Bayesian learning of effective chemical master equations in crowded intracellular conditions

TL;DR

This paper introduces a Bayesian machine learning approach to derive effective chemical master equations that account for crowding effects in intracellular environments, improving the modeling of stochastic reaction kinetics.

Contribution

It presents a novel method combining Bayesian optimization and Gaussian process regression to learn crowding-aware propensity functions from cellular automata simulations.

Findings

Accurately predicts molecule number distributions in crowded conditions.

Extends small training data to physiologically relevant crowding levels.

Shows good agreement with detailed CA simulations.

Abstract

Biochemical reactions inside living cells often occur in the presence of crowders -- molecules that do not participate in the reactions but influence the reaction rates through excluded volume effects. However the standard approach to modelling stochastic intracellular reaction kinetics is based on the chemical master equation (CME) whose propensities are derived assuming no crowding effects. Here, we propose a machine learning strategy based on Bayesian Optimisation utilising synthetic data obtained from spatial cellular automata (CA) simulations (that explicitly model volume-exclusion effects) to learn effective propensity functions for CMEs. The predictions from a small CA training data set can then be extended to the whole range of parameter space describing physiologically relevant levels of crowding by means of Gaussian Process regression. We demonstrate the method on an enzyme-catalyzed reaction and a genetic feedback loop, showing good agreement between the time-dependent distributions of molecule numbers predicted by the effective CME and CA simulations.