 30-40 species of bacteria, we can assume that each of the common types contribute to approximately 1% of the total surface area of the intestine. Considering the clustering effect of cells, we assume that some regions would have much higher cell densities than others, such that the uneven distribution may result in a tenfold fluctuation in cell density. We hypothesize that the relative cell density in our model could be as high as 0.1.<br />
<br />
Cell density has dramatic effect on the overall effect of quorum sensing system, as supported by a recent study investigating the synchronization of repressilators by quorum sensing mechanisms [1]. Therefore, we also model our system with different cell densities, as can be seen in the results.<br />
<br />
===Results===<br />
To see the effect of quorum sensing mechanism on overall GLP1 expression in a cell population with uneven distributed fatty acid input, we model cells with and without quorum sensing and compare their spatial - temporal GLP1 expression, with relative cell density of 0.1<br />
The results show that species which are not regulated by the quorum sensing module, such as FA, X_FadR, and TetR1, show no difference in the spatial temporal expression pattern between system with and without the quorum sensing system. <br />
<br />
However, species affected by the quorum sensing module, such as LacI and GLP1, show striking difference in their spatial temporal concentration pattern. Within the given time span, systems with a quorum sensing module produces GLP1 over a broader spatial region, resulting in more total GLP1. <br />
<br />
===Species unregulated by the quorum sensing module===<br />
<br />
====FA====<br />
<br />
{{:Team:NTU-Taida/Templates/Vid|num=4|width=600px|name=NTU-Taida-Model-Combined-video4.gif}}<br />
<br />
====X_fadR====<br />
{{:Team:NTU-Taida/Templates/Vid|num=5|width=600px|name=NTU-Taida-Model-Combined-video5.gif}}<br />
{{:Team:NTU-Taida/Templates/Vid|num=6|width=600px|name=NTU-Taida-Model-Combined-video6.gif}}<br />
<br />
===Species regulated by the quorum sensing module===<br />
====LacI====<br />
{{:Team:NTU-Taida/Templates/Vid|num=7|width=450px|name=NTU-Taida-Model-Combined-video7.gif}}<br />
The expression of LacI is inhibited by TetR proteins, and therefore is regulated by the quorum sensing module. Although the concentration of TetR1 is the same in systems with and without quorum sensing, cells with quorum sensing produce TetR2 as the output of the quorum sensing module and therefore result in overall more total TetR proteins. Thus, the repression of LacI is more significant in systems with the quorum sensing module. <br />
<br />
====GLP1====<br />
{{:Team:NTU-Taida/Templates/Vid|num=8|width=600px|name=NTU-Taida-Model-Combined-video8.gif}}<br />
As the expression of GLP1 is repressed by LacI proteins, GLP1 also displays different spatial-temporal concentration pattern between the two systems. With quorum sensing module, the system produces more GLP1 overall.<br />
<br />
===Effect of cell density===<br />
<br />
Relative cell density plays a critical role in determining whether we can see a significant difference between systems with and without quorum sensing. We simulated the spatial-temporal response of GLP1 of four systems, all of them with the quorum sensing module but with relative cell densities of 0.2, 0.1, and 0.01, respectively. <br />
<br />
Then we compare their response to that of system without quorum sensing to determine if there exists a threshold of cell density, below which the effect of quorum sensing module is unperceivable. <br />
<br />
{{:Team:NTU-Taida/Templates/Vid|num=9|width=600px|name=NTU-Taida-Model-Combined-video9.gif}}<br />
<br />
We can see from Video 9 that the system with a relative cell density of 0.2 differs most with the system without the quorum sensing module. The system with a relative cell density of 0.1 shows moderate difference. The system with a relative cell density of 0.05 displays very subtle difference. There is no difference between the system with a relative cell density of 0.01 and the system with no quorum sensing module. Therefore, the threshold of relative cell density may lie between 0.05 and 0.01.<br />
<br />
<br />
==3D Cell population response model==<br />
<br />
Finally, we construct a full 3D model, combing the consideration on the x-y plane and the x-z plane. Our goal is to simulate the effect of non-uniform production of fatty acid due to the spatially limited lipase activity. We modeled the intestine by a cylindrical tube, with a fat source limited to the z=0 plane, to simulate the situations similar to that shown in Figure 7, and examine the effect of Quorum sensing. <br />
<br />
[[File:NTU-Taida-Model-Combined-fig7.png|600px|center|thumb|Figure 7]]<br />
<br />
The equations used are the same as those in the 2D cell population response model, but with the equations governing diffusions changing from the two-dimension form to their three-dimension counterparts.<br />
<br />
{{:Team:NTU-Taida/Templates/Vid|num=10-11|width=600px|name=NTU-Taida-Model-Combined-video10-11.gif}}<br />
<br />
Video 10 shows the result of system without quorum sensing module while Video 11 shows the result of system with quorum sensing module. From Video 10 and 11, we can see that GLP-1 starts to be expressed at similar time point at the intestinal wall on the z=0 plane. However, the GLP-1 expression spreads faster along the z-axis in system with quorum sensing.<br />
<br />
==Reference==<br />
<ol id='Ref'><br />
<li>Jordi Garcia-Ojalvo , Michael B. Elowitz, and Steven H. Strogatz , Modeling a synthetic multicellular clock: Repressilators coupled by quorum sensing, pnas,2004</li><br />
</ol><br />
<!--EOF--><br />
{{:Team:NTU-Taida/Templates/ContentEnd}}{{:Team:NTU-Taida/Templates/Footer|ActiveNavbar=Modeling, #nav-Modeling-Combined}}</div>Lbwanghttp://2012.igem.org/Team:NTU-Taida/Modeling/2D-3D-CombinedTeam:NTU-Taida/Modeling/2D-3D-Combined2012-10-26T22:59:18Z<p>Lbwang: /* Spatial-temporal Model Equations */</p>
<hr />
<div>{{:Team:NTU-Taida/Templates/Header}}{{:Team:NTU-Taida/Templates/Navbar}}{{:Team:NTU-Taida/Templates/Sidebar|Title=2D &amp; 3D Combined Model}}{{:Team:NTU-Taida/Templates/ContentStart}}<br />
{{:Team:NTU-Taida/Templates/BSHero|Title=2D &amp; 3D Combined Model|Content=<p></p>}}<br />
<br />
== Overview ==<br />
<p style="text-indent: 2em;"><br />
With the single cell model, fatty acid reaction-absorption model, and system analysis, we have verified the filter function of our circuit, simulated the real physiological fatty acid level at intestinal wall, and adjust our filter threshold to fit to the real condition. Next, we want to combine them together and see what would happen when we put cells in the intestine after a fatty meal.<br />
</p><br />
<p style="text-indent: 2em;"><br />
