Hybrid discrete/continuum algorithms for stochastic reaction networks

Safta, Cosmin; Sargsyan, Khachik; Debusschere, Bert; Najm, Habib N.

doi:10.1016/j.jcp.2014.10.026

Title: Hybrid discrete/continuum algorithms for stochastic reaction networks

Journal Article · Wed Oct 22 00:00:00 EDT 2014 · Journal of Computational Physics

DOI:https://doi.org/10.1016/j.jcp.2014.10.026· OSTI ID:1121280

Safta, Cosmin ^[1]; Sargsyan, Khachik ^[1];

^[1];

^[1]

Sandia National Lab. (SNL-CA), Livermore, CA (United States)

Direct solutions of the Chemical Master Equation (CME) governing Stochastic Reaction Networks (SRNs) are generally prohibitively expensive due to excessive numbers of possible discrete states in such systems. To enhance computational efficiency we develop a hybrid approach where the evolution of states with low molecule counts is treated with the discrete CME model while that of states with large molecule counts is modeled by the continuum Fokker-Planck equation. The Fokker-Planck equation is discretized using a 2nd order finite volume approach with appropriate treatment of flux components to avoid negative probability values. The numerical construction at the interface between the discrete and continuum regions implements the transfer of probability reaction by reaction according to the stoichiometry of the system. As a result, the performance of this novel hybrid approach is explored for a two-species circadian model with computational efficiency gains of about one order of magnitude.

View Accepted Manuscript (DOE)

View Accepted Manuscript (Publisher)

Cite

Export

Save

Research Organization:: Sandia National Lab. (SNL-CA), Livermore, CA (United States)

Sponsoring Organization:: USDOE National Nuclear Security Administration (NNSA); USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR)

Grant/Contract Number:: AC04-94AL85000; 07-012783

OSTI ID:: 1121280

Alternate ID(s):: OSTI ID: 1246992

Report Number(s):: SAND-2013-10187J; 485627

Journal Information:: Journal of Computational Physics, Vol. 281, Issue C; ISSN 0021-9991

Publisher:: ElsevierCopyright Statement

Country of Publication:: United States

Language:: English

Citation Metrics:

Cited by: 11 works

Citation information provided by
Web of Science

References (38)

