Simulation-free estimation of reaction propensities in cellular reactions and gene signaling networks

Abstract

Classical reaction kinetics based on deterministic rates laws are not valid for the description of cellular events in which the small number of molecules introduces stochasticity with discrete instead of continuous state transitions. Stochastic models are suitable for simulating transcriptional and translational events inside biological cells, but are impractical for solving inverse problems, which aim to estimate unknown reaction propensities from experimental observations. We introduce a new mathematical framework of Ito stochastic differential equations for the modeling of discrete cellular events and the robust and consistent parameter estimation of cellular dynamics where classical reaction kinetics is invalid. The results supported by case studies on gene expression in B. subtilis cells and viral gene transcription and translation inside non-lytic viral cells demonstrate that the proposed methodology performs as reliable as the gold standard Gillespie algorithm for simulating cellular events. More importantly, the new Ito process framework is ideal for estimating unknown reaction propensities from data as readily as in deterministic parameter estimation by using the novel ‘SPE – simulation free parameter estimation’ approach. Also, the computation time for the stochastic differential equation models is significantly low when compared to discrete event simulations.