2007/08/31 by David F. Anderson · 378 citations
Biochemistry, Genetics and Molecular Biology · Chemistry · Decision Sciences · Mathematics · #Algorithm #Applied mathematics #Biological system #Chemical reaction #Chemistry #Computer science #Gene Regulatory Network Analysis #Jump #Machine learning #Markov chain #Markov process #Mathematical optimization #Mathematics #Microbial Metabolic Engineering and Bioproduction #Physics #Poisson distribution #Representation (politics) #Simulation Techniques and Applications #Statistical physics #Statistics #q-bio.MN #q-bio.QM
paper · pdf · doi:10.1063/1.2799998
published in The Journal of Chemical Physics 127(21), 214107 (American Institute of Physics) · 25 pages, 1 figure. Some minor changes made to add clarity
arxiv created 2007/08/31 · openalex publication_date 2007/12/06 · arxiv updated 2015/05/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/06
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.