Automated Generation of Conditional Moment Equations for Stochastic Reaction Networks

The dynamics of biochemical reaction networks require a stochastic description when copy number fluctuations become significant. Such description is provided by moment equations that capture the statistical properties of the involved molecular components such as their average abundance and variability. Certain applications require a special form of moment equations, where the statistics of some components are described conditionally on complete trajectories of other components. Typical examples include information theoretical analyses of biochemical networks, model reduction and subnetwork simulation, or statistical inference where time-varying molecular signals are inferred from counting observations. These conditional moment equations have so far been limited to relatively simple reaction systems as their manual derivation becomes difficult for systems involving many components and interactions. Here, we present a Python tool for the automated derivation of moment equations conditional on complete time trajectories for arbitrary user-defined reaction systems and showcase its utility in the context of subnetwork simulation. With this automated tool, conditional moment equations become applicable to a broad class of biochemical systems.