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Our synthetic biology constructions feature tens of parameters and at this scale human brains can only guess how the whole system would work. We of course needed mathematical modelling in order to check the effectiveness of the genetic circuit.

In the particular case of our circuit and final use of the bacteria, the modelling team also had to give the specificities (size, number of bacteria, IPTG gradient specificities) of the measuring device we intend to produce.

In the next pages we expose which algorithms we used for both deterministic modelling and stochastic modelling, explain our MATLAB scripts (available here) and finally give the results of our simulations.

Deterministic Modelling :
Our equations and how we obtained them.
Our algorithms
Isoclines and Hysteresis

Stochastic Modelling
Geoffrey
Gillespie algorithm
Mean, standard deviation and statistical properties