A rigorous derivation of the chemical master equation Gillespie, Daniel T. Physica A: Statistical Mechanics and its Applications, Vol. 188, Issue 1-3 https://doi.org/10.1016/0378-4371(92)90283-V	journal	September 1992
A general method for numerically simulating the stochastic time evolution of coupled chemical reactions Gillespie, Daniel T. Journal of Computational Physics, Vol. 22, Issue 4 https://doi.org/10.1016/0021-9991(76)90041-3	journal	December 1976
Exact stochastic simulation of coupled chemical reactions Gillespie, Daniel T. The Journal of Physical Chemistry, Vol. 81, Issue 25 https://doi.org/10.1021/j100540a008	journal	December 1977
Efficient Exact Stochastic Simulation of Chemical Systems with Many Species and Many Channels Gibson, Michael A.; Bruck, Jehoshua The Journal of Physical Chemistry A, Vol. 104, Issue 9 https://doi.org/10.1021/jp993732q	journal	March 2000
Stiffness in stochastic chemically reacting systems: The implicit tau-leaping method Rathinam, Muruhan; Petzold, Linda R.; Cao, Yang The Journal of Chemical Physics, Vol. 119, Issue 24 https://doi.org/10.1063/1.1627296	journal	December 2003
Approximate accelerated stochastic simulation of chemically reacting systems Gillespie, Daniel T. The Journal of Chemical Physics, Vol. 115, Issue 4 https://doi.org/10.1063/1.1378322	journal	July 2001
Approximate simulation of coupled fast and slow reactions for stochastic chemical kinetics Haseltine, Eric L.; Rawlings, James B. The Journal of Chemical Physics, Vol. 117, Issue 15 https://doi.org/10.1063/1.1505860	journal	October 2002
The numerical stability of leaping methods for stochastic simulation of chemically reacting systems Cao, Yang; Petzold, Linda R.; Rathinam, Muruhan The Journal of Chemical Physics, Vol. 121, Issue 24 https://doi.org/10.1063/1.1823412	journal	January 2004
The slow-scale stochastic simulation algorithm Cao, Yang; Gillespie, Daniel T.; Petzold, Linda R. The Journal of Chemical Physics, Vol. 122, Issue 1 https://doi.org/10.1063/1.1824902	journal	January 2005
Multiscale stochastic simulation algorithm with stochastic partial equilibrium assumption for chemically reacting systems Cao, Yang; Gillespie, Dan; Petzold, Linda Journal of Computational Physics, Vol. 206, Issue 2 https://doi.org/10.1016/j.jcp.2004.12.014	journal	July 2005
Nested stochastic simulation algorithms for chemical kinetic systems with multiple time scales E., Weinan; Liu, Di; Vanden-Eijnden, Eric Journal of Computational Physics, Vol. 221, Issue 1 https://doi.org/10.1016/j.jcp.2006.06.019	journal	January 2007
A new look at the chemical master equation Sandu, Adrian Numerical Algorithms, Vol. 65, Issue 3 https://doi.org/10.1007/s11075-013-9758-z	journal	September 2013
The finite state projection algorithm for the solution of the chemical master equation Munsky, Brian; Khammash, Mustafa The Journal of Chemical Physics, Vol. 124, Issue 4 https://doi.org/10.1063/1.2145882	journal	January 2006
A multiple time interval finite state projection algorithm for the solution to the chemical master equation Munsky, Brian; Khammash, Mustafa Journal of Computational Physics, Vol. 226, Issue 1 https://doi.org/10.1016/j.jcp.2007.05.016	journal	September 2007
The Finite State Projection Approach for the Analysis of Stochastic Noise in Gene Networks Munsky, Brian; Khammash, Mustafa IEEE Transactions on Automatic Control, Vol. 53, Issue Special Issue https://doi.org/10.1109/TAC.2007.911361	journal	January 2008
An optimal Finite State Projection Method Sunkara, Vikram; Hegland, Markus Procedia Computer Science, Vol. 1, Issue 1 https://doi.org/10.1016/j.procs.2010.04.177	journal	May 2010
A solver for the stochastic master equation applied to gene regulatory networks Hegland, Markus; Burden, Conrad; Santoso, Lucia Journal of Computational and Applied Mathematics, Vol. 205, Issue 2 https://doi.org/10.1016/j.cam.2006.02.053	journal	August 2007
Stochastic chemical kinetics and the total quasi-steady-state assumption: Application to the stochastic simulation algorithm and chemical master equation MacNamara, Shev; Bersani, Alberto M.; Burrage, Kevin The Journal of Chemical Physics, Vol. 129, Issue 9 https://doi.org/10.1063/1.2971036	journal	January 2008
Multiscale Modeling of Chemical Kinetics via the Master Equation MacNamara, Shev; Burrage, Kevin; Sidje, Roger B. Multiscale Modeling & Simulation, Vol. 6, Issue 4 https://doi.org/10.1137/060678154	journal	January 2008
Inexact Uniformization Method for Computing Transient Distributions of Markov Chains Sidje, Roger B.; Burrage, Kevin; MacNamara, Shev SIAM Journal on Scientific Computing, Vol. 29, Issue 6 https://doi.org/10.1137/060662629	journal	January 2007
A modified uniformization method for the solution of the chemical master equation Zhang, Jingwei; Watson, Layne T.; Cao, Yang Computers & Mathematics with Applications, Vol. 59, Issue 1 https://doi.org/10.1016/j.camwa.2009.04.021	journal	January 2010
Reduction and solution of the chemical master equation using time scale separation and finite state projection Peleš, Slaven; Munsky, Brian; Khammash, Mustafa The Journal of Chemical Physics, Vol. 125, Issue 20 https://doi.org/10.1063/1.2397685	journal	November 2006
Adaptive Discrete Galerkin Methods Applied to the Chemical Master Equation Deuflhard, P.; Huisinga, W.; Jahnke, T. SIAM Journal on Scientific Computing, Vol. 30, Issue 6 https://doi.org/10.1137/070689759	journal	January 2008
Spectral approximation of solutions to the chemical master equation Engblom, Stefan Journal of Computational and Applied Mathematics, Vol. 229, Issue 1 https://doi.org/10.1016/j.cam.2008.10.029	journal	July 2009
Radial Basis Function Collocation for the Chemical Master Equation Zhang, Jingwei; Watson, Layne T.; Beattie, Christopher A. International Journal of Computational Methods, Vol. 07, Issue 03 https://doi.org/10.1142/S0219876210002234	journal	September 2010
Solving chemical master equations by adaptive wavelet compression Jahnke, Tobias; Udrescu, Tudor Journal of Computational Physics, Vol. 229, Issue 16 https://doi.org/10.1016/j.jcp.2010.04.015	journal	August 2010
Chemical Master Equation and Langevin regimes for a gene transcription model Khanin, Raya; Higham, Desmond J. Theoretical Computer Science, Vol. 408, Issue 1 https://doi.org/10.1016/j.tcs.2008.07.007	journal	November 2008
Fokker–Planck approximation of the master equation in molecular biology Sjöberg, Paul; Lötstedt, Per; Elf, Johan Computing and Visualization in Science, Vol. 12, Issue 1 https://doi.org/10.1007/s00791-006-0045-6	journal	February 2007
Accurate hybrid stochastic simulation of a system of coupled chemical or biochemical reactions Salis, Howard; Kaznessis, Yiannis The Journal of Chemical Physics, Vol. 122, Issue 5 https://doi.org/10.1063/1.1835951	journal	February 2005
On the origins of approximations for stochastic chemical kinetics Haseltine, Eric L.; Rawlings, James B. The Journal of Chemical Physics, Vol. 123, Issue 16 https://doi.org/10.1063/1.2062048	journal	October 2005
Hybrid method for the chemical master equation Hellander, Andreas; Lötstedt, Per Journal of Computational Physics, Vol. 227, Issue 1 https://doi.org/10.1016/j.jcp.2007.07.020	journal	November 2007
StochKit2: software for discrete stochastic simulation of biochemical systems with events Sanft, K. R.; Wu, S.; Roh, M. Bioinformatics, Vol. 27, Issue 17 https://doi.org/10.1093/bioinformatics/btr401	journal	July 2011
Mechanisms of noise-resistance in genetic oscillators Vilar, J. M. G.; Kueh, H. Y.; Barkai, N. Proceedings of the National Academy of Sciences, Vol. 99, Issue 9 https://doi.org/10.1073/pnas.092133899	journal	April 2002
Near-Critical Phenomena in Intracellular Metabolite Pools Elf, Johan; Paulsson, Johan; Berg, Otto G. Biophysical Journal, Vol. 84, Issue 1 https://doi.org/10.1016/S0006-3495(03)74839-5	journal	January 2003
Towards the ultimate conservative difference scheme. V. A second-order sequel to Godunov's method van Leer, Bram Journal of Computational Physics, Vol. 32, Issue 1 https://doi.org/10.1016/0021-9991(79)90145-1	journal	July 1979
Weak solutions of nonlinear hyperbolic equations and their numerical computation Lax, Peter D. Communications on Pure and Applied Mathematics, Vol. 7, Issue 1 https://doi.org/10.1002/cpa.3160070112	journal	February 1954
High resolution schemes for hyperbolic conservation laws Harten, Ami Journal of Computational Physics, Vol. 49, Issue 3 https://doi.org/10.1016/0021-9991(83)90136-5	journal	March 1983
Python for Scientific Computing Oliphant, Travis E. Computing in Science & Engineering, Vol. 9, Issue 3 https://doi.org/10.1109/MCSE.2007.58	journal	January 2007

