Team:UC Chile/Cyanolux/Modelling

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{{UC_Chile4}}
{{UC_Chile4}}
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<h1>Why Modelling?:</h1>
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Synechocystis transcriptional circadian oscillation makes  it an exceptional chassis if time control of synthetic metabolic processes is desired.
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Nevertheless, the  functionality of some of these processes depends upon precise timing.
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While there are hundreds of genes known to oscillate in Synechocystis genome -each with its own peak, strenght and amplitude- it can be tricky to choose the right ones.
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Here is where our modeling approach comes on stage.
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<font size="4">Why?</font>
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<h1>Model Overview:</h1>
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To express circadian under circadian oscillation it was essential to identify the ideal promoters that can yield highest substrate concentrations at the exact time our biolamp is on i.e. by night.
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<h2>Model Application</h2>
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Our model works as a user-friendly black box. The user´s input is the desired time of protein concentration peak and the program´s output is a list of suggested promoters.
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It can be adjusted to take as input the time on which enzymatic products concentration peaks , or to maximize an intermediate metabolite that depends not just on production but also consumption.
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Finally, its logical design can be applied to any other organism that exhibits circadian oscillation.
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<html><center><img src="https://static.igem.org/mediawiki/2012/9/93/Boxextended.jpg" align="left" width="720"></center></html>
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Based on literature (ref) we found that suitable promoters to start our model were sigE (sll1689), Transaldolase (slr1793) and Cytochrome aa3 (sll1898).
 
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Therefore, in the following section we explain how to model the oscillation in product generation under three circadian promoters: sigE (sll1689), Transaldolase (slr1793) and Cytochrome aa3 (sll1898).
 
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<font size="4">Methodology</font>
 
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Product generation by promoter
 
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From known sigE (sll1689) production data we could build up a model using MatLab software.  (Please check our script!).
 
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Basically, what we have after data adjustment is a sine function consistent with the oscillatory nature of the circadian rhythm.
 
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Generation = C*sen(2π(t-(peak-6))/12)+1
 
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The C parameter was optimized using Excel Solver’s algorithm of least squares.
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<h2>What´s inside the box?</h2>
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<html><center><img src="https://static.igem.org/mediawiki/2012/c/c0/Openbb.jpg" align="left" width="320"></center></html>We took all the microarray data available of promoter of Synechocystis grown on normal conditions. Conveniently, these arrays already have a filter: they only contain cycling promoters
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The microarray data points were adjusted by a least squares algorithm into sine functions for each promoter.
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<html><center><img src="https://static.igem.org/mediawiki/2012/2/2f/Equa1.scheme.jpg" align="left" width="606"></center></html>
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Where k, theta and y are parameters to adjust.
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x is protein concentration
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This equation accounts for protein production and its included into this form of universal balance equation:
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<html><center><img src="https://static.igem.org/mediawiki/2012/2/24/Equa2.2.jpg" align="left" width="706"></center></html>
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Where HL is protein´s half life
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The resulting plot of this equation predicts protein concentration over time.
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As a complement, we developed a list of relative promoter strengths. We took one promoter present in all datasets to make a relative scale, then,  we transformed it to an absolute scale using a promoter quantitatively characterized in literature by comparing it to the relative scale promoter.
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<h1>Extended Model</h1>
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The approach can be extended to consider as input the product of the protein enzymatic activity instead of the protein itself.
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Moreover, it can be adjusted to a two-protein model in which protein 1 produces the metabolite and protein 2 consumes it.
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<h1>Applying the model: Synechocystis promoters</h1>
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We applied our model to solve the question of which promoters should we use to meet our [https://2012.igem.org/Team:UC_Chile/Cyanolux/Project_short#Strategy strategy goals] 
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The results are shown below:
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For Transaldolase (slr1793) and Cytochrome aa3 (sll1898) a microarray data was adjusted (using the same algorithm of least squares) to obtain:
 
Promoter Peak hour
Promoter Peak hour
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sigE production=0,8028*sen(π(t-2)/12)+1
sigE production=0,8028*sen(π(t-2)/12)+1
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[[File:sigeprodction.jpg]]
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[[File:sigeprodction.jpg|center]]
Pta production=0,6246*sen(π(t-8)/12)+1
Pta production=0,6246*sen(π(t-8)/12)+1
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[[File:ptaproductoihj.jpg]]
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[[File:ptaproductoihj.jpg|center]]
Pcaa3 production=0,9493*sen(π(t-3)/12)+1
Pcaa3 production=0,9493*sen(π(t-3)/12)+1
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[[File:pcaa3production.jpg]]
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[[File:pcaa3production.jpg|center]]
<font size="3">Solving ODE’s</font>
<font size="3">Solving ODE’s</font>
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As there is no entries nor exits (closed system) the expression becomes
As there is no entries nor exits (closed system) the expression becomes
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Entries-exits+generation-consumption= accumulation
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Generation-consumption= accumulation
For LuxAB we know
For LuxAB we know
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Using Matlab to solve this ODE
Using Matlab to solve this ODE
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[[File:plot10000_uc_chile.jpg]]
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For LuxCDEG
For LuxCDEG
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dY/dt=k_1*sen((π*(t-8))/12)+1-ln(2)/t_m *Y(t)
dY/dt=k_1*sen((π*(t-8))/12)+1-ln(2)/t_m *Y(t)
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MatLab result
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Finally we have the protein concentrations at different times
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Finally we had the protein concentrations at different times
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This combination of promoters was the one that best fits our strategy: Maximize substrate concentration during dusk hours
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<html><center><img src="https://static.igem.org/mediawiki/2012/4/41/Finalmodelhdhjvsd.jpg" align="left" width="706"></center></html>
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Latest revision as of 03:53, 27 October 2012

Project: Luxilla - Pontificia Universidad Católica de Chile, iGEM 2012