Statistical physics approaches to subnetwork dynamics in biochemical systems

TL;DR

This paper introduces a Gaussian variational approximation method for reducing large biochemical network models to focus on a subnetwork, capturing effects of the larger system including memory and noise, with improved accuracy and efficiency.

Contribution

It develops a novel model reduction technique incorporating memory and noise effects, applicable to stochastic biochemical networks, and demonstrates its effectiveness on a real signaling pathway.

Findings

The method accurately predicts subnetwork dynamics with memory and noise effects.

It is computationally more efficient than existing projection methods.

Application to EGFR pathway shows improved prediction accuracy.

Abstract

We apply a Gaussian variational approximation to model reduction in large biochemical networks of unary and binary reactions. We focus on a small subset of variables (subnetwork) of interest, e.g. because they are accessible experimentally, embedded in a larger network (bulk). The key goal is to write dynamical equations reduced to the subnetwork but still retaining the effects of the bulk. As a result, the subnetwork-reduced dynamics contains a memory term and an extrinsic noise term with non-trivial temporal correlations. We first derive expressions for this memory and noise in the linearized (Gaussian) dynamics and then use a perturbative power expansion to obtain first order nonlinear corrections. For the case of vanishing intrinsic noise, our description is explicitly shown to be equivalent to projection methods up to quadratic terms, but it is applicable also in the presence of stochastic fluctuations in the original dynamics. An example from the Epidermal Growth Factor Receptor (EGFR) signalling pathway is provided to probe the increased prediction accuracy and computational efficiency of our method.