Team:Technion-Israel/Modeling

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Revision as of 08:19, 13 October 2014


Safie by Technion-Israel

Why Should it Work

Why Alpha System Should Work – a deterministic model of alpha system

When modelling our system, we began with the simplest method known – deterministic rate equations. Moreover, from the design it was clear that the most important benchmark for the signal within the system would be the concentration of AHL as a function of time, so we began by modelling this part of our system. It took only a simple derivation (see [1]) to obtain these equations which characterize this part of the system:

(d[mRNALuxI])/(dt) = (vB + vAkA[AHL]2)/(1 + kA[AHL]2) − γmRNALuxI[mRNALuxI] + GateI
(d[LuxI])/(dt) = αLuxI[mRNALuxI] − γLuxI[LuxI]
(d[AHL])/(dt) = αAHL[AHL] − γAHL[AHL]

(For a glossary see [1]).

We began to analyze this system by attempting to simplify it, by assuming a steady state solution wherever possible. Using this method (see [2]) we managed to obtain this equation:

(d[AHL])/(dt) = (vB + vAkA[AHL]2)/(1 + kA[AHL]2) − γAHL[AHL] + GateI

It is clear from the goals of our system, that we want to have some sort of bi-stability in the result, when Gate I is small (see [2]). The answer to whether this condition is met, would obviously depend on the constants of the system for which we could not find a reliable source, but using a simple geometric analysis of the phase space (see [3]), we were able to produce a graph showing for which values of (v_A,v_B) we could configure the system (by changing the IPTG concentration and the OD) to show bi-stability:

map of bi-stability in the alpha system

Why Should it Fail
Synthetic Biofilm Formation

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