The combined model is composed of three different sections. 2D combined model simulates the GLP1 response of Pepdex E-coli cells after the food intake in the x-y cross-sectional plane. 2D Cell population response model further considers the possible uneven concentration of fatty acid along the z-axis due to non-uniform distribution of lipase and simulates how the quorum sensing system assists our system to overcame this possible limitation and enhance the response. Finally, 3D Cell population response model incorporates all the consideration to generate a full model to visualize the dynamic behavior of our system.<br />
</p><br />
<br />
<br />
==2D Combined Model==<br />
So far, we have the spatial-temporal concentration of fatty acid, and cells with suitable threshold. In this model, we want to see what would happen when we put cells in the intestine after a meal. <br />
<br />
[[File:NTU-Taida-Model-Combined-fig1.png|600px|center|thumb|Figure 1]]<br />
<br />
We achieve this by further coupling the single cell ODEs (with parameters adjusted by system analysis) locally to the fatty acid reaction-absorption model at the intestinal wall, as shown in Figure 2.<br />
<br />
[[File:NTU-Taida-Model-Combined-fig2.png|600px|center|thumb|Figure 2]]<br />
<br />
Besides to see the cell response when combined with the environmental input, we also want to simulate the prolonged effect of the quorum sensing module with physiological input. Therefore, we simulate system with and without quorum sensing modules and compare their results.<br />
<br />
===Spatial-temporal Model Equations ===<br />
The equations used in our 2D combined model mainly come from the reaction-absorption model and the single cell model. The following three equations are the same as those in the reaction-absorption model, which simulates the change in fatty acid concentration in time and space. <br />
<br />
{{:Team:NTU-Taida/Templates/Eq|num=1|eq=<br />
\frac{d fat}{d t} = -\frac{k_{cat}[E]_t\cdot[S]}{K_m + [S]} <br />
}}<br />
<br />
{{:Team:NTU-Taida/Templates/Eq|num=2|eq=<br />
\frac{d FA}{d t} = 3 \cdot \frac{k_{cat}[E]_t\cdot[S]}{K_m + [S]} <br />
}}<br />
<br />
{{:Team:NTU-Taida/Templates/Eq|num=3|eq=<br />
J=(C_1 - C_2)(D_{FA}/d) <br />
}}<br />
<br />
Other equations in the model are almost the same as those derived in our single cell model, with slightly difference in those for AHL, which will be discussed thoroughly in the 2D Cell population response model. The equations are shown as below.<br />
<br />
{{:Team:NTU-Taida/Templates/Eq|num=4|eq=<br />
\frac{d FadR}{d t} = \alpha_{FadR} - \gamma_{FadR} \cdot FadR <br />
}}<br />
<br />
$$X_{FadR} = \frac{FadR \cdot \beta_{FA}^{n2}}{FA^{n2} + \beta_{FA}^{n2}}$$<br />
{{:Team:NTU-Taida/Templates/Eq|num=5|eq=<br />
}}<br />
<br />
$$\frac{dTetR_1}{dt} = \frac{\alpha_{TetR_1} \cdot {\beta_{FadR}^{n1}}}{\beta_{FadR}^{n1} + X_{FadR}^{n1}} - \gamma_{TetR_1} \cdot TetR_1 $$<br />
{{:Team:NTU-Taida/Templates/Eq|num=6|eq=<br />
}}<br />
<br />
$$\frac{d TetR_2}{d t} = \frac{\alpha_{TetR_2} \cdot R^{n3}}{\beta_R^{n3} + R^{n3}} - \gamma_{TetR_2} \cdot TetR_2$$<br />
{{:Team:NTU-Taida/Templates/Eq|num=7|eq=<br />
}}<br />
<br />
$$\frac{d LuxI}{d t} = \frac{\alpha_{LuxI} \cdot \beta_{FadR}^{n1}}{\beta_{FadR}^{n1} + X_{FadR}^{n1}} - \gamma_{LuxI} \cdot LuxI$$<br />
{{:Team:NTU-Taida/Templates/Eq|num=8|eq=<br />
}}<br />
<br />
{{:Team:NTU-Taida/Templates/Eq|num=9|eq=<br />
\frac{\partial^2 AHL}{\partial x^2} + \frac{\partial^2 AHL}{\frac y^2} - \frac{1}{D_{AHL} \cdot \frac{\partial AHL}{\partial t}} = 0<br />
}}<br />
<br />
$$R(AHL) = - \gamma_{AHL_{ext}} \cdot AHL + cd(k_{s1}LuxI - k_{s0}AHL)$$<br />
{{:Team:NTU-Taida/Templates/Eq|num=10|eq=<br />
}}<br />
<br />
$$\frac{d R}{d t} = \rho (LuxR)^2(AHL_i)^2 - \gamma_R \cdot R$$<br />
{{:Team:NTU-Taida/Templates/Eq|num=11|eq=<br />
}}<br />
<br />
$$\frac{d LacI}{d t} = \frac{\alpha_{LacI}}{1 + (\frac{TetR_1 + TetR_2}{\beta_{TetR}})^{n5}} - \gamma_{LacI} \cdot LacI$$<br />
{{:Team:NTU-Taida/Templates/Eq|num=12|eq=<br />
}}<br />
<br />
$$\frac{d GLP1}{d t} = \frac{\alpha_{GLP1}}{1 + (\frac{LacI}{\beta_{LacI}})^{n6}} - \gamma_{GLP1} \cdot GLP1$$<br />
{{:Team:NTU-Taida/Templates/Eq|num=13|eq=<br />
}}<br />
<br />
<br />
For the control group without the quorum sensing module, we simply discard the terms related to quorum sensing system in the ODE set.<br />
<br />
===Results===<br />
<br />
{{:Team:NTU-Taida/Templates/Vid|num=1-3|width=600px|name=NTU-Taida-Model-Combined-video1-3.gif}}<br />
<br />
[[FIle:NTU-Taida-Model-2D3D-vedio1-3.gif|450px|thumb|center|video1-3]]<br />
<br />
<br />
Video 1 shows the spatial temporal concentration change of fatty acid. Video 2 and three show the corresponding spatial temporal response of GLP-1 expression in system without and with quorum sensing module, respectively.<br />
<br />
We can see from the videos that the fatty acid concentration at the intestinal wall first increases rapidly, turning on the circuits in the cells and resulting in GLP-1 expression at the intestinal wall. Then due to the absorption of fatty acid, the concentration gradually falls and the GLP-1 concentration started to decrease. Notice that the GLP1 expression in the system with Quorum sensing, shown in Video 3, lasts longer than that of the system without quorum sensing, shown in Video 2. Consistent to the single cell model, the system with QS has more prolonged response compared to the one without it.<br />
<br />
==Cell Population Response Model==<br />
<br />
We have assumed that fat distributes uniformly along the z-axis in the lumen after a meal in the previous models. However, in real situation in human body, lipase only exists in certain segments of the intestine. Therefore, fat hydrolysis will only take place in those segments and there will be no fatty acid produced outside these segments, as shown in Figure 3. Cells residing in the segments without lipase activity can only sense the fatty acid diffused from the source segments. Because AHL diffuses faster than fatty acid, we incorporate the quorum sensing system to enable faster recruitment of more bacteria to express GLP-1 in regions without lipase.<br />
<br />
Quorum sensing module enables cells to communicate with each other, as the uneven distribution of fatty acid in the intestines may cause gaps in individual detection. Cells with the quorum sensing module can respond to food intake event as long as their neighboring cells have detected fatty acid, enhancing the overall response to the food intake (Figure 4). However, the communication between cells via AHL can’t be seen when only viewing a single cell. Therefore, we construct spatial temporal models with COMSOL Multiphysics in order to gain insights into the influence of cell-cell communication mediated via the quorum sensing module on the overall GLP1 expression.<br />
