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

Title: Scaling methods for accelerating kinetic Monte Carlo simulations of chemical reaction networks

Abstract

Various kinetic Monte Carlo algorithms become inefficient when some of the population sizes in a system are large, which gives rise to a large number of reaction events per unit time. In this work, we present a new acceleration algorithm based on adaptive and heterogeneous scaling of reaction rates and stoichiometric coefficients. The algorithm is conceptually related to the commonly used idea of accelerating a stochastic simulation by considering a subvolume λΩ (0 < λ < 1) within a system of interest, which reduces the number of reaction events per unit time occurring in a simulation by a factor 1/λ at the cost of greater error in unbiased estimates of first moments and biased overestimates of second moments. Our new approach offers two unique benefits. First, scaling is adaptive and heterogeneous, which eliminates the pitfall of overaggressive scaling. Second, there is no need for an a priori classification of populations as discrete or continuous (as in a hybrid method), which is problematic when discreteness of a chemical species changes during a simulation. The method requires specification of only a single algorithmic parameter, Nc, a global critical population size above which populations are effectively scaled down to increase simulation efficiency. Themore » method, which we term partial scaling, is implemented in the open-source BioNetGen software package. We demonstrate that partial scaling can significantly accelerate simulations without significant loss of accuracy for several published models of biological systems. Finally, these models characterize activation of the mitogen-activated protein kinase ERK, prion protein aggregation, and T-cell receptor signaling.« less

Authors:
ORCiD logo [1]; ORCiD logo [1]; ORCiD logo [1]
+ Show Author Affiliations
  1. Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
Publication Date:
Research Org.:
Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)
Sponsoring Org.:
USDOE National Nuclear Security Administration (NNSA); USDOE Laboratory Directed Research and Development (LDRD) Program
OSTI Identifier:
1544696
Alternate Identifier(s):
OSTI ID: 1529038
Report Number(s):
LA-UR-19-22745
Journal ID: ISSN 0021-9606
Grant/Contract Number:  
89233218CNA000001; Center for Nonlinear Studies
Resource Type:
Accepted Manuscript
Journal Name:
Journal of Chemical Physics
Additional Journal Information:
Journal Volume: 150; Journal Issue: 24; Journal ID: ISSN 0021-9606
Publisher:
American Institute of Physics (AIP)
Country of Publication:
United States
Language:
English
Subject:
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CHEMISTRY

Citation Formats

Lin, Yen Ting, Feng, Song, and Hlavacek, William Scott. Scaling methods for accelerating kinetic Monte Carlo simulations of chemical reaction networks. United States: N. p., 2019. Web. doi:10.1063/1.5096774.
Copy to clipboard
Lin, Yen Ting, Feng, Song, & Hlavacek, William Scott. Scaling methods for accelerating kinetic Monte Carlo simulations of chemical reaction networks. United States. https://doi.org/10.1063/1.5096774
Copy to clipboard
Lin, Yen Ting, Feng, Song, and Hlavacek, William Scott. Mon . "Scaling methods for accelerating kinetic Monte Carlo simulations of chemical reaction networks". United States. https://doi.org/10.1063/1.5096774. https://www.osti.gov/servlets/purl/1544696.
Copy to clipboard
@article{osti_1544696,
title = {Scaling methods for accelerating kinetic Monte Carlo simulations of chemical reaction networks},
author = {Lin, Yen Ting and Feng, Song and Hlavacek, William Scott},
abstractNote = {Various kinetic Monte Carlo algorithms become inefficient when some of the population sizes in a system are large, which gives rise to a large number of reaction events per unit time. In this work, we present a new acceleration algorithm based on adaptive and heterogeneous scaling of reaction rates and stoichiometric coefficients. The algorithm is conceptually related to the commonly used idea of accelerating a stochastic simulation by considering a subvolume λΩ (0 < λ < 1) within a system of interest, which reduces the number of reaction events per unit time occurring in a simulation by a factor 1/λ at the cost of greater error in unbiased estimates of first moments and biased overestimates of second moments. Our new approach offers two unique benefits. First, scaling is adaptive and heterogeneous, which eliminates the pitfall of overaggressive scaling. Second, there is no need for an a priori classification of populations as discrete or continuous (as in a hybrid method), which is problematic when discreteness of a chemical species changes during a simulation. The method requires specification of only a single algorithmic parameter, Nc, a global critical population size above which populations are effectively scaled down to increase simulation efficiency. The method, which we term partial scaling, is implemented in the open-source BioNetGen software package. We demonstrate that partial scaling can significantly accelerate simulations without significant loss of accuracy for several published models of biological systems. Finally, these models characterize activation of the mitogen-activated protein kinase ERK, prion protein aggregation, and T-cell receptor signaling.},
doi = {10.1063/1.5096774},
journal = {Journal of Chemical Physics},
number = 24,
volume = 150,
place = {United States},
year = {Mon Jun 24 00:00:00 EDT 2019},
month = {Mon Jun 24 00:00:00 EDT 2019}
}
Copy to clipboard
Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record
https://doi.org/10.1063/1.5096774
Copyright Statement
Other availability
Search WorldCat Search WorldCat to find libraries that may hold this journal
Citation Metrics:
Cited by: 2 works
Citation information provided by
Web of Science

