Fluctuation-Preserving Coarse Graining for Biochemical Systems

Finite stochastic Markov models play a major role in modeling biological systems. Such models are a coarse-grained description of the underlying microscopic dynamics and can be considered mesoscopic. The level of coarse-graining is to a certain extent arbitrary since it depends on the resolution of accommodating measurements. Here we present a systematic way to simplify such stochastic descriptions which preserves both the meso-micro and the meso-macro connections. The former is achieved by demanding locality, the latter by considering cycles on the network of states. Our method preserves fluctuations of observables much better than naive approaches.