The linear-noise approximation and the chemical master equation exactly agree up to second-order moments for a class of chemical systems

TL;DR

This paper demonstrates that the linear-noise approximation (LNA) precisely matches the chemical master equation up to second-order moments for certain chemical systems, including some with second-order reactions, regardless of molecule count.

Contribution

It extends the known agreement between LNA and the chemical master equation to a subset of systems with second-order reactions, beyond zero and first-order reactions.

Findings

LNA exactly agrees with the chemical master equation up to second-order moments for specific systems.

This agreement holds regardless of the number of molecules involved.

The result broadens the applicability of LNA in chemical system analysis.

Abstract

It is well known that the linear-noise approximation (LNA) exactly agrees with the chemical master equation, up to second-order moments, for chemical systems composed of zero and first-order reactions. Here we show that this is also a property of the LNA for a subset of chemical systems with second-order reactions. This agreement is independent of the number of interacting molecules.