  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.
