# Reduction for stochastic biochemical reaction networks with multiscale conservations

## TL;DR

This paper addresses the challenge of accurately approximating stochastic biochemical reaction networks with multiple timescales and conservation laws by proposing a modified multiscale approximation method.

## Contribution

It introduces a novel modification to the existing multiscale approximation approach to improve accuracy in networks with conservation laws and virtual slow species.

## Key findings

- Improved approximation accuracy in complex biochemical networks
- Effective handling of conservation laws in stochastic simulations
- Enhanced applicability of multiscale methods

## Abstract

Biochemical reaction networks frequently consist of species evolving on multiple timescales. Stochastic simulations of such networks are often computationally challenging and therefore various methods have been developed to obtain sensible stochastic approximations on the timescale of interest. One of the rigorous and popular approaches is the multiscale approximation method for continuous time Markov processes. In this approach, by scaling species abundances and reaction rates, a family of processes parameterized by a scaling parameter is defined. The limiting process of this family is then used to approximate the original process. However, we find that such approximations become inaccurate when combinations of species with disparate abundances either constitute conservation laws or form virtual slow auxiliary species. To obtain more accurate approximation in such cases, we propose here an appropriate modification of the original method.