Difference between revisions of "Team:Valencia UPV/Modeling"

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<p>Take a sit and enjoy this wander in our mathematical chaos!</p>
 
<p>Take a sit and enjoy this wander in our mathematical chaos!</p>
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PRUEBA
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Degradations are considered as first order reactions. Production rates that gobern each process are the same for all proteins, as they are preceeded by the same promotor. However, this could be changed by using promotors with different strength. Thus, each protein could have an individualized production rate (transcription + translation).
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\begin{equation}
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[\dot{A}]=k_{P_A}\cdot[mA]-d_A[A]\longrightarrow
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\begin{bmatrix}\dot{m}A \\\dot{A} \\\end{bmatrix}=
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\begin{bmatrix}-d_{mA}& 0 \\k_{P_A}&-d_A\\\end{bmatrix}
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\begin{bmatrix}mA\\A\\\end{bmatrix}+
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\begin{bmatrix}k_{mA}c_{gA}\\0\\\end{bmatrix}\end{equation}
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\\ As genes encoding proteins A, B, C and D,  follow the same transcription pathway, we will write their equations taking A as reference.\\
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Expressing each concentration as a "x" variable:\\•
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$$[gA]=x_1 \qquad\quad [RNA_p]=x_2 \qquad\quad [gA·RNA_p]=x_3$$
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$$[mA]=x_4\qquad\quad [A]=x_5$$
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Where A is E-PIF6.
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\begin{equation}
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\dot{x_{1}}=-k_{1_{A}}\cdot x_{1} \cdot x_{2}+k_{-1_{A}}\cdot x_{3}+k_{mA}\cdot x_{3}
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\end{equation}
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$$
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\dot{x_{2}}=0 $$
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The expression above means that $[RNA_{pol}]$  inside the cell is high enough to consider it in excess.
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PRUEBA
 
 
 
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Revision as of 11:49, 18 September 2015

Link title Valencia UPV iGEM 2015

Overview

When new things are created, there is no clue about its behavior, which causes uncertainty. This is the reason why modeling has become a significant part of any project.

We started by figuring out how it should work in a tree diagram, keeping the idea simple:




Basically, our aim is the biological design of a decoder that only expresses the codified genetic information when, where and which is desired by the user. The biological components that allow us this implementation in living organisms are two switches, two recombinases and a library of different binding domains. All those elements have been coordinated in this cascade of three different levels.




Our deterministic model uses mathematical information contained in its equations, in order to provide results that depict the behavior of our device. After deterministic model, it is time to test our biological machine in different conditions.

As organisms are supposed to be in a closed device, environmental variability was not the critical point. We have analyzed the influence of different color combinations of light, duration of those, numbers of gene copies and values of tetramerization.

One of the main points when innovative devices are being tested, is “how”. How does AladDNA behave? This is the main question that we want to answer with our modeling task.

Take a sit and enjoy this wander in our mathematical chaos!

PRUEBA Degradations are considered as first order reactions. Production rates that gobern each process are the same for all proteins, as they are preceeded by the same promotor. However, this could be changed by using promotors with different strength. Thus, each protein could have an individualized production rate (transcription + translation). \begin{equation} [\dot{A}]=k_{P_A}\cdot[mA]-d_A[A]\longrightarrow \begin{bmatrix}\dot{m}A \\\dot{A} \\\end{bmatrix}= \begin{bmatrix}-d_{mA}& 0 \\k_{P_A}&-d_A\\\end{bmatrix} \begin{bmatrix}mA\\A\\\end{bmatrix}+ \begin{bmatrix}k_{mA}c_{gA}\\0\\\end{bmatrix}\end{equation} \\ As genes encoding proteins A, B, C and D, follow the same transcription pathway, we will write their equations taking A as reference.\\ Expressing each concentration as a "x" variable:\\• $$[gA]=x_1 \qquad\quad [RNA_p]=x_2 \qquad\quad [gA·RNA_p]=x_3$$ $$[mA]=x_4\qquad\quad [A]=x_5$$ Where A is E-PIF6. \begin{equation} \dot{x_{1}}=-k_{1_{A}}\cdot x_{1} \cdot x_{2}+k_{-1_{A}}\cdot x_{3}+k_{mA}\cdot x_{3} \end{equation} $$ \dot{x_{2}}=0 $$ The expression above means that $[RNA_{pol}]$ inside the cell is high enough to consider it in excess. PRUEBA