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Biochemical reaction networks frequently consist of species evolving onmultiple timescales. Stochastic simulations of such networks are oftencomputationally challenging and therefore various methods have been developedto obtain sensible stochastic approximations on the timescale of interest. Oneof the rigorous and popular approaches is the multiscale approximation methodfor continuous time Markov processes. In this approach, by scaling speciesabundances and reaction rates, a family of processes parameterized by a scalingparameter is defined. The limiting process of this family is then used toapproximate the original process. However, we find that such approximationsbecome inaccurate when combinations of species with disparate abundances eitherconstitute conservation laws or form virtual slow auxiliary species. To obtainmore accurate approximation in such cases, we propose here an appropriatemodification of the original method.

Reduction for stochastic biochemical reaction networks with multiscale conservations