Building Stochastic Feedback Models from Limited Data; A Maximum Entropy-Based Solution

Abstract

We present a general, maximum entropy-based method for modeling stochastic feedback dynamics of small chemical and biochemical systems. Our method, Maximum Caliber, uses experimental data in the form of dynamical averages and correlations to construct ensembles of system trajectories. These theoretical ensembles are used to infer long-time dynamics from short-time trajectories. In particular, the method does not have to invoke complex reaction schemes to predict dynamical features such as multistability. On the other hand, traditional stochastic modeling methods often require knowledge of rates and reaction networks. Such parameters are rarely validated independently of the experimental curve-fitting. Maximum Caliber requires both fewer assumptions regarding the reaction network and fewer parameters to capture the effects of feedback. We demonstrate the principle on the genetic toggle switch and the circadian clock.