A Numerical Aggregation Algorithm for the Enzyme-catalyzed Substrate Conversion

and moreover, if reaction frequencies of different reaction types
differ in orders of magnitude, models possess the mathematical
property of stiffness, which renders system analysis difficult and
often even impossible with traditional methods. Recently, an
accelerated stochastic simulation technique based on a system
partitioning, the slow-scale stochastic simulation algorithm, has been
applied to the enzyme-catalyzed substrate conversion to circumvent
the inefficiency of standard stochastic simulation in the presence of
stiffness.
We propose a numerical algorithm based on a similar partitioning but
without resorting to simulation. The algorithm exploits the connection
to continuous-time Markov chains and decomposes the overall problem to
significantly smaller subproblems that become tractable. Numerical
results show enormous efficiency improvements relative to accelerated
stochastic simulation.