Analysing a bistable switch in systems biology with stochastic simulations

Sammanfattning: We analyse biological switches with the aid of computers and the Gillespie method, a stochastic solver. Stochastic calculations can lead to spontaneous switches which are, in part, determined by a subset of the parameters. In a deterministic description this is hidden. Initial analysis using a deterministic description of the system will reveal that by applying certain constraints on the system we can greatly simplify the calculations. This gives us a quick and simple way to calculate not only how many fixed points a system has for any specified set of parameters, but also the equilibrium concentrations. This is in great contrast to when the calculations are done stochastically, where you unlock certain behaviours and loose others, such as being able to accurately calculate equilibrium concentrations (number of molecules). We will also see that, as a rough estimate, the highest equilibrium concentration is dependent on a specific parameter, namely the quotient between the production and degradation rate. Finally we also look at a system in which an external signal is added, driving the system to switch.