Coarse-graining biochemical complexity

Ilya Nemenman, Los Alamos National Lab

To decrease the complexity involved in analysis of large stochastic biochemical networks, one often coarse-grains them to a level of effective deterministic reactions (such as the famous Hill law), sometimes infused with Poisson/Langevin noise. When is such description fair? To understand this, we developed a novel technique, which has its roots in statistical field theory and adiabatic quantum mechanics. The technique allows us to derive rigorous laws describing coarse-grained, effective stochastic dynamics. We found that, for complex reactions, stochasticity results in corrections to the mean reaction rates, which are intimately related to stochastic pumping effect, and to the Berry phase in quantum mechanics. Additionally, the noise variance for coarse-grained reactions differs substantially from the usual Poisson statistics, and both effects must be accounted for in careful analytical or numerical studies. I will illustrate these points using a simple example of a Michaelis-Menten enzyme.