Biochemical reaction systems with a low to moderate number of molecules are typically modeled as discrete jump Markov processes. These systems are oftentimes simulated using the Gillespie Algorithm or the Next Reaction Method , which are exact simulation methods . In this paper we make explicit use of the fact that the initiation times of each reaction are given by the firing times of an independent, unit Poisson process with integrated propensity function. We use this representation to develop a modified version of the Next Reaction Method . We then demonstrate how this modified Next Reaction Method is the appropriate method to use to simulate systems in which the rate constants are functions of time (that is, systems that are time dependent Markov Processes). Finally, we extend our modified Next Reaction Method to systems with delays and compare its efficiency with those of the recent algorithms designed for systems with delays.
Chemical reaction systems with a low to moderate number of molecules are typically modeled as discrete jump Markov processes. These systems are oftentimes simulated with methods that produce statistically exact sample paths such as the Gillespie Algorithm or the Next Reaction Method . In this paper we make explicit use of the fact that the initiation times of the reactions can be represented as the firing times of independent, unit rate Poisson processes with internal times given by integrated propensity functions. Using this representation we derive a modified Next Reaction Method and, in a way that achieves efficiency over existing approaches for exact simulation, extend it to systems with time dependent propensities as well as to systems with delays.
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Biochemical
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using
with methods that produce statistically exact sample paths such as
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, which are exact simulation methods
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each reaction are given by the
the reactions can be represented as the
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an
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Poisson process with integrated propensity function. We use this representation to develop a modified version of the
rate Poisson processes with internal times given by integrated propensity functions. Using this representation we derive a modified
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. We then demonstrate how this modified Next Reaction Method is the appropriate method to use to simulate systems in which the rate constants are functions of time (that is, systems that are time dependent Markov Processes). Finally, we extend our modified Next Reaction Method
and, in a way that achieves efficiency over existing approaches for exact simulation, extend it
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delays and compare its efficiency with those of the recent algorithms designed for
time dependent propensities as well as to