<br />
[[File:NTU-Taida-Model-Combined-fig3.png|600px|center|thumb|Figure 3]]<br />
[[File:NTU-Taida-Model-Combined-fig4.png|600px|center|thumb|Figure 4]]<br />
<br />
==2D Cell Population Response Model==<br />
We start our effort with a 2D spatial temporal model. When E.coli cells colonize the intestine, they tend to attach onto the intestinal walls instead of distributing evenly throughout the intestine lumen. Therefore, we first view our system as a two dimensional system, with the modeling plane in the x-z (or either y-z) dimension.<br />
<br />
===Geometry Design===<br />
[[File:NTU-Taida-Model-Combined-fig5.png|600px|center|thumb|Figure 5]]<br />
<br />
With this in mind, we construct a plane in 2D geometry and couple the ODEs derived in our single cell model to simulate the presence of cells.<br />
<br />
To model the effect of quorum sensing, we establish an uneven distribution of fatty acid by giving a constant concentration source of fatty acid in the middle of our modeled plane, as shown in Figure 6. There are no cells within the circular fatty acid source. As time goes on, fatty acids diffuse from the source and establish a concentric gradient. To see the effect of quorum sensing mechanism on overall GLP1 expression in a cell population with uneven distributed fatty acid input, we model cells with and without quorum sensing and compare their spatial –temporal GLP1 expression.<br />
[[File:NTU-Taida-Model-Combined-fig6.png|600px|center|thumb|Figure 6]]<br />
<br />
===Spatial-temporal Model Equations===<br />
The first equation used in our model describes the free diffusion of fatty acids from the central source.<br />
<br />
{{:Team:NTU-Taida/Templates/Eq|num=1|eq=<br />
\partial^2 = 0<br />
}}<br />
<br />
Other equations in the model are almost the same as those derived in our single cell model, except for the ones for AHL. For AHL, we have to set up a partial differential equation describing both the diffusion and the reaction event of AHL. We assume that AHL diffusion into and out of cells is fast and do not model this diffusion process explicitly. Therefore, in contrast to the single-cell model, we only use one species called AHL instead of an internal AHL concentration AHLi and an external AHL concentration AHLe. <br />
<br />
For the reaction term of AHL, we first discard the terms describing the diffusion into and out of the cell membrane in the ODEs of AHLi and AHLe in the single cell model. <br />
As previously mentioned, we assume that the diffusion AHL diffusion into and out of cells is fast. Therefore, we simply account for the diffusion of AHL across cell membrane by multiplying the intracellular AHLi terms by the relative cell density, which will be described in the next section. With these considerations, we combine the two equations of AHLi and AHLe (Eq . and Eq. )into one reaction equation (Eq. ).<br />
<br />
{{:Team:NTU-Taida/Templates/Eq|num=3|eq=xxxxxyyyyyzzzz<br />
}}<br />
<br />
{{:Team:NTU-Taida/Templates/Eq|num=4|eq=xxxxxyyyyyzzzz<br />
}}<br />
<br />
{{:Team:NTU-Taida/Templates/Eq|num=5|eq=xxxxxyyyyyzzzz<br />
}}<br />
<br />
With the help of COMSOL Multiphysics, we can consider both the diffusion and reaction terms of AHL by giving the diffusion (Eq. 2) and reaction (Eq. 5) equations above, without the need to solve the explicit PDE of AHL.<br />
<br />
The diffusion of AHL is modeled by a free diffusion equation.<br />
{{:Team:NTU-Taida/Templates/Eq|num=2|eq=xxxxxyyyyyzzzz<br />
}}<br />
<br />
Other equations in the model are the same as those derived in our single cell model.<br />
For the control group without the quorum sensing module, we discard the terms related to quorum sensing system in the ODE set.<br />
<br />
==Relative Cell density==<br />
The relative cell density is defined as the ratio of the total area E.coli cells occupy to the area of the intestinal wall. By multiplying the intracellular AHL synthesis and degradation terms by the relative cell density, we assume that as a cell synthesizes or degrades AHL, the addition or reduction of AHL molecules is dispersed evenly through the neighboring area. (Mind that the diffusion of these AHL molecules on global scale is still governed by the free diffusion equation.)<br />
<br />
We calculated the relative cell density by assuming there are 1014 bacteria cells residing in the intestine, which has a total surface area of 200 m2. Thus, the average cell density is 5*1011 cells/m2. We can measure the surface area of each individual cell by multiplying their length by their width, giving a surface area of 10-12 m2 per cell. Multiplying the surface area per cell and the average cell density gives the area density of total cells as 0.5. <br />
Since 99% of the gut flora consists of 30-40 species of bacteria, we can assume that each of the common types contribute to approximately 1% of the total surface area of the intestine. Considering the clustering effect of cells, we assume that some regions would have much higher cell densities than others, such that the uneven distribution may result in a tenfold fluctuation in cell density. We hypothesize that the relative cell density in our model could be as high as 0.1.<br />
<br />
Cell density has dramatic effect on the overall effect of quorum sensing system, as supported by a recent study investigating the synchronization of repressilators by quorum sensing mechanisms [1]. Therefore, we also model our system with different cell densities, as can be seen in the results.<br />
<br />
===Results===<br />
To see the effect of quorum sensing mechanism on overall GLP1 expression in a cell population with uneven distributed fatty acid input, we model cells with and without quorum sensing and compare their spatial - temporal GLP1 expression, with relative cell density of 0.1<br />
The results show that species which are not regulated by the quorum sensing module, such as FA, X_FadR, and TetR1, show no difference in the spatial temporal expression pattern between system with and without the quorum sensing system. <br />
<br />
However, species affected by the quorum sensing module, such as LacI and GLP1, show striking difference in their spatial temporal concentration pattern. Within the given time span, systems with a quorum sensing module produces GLP1 over a broader spatial region, resulting in more total GLP1. <br />
<br />
===Species unregulated by the quorum sensing module===<br />
<br />
====FA====<br />
<br />
{{:Team:NTU-Taida/Templates/Vid|num=4|width=600px|name=NTU-Taida-Model-Combined-video4.gif}}<br />
<br />
====X_fadR====<br />
{{:Team:NTU-Taida/Templates/Vid|num=5|width=600px|name=NTU-Taida-Model-Combined-video5.gif}}<br />
{{:Team:NTU-Taida/Templates/Vid|num=6|width=600px|name=NTU-Taida-Model-Combined-video6.gif}}<br />
<br />
===Species regulated by the quorum sensing module===<br />
