Spectral neural approximations for models of transcriptional dynamics

Abstract

AbstractTranscriptional systems involving discrete, stochastic events are naturally modeled using Chemical Master Equations (CMEs). These can be solved for microstate probabilities over time and state space for a better understanding of biological rates and system dynamics. However, closed form solutions to CMEs are available in only the simplest cases. Probing systems of higher complexity is challenging due to the computational cost of finding solutions and often compromises accuracy by treating infinite systems as finite. We use statistical understanding of system behavior and the generalizability of neural networks to approximate steady-state joint distribution solutions for a two-species model of the life cycle of RNA. We define a set of kernel functions using moments of the system and learn optimal weights for kernel functions with a neural network trained to minimize statistical distance between approximated and numerically calculated distributions. We show that this method of kernel weight regression (KWR) approximation is as accurate as lower-order generating-function solutions to the system, but faster; KWR approximation reduces the time for likelihood evaluation by several orders of magnitude. KWR also generalizes to produce probability predictions for system rates outside of training sets, thereby enabling efficient transcriptional parameter exploration and system analysis.