Search Menu
DOE PAGES title logo U.S. Department of Energy
Office of Scientific and Technical Information
Search Scholarly Publications

Title: A hybrid multiscale Monte Carlo algorithm (HyMSMC) to cope with disparity in time scales and species populations in intracellular networks

Abstract

Background: The fundamental role that intrinsic stochasticity plays in cellular functions has been shown via numerous computational and experimental studies. In the face of such evidence, it is important that intracellular networks are simulated with stochastic algorithms that can capture molecular fluctuations. However, separation of time scales and disparity in species population, two common features of intracellular networks, make stochastic simulation of such networks computationally prohibitive. While recent work has addressed each of these challenges separately, a generic algorithm that can simultaneously tackle disparity in time scales and population scales in stochastic systems is currently lacking. In this paper, we propose the hybrid, multiscale Monte Carlo (HyMSMC) method that fills in this void. Results: The proposed HyMSMC method blends stochastic singular perturbation concepts, to deal with potential stiffness, with a hybrid of exact and coarse-grained stochastic algorithms, to cope with separation in population sizes. In addition, we introduce the computational singular perturbation (CSP) method as a means of systematically partitioning fast and slow networks and computing relaxation times for convergence. We also propose a new criteria of convergence of fast networks to stochastic low-dimensional manifolds, which further accelerates the algorithm. Conclusion: We use several prototype and biological examples, including amore » gene expression model displaying bistability, to demonstrate the efficiency, accuracy and applicability of the HyMSMC method. Bistable models serve as stringent tests for the success of multiscale MC methods and illustrate limitations of some literature methods.« less

Authors:
 [1];  [1];  [1]
+ Show Author Affiliations
  1. Univ. of Delaware, Newark, DE (United States). Dept. of Chemical Engineering
Publication Date:
Research Org.:
Johns Hopkins Univ., Baltimore, MD (United States); Univ. of Delaware, Newark, DE (United States)
Sponsoring Org.:
USDOE Office of Science (SC), Biological and Environmental Research (BER). Biological Systems Science Division
OSTI Identifier:
1626335
Grant/Contract Number:  
FG02-04ER25626
Resource Type:
Accepted Manuscript
Journal Name:
BMC Bioinformatics
Additional Journal Information:
Journal Volume: 8; Journal Issue: 1; Journal ID: ISSN 1471-2105
Publisher:
BioMed Central
Country of Publication:
United States
Language:
English
Subject:
59 BASIC BIOLOGICAL SCIENCES; 97 MATHEMATICS AND COMPUTING; Biochemistry & Molecular Biology; Biotechnology & Applied Microbiology; Mathematical & Computational Biology

