Model order reduction for Linear Noise Approximation using time-scale separation (Extended Version)

TL;DR

This paper presents a method for reducing the complexity of biomolecular systems modeled with Linear Noise Approximation by exploiting time-scale separation, providing accurate approximations of slow variable dynamics.

Contribution

We develop a model reduction technique for Linear Noise Approximation systems with multiple time-scales using singular perturbation methods, achieving accurate moment approximations.

Findings

Reduced models approximate original slow variable moments within O(ε)

Method effectively captures time-scale separation in biomolecular systems

Illustrated with a biomolecular example demonstrating accuracy

Abstract

In this paper, we focus on model reduction of biomolecular systems with multiple time-scales, modeled using the Linear Noise Approximation. Considering systems where the Linear Noise Approximation can be written in singular perturbation form, with $\epsilon$ as the singular perturbation parameter, we obtain a reduced order model that approximates the slow variable dynamics of the original system. In particular, we show that, on a finite time-interval, the first and second moments of the reduced system are within an $O(\epsilon)$-neighborhood of the first and second moments of the slow variable dynamics of the original system. The approach is illustrated on an example of a biomolecular system that exhibits time-scale separation.