Limits on the suppression of molecular fluctuations and oscillation dephasing in stochastic reaction networks

Many efforts in synthetic biology have been dedicated to designing ultra-reliable gene networks, but so far there has been little theory capable of providing guidance on the experimental design, because small differences in rate functions or topology can sometimes change the dynamics drastically. Here we aim to identify general principles in stochastic reaction networks that apply regardless of parameters and the form of rate functions. First we studied the noise suppression in multi-component networks and asked if it is possible to design systems where the components control and mutually suppress the noise in each other. Specifically, we find that in any N-component system, regardless of how each component affects other's production rates, it is impossible to suppress fluctuations below the uncontrolled equivalents for all components. We next examined whether there exist similar design principles in oscillatory behaviours in stochastic reaction networks. We studied a broad class of feedback, allowing arbitrary time delay and control functions, and found that even when all the rest of the feedback loop is optimal for generating sustained oscillations, the information loss from one single reaction step can lead to severe constraints in the autocorrelation and power spectrum.