2010/05/15 by Aleksandra M. Walczak, Andrew Mugler, Chris H. Wiggins +1 · 1 citation
Biochemistry, Genetics and Molecular Biology · #Diffusion and Search Dynamics #Gene Regulatory Network Analysis #Mathematical model #Monte Carlo method #Noise (video) #Parametric model #Parametric statistics #Single-cell and spatial transcriptomics #Stochastic modelling #Stochastic process #q-bio.MN
paper · pdf · doi:10.1007/978-1-61779-833-7_13
published as Methods Mol. Biol. (2012) 880, 273-322
arxiv created 2010/05/15 · openalex publication_date 2012/01/01 · arxiv updated 2015/03/16 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
Recent single-cell experiments have revived interest in the unavoidable or intrinsic noise in biochemical and genetic networks arising from the small number of molecules of the participating species. That is, rather than modeling regulatory networks in terms of the deterministic dynamics of concentrations, we model the dynamics of the probability of a given copy number of the reactants in single cells. Most of the modeling activity of the last decade has centered on stochastic simulation, i.e., Monte Carlo methods for generating stochastic time series. Here we review the mathematical description in terms of probability distributions, introducing the relevant derivations and illustrating several cases for which analytic progress can be made either instead of or before turning to numerical computation. Analytic progress can be useful both for suggesting more efficient numerical methods and for obviating the computational expense of, for example, exploring parametric dependence.