====LacI====<br />
{{:Team:NTU-Taida/Templates/Vid|num=7|width=450px|name=NTU-Taida-Model-Combined-video7.gif}}<br />
The expression of LacI is inhibited by TetR proteins, and therefore is regulated by the quorum sensing module. Although the concentration of TetR1 is the same in systems with and without quorum sensing, cells with quorum sensing produce TetR2 as the output of the quorum sensing module and therefore result in overall more total TetR proteins. Thus, the repression of LacI is more significant in systems with the quorum sensing module. <br />
<br />
====GLP1====<br />
{{:Team:NTU-Taida/Templates/Vid|num=8|width=600px|name=NTU-Taida-Model-Combined-video8.gif}}<br />
As the expression of GLP1 is repressed by LacI proteins, GLP1 also displays different spatial-temporal concentration pattern between the two systems. With quorum sensing module, the system produces more GLP1 overall.<br />
<br />
===Effect of cell density===<br />
<br />
Relative cell density plays a critical role in determining whether we can see a significant difference between systems with and without quorum sensing. We simulated the spatial-temporal response of GLP1 of four systems, all of them with the quorum sensing module but with relative cell densities of 0.2, 0.1, and 0.01, respectively. <br />
<br />
Then we compare their response to that of system without quorum sensing to determine if there exists a threshold of cell density, below which the effect of quorum sensing module is unperceivable. <br />
<br />
{{:Team:NTU-Taida/Templates/Vid|num=9|width=600px|name=NTU-Taida-Model-Combined-video9.gif}}<br />
<br />
We can see from Video 9 that the system with a relative cell density of 0.2 differs most with the system without the quorum sensing module. The system with a relative cell density of 0.1 shows moderate difference. The system with a relative cell density of 0.05 displays very subtle difference. There is no difference between the system with a relative cell density of 0.01 and the system with no quorum sensing module. Therefore, the threshold of relative cell density may lie between 0.05 and 0.01.<br />
<br />
<br />
==3D Cell population response model==<br />
<br />
Finally, we construct a full 3D model, combing the consideration on the x-y plane and the x-z plane. Our goal is to simulate the effect of non-uniform production of fatty acid due to the spatially limited lipase activity. We modeled the intestine by a cylindrical tube, with a fat source limited to the z=0 plane, to simulate the situations similar to that shown in Figure 7, and examine the effect of Quorum sensing. <br />
<br />
[[File:NTU-Taida-Model-Combined-fig7.png|600px|center|thumb|Figure 7]]<br />
<br />
The equations used are the same as those in the 2D cell population response model, but with the equations governing diffusions changing from the two-dimension form to their three-dimension counterparts.<br />
<br />
{{:Team:NTU-Taida/Templates/Vid|num=10-11|width=600px|name=NTU-Taida-Model-Combined-video10-11.gif}}<br />
<br />
Video 10 shows the result of system without quorum sensing module while Video 11 shows the result of system with quorum sensing module. From Video 10 and 11, we can see that GLP-1 starts to be expressed at similar time point at the intestinal wall on the z=0 plane. However, the GLP-1 expression spreads faster along the z-axis in system with quorum sensing.<br />
<br />
==Reference==<br />
<ol id='Ref'><br />
<li>Jordi Garcia-Ojalvo , Michael B. Elowitz, and Steven H. Strogatz , Modeling a synthetic multicellular clock: Repressilators coupled by quorum sensing, pnas,2004</li><br />
</ol><br />
<!--EOF--><br />
{{:Team:NTU-Taida/Templates/ContentEnd}}{{:Team:NTU-Taida/Templates/Footer|ActiveNavbar=Modeling, #nav-Modeling-Combined}}</div>Lbwanghttp://2012.igem.org/Team:NTU-Taida/SafetyTeam:NTU-Taida/Safety2012-10-26T22:53:11Z<p>Lbwang: /* Testing Function */</p>
<hr />
<div>{{:Team:NTU-Taida/Templates/Header}}{{:Team:NTU-Taida/Templates/Navbar}}{{:Team:NTU-Taida/Templates/Sidebar}}{{:Team:NTU-Taida/Templates/ContentStart}}<br />
{{:Team:NTU-Taida/Templates/BSHero|Title=Safety|Content=<p>Use this page to answer the questions on the <a href='/Safety'>safety page</a>.</p>}}<br />
<br />
==Question 1 ==<br />
'''Would any of your project ideas raise safety issues in terms of:'''<br />
*'''researcher safety,'''<br />
*'''public safety, or'''<br />
*'''environmental safety?'''<br />
The biosafety concerns can be simplified to an equation, Risk= probabilityX Hazard. <br />
In our project, the questions we deal with are basically human disease-oriented. We try to prevent any concern regarding potential harms to human. <br />
<br />
As for the researchers, our research is conducted in a safely regulated laboratory, and the ideas of our project do not require etiologic agents, hosts or vectors for experiment. Also no toxic reagent or high risk chemical compound is used. In all, our project hasn’t yet raised researcher safety issues thus far. <br />
For we do not apply any virulent genes or etiologic agents, there seems no additional threats on public safety. Furthermore, the non-pathogenic E. coli we try to deliver into human body can be easily eliminated by antibiotic use if infection arises and is the main concern of patient's safety. <br />
<br />
However, the antibiotics resistance plasmid used in our project may harbor the threats of horizontal gene transfer, which will enhance the virulence of other Escherichia coli in the environment. Though a self-destruction mechanism is designed in our project, we are still aware of the risk on environmental safety. The rules and regulations of concern will be under close supervision of Environmental Protection and Occupational Safety and Hygiene Unit of NTUCM.<br />
<br />
==Question 2 ==<br />
'''Do any of the new BioBrick parts (or devices) that you made this year raise any safety issues? If yes,'''<br />
* '''Did you document these issues in the Registry?'''<br />
* '''How did you manage to handle the safety issue?'''<br />
* '''How could other teams learn from your experience?'''<br />
<br />
The most common question people would have judged us is how we make sure that it is safe to deliver this bug into human intestine. As we noted, the output we would like to deliver, GLP-1, is innate and has no significant harms to the human body. Cell penetrating peptides, which is another peptide we are going to deliver into gastroenterological tract, do no harm as well, since it has a pretty short half life (<15 mins) inside GI tract. <br />
<br />
