  There exist several methods for simulating biological and physical systems as
represented by chemical reaction networks. Systems with low numbers of
particles are frequently modelled as discrete-state Markov jump processes and
are typically simulated via a stochastic simulation algorithm (SSA). An SSA,
while accurate, is often unsuitable for systems with large numbers of
individuals, and can become prohibitively expensive with increasing reaction
frequency. Large systems are often modelled deterministically using ordinary
differential equations, sacrificing accuracy and stochasticity for
computational efficiency and analytical tractability. In this paper, we present
a novel hybrid technique for the accurate and efficient simulation of large
chemical reaction networks. This technique, which we name the mass-conversion
method, couples a discrete-state Markov jump process to a system of ordinary
differential equations by simulating a reaction network using both techniques
simultaneously. Individual molecules in the network are represented by exactly
one regime at any given time, and may switch their governing regime depending
on particle density. In this manner, we model high copy-number species using
the cheaper continuum method and low copy-number species using the more
expensive, discrete-state stochastic method to preserve the impact of
stochastic fluctuations at low copy number. The motivation, as with similar
methods, is to retain the advantages while mitigating the shortfalls of each
method. We demonstrate the performance and accuracy of our method for several
test problems that exhibit varying degrees of inter-connectivity and complexity
by comparing averaged trajectories obtained from both our method and from exact
stochastic simulation.
