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Stochastic Models of Biological Processes

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Encyclopedia of Complexity and Systems Science

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Abbreviations

Brownian dynamics:

A level of detail in which each molecule is represented by a point-like particle and molecules move in response to diffusion and collisions

Chemical Fokker–Planck equation (CFPE):

Master equation for well-mixed systems that corresponds to the chemical Langevin equation

Chemical master equation (CME):

Master equation for the probability that the system has specific integer copy numbers for each type of chemical species; it is exact for a well-mixed system

Chemical Langevin equation (CLE):

Approximate stochastic differential equation for well-mixed systems which is based on continuous Gaussian statistics

Direct method:

An implementation of the Gillespie algorithm

Extrinsic noise:

In genetic noise studies, expression fluctuations of a gene that arise from upstream genes or global fluctuations

First‐reaction method:

An implementation of the Gillespie algorithm

Gillespie algorithm:

Exact algorithm for simulating individual trajectories of the CME

Hybrid algorithms:

Algorithms that are designed to efficiently simulate systems that have multiple timescales

Individual‐based spatial models:

Models that track individual molecules as they diffuse or react

Intrinsic noise:

Expression fluctuations of a gene that arise from that particular gene

Jump process:

A process in which the system abruptly changes from one state to another

Optimized direct method:

A computationally efficient implementation of the Gillespie algorithm

Population‐based spatial models:

Models that track how many molecules of each chemical species are in various spatial compartments

Reaction channel:

A possible reaction between specified reactant and product chemical species (the terminology distinguishes this meaning from an individual reaction event between single molecules)

Reaction‐diffusion equation:

Deterministic partial differential equation that combines mass action reaction kinetics and normal chemical diffusion

Reaction‐diffusion master equation (RDME):

Chemical master equation that accounts for diffusion as well as reactions

Reaction rate equation (RRE):

Deterministic ordinary differential equation for the net production rate of each chemical species from chemical reactions

Spatial chemical Langevin equation:

Chemical Langevin equation that accounts for diffusion as well as reactions

Stochastic simulation algorithm (SSA):

Alternative term for the Gillespie algorithm

Stoichiometric matrix (ν):

Matrix that gives the net production of each chemical species, for each chemical reaction

Tau‐leaping method:

Approximate simulation method for well-mixed systems in which molecule numbers are updated using discrete Poisson statistics

Well‐mixed hypothesis:

Assumption that mixing processes occur faster than the relevant reaction processes

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Acknowledgments

This work was funded by the US Department of Energy.

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Authors and Affiliations

  1. Physical Biosciences Division, Lawrence Berkeley National Laboratory, Berkeley, USA

    Steven S. Andrews, Tuan Dinh & Adam P. Arkin

  2. Department of Bioengineering and Howard Hughes Medical Institute, University of California, Berkeley, USA

    Adam P. Arkin

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    Robert A. Meyers Ph. D. (Editor-in-Chief) (Editor-in-Chief)

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Andrews, S.S., Dinh, T., Arkin, A.P. (2009). Stochastic Models of Biological Processes. In: Meyers, R. (eds) Encyclopedia of Complexity and Systems Science. Springer, New York, NY. https://doi.org/10.1007/978-0-387-30440-3_524

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