What’s more, intestine is an organ with an abundance of normal flora, mainly consisting of Streptococcus and Lactobacillus in the middle intestine. In ileum and section close to ileo-cecal valve, bacteroides and coliform bacteria are dominant. First, for the E. coli itself, it’s very hard to colonize in the GI tract as it would face a bunch of competitors over nutrients and space. Second, the bugs we are going to deliver inside human body is pretty fragile, which can be easily eliminated by some antibiotics, 2nd generation cephalosporin, high ampicillin plus sulbactam, or erythromycin, which is ideal of usage in our cases, since it not only provided anti-microbial effects, but also increases the motility of intestine. Above all, the design we are going to bring to synthetic biology community has little safety concerns, and can be easily circumvented or adjusted.<br />
<br />
==Question 3 ==<br />
'''Is there a local biosafety group, committee, or review board at your institution?<br />
*'''If yes, what does your local biosafety group think about your project?'''<br />
*'''If no, which specific biosafety rules or guidelines do you have to consider in your country?'''<br />
<br />
In National Taiwan University, College of Medicine, where the experiments of our project are conducted, Environmental Protection and Occupational Safety and Hygiene Unit of NTUCM takes charge of promoting and supervising safety and health issues.<br />
Before beginning of our project, our team members and advisors have attended the safety education series and training courses held by this unit. All of us were qualified by passing the tests at the end of the training to be sure that all the rules of concern are well understood. The application of our project was also verified and qualified. All experiments are conducted under the biosafety rules of Environmental Protection and Occupational Safety and Hygiene Unit of NTUCM, of which all of our experimental procedures, equipments, facilities were under close supervision.<br />
http://www.mc.ntu.edu.tw/department/safety/index.htm<br />
<br />
==Question 4 ==<br />
'''Do you have any other ideas how to deal with safety issues that could be useful for future iGEM competitions? How could parts, devices and systems be made even safer through biosafety engineering?'''<br />
<br />
As our opinion, we think that for every iGEM teams' circuit design, a mechanism to turn off is necessary. In order to improve the iGEM competition safety concern, we would like to suggest a turn-off mechanism as requirement. Also, the microorganisms should be kept dependent on controlled conditions in the lab to prohibit the unwanted spreading and multiplication outside the lab. Moreover, a suicide switch for all BioBricks or dependence on special nutrients lack in nature for organisms should be engineered in case organisms escape and cause safety concern. The most important thing is that every team and the advisor should know their potential danger and the ways to assess the risk. This aim could be approached by emphasizing the safety rules. Creating a page on the registry for the teams to explain their event tree analysis and fault tree analysis would be an easiest method to increase safety when working with BioBrick parts.<br />
<br />
For our PepdEx system, we proposed two layers of safety regulations: (1) temperature inducible suicide system to prevent gene recombination/pollution, and (2) RNA interaction/competitive inhibition to prevent horizontal gene transfer. Detailed descriptions can be found in our "Project" section.<br />
<br />
== Testing Function ==<br />
<br />
{{:Team:NTU-Taida/Templates/Eq|num=1|eq=a_x+c}}<br />
<br />
When \(a \ne 0\), there are two solutions to \(ax^2 + bx + c = 0\) and they are<br />
$$x = {-b \pm \sqrt{b^2-4ac} \over 2a}.$$<br />
<br />
<html><iframe width="420" height="315" src="http://www.youtube.com/embed/04854XqcfCY" frameborder="0" allowfullscreen></iframe></html><br />
<br />
<!--EOF --><br />
{{:Team:NTU-Taida/Templates/ContentEnd}}{{:Team:NTU-Taida/Templates/Footer|ActiveNavbar=Safety}}</div>Lbwanghttp://2012.igem.org/Team:NTU-Taida/SafetyTeam:NTU-Taida/Safety2012-10-26T22:52:57Z<p>Lbwang: /* Testing Function */</p>
<hr />
<div>{{:Team:NTU-Taida/Templates/Header}}{{:Team:NTU-Taida/Templates/Navbar}}{{:Team:NTU-Taida/Templates/Sidebar}}{{:Team:NTU-Taida/Templates/ContentStart}}<br />
{{:Team:NTU-Taida/Templates/BSHero|Title=Safety|Content=<p>Use this page to answer the questions on the <a href='/Safety'>safety page</a>.</p>}}<br />
<br />
==Question 1 ==<br />
'''Would any of your project ideas raise safety issues in terms of:'''<br />
*'''researcher safety,'''<br />
*'''public safety, or'''<br />
*'''environmental safety?'''<br />
The biosafety concerns can be simplified to an equation, Risk= probabilityX Hazard. <br />
In our project, the questions we deal with are basically human disease-oriented. We try to prevent any concern regarding potential harms to human. <br />
<br />
As for the researchers, our research is conducted in a safely regulated laboratory, and the ideas of our project do not require etiologic agents, hosts or vectors for experiment. Also no toxic reagent or high risk chemical compound is used. In all, our project hasn’t yet raised researcher safety issues thus far. <br />
For we do not apply any virulent genes or etiologic agents, there seems no additional threats on public safety. Furthermore, the non-pathogenic E. coli we try to deliver into human body can be easily eliminated by antibiotic use if infection arises and is the main concern of patient's safety. <br />
<br />
However, the antibiotics resistance plasmid used in our project may harbor the threats of horizontal gene transfer, which will enhance the virulence of other Escherichia coli in the environment. Though a self-destruction mechanism is designed in our project, we are still aware of the risk on environmental safety. The rules and regulations of concern will be under close supervision of Environmental Protection and Occupational Safety and Hygiene Unit of NTUCM.<br />
<br />
==Question 2 ==<br />
'''Do any of the new BioBrick parts (or devices) that you made this year raise any safety issues? If yes,'''<br />
* '''Did you document these issues in the Registry?'''<br />
* '''How did you manage to handle the safety issue?'''<br />
* '''How could other teams learn from your experience?'''<br />
<br />
The most common question people would have judged us is how we make sure that it is safe to deliver this bug into human intestine. As we noted, the output we would like to deliver, GLP-1, is innate and has no significant harms to the human body. Cell penetrating peptides, which is another peptide we are going to deliver into gastroenterological tract, do no harm as well, since it has a pretty short half life (<15 mins) inside GI tract. <br />
<br />