Citation Formats

Samant, Asawari, Ogunnaike, Babatunde A., and Vlachos, Dionisios G. A hybrid multiscale Monte Carlo algorithm (HyMSMC) to cope with disparity in time scales and species populations in intracellular networks. United States: N. p., 2007. Web. doi:10.1186/1471-2105-8-175.
Copy to clipboard
Samant, Asawari, Ogunnaike, Babatunde A., & Vlachos, Dionisios G. A hybrid multiscale Monte Carlo algorithm (HyMSMC) to cope with disparity in time scales and species populations in intracellular networks. United States. https://doi.org/10.1186/1471-2105-8-175
Copy to clipboard
Samant, Asawari, Ogunnaike, Babatunde A., and Vlachos, Dionisios G. Thu . "A hybrid multiscale Monte Carlo algorithm (HyMSMC) to cope with disparity in time scales and species populations in intracellular networks". United States. https://doi.org/10.1186/1471-2105-8-175. https://www.osti.gov/servlets/purl/1626335.
Copy to clipboard
@article{osti_1626335,
title = {A hybrid multiscale Monte Carlo algorithm (HyMSMC) to cope with disparity in time scales and species populations in intracellular networks},
author = {Samant, Asawari and Ogunnaike, Babatunde A. and Vlachos, Dionisios G.},
abstractNote = {Background: The fundamental role that intrinsic stochasticity plays in cellular functions has been shown via numerous computational and experimental studies. In the face of such evidence, it is important that intracellular networks are simulated with stochastic algorithms that can capture molecular fluctuations. However, separation of time scales and disparity in species population, two common features of intracellular networks, make stochastic simulation of such networks computationally prohibitive. While recent work has addressed each of these challenges separately, a generic algorithm that can simultaneously tackle disparity in time scales and population scales in stochastic systems is currently lacking. In this paper, we propose the hybrid, multiscale Monte Carlo (HyMSMC) method that fills in this void. Results: The proposed HyMSMC method blends stochastic singular perturbation concepts, to deal with potential stiffness, with a hybrid of exact and coarse-grained stochastic algorithms, to cope with separation in population sizes. In addition, we introduce the computational singular perturbation (CSP) method as a means of systematically partitioning fast and slow networks and computing relaxation times for convergence. We also propose a new criteria of convergence of fast networks to stochastic low-dimensional manifolds, which further accelerates the algorithm. Conclusion: We use several prototype and biological examples, including a gene expression model displaying bistability, to demonstrate the efficiency, accuracy and applicability of the HyMSMC method. Bistable models serve as stringent tests for the success of multiscale MC methods and illustrate limitations of some literature methods.},
doi = {10.1186/1471-2105-8-175},
journal = {BMC Bioinformatics},
number = 1,
volume = 8,
place = {United States},
year = {Thu May 24 00:00:00 EDT 2007},
month = {Thu May 24 00:00:00 EDT 2007}
}
Copy to clipboard
Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record
https://doi.org/10.1186/1471-2105-8-175
Copyright Statement
Other availability
Search WorldCat Search WorldCat to find libraries that may hold this journal
Save / Share:
Export Metadata
Save to My Library
You must Sign In or Create an Account in order to save documents to your library.

Works referenced in this record:

Directed cell migration towards softer environments
journal, July 2022

Binomial distribution based τ-leap accelerated stochastic simulation
journal, January 2005

  • Chatterjee, Abhijit; Vlachos, Dionisios G.; Katsoulakis, Markos A.
  • The Journal of Chemical Physics, Vol. 122, Issue 2
  • DOI: 10.1063/1.1833357

Binomial leap methods for simulating stochastic chemical kinetics
journal, December 2004

  • Tian, Tianhai; Burrage, Kevin
  • The Journal of Chemical Physics, Vol. 121, Issue 21
  • DOI: 10.1063/1.1810475

Multiscale spatial Monte Carlo simulations: Multigriding, computational singular perturbation, and hierarchical stochastic closures
journal, February 2006

  • Chatterjee, Abhijit; Vlachos, Dionisios G.
  • The Journal of Chemical Physics, Vol. 124, Issue 6
  • DOI: 10.1063/1.2166380

Accurate hybrid stochastic simulation of a system of coupled chemical or biochemical reactions
journal, February 2005

  • Salis, Howard; Kaznessis, Yiannis
  • The Journal of Chemical Physics, Vol. 122, Issue 5
  • DOI: 10.1063/1.1835951

R-leaping: Accelerating the stochastic simulation algorithm by reaction leaps
journal, August 2006

  • Auger, Anne; Chatelain, Philippe; Koumoutsakos, Petros
  • The Journal of Chemical Physics, Vol. 125, Issue 8
  • DOI: 10.1063/1.2218339

The slow-scale stochastic simulation algorithm
journal, January 2005

  • Cao, Yang; Gillespie, Daniel T.; Petzold, Linda R.
  • The Journal of Chemical Physics, Vol. 122, Issue 1
  • DOI: 10.1063/1.1824902

Stochastic Gene Expression in a Single Cell
journal, August 2002

A general method for numerically simulating the stochastic time evolution of coupled chemical reactions
journal, December 1976

Approximate simulation of coupled fast and slow reactions for stochastic chemical kinetics
journal, October 2002

