Team:ULB-Brussels/Project/Mathematical

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==Introduction==
==Introduction==
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In these expressions, [x] is the concentration of activated genes, p is called the Hill coefficient,
In these expressions, [x] is the concentration of activated genes, p is called the Hill coefficient,
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k is the activation coefficient and \alpha is the maximum expression level of the promotor.
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k is the activation coefficient and α is the maximum expression level of the promotor.
For each block of the system, we can obtain a dynamical equation by considering its interactions
For each block of the system, we can obtain a dynamical equation by considering its interactions
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Where, [x]-i is the concentration of the gene i, R(Ha([x]);Hp([x])) is the regulating function
Where, [x]-i is the concentration of the gene i, R(Ha([x]);Hp([x])) is the regulating function
which is a combination of Hill functions. The second term of the right side is the destruction
which is a combination of Hill functions. The second term of the right side is the destruction
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term, where °i is the maximum destruction rate of the gene i.
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term, where γi is the maximum destruction rate of the gene i.
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We must bear in mind, however that the robustness of a given operational regime with respect to
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external perturbations strongly depends on the value of the Hill coefficients. [16] In particular,
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the robustness is expected to increase with the value of the hill coefficient. The cooperativity
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behaviour is also a function of the Hill coefficient. For these reasons we will consider a situation
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for which p = 2.
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==A first simplified model==

Revision as of 00:08, 22 October 2009

iGEM Team:ULB-Brussels Wiki

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Introduction

Synthetic biology is a recent development in biology which aims at producing useful material via biological agents. In this context, a biological system can be seen as a complex network composed of different functional parts ( [14]). Mathematical tools allow one to make prediction on the dynamical behaviour of a given bio-system. We aim at studying ft the system which has been built in the second section of this report. We already know from our experiment that our system is able to produce glue in the presence of IPTG inductor. We now address the following question: what is the influence of the different parameters on the global dynamics (degradation rate, production rate, level of initial quantity for the C2P22 repressor,...) with and without IPTG. In order to achieve this task, we will consider three different models: the first one shows the basal property we are looking for: a system able to produce glue. The two next models can be seen as two different steps of improvement. The purpose of these models is to improve the experimental control of the glue production. Parameters values result from the literature and previous iGEM team wiki’s. We know these remain qualitative and that lab work should be carried out to specify them more precisely.

  • Hill function for activator

EQUATION1

  • Hill function for repressor

EQUATION2

In these expressions, [x] is the concentration of activated genes, p is called the Hill coefficient, k is the activation coefficient and α is the maximum expression level of the promotor.

For each block of the system, we can obtain a dynamical equation by considering its interactions with the other blocks of the system. For each block we can build an equation of the following form:

EQUATION3

Where, [x]-i is the concentration of the gene i, R(Ha([x]);Hp([x])) is the regulating function which is a combination of Hill functions. The second term of the right side is the destruction term, where γi is the maximum destruction rate of the gene i.

We must bear in mind, however that the robustness of a given operational regime with respect to external perturbations strongly depends on the value of the Hill coefficients. [16] In particular, the robustness is expected to increase with the value of the hill coefficient. The cooperativity behaviour is also a function of the Hill coefficient. For these reasons we will consider a situation for which p = 2.

A first simplified model