Cited By (3)

Approximation and inference methods for stochastic biochemical kinetics—a tutorial review Schnoerr, David; Sanguinetti, Guido; Grima, Ramon Journal of Physics A: Mathematical and Theoretical, Vol. 50, Issue 9 https://doi.org/10.1088/1751-8121/aa54d9	journal	January 2017
Hybrid framework for the simulation of stochastic chemical kinetics Duncan, Andrew; Erban, Radek; Zygalakis, Konstantinos Journal of Computational Physics, Vol. 326 https://doi.org/10.1016/j.jcp.2016.08.034	journal	December 2016
Approximate Numerical Integration of the Chemical Master Equation for Stochastic Reaction Networks Mikeev, Linar; Sandmann, Werner arXiv https://doi.org/10.48550/arxiv.1907.10245	preprint	January 2019

Similar Records

Hybrid discrete/continuum algorithms for stochastic reaction networks

Journal Article · Thu Jan 15 00:00:00 EST 2015 · Journal of Computational Physics · OSTI ID:1121280

Safta, Cosmin; Sargsyan, Khachik; Debusschere, Bert

Adaptive hybrid simulations for multiscale stochastic reaction networks

Journal Article · Wed Jan 21 00:00:00 EST 2015 · Journal of Chemical Physics · OSTI ID:1121280

Hepp, Benjamin; Gupta, Ankit; Khammash, Mustafa

A master equation and moment approach for biochemical systems with creation-time-dependent bimolecular rate functions

Journal Article · Sun Dec 07 00:00:00 EST 2014 · Journal of Chemical Physics · OSTI ID:1121280

El-Samad, Hana

Related Subjects

97 MATHEMATICS AND COMPUTING
Chemical Master Equation
Fokker–Planck equation
finite volume
Flux splitting
hybrid discrete-continuum models

Title: Hybrid discrete/continuum algorithms for stochastic reaction networks

Citation Formats

References (38)

Cited By (3)

Similar Records

Related Subjects