  • Haseltine, Eric L.; Rawlings, James B.
  • The Journal of Chemical Physics, Vol. 117, Issue 15
  • DOI: 10.1063/1.1505860

Stochastic chemical kinetics and the quasi-steady-state assumption: Application to the Gillespie algorithm
journal, March 2003

  • Rao, Christopher V.; Arkin, Adam P.
  • The Journal of Chemical Physics, Vol. 118, Issue 11
  • DOI: 10.1063/1.1545446

The chemical Langevin equation
journal, July 2000

  • Gillespie, Daniel T.
  • The Journal of Chemical Physics, Vol. 113, Issue 1
  • DOI: 10.1063/1.481811

The CSP method for simplifying kinetics
journal, April 1994

  • Lam, S. H.; Goussis, D. A.
  • International Journal of Chemical Kinetics, Vol. 26, Issue 4
  • DOI: 10.1002/kin.550260408

Stiffness in stochastic chemically reacting systems: The implicit tau-leaping method
journal, December 2003

  • Rathinam, Muruhan; Petzold, Linda R.; Cao, Yang
  • The Journal of Chemical Physics, Vol. 119, Issue 24
  • DOI: 10.1063/1.1627296

Efficient Exact Stochastic Simulation of Chemical Systems with Many Species and Many Channels
journal, March 2000

  • Gibson, Michael A.; Bruck, Jehoshua
  • The Journal of Physical Chemistry A, Vol. 104, Issue 9
  • DOI: 10.1021/jp993732q

Quasiequilibrium approximation of fast reaction kinetics in stochastic biochemical systems
journal, May 2005

  • Goutsias, John
  • The Journal of Chemical Physics, Vol. 122, Issue 18
  • DOI: 10.1063/1.1889434

Efficient step size selection for the tau-leaping simulation method
journal, January 2006

  • Cao, Yang; Gillespie, Daniel T.; Petzold, Linda R.
  • The Journal of Chemical Physics, Vol. 124, Issue 4
  • DOI: 10.1063/1.2159468

Higher order corrections in the approximation of low-dimensional manifolds and the construction of simplified problems with the CSP method
journal, November 2005

  • Valorani, Mauro; Goussis, Dimitris A.; Creta, Francesco
  • Journal of Computational Physics, Vol. 209, Issue 2
  • DOI: 10.1016/j.jcp.2005.03.033

Approximate accelerated stochastic simulation of chemically reacting systems
journal, July 2001

  • Gillespie, Daniel T.
  • The Journal of Chemical Physics, Vol. 115, Issue 4
  • DOI: 10.1063/1.1378322

Multiscale stochastic simulation algorithm with stochastic partial equilibrium assumption for chemically reacting systems
journal, July 2005

  • Cao, Yang; Gillespie, Dan; Petzold, Linda
  • Journal of Computational Physics, Vol. 206, Issue 2
  • DOI: 10.1016/j.jcp.2004.12.014

Nested stochastic simulation algorithm for chemical kinetic systems with disparate rates
journal, November 2005

  • E., Weinan; Liu, Di; Vanden-Eijnden, Eric
  • The Journal of Chemical Physics, Vol. 123, Issue 19
  • DOI: 10.1063/1.2109987

Stochasticity in Transcriptional Regulation: Origins, Consequences, and Mathematical Representations
journal, December 2001

Stochastic Gene Expression in a Single Cell
journal, August 2002

A general method for numerically simulating the stochastic time evolution of coupled chemical reactions
journal, December 1976

Exact stochastic simulation of coupled chemical reactions
journal, December 1977

  • Gillespie, Daniel T.
  • The Journal of Physical Chemistry, Vol. 81, Issue 25
  • DOI: 10.1021/j100540a008

Efficient Exact Stochastic Simulation of Chemical Systems with Many Species and Many Channels
journal, March 2000