What’s more, intestine is an organ with an abundance of normal flora, mainly consisting of Streptococcus and Lactobacillus in the middle intestine. In ileum and section close to ileo-cecal valve, bacteroides and coliform bacteria are dominant. First, for the E. coli itself, it’s very hard to colonize in the GI tract as it would face a bunch of competitors over nutrients and space. Second, the bugs we are going to deliver inside human body is pretty fragile, which can be easily eliminated by some antibiotics, 2nd generation cephalosporin, high ampicillin plus sulbactam, or erythromycin, which is ideal of usage in our cases, since it not only provided anti-microbial effects, but also increases the motility of intestine. Above all, the design we are going to bring to synthetic biology community has little safety concerns, and can be easily circumvented or adjusted.<br />
<br />
==Question 3 ==<br />
'''Is there a local biosafety group, committee, or review board at your institution?<br />
*'''If yes, what does your local biosafety group think about your project?'''<br />
*'''If no, which specific biosafety rules or guidelines do you have to consider in your country?'''<br />
<br />
In National Taiwan University, College of Medicine, where the experiments of our project are conducted, Environmental Protection and Occupational Safety and Hygiene Unit of NTUCM takes charge of promoting and supervising safety and health issues.<br />
Before beginning of our project, our team members and advisors have attended the safety education series and training courses held by this unit. All of us were qualified by passing the tests at the end of the training to be sure that all the rules of concern are well understood. The application of our project was also verified and qualified. All experiments are conducted under the biosafety rules of Environmental Protection and Occupational Safety and Hygiene Unit of NTUCM, of which all of our experimental procedures, equipments, facilities were under close supervision.<br />
http://www.mc.ntu.edu.tw/department/safety/index.htm<br />
<br />
==Question 4 ==<br />
'''Do you have any other ideas how to deal with safety issues that could be useful for future iGEM competitions? How could parts, devices and systems be made even safer through biosafety engineering?'''<br />
<br />
As our opinion, we think that for every iGEM teams' circuit design, a mechanism to turn off is necessary. In order to improve the iGEM competition safety concern, we would like to suggest a turn-off mechanism as requirement. Also, the microorganisms should be kept dependent on controlled conditions in the lab to prohibit the unwanted spreading and multiplication outside the lab. Moreover, a suicide switch for all BioBricks or dependence on special nutrients lack in nature for organisms should be engineered in case organisms escape and cause safety concern. The most important thing is that every team and the advisor should know their potential danger and the ways to assess the risk. This aim could be approached by emphasizing the safety rules. Creating a page on the registry for the teams to explain their event tree analysis and fault tree analysis would be an easiest method to increase safety when working with BioBrick parts.<br />
<br />
For our PepdEx system, we proposed two layers of safety regulations: (1) temperature inducible suicide system to prevent gene recombination/pollution, and (2) RNA interaction/competitive inhibition to prevent horizontal gene transfer. Detailed descriptions can be found in our "Project" section.<br />
<br />
== Testing Function ==<br />
<br />
{{:Team:NTU-Taida/Templates/Eq|num=1|eq=a_x+c}}<br />
<br />
When \(a \ne 0\), there are two solutions to \(ax^2 + bx + c = 0\) and they are<br />
$$x = {-b \pm \sqrt{b^2-4ac} \over 2a}.$$<br />
<br />
<iframe width="420" height="315" src="http://www.youtube.com/embed/04854XqcfCY" frameborder="0" allowfullscreen></iframe><br />
<br />
<!--EOF --><br />
{{:Team:NTU-Taida/Templates/ContentEnd}}{{:Team:NTU-Taida/Templates/Footer|ActiveNavbar=Safety}}</div>Lbwanghttp://2012.igem.org/Team:NTU-Taida/Modeling/2D-3D-CombinedTeam:NTU-Taida/Modeling/2D-3D-Combined2012-10-26T20:57:39Z<p>Lbwang: </p>
<hr />
<div>{{:Team:NTU-Taida/Templates/Header}}{{:Team:NTU-Taida/Templates/Navbar}}{{:Team:NTU-Taida/Templates/Sidebar|Title=2D &amp; 3D Combined Model}}{{:Team:NTU-Taida/Templates/ContentStart}}<br />
{{:Team:NTU-Taida/Templates/BSHero|Title=2D &amp; 3D Combined Model|Content=<p>With the single cell model, fatty acid reaction-absorption model, and system analysis, we have verified the filter function of our circuit, simulated the real physiological fatty acid level at intestinal wall, and adjust our filter threshold to fit to the real condition. Next, we want to combine them together and see what would happen when we put cells in the intestine after a fatty meal.</p><br />
<p>The combined model is composed of three different sections. 2D combined model simulates the GLP1 response of Pepdex E-coli cells after the food intake in the x-y cross-sectional plane. 2D Cell population response model further considers the possible uneven concentration of fatty acid along the z-axis due to non-uniform distribution of lipase and simulates how the quorum sensing system assists our system to overcame this possible limitation and enhance the response. Finally, 3D Cell population response model incorporates all the consideration to generate a full model to visualize the dynamic behavior of our system.</p>}}<br />
<br />
==2D Combined Model==<br />
So far, we have the spatial-temporal concentration of fatty acid, and cells with suitable threshold. In this model, we want to see what would happen when we put cells in the intestine after a meal. <br />
<br />
[[File:NTU-Taida-Model-Combined-fig1.png|600px|center|thumb|Figure 1]]<br />
<br />
We achieve this by further coupling the single cell ODEs (with parameters adjusted by system analysis) locally to the fatty acid reaction-absorption model at the intestinal wall, as shown in Figure 2.<br />
<br />
[[File:NTU-Taida-Model-Combined-fig2.png|600px|center|thumb|Figure 2]]<br />
<br />
Besides to see the cell response when combined with the environmental input, we also want to simulate the prolonged effect of the quorum sensing module with physiological input. Therefore, we simulate system with and without quorum sensing modules and compare their results.<br />
<br />
===Spatial-temporal Model Equations ===<br />
The equations used in our 2D combined model mainly come from the reaction-absorption model and the single cell model. The following three equations are the same as those in the reaction-absorption model, which simulates the change in fatty acid concentration in time and space. <br />
<br />
{{:Team:NTU-Taida/Templates/EqN|eq=<br />
\frac{d fat}{d t} = -\frac{k_{cat}[E]_t\cdot[S]}{K_m + [S]} <br />
}}<br />
<br />
{{:Team:NTU-Taida/Templates/EqN|eq=<br />
\frac{d FA}{d t} = 3 \cdot {k_{cat}[E]_t\cdot[S]}{K_m + [S]} <br />
}}<br />
<br />
{{:Team:NTU-Taida/Templates/EqN|eq=<br />
J=(C_1 - C_2)(D_{FA}/d) <br />
