Adjusting Noise in the Genetic Toggle Switch through Stochastic Circuit Design

Bistable genetic circuits are important regulatory elements that can serve as biological switches. However, for a switch to function correctly, the noise inherent to the circuit needs to be taken into account, as it affects the robustness of the system. Using the example of a genetic toggle switch, we analyse the dependence of its intrinsic noise on the biochemical properties of the circuit. To that end, the circuit is described stochastically, and the variances of mRNA and protein fluctuations in each stable expression state are formulated as functions of relevant circuit parameters. This is done with the help of the linear noise approximation. As the obtained dependence is highly complex and difficult to interpret, simplified models with increasing complexity are analyzed successively. First, mRNA levels are eliminated assuming infinitely fast mRNA dynamics. Based on this model, influences of mutual inhibition dynamics and of the distribution of time-scales between the two gene expression systems are evaluated. By introducing translational bursts into the model, the interplay between mRNA and protein dynamics can be studied for quickly degrading mRNAs. Finally, special cases of the full stochastic model are discussed. Our results are verified by stochastic simulations and interpreted from a biological point of view. This enables to suggest genetic modifications for the targeted modulation of transition probabilities between distinct expression states.