  • Gibson, Michael A.; Bruck, Jehoshua
  • The Journal of Physical Chemistry A, Vol. 104, Issue 9
  • DOI: 10.1021/jp993732q

Approximate accelerated stochastic simulation of chemically reacting systems
journal, July 2001

  • Gillespie, Daniel T.
  • The Journal of Chemical Physics, Vol. 115, Issue 4
  • DOI: 10.1063/1.1378322

Binomial distribution based τ-leap accelerated stochastic simulation
journal, January 2005

  • Chatterjee, Abhijit; Vlachos, Dionisios G.; Katsoulakis, Markos A.
  • The Journal of Chemical Physics, Vol. 122, Issue 2
  • DOI: 10.1063/1.1833357

Binomial leap methods for simulating stochastic chemical kinetics
journal, December 2004

  • Tian, Tianhai; Burrage, Kevin
  • The Journal of Chemical Physics, Vol. 121, Issue 21
  • DOI: 10.1063/1.1810475

R-leaping: Accelerating the stochastic simulation algorithm by reaction leaps
journal, August 2006

  • Auger, Anne; Chatelain, Philippe; Koumoutsakos, Petros
  • The Journal of Chemical Physics, Vol. 125, Issue 8
  • DOI: 10.1063/1.2218339

Stiffness in stochastic chemically reacting systems: The implicit tau-leaping method
journal, December 2003

  • Rathinam, Muruhan; Petzold, Linda R.; Cao, Yang
  • The Journal of Chemical Physics, Vol. 119, Issue 24
  • DOI: 10.1063/1.1627296

Avoiding negative populations in explicit Poisson tau-leaping
journal, August 2005

  • Cao, Yang; Gillespie, Daniel T.; Petzold, Linda R.
  • The Journal of Chemical Physics, Vol. 123, Issue 5
  • DOI: 10.1063/1.1992473

A “partitioned leaping” approach for multiscale modeling of chemical reaction dynamics
journal, October 2006

  • Harris, Leonard A.; Clancy, Paulette
  • The Journal of Chemical Physics, Vol. 125, Issue 14
  • DOI: 10.1063/1.2354085

The slow-scale stochastic simulation algorithm
journal, January 2005

  • Cao, Yang; Gillespie, Daniel T.; Petzold, Linda R.
  • The Journal of Chemical Physics, Vol. 122, Issue 1
  • DOI: 10.1063/1.1824902

Multiscale stochastic simulation algorithm with stochastic partial equilibrium assumption for chemically reacting systems
journal, July 2005

  • Cao, Yang; Gillespie, Dan; Petzold, Linda
  • Journal of Computational Physics, Vol. 206, Issue 2
  • DOI: 10.1016/j.jcp.2004.12.014

Accurate hybrid stochastic simulation of a system of coupled chemical or biochemical reactions
journal, February 2005

  • Salis, Howard; Kaznessis, Yiannis
  • The Journal of Chemical Physics, Vol. 122, Issue 5
  • DOI: 10.1063/1.1835951

An equation-free probabilistic steady-state approximation: Dynamic application to the stochastic simulation of biochemical reaction networks
journal, December 2005

  • Salis, Howard; Kaznessis, Yiannis N.
  • The Journal of Chemical Physics, Vol. 123, Issue 21
  • DOI: 10.1063/1.2131050

Overcoming stiffness in stochastic simulation stemming from partial equilibrium: A multiscale Monte Carlo algorithm
journal, October 2005

  • Samant, A.; Vlachos, D. G.
  • The Journal of Chemical Physics, Vol. 123, Issue 14
  • DOI: 10.1063/1.2046628

Stochastic chemical kinetics and the quasi-steady-state assumption: Application to the Gillespie algorithm
journal, March 2003

  • Rao, Christopher V.; Arkin, Adam P.
  • The Journal of Chemical Physics, Vol. 118, Issue 11
  • DOI: 10.1063/1.1545446

Approximate simulation of coupled fast and slow reactions for stochastic chemical kinetics
journal, October 2002

