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| − | <h1 class="h-sectionT">MODEL OF RFP PRODUCTION</h1> | + | <h1 class="h-sectionT">MATHEMATICS SECTION</h1> |
| | + | <p>According to our bench project we divided the Math Modelling in two: (1) RFP production taking in account the regulation of MerR gene, which turns RFP expression possible only in the presence of Mercury. This model allow us to understand the force of the new promoters we designed by the speed of RFP’s production; (2) A model to predict the production of the complex Omp-A-Phytochelatin and bioaccumulation of mercury.</p> |
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| − | <h3 style="color:#b54df5;margin-left: 2em">1. Modelling</h3>
| + | <div class="imgCentralizada" > |
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| − | <p>We want to characterize the promoter’s velocity of expression due to presence of mercury, so we will attach an RFP gene to it to produce.</p>
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| − | <p>First we will model the production of RFP due to Hg<sup>2+</sup> at stationary time phase with this configuration. Then we add the initial phase consideration</p>
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| − | <h3 style="color:#b54df5;margin-left: 2em">1.1 Stationary time phase. </h3>
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| − | <p>The GMO we have is:</p>
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| − | <div class="imgCentralizada"><img src="https://static.igem.org/mediawiki/2016/thumb/1/1b/UFAM_UEA_Team_math_%281%29.png/799px-UFAM_UEA_Team_math_%281%29.png" /> | + | |
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| − | <p>Where MerR is a repressor and releases when H2+ is presented in the interior of the cell, we will note this amount as Hgin and the exterior as Hgout. And Promoter nP is the promoter which velocity we want to characterize. The activation of the gene in the pressence of Hgin is represented like:</p>
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| − | <div class="imgCentralizada"><img src="https://static.igem.org/mediawiki/2016/8/8f/UFAM_UEA_Team_math_%282%29.png" />
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| − | <p>where G is the inactive form of gene repressed by merR, and X is its active form. Through the law of mass action we derive the diferential equation</p>
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| − | <p>(1)<img src="https://static.igem.org/mediawiki/2016/6/6b/UFAM_UEA_Team_math_%283%29.png" width=250 height=60/> <p>
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| − | <p>At the equillibrium state, ie. <img src="
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| − | https://static.igem.org/mediawiki/2016/4/47/UFAM_UEA_Team_math_%284%29.png" width=80 height=40/>, we have that the proportion of genes in the activated gene is</p>
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| − | <p>(2)<img src="
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| − | https://static.igem.org/mediawiki/2016/1/17/UFAM_UEA_Team_math_%285%29.png" width=250 height=60/></p>
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| − | <p>Where <img src="
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| − | https://static.igem.org/mediawiki/2016/3/30/UFAM_UEA_Team_math_%286%29.png" width=80 height=40/></p>
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| − | <p>So this is the average production rate of a typical gene, so the average mRNA production will be</p>
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| − | <p>(3)<img src="
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| − | https://static.igem.org/mediawiki/2016/5/5e/UFAM_UEA_Team_math_%287%29.png" width=350 height=80/></p>
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| − | <p>Where α is the production of mRNA due to the stochastic nature of the binding of merR for repressing the RNA Polymerase and δ1 is the degradation factor of mRNA. The reaction for production of RFP from mRNA is</p>
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| − | <div class="imgCentralizada"><img src="https://static.igem.org/mediawiki/2016/4/43/UFAM_UEA_Team_math_%288%29.png" />
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| − | <p>so we derive the diferential equation</p>
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| − | <p>(4)<img src="
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| − | https://static.igem.org/mediawiki/2016/7/73/UFAM_UEA_Team_math_%289%29.png" width=350 height=80/></p>
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| − | <p>where δ2 is the degradation constant of [RFP]. The variation of exterior mercury is </p>
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| − | <div class="imgCentralizada"><img src="https://static.igem.org/mediawiki/2016/3/38/UFAM_UEA_Team_math_%2810%29.png" />
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| − | <p>from here we derive the differential equation</p>
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| − | <p>(5)<img src="
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| − | https://static.igem.org/mediawiki/2016/1/1e/UFAM_UEA_Team_math_%2811%29.png" width=350 height=80/></p>
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| − | <p>As the interior mercury is used by the inactive form of the gene, the variation of Hgin<sup>2+</sup> is</p>
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| − | <p>(6)<img src="
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| − | https://static.igem.org/mediawiki/2016/thumb/7/7f/UFAM_UEA_Team_math_%2812%29.png/800px-UFAM_UEA_Team_math_%2812%29.png" width=350 height=80/></p>
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| − | <p>To solve this system we will assume that the permeability of the cell memebrane to mercury is instantaneus then we have that <img src="
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| − | https://static.igem.org/mediawiki/2016/7/76/UFAM_UEA_Team_math_%2813%29.png" width=80 height=40/> then <img src="
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| − | https://static.igem.org/mediawiki/2016/c/c5/UFAM_UEA_Team_math_%2814%29.png" width=80 height=40/> so we have that the variation of the interior mercury is</p>
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| | + | <a href="https://static.igem.org/mediawiki/2016/2/22/UFAM_UEA_MATH_%281%29.pdf" target="blank"><img style="width:15em; heigth:15em" src="https://static.igem.org/mediawiki/2016/b/ba/UFAM_UEA_MATH_%283%29.png"/></a> |
| | + | <a href="https://static.igem.org/mediawiki/2016/b/b4/UFAM_UEA_MATH_%282%29.pdf" target="blank"><img style="width:13em; heigth:13em" src="https://static.igem.org/mediawiki/2016/5/5b/UFAM_UEA_MATH_%284%29.png"/></a> |
| | + | </div> |
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| | </div> | | </div> |
MATHEMATICS SECTION
According to our bench project we divided the Math Modelling in two: (1) RFP production taking in account the regulation of MerR gene, which turns RFP expression possible only in the presence of Mercury. This model allow us to understand the force of the new promoters we designed by the speed of RFP’s production; (2) A model to predict the production of the complex Omp-A-Phytochelatin and bioaccumulation of mercury.
