A modified next reaction method for simulating chemical systems with time dependent propensities and delays.

By David F. Anderson. Journal of Chemical Physics, 2007

357 citations recorded by the source corpus.

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.

Subfields: Management Science and Operations Research, Molecular Biology

View Paper: https://www.semanticscholar.org/paper/2c97d56707878a3a1d926f385f68be07e4722d7b

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In Management Science and Operations Research

In Molecular Biology

Citations in the corpus

Simulating the evolution of soot mixing state with a particle-resolved aerosol model (2008, methodology): “Anderson [2007, 2008] developed efficient simulation algorithms based on the Next Reaction Method and the tau-leaping method.”
Malliavin Calculus for Fractional Delay Equations (2009, background): “In spite of this lack of theoretical results, the need for suitable oscillating dynamical models with delays is obvious in the applied literature, and involves problems in signal or disease transmission [6, 32, 35], biochemical reactions [2] or gene regulation [5, 25].”
Stochastic switching in biology: from genotype to phenotype (2017, methodology): “These include the next reaction method [109] and the modified next reaction method [4].”
Continuous Time Markov Chain Models for Chemical Reaction Networks (2011, methodology): “For example, the above equation suggests a simulation strategy equivalent to the next reaction method [1, 19].”