}}<br />
<br />
Other equations in the model are almost the same as those derived in our single cell model, with slightly difference in those for AHL, which will be discussed thoroughly in the 2D Cell population response model. The equations are shown as below.<br />
<br />
'''TRY TO TYPE YOURSELF FOLLOWING THE EXAMPLE ABOVE'''<br />
'''TRY TO TYPE YOURSELF FOLLOWING THE EXAMPLE ABOVE'''<br />
'''TRY TO TYPE YOURSELF FOLLOWING THE EXAMPLE ABOVE'''<br />
'''TRY TO TYPE YOURSELF FOLLOWING THE EXAMPLE ABOVE'''<br />
<br />
For the control group without the quorum sensing module, we simply discard the terms related to quorum sensing system in the ODE set.<br />
<br />
<br />
===Results===<br />
<br />
{{:Team:NTU-Taida/Templates/Vid|num=1-3|width=600px|name=NTU-Taida-Model-Combined-video1-3.gif}}<br />
<br />
Video 1 shows the spatial temporal concentration change of fatty acid. Video 2 and three show the corresponding spatial temporal response of GLP-1 expression in system without and with quorum sensing module, respectively.<br />
<br />
We can see from the videos that the fatty acid concentration at the intestinal wall first increases rapidly, turning on the circuits in the cells and resulting in GLP-1 expression at the intestinal wall. Then due to the absorption of fatty acid, the concentration gradually falls and the GLP-1 concentration started to decrease. Notice that the GLP1 expression in the system with Quorum sensing, shown in Video 3, lasts longer than that of the system without quorum sensing, shown in Video 2. Consistent to the single cell model, the system with QS has more prolonged response compared to the one without it.<br />
<br />
<br />
==Cell Population Response Model==<br />
<br />
We have assumed that fat distributes uniformly along the z-axis in the lumen after a meal in the previous models. However, in real situation in human body, lipase only exists in certain segments of the intestine. Therefore, fat hydrolysis will only take place in those segments and there will be no fatty acid produced outside these segments, as shown in Figure 3. Cells residing in the segments without lipase activity can only sense the fatty acid diffused from the source segments. Because AHL diffuses faster than fatty acid, we incorporate the quorum sensing system to enable faster recruitment of more bacteria to express GLP-1 in regions without lipase.<br />
<br />
Quorum sensing module enables cells to communicate with each other, as the uneven distribution of fatty acid in the intestines may cause gaps in individual detection. Cells with the quorum sensing module can respond to food intake event as long as their neighboring cells have detected fatty acid, enhancing the overall response to the food intake (Figure 4). However, the communication between cells via AHL can’t be seen when only viewing a single cell. Therefore, we construct spatial temporal models with COMSOL Multiphysics in order to gain insights into the influence of cell-cell communication mediated via the quorum sensing module on the overall GLP1 expression.<br />
<br />
[[File:NTU-Taida-Model-Combined-fig3.png|600px|center|thumb|Figure 3]]<br />
[[File:NTU-Taida-Model-Combined-fig4.png|600px|center|thumb|Figure 4]]<br />
<br />
==2D Cell Population Response Model==<br />
We start our effort with a 2D spatial temporal model. When E.coli cells colonize the intestine, they tend to attach onto the intestinal walls instead of distributing evenly throughout the intestine lumen. Therefore, we first view our system as a two dimensional system, with the modeling plane in the x-z (or either y-z) dimension.<br />
<br />
===Geometry Design===<br />
[[File:NTU-Taida-Model-Combined-fig5.png|600px|center|thumb|Figure 5]]<br />
<br />
With this in mind, we construct a plane in 2D geometry and couple the ODEs derived in our single cell model to simulate the presence of cells.<br />
<br />
To model the effect of quorum sensing, we establish an uneven distribution of fatty acid by giving a constant concentration source of fatty acid in the middle of our modeled plane, as shown in Figure 6. There are no cells within the circular fatty acid source. As time goes on, fatty acids diffuse from the source and establish a concentric gradient. To see the effect of quorum sensing mechanism on overall GLP1 expression in a cell population with uneven distributed fatty acid input, we model cells with and without quorum sensing and compare their spatial –temporal GLP1 expression.<br />
[[File:NTU-Taida-Model-Combined-fig6.png|600px|center|thumb|Figure 6]]<br />
<br />
===Spatial-temporal Model Equations===<br />
The first equation used in our model describes the free diffusion of fatty acids from the central source.<br />
<br />
{{:Team:NTU-Taida/Templates/Eq|num=1|eq=xxxxxyyyyyzzzz<br />
}}<br />
<br />
Other equations in the model are almost the same as those derived in our single cell model, except for the ones for AHL. For AHL, we have to set up a partial differential equation describing both the diffusion and the reaction event of AHL. We assume that AHL diffusion into and out of cells is fast and do not model this diffusion process explicitly. Therefore, in contrast to the single-cell model, we only use one species called AHL instead of an internal AHL concentration AHLi and an external AHL concentration AHLe. <br />
<br />
For the reaction term of AHL, we first discard the terms describing the diffusion into and out of the cell membrane in the ODEs of AHLi and AHLe in the single cell model. <br />
As previously mentioned, we assume that the diffusion AHL diffusion into and out of cells is fast. Therefore, we simply account for the diffusion of AHL across cell membrane by multiplying the intracellular AHLi terms by the relative cell density, which will be described in the next section. With these considerations, we combine the two equations of AHLi and AHLe (Eq . and Eq. )into one reaction equation (Eq. ).<br />
<br />
{{:Team:NTU-Taida/Templates/Eq|num=3|eq=xxxxxyyyyyzzzz<br />
}}<br />
<br />
{{:Team:NTU-Taida/Templates/Eq|num=4|eq=xxxxxyyyyyzzzz<br />
}}<br />
<br />
{{:Team:NTU-Taida/Templates/Eq|num=5|eq=xxxxxyyyyyzzzz<br />
}}<br />
<br />
With the help of COMSOL Multiphysics, we can consider both the diffusion and reaction terms of AHL by giving the diffusion (Eq. 2) and reaction (Eq. 5) equations above, without the need to solve the explicit PDE of AHL.<br />
<br />
The diffusion of AHL is modeled by a free diffusion equation.<br />
{{:Team:NTU-Taida/Templates/Eq|num=2|eq=xxxxxyyyyyzzzz<br />
}}<br />
<br />
Other equations in the model are the same as those derived in our single cell model.<br />
For the control group without the quorum sensing module, we discard the terms related to quorum sensing system in the ODE set.<br />
<br />
==Relative Cell density==<br />
