Stochasticity and robustness in bi-stable systems

The genetic bi-stable switch (toggle switch) consists of two genes which repress one another through their synthesised proteins. In the stochastic bi-stable case, the toggle switch exhibits noise induced flips. Using simulation based techniques, we identified three methods for reducing the random flipping probability, namely: (i) increasing the system size, (ii) increasing the synthesis rate, and (iii) increasing the Hill coefficient. Our heat-maps showed that for large parts of parameter space the toggle switch displays extremely low noise induced flipping probability, and consequently high robustness. We also analysed the noise analytically. The area of validity of the analytical approach was found to be constrained to low Hill coefficients and high synthesis rate (both conditions within biological realistic parameters). Most importantly, we observed that increasing the synthesis rate is more efficient in reducing the noise compared to the increase in system size, for systems affected by negative feedback.