Structured Projection-Based Model Reduction with Application to Stochastic Biochemical Networks

TL;DR

This paper introduces a structured projection-based model reduction technique for stochastic biochemical networks, specifically applied to the Linear Noise Approximation of the Chemical Master Equation, ensuring convergence and preserving network structure.

Contribution

It develops a novel structured projection-based reduction algorithm with convex optimization, demonstrating convergence and applicability to biochemical network models.

Findings

Reduced order LNA converges in mean square to the full model

Structured projections can be computed via convex optimization or basic linear algebra

Algorithms successfully applied to yeast glycolysis pathway model

Abstract

The Chemical Master Equation (CME) is well known to provide the highest resolution models of a biochemical reaction network. Unfortunately, even simulating the CME can be a challenging task. For this reason more simple approximations to the CME have been proposed. In this work we focus on one such model, the Linear Noise Approximation. Specifically, we consider implications of a recently proposed LNA time-scale separation method. We show that the reduced order LNA converges to the full order model in the mean square sense. Using this as motivation we derive a network structure preserving reduction algorithm based on structured projections. We present convex optimisation algorithms that describe how such projections can be computed and we discuss when structured solutions exits. We also show that for a certain class of systems, structured projections can be found using basic linear algebra and no optimisation is necessary. The algorithms are then applied to a linearised stochastic LNA model of the yeast glycolysis pathway.