The relative cell density is defined as the ratio of the total area E.coli cells occupy to the area of the intestinal wall. By multiplying the intracellular AHL synthesis and degradation terms by the relative cell density, we assume that as a cell synthesizes or degrades AHL, the addition or reduction of AHL molecules is dispersed evenly through the neighboring area. (Mind that the diffusion of these AHL molecules on global scale is still governed by the free diffusion equation.)<br />
<br />
We calculated the relative cell density by assuming there are 1014 bacteria cells residing in the intestine, which has a total surface area of 200 m2. Thus, the average cell density is 5*1011 cells/m2. We can measure the surface area of each individual cell by multiplying their length by their width, giving a surface area of 10-12 m2 per cell. Multiplying the surface area per cell and the average cell density gives the area density of total cells as 0.5. <br />
Since 99% of the gut flora consists of 30-40 species of bacteria, we can assume that each of the common types contribute to approximately 1% of the total surface area of the intestine. Considering the clustering effect of cells, we assume that some regions would have much higher cell densities than others, such that the uneven distribution may result in a tenfold fluctuation in cell density. We hypothesize that the relative cell density in our model could be as high as 0.1.<br />
<br />
Cell density has dramatic effect on the overall effect of quorum sensing system, as supported by a recent study investigating the synchronization of repressilators by quorum sensing mechanisms [1]. Therefore, we also model our system with different cell densities, as can be seen in the results.<br />
<br />
===Results===<br />
To see the effect of quorum sensing mechanism on overall GLP1 expression in a cell population with uneven distributed fatty acid input, we model cells with and without quorum sensing and compare their spatial - temporal GLP1 expression, with relative cell density of 0.1<br />
The results show that species which are not regulated by the quorum sensing module, such as FA, X_FadR, and TetR1, show no difference in the spatial temporal expression pattern between system with and without the quorum sensing system. <br />
<br />
However, species affected by the quorum sensing module, such as LacI and GLP1, show striking difference in their spatial temporal concentration pattern. Within the given time span, systems with a quorum sensing module produces GLP1 over a broader spatial region, resulting in more total GLP1. <br />
<br />
===Species unregulated by the quorum sensing module===<br />
<br />
====FA====<br />
<br />
{{:Team:NTU-Taida/Templates/Vid|num=4|width=600px|name=NTU-Taida-Model-Combined-video4.gif}}<br />
<br />
====X_fadR====<br />
{{:Team:NTU-Taida/Templates/Vid|num=5|width=600px|name=NTU-Taida-Model-Combined-video5.gif}}<br />
{{:Team:NTU-Taida/Templates/Vid|num=6|width=600px|name=NTU-Taida-Model-Combined-video6.gif}}<br />
<br />
===Species regulated by the quorum sensing module===<br />
====LacI====<br />
{{:Team:NTU-Taida/Templates/Vid|num=7|width=450px|name=NTU-Taida-Model-Combined-video7.gif}}<br />
The expression of LacI is inhibited by TetR proteins, and therefore is regulated by the quorum sensing module. Although the concentration of TetR1 is the same in systems with and without quorum sensing, cells with quorum sensing produce TetR2 as the output of the quorum sensing module and therefore result in overall more total TetR proteins. Thus, the repression of LacI is more significant in systems with the quorum sensing module. <br />
<br />
====GLP1====<br />
{{:Team:NTU-Taida/Templates/Vid|num=8|width=600px|name=NTU-Taida-Model-Combined-video8.gif}}<br />
As the expression of GLP1 is repressed by LacI proteins, GLP1 also displays different spatial-temporal concentration pattern between the two systems. With quorum sensing module, the system produces more GLP1 overall.<br />
<br />
===Effect of cell density===<br />
<br />
Relative cell density plays a critical role in determining whether we can see a significant difference between systems with and without quorum sensing. We simulated the spatial-temporal response of GLP1 of four systems, all of them with the quorum sensing module but with relative cell densities of 0.2, 0.1, and 0.01, respectively. <br />
<br />
Then we compare their response to that of system without quorum sensing to determine if there exists a threshold of cell density, below which the effect of quorum sensing module is unperceivable. <br />
<br />
{{:Team:NTU-Taida/Templates/Vid|num=9|width=600px|name=NTU-Taida-Model-Combined-video9.gif}}<br />
<br />
We can see from Video 9 that the system with a relative cell density of 0.2 differs most with the system without the quorum sensing module. The system with a relative cell density of 0.1 shows moderate difference. The system with a relative cell density of 0.05 displays very subtle difference. There is no difference between the system with a relative cell density of 0.01 and the system with no quorum sensing module. Therefore, the threshold of relative cell density may lie between 0.05 and 0.01.<br />
<br />
<br />
==3D Cell population response model==<br />
<br />
Finally, we construct a full 3D model, combing the consideration on the x-y plane and the x-z plane. Our goal is to simulate the effect of non-uniform production of fatty acid due to the spatially limited lipase activity. We modeled the intestine by a cylindrical tube, with a fat source limited to the z=0 plane, to simulate the situations similar to that shown in Figure 7, and examine the effect of Quorum sensing. <br />
<br />
[[File:NTU-Taida-Model-Combined-fig7.png|600px|center|thumb|Figure 7]]<br />
<br />
The equations used are the same as those in the 2D cell population response model, but with the equations governing diffusions changing from the two-dimension form to their three-dimension counterparts.<br />
<br />
{{:Team:NTU-Taida/Templates/Vid|num=10-11|width=600px|name=NTU-Taida-Model-Combined-video10-11.gif}}<br />
<br />
Video 10 shows the result of system without quorum sensing module while Video 11 shows the result of system with quorum sensing module. From Video 10 and 11, we can see that GLP-1 starts to be expressed at similar time point at the intestinal wall on the z=0 plane. However, the GLP-1 expression spreads faster along the z-axis in system with quorum sensing.<br />
<br />
==Reference==<br />
<ol id='Ref'><br />
<li>Jordi Garcia-Ojalvo , Michael B. Elowitz, and Steven H. Strogatz , Modeling a synthetic multicellular clock: Repressilators coupled by quorum sensing, pnas,2004</li><br />
</ol><br />
<!--EOF--><br />
{{:Team:NTU-Taida/Templates/ContentEnd}}{{:Team:NTU-Taida/Templates/Footer|ActiveNavbar=Modeling, #nav-Modeling-Combined}}</div>Lbwang