Team:Grenoble/Modeling/Signaling

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1- How sensitive is the signaling module? And what dipeptide concentration should be present in order to trigger a response?
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2- How long does it take for the dipeptide to trigger a response?
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Revision as of 08:33, 22 September 2012

iGEM Grenoble 2012

iGEM Grenoble iGEM
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Overview



The design of signaling module is given by the figure below:
Once the dipeptide molecule is fixed to the TAP receptor, it activates the phosphorylation of OmpR. OmpR* (the phosphorylated form of OmpR) is the transcription factor that activates the gene expression of cya.
This approach arises a few questions we cannot answer without computer models:

1- How sensitive is the signaling module? And what dipeptide concentration should be present in order to trigger a response?

2- How long does it take for the dipeptide to trigger a response?

Answering these two questions will help us assess the sensitivity and the rapidity of the whole system (ie the signaling module, the amplification module and the quorum sensing).

To answer these questions, we need to set the ordinary equations that govern AC evolution. Thus we can plot the evolution of AC concentration versus initial dipeptide concentration (sensitivity) as well as the temporal evolution of AC concentration (rapidity).

ODEs

Let’s begin by considering the cya gene activation by the transcription factor OmpR*.
It’s a gene activation, so the transcription rate is given by a hill function:



Where Vm is the maximal transcription rate, k is the activation coefficient, p is the basal production coefficient and α the degradation coefficient.
For OmpR phosphorylation, we considered in the literature a model that takes into account the enzymatic mechanism of the Histidine Kinase EnvZ as well as the phosphotransfer and the phosphatase.
The model we use is a phenomenological extension of the Goldbeter-Koshland biochemical switch model.[1]
The resulting equation governs [OmpR*] temporal evolution (the square brackets denote concentration) and highlights the fact that the phosphorylation is activated by dipeptide.



where K and K’ are the dimensionless Michaelis-Menten coefficients.
Since the process involved in the production of the new protein AC proceed at much slower timescale than the phosphorylation process that aims at chemically modifying the existing protein OmpR, time derivative of [OmpR*] is null (click here for more explanation) and [OmpR] and [OmpR*] are linked by a conservation law:
[OmpR*]+[OmpR]=[OmpR]tot

Once we’ve set the derivative equation of OmpR* equals to zero and replaced the value of [OmpR] and [OmpR*] by their expressions involving the total quantity of OmpR, we get a second order polynomial equation of [OmpR*]:



If we define the coefficients



We notice that the coefficient “a” is always negative because the dephosphorylation rate of OmpR* is lower in value than the phosphorylation rate .As a product of kinetic parameters, the coefficient “c” is positive.
For the reasons given above the determinant is positive:

Δ=b²-4 a c>0


We have then two float roots x and y. Their product is given by x.y = c/a. As “a” and “c” have opposite signs, x and y have opposite signs: We choose the positive root.

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