  • Haseltine, Eric L.; Rawlings, James B.
  • The Journal of Chemical Physics, Vol. 117, Issue 15
  • DOI: 10.1063/1.1505860

Nested stochastic simulation algorithm for chemical kinetic systems with disparate rates
journal, November 2005

  • E., Weinan; Liu, Di; Vanden-Eijnden, Eric
  • The Journal of Chemical Physics, Vol. 123, Issue 19
  • DOI: 10.1063/1.2109987

Quasiequilibrium approximation of fast reaction kinetics in stochastic biochemical systems
journal, May 2005

  • Goutsias, John
  • The Journal of Chemical Physics, Vol. 122, Issue 18
  • DOI: 10.1063/1.1889434

The chemical Langevin equation
journal, July 2000

  • Gillespie, Daniel T.
  • The Journal of Chemical Physics, Vol. 113, Issue 1
  • DOI: 10.1063/1.481811

Numerical Techniques for Multi-Scale Dynamical Systems with Stochastic Effects
journal, January 2003

Multiscale spatial Monte Carlo simulations: Multigriding, computational singular perturbation, and hierarchical stochastic closures
journal, February 2006

  • Chatterjee, Abhijit; Vlachos, Dionisios G.
  • The Journal of Chemical Physics, Vol. 124, Issue 6
  • DOI: 10.1063/1.2166380

Using CSP to Understand Complex Chemical Kinetics
journal, March 1993

The CSP method for simplifying kinetics
journal, April 1994

  • Lam, S. H.; Goussis, D. A.
  • International Journal of Chemical Kinetics, Vol. 26, Issue 4
  • DOI: 10.1002/kin.550260408

Higher order corrections in the approximation of low-dimensional manifolds and the construction of simplified problems with the CSP method
journal, November 2005

  • Valorani, Mauro; Goussis, Dimitris A.; Creta, Francesco
  • Journal of Computational Physics, Vol. 209, Issue 2
  • DOI: 10.1016/j.jcp.2005.03.033

Efficient step size selection for the tau-leaping simulation method
journal, January 2006

  • Cao, Yang; Gillespie, Daniel T.; Petzold, Linda R.
  • The Journal of Chemical Physics, Vol. 124, Issue 4
  • DOI: 10.1063/1.2159468

A multi-algorithm, multi-timescale method for cell simulation
journal, January 2004

    Sort by:
    [ × clear filter / sort ]

    Works referencing / citing this record:

    Computational singular perturbation analysis of brain lactate metabolism
    journal, December 2019

    Slow-scale split-step tau-leap method for stiff stochastic chemical systems
    journal, December 2019

    • Reshniak, Viktor; Khaliq, Abdul; Voss, David
    • Journal of Computational and Applied Mathematics, Vol. 361
    • DOI: 10.1016/j.cam.2019.03.044

    Stochastic Kinetic Modeling of Vesicular Stomatitis Virus Intracellular Growth
    journal, May 2009

    • Hensel, Sebastian C.; Rawlings, James B.; Yin, John
    • Bulletin of Mathematical Biology, Vol. 71, Issue 7
    • DOI: 10.1007/s11538-009-9419-5

    Hybrid deterministic/stochastic simulation of complex biochemical systems
    journal, January 2017

    • Lecca, Paola; Bagagiolo, Fabio; Scarpa, Marina
    • Molecular BioSystems, Vol. 13, Issue 12
    • DOI: 10.1039/c7mb00426e

    Computational singular perturbation analysis of brain lactate metabolism
    journal, December 2019

    FERN – a Java framework for stochastic simulation and evaluation of reaction networks
    journal, August 2008

    • Erhard, Florian; Friedel, Caroline C.; Zimmer, Ralf
    • BMC Bioinformatics, Vol. 9, Issue 1
    • DOI: 10.1186/1471-2105-9-356
      Sort by:
      [ × clear filter / sort ]

      Similar Records in DOE PAGES and OSTI.GOV collections: