Team:USP-UNESP-Brazil/Plasmid Plug n Play/Modeling

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</ul>
</ul>
</p>
</p>
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<p>To estimate the concentration of the variables, we need the volume of <em>''E. coli''</em>. According to [2]<br /><span class="math"><em>V</em><sub><em>e</em><em>c</em></sub> = 0.7*10<sup>−15</sup><em>L</em></span><br /> Using this estimate, it is possible to calculate the concentration of one molecule inside the bacteria in molar concentration <br /><span class="math">1<em>M</em> = 1<em>m</em><em>o</em><em>l</em> / 1<em>L</em> = 6*10<sup>23</sup><em>m</em><em>o</em><em>l</em><em>e</em><em>c</em><em>u</em><em>l</em><em>e</em><em>s</em> / <em>L</em></span><br /></p>
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<p>To estimate the concentration of the variables, we need the volume of <em>''E. coli''</em>. According to [2],  $V_{ec} = 0.7 \hspace{0.2cm}(\mu m)^3 = 0.7$ $10^{-15} L$. Using this estimation, it is possible to calculate the concentration of one molecule inside the bacteria in molar concentration <br /><span class="math">1<em>M</em> = 1<em>m</em><em>o</em><em>l</em> / 1<em>L</em> = 6*10<sup>23</sup><em>m</em><em>o</em><em>l</em><em>e</em><em>c</em><em>u</em><em>l</em><em>e</em><em>s</em> / <em>L</em></span><br /></p>
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<p><br /><span class="math">$[1 molec] = \frac{1}{0.7*10^{-15} L} = \frac{1}{6*10^{23}  
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0.7*10^{-15}}M \simeq 10^{-9} M = 1 nM$</span><br /></p>
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\begin{align}
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[1 molec] = \frac{1}{0.7*10^{-15} L} = \frac{1}{6*10^{23} 0.7*10^{-15}}M \simeq 1 nM
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\end{align}
<h3 id="plasmid-concentration">Plasmid concentration</h3>
<h3 id="plasmid-concentration">Plasmid concentration</h3>
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\end{align}
\end{align}
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<p>So, the concentration of the protein per Plug&Play plasmid, for both CRE and FLP recombinases, is given by:</p>
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<p>So, an estimative of protein concentration per Plug&Play plasmid, for both CRE and FLP recombinases, is given by:</p>
\begin{align}
\begin{align}
[Prot] = \frac{k_{transl} k_{transc}}{k_{dProt} k_{dRNA} n_{bp}^2/3 } \simeq 2000 nM
[Prot] = \frac{k_{transl} k_{transc}}{k_{dProt} k_{dRNA} n_{bp}^2/3 } \simeq 2000 nM
\end{align}
\end{align}
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<p>This result is an estimation of the amount of protein (CRE or FLP) produced by each Plug&Play plasmid and consequently, the total concentration should be higher than <span class="math">$2000 nM$</span> and dependent of the kind of Plug&Ply plasmid (high or low copy). Therefore, there is no significant change in the results presented here for concentrations higher than <span class="math">$2000 nM$</span>. This might occur because there are plenty of recombinase monomers to perform the recombination for concentrations higher than <span class="math">$2000 nM$</span>. Because of this, the following results are presented using <span class="math">$2000 nM$</span> of monomer concentration.</p>
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<p>This result is an estimation of the amount of protein (CRE or FLP) produced by each Plug&Play plasmid and consequently, the total concentration should be higher than 2000 $nM$ and dependent of the kind of Plug&Ply plasmid (high or low copy). Therefore, there is no significant change in the results presented here for concentrations higher than 2000 $nM$. This might occur because there are plenty of recombinase monomers to perform the recombination for concentrations higher than 2000 $nM$. Because of this, the following results are presented using 2000 $nM$ of monomer concentration.</p>
<h3 id="orf-concentration">ORF concentration</h3>
<h3 id="orf-concentration">ORF concentration</h3>
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[So] = \frac{m_{dna} 2*10^{-15}}{50*10^{-6}} \simeq m_{dna} 0.4*10^{-10} M = m_{dna}*0.04  nM.
[So] = \frac{m_{dna} 2*10^{-15}}{50*10^{-6}} \simeq m_{dna} 0.4*10^{-10} M = m_{dna}*0.04  nM.
\end{align}  
\end{align}  
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This means, for example, that in order to obtain <span class="math">10</span> <span class="math"><em>n</em><em>M</em></span> of concentration <span class="math">250</span> <span class="math"><em>n</em><em>g</em></span> of DNA are needed in a solution of <span class="math">50<em>μ</em><em>L</em></span>.</p>
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This means, for example, that in order to obtain 10 nM of concentration 250 ''ng'' of DNA are needed in a solution of 50 $\mu L$.</p>
<h1 id="results">Results</h1>
<h1 id="results">Results</h1>
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<p>For CRE recombinase, linear DNA degradation do not play a fundamental role in our system and it can even be disregarded, figure 3. This may occur because the circularization of linear DNA by recombinases is faster than the degradation of it. For FLP, however, linear DNA degradation is an important effect and must be taken in account, figure 4. This occurs because the association of the first and second monomers for CRE is significantly higher than for FLP.</p>
<p>For CRE recombinase, linear DNA degradation do not play a fundamental role in our system and it can even be disregarded, figure 3. This may occur because the circularization of linear DNA by recombinases is faster than the degradation of it. For FLP, however, linear DNA degradation is an important effect and must be taken in account, figure 4. This occurs because the association of the first and second monomers for CRE is significantly higher than for FLP.</p>
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<p>In the following analysis we evaluated the concentration of plasmids with the inserted ORF as a function of the DNA mass  in the solution during eletroporation and the variable <span class="math"><em>c</em></span> (the fraction of ORF concentration that enters in the bacteria), Figs 5 and 6. We are interested in concentrations of Plug&Play plasmids with the ORF inserted higher than <span class="math">1</span> <span class="math"><em>n</em><em>M</em></span> which means that, in average, there will be at least one plasmid with the ORF in the bacteria, represented by the red region on the Figs. 5 and 6. According to our results an amount of <span class="math">10000</span> <span class="math"><em>n</em><em>g</em></span> of DNA might be satisfactory when using CRE. Nevertheless, when using FLP this amount might not be enough and the amount needed is highly dependent of the linear DNA degradation rate.</p>
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<p>In the following analysis we evaluated the concentration of plasmids with the inserted ORF as a function of the DNA mass  in the solution during eletroporation and the variable <span class="math"><em>c</em></span> (the fraction of ORF concentration that enters in the bacteria), Figs 5 and 6. We are interested in concentrations of Plug&Play plasmids with the ORF inserted higher than 1 $nM$ which means that, in average, there will be at least one plasmid with the ORF in the bacteria, represented by the red region on the Figs. 5 and 6. According to our results an amount of 10000 $ng$ of DNA might be satisfactory when using CRE. Nevertheless, when using FLP this amount might not be enough and the amount needed is highly dependent of the linear DNA degradation rate.</p>
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<p>One possible strategy to improve the recombination without increasing this amount of DNA is to reduce the volume of the solution before eletroporation, which increase the ORF concentration in the solution. Values lower than <span class="math">10000</span> <span class="math"><em>n</em><em>g</em></span> of DNA may also be satisfactory since the ORF has a antibiotics resistance gene and once the ORF had been inserted the bacteria tend to keep and replicate the plasmid.</p>
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<p>One possible strategy to improve the recombination without increasing this amount of DNA is to reduce the volume of the solution before eletroporation, which increase the ORF concentration in the solution. Values lower than 10000 $ng$ of DNA may also be satisfactory since the ORF has a antibiotics resistance gene and once the ORF had been inserted the bacteria tend to keep and replicate the plasmid.</p>
{{:Team:USP-UNESP-Brazil/Templates/RImage | image=ORFxc.jpg | caption=Fig. 5. The concentration of plasmids with the ORF inserted as a function of ORF mass in concentration and <span class="math"><em>c</em></span> (the fraction of ORF concentration that enters in the bacteria) for CRE recombinase. We suppose that eletroporation was done in a solution of 50 <span class="math"><em>μ</em><em>L</em></span>.| size=600px }}
{{:Team:USP-UNESP-Brazil/Templates/RImage | image=ORFxc.jpg | caption=Fig. 5. The concentration of plasmids with the ORF inserted as a function of ORF mass in concentration and <span class="math"><em>c</em></span> (the fraction of ORF concentration that enters in the bacteria) for CRE recombinase. We suppose that eletroporation was done in a solution of 50 <span class="math"><em>μ</em><em>L</em></span>.| size=600px }}
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<h1 id="discussion">Discussion</h1>
<h1 id="discussion">Discussion</h1>
<p>In order to identify differences between FLP and CRE, we compared the two enzymes using two analyses. Our results point to an obvious choice for the CRE-lox recombination system since it is less affected by DNA degradation and improves the insertion of the ORF compared with FLP-FRT system.</p>
<p>In order to identify differences between FLP and CRE, we compared the two enzymes using two analyses. Our results point to an obvious choice for the CRE-lox recombination system since it is less affected by DNA degradation and improves the insertion of the ORF compared with FLP-FRT system.</p>
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<p>In our model we have considered all lox sites as loxP. However, there are mutated loxP and a combination of them can improve the insertion of the target gene (ORF) [4]. We have chosen to use lox66 and lox71 in our experimental design. We did not introduced the lox66 and lox71 in the model for two main reasons: there are no references about the values of rate constants for altered loxP and we prefer to keep the simplicity and clarity of the model. In order to take these variables in consideration, it would be necessary to use more equations and extra hypothesis.</p>
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<p>In our model we have considered all lox sites as loxP. However, there are mutated loxP and a combination of them can improve the insertion of the target gene (ORF) [4]. We have chosen to use lox66 and lox71 in our experimental design. Nevertheless, we did not introduce the lox66 and lox71 in the model for two main reasons: there are no references about the values of rate constants for altered loxP and we prefer to keep the simplicity and clarity of the model. In order to take these variables in consideration, it would be necessary to use more equations and extra hypothesis.</p>
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<p>Although we did not consider the mutated loxP, we have some considerations about it. The insertion reaction is favored over the excision reaction by roughly fivefold using mutated recombination, when using CRE recombinases <span class="citation"></span>. This occurs because the double mutated loxP has a very low affinity for the CRE monomers. So, an intuitive conclusion is that the combination we chose may optimize the insertion of the ORF in the Plug&Play plasmid. Nevertheless, this conclusion could be false because the altered loxP demands more time in the circularization step since it has a lower association constant for CRE recombinase. This extra amount of time could be such, that the degradation of linear DNA plays a fundamental role in the process. However, as it is illustrated, in the case of CRE recombinases the degradation of linear DNA is not a fundamental variable and it may not interfere. Because of this, the combination of mutated loxP must optimize the amount of ORF inserted in the plasmid.</p>
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<p>Although we did not consider the mutated loxP, we have some considerations about it. The insertion reaction is favored over the excision reaction by roughly fivefold using mutated recombination, when using CRE recombinases [4]. This occurs because the double mutated loxP has a very low affinity for the CRE monomers. So, an intuitive conclusion is that the combination we chose may optimize the insertion of the ORF in the Plug&Play plasmid. Nevertheless, this conclusion could be false because the altered loxP demands more time in the circularization step since it has a lower association constant for CRE recombinase. This extra amount of time could be such that the degradation of linear DNA plays a fundamental role in the process. However, as it is illustrated in Fig. 3, in the case of CRE recombinases, the degradation of linear DNA is not a fundamental variable and it may not interfere. Because of that, we may conclude that the combination of mutated loxP must optimize the amount of ORF inserted in the plasmid.</p>
<h1 id="Appendix">Appendix</h1>
<h1 id="Appendix">Appendix</h1>

Latest revision as of 02:42, 27 September 2012