Figures / Tables:

FIG. 1 FIG. 1: Simulations based on Eqs. (1). In the six panels at left (a–f), we compare stochastic sample paths found using an SSA to the corresponding deterministic trajectories found by numerically integrating the ODEs in Eq. (2). We consider a range of system sizes (without changing intensive parameters): Ω =more » 104 (a and b), 102 (c and d), and 3 (e and f). The model parameters are $κ_1$ = 3, $κ_2$ = 300, and $κ_3$ = 1.5. In the top panels (a, c and e), we compare the random variable $N_1/Ω$ to the deterministic quantity $n_1$. Similarly, in the bottom panels (b, d and f), we compare $N_2/Ω$ to $n_2$. For panels (a–f), as indicated by the legend of each panel, we plot a single stochastic sample path, the first moment estimated by averaging over 500 sample paths, and the corresponding deterministic trajectory. In panels (g and h), we plot the marginal stationary distributions for $N_1/Ω$ and $N_2/Ω$, each measured from 10 5 sample paths. Note that, when Ω = 3, the probability distribution of $N_1/Ω$ is skewed to the right (g), leading to a first moment estimation that deviates noticeably from the continuum limit (e). Time and volume each have arbitrary units (a.u.).« less
All figures and tables (9 total)
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:

Stochastic Simulation of Chemical Kinetics
journal, May 2007

It’s a noisy business! Genetic regulation at the nanomolar scale
journal, February 1999

Generalizing Gillespie’s Direct Method to Enable Network-Free Simulations
journal, March 2018

  • Suderman, Ryan; Mitra, Eshan D.; Lin, Yen Ting
  • Bulletin of Mathematical Biology, Vol. 81, Issue 8
  • DOI: 10.1007/s11538-018-0418-2

Rule-based modeling: a computational approach for studying biomolecular site dynamics in cell signaling systems: Computational approach for studying biomolecular site dynamics in cell signaling systems
journal, September 2013

  • Chylek, Lily A.; Harris, Leonard A.; Tung, Chang-Shung
  • Wiley Interdisciplinary Reviews: Systems Biology and Medicine, Vol. 6, Issue 1
  • DOI: 10.1002/wsbm.1245

Kinetic Monte Carlo method for rule-based modeling of biochemical networks
journal, September 2008

Efficient modeling, simulation and coarse-graining of biological complexity with NFsim
journal, December 2010

  • Sneddon, Michael W.; Faeder, James R.; Emonet, Thierry
  • Nature Methods, Vol. 8, Issue 2
  • DOI: 10.1038/nmeth.1546

Specification, annotation, visualization and simulation of a large rule-based model for ERBB receptor signaling
journal, January 2012

  • Creamer, Matthew S.; Stites, Edward C.; Aziz, Meraj
  • BMC Systems Biology, Vol. 6, Issue 1
  • DOI: 10.1186/1752-0509-6-107

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

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

Breakdown of Fast-Slow Analysis in an Excitable System with Channel Noise
journal, September 2013

Transcriptional Bursting Diversifies the Behaviour of a Toggle Switch: Hybrid Simulation of Stochastic Gene Expression
journal, January 2013

  • Bokes, Pavol; King, John R.; Wood, Andrew T. A.
  • Bulletin of Mathematical Biology, Vol. 75, Issue 2
  • DOI: 10.1007/s11538-013-9811-z

Stochastic hybrid model of spontaneous dendritic NMDA spikes
journal, January 2014

Path-Integral Methods for Analyzing the Effects of Fluctuations in Stochastic Hybrid Neural Networks
journal, February 2015

Gene expression dynamics with stochastic bursts: Construction and exact results for a coarse-grained model
journal, February 2016

Bursting noise in gene expression dynamics: linking microscopic and mesoscopic models
journal, January 2016

  • Lin, Yen Ting; Galla, Tobias
  • Journal of The Royal Society Interface, Vol. 13, Issue 114
  • DOI: 10.1098/rsif.2015.0772

Stochastic switching in biology: from genotype to phenotype
journal, February 2017

  • Bressloff, Paul C.
  • Journal of Physics A: Mathematical and Theoretical, Vol. 50, Issue 13
  • DOI: 10.1088/1751-8121/aa5db4

Feynman-Kac formula for stochastic hybrid systems
journal, January 2017

Efficient analysis of stochastic gene dynamics in the non-adiabatic regime using piecewise deterministic Markov processes
journal, January 2018

  • Lin, Yen Ting; Buchler, Nicolas E.
  • Journal of The Royal Society Interface, Vol. 15, Issue 138
  • DOI: 10.1098/rsif.2017.0804

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

Relaxation oscillations and hierarchy of feedbacks in MAPK signaling
journal, January 2017

  • Kochańczyk, Marek; Kocieniewski, Paweł; Kozłowska, Emilia
  • Scientific Reports, Vol. 7, Issue 1
  • DOI: 10.1038/srep38244

Dynamics of the nucleated polymerization model of prion replication
journal, February 2007

Stochastic effects and bistability in T cell receptor signaling
journal, September 2008

  • Lipniacki, Tomasz; Hat, Beata; Faeder, James R.
  • Journal of Theoretical Biology, Vol. 254, Issue 1
  • DOI: 10.1016/j.jtbi.2008.05.001

BioNetGen 2.2: advances in rule-based modeling
journal, July 2016

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

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

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

Stochastic Processes and Statistical Physics
journal, July 1949

Extinction Times for Birth-Death Processes: Exact Results, Continuum Asymptotics, and the Failure of the Fokker--Planck Approximation
journal, January 2005

  • Doering, Charles R.; Sargsyan, Khachik V.; Sander, Leonard M.
  • Multiscale Modeling & Simulation, Vol. 3, Issue 2
  • DOI: 10.1137/030602800

Features of Fast Living: On the Weak Selection for Longevity in Degenerate Birth-Death Processes
journal, April 2012

  • Lin, Yen Ting; Kim, Hyejin; Doering, Charles R.
  • Journal of Statistical Physics, Vol. 148, Issue 4
  • DOI: 10.1007/s10955-012-0479-9

Demographic stochasticity and evolution of dispersion I. Spatially homogeneous environments
journal, March 2014

  • Lin, Yen Ting; Kim, Hyejin; Doering, Charles R.
  • Journal of Mathematical Biology, Vol. 70, Issue 3
  • DOI: 10.1007/s00285-014-0776-9

Demographic stochasticity and evolution of dispersion II: Spatially inhomogeneous environments
journal, March 2014

  • Lin, Yen Ting; Kim, Hyejin; Doering, Charles R.
  • Journal of Mathematical Biology, Vol. 70, Issue 3
  • DOI: 10.1007/s00285-014-0756-0

A Power Series Expansion of the Master Equation
journal, April 1961

  • Kampen, N. G. van
  • Canadian Journal of Physics, Vol. 39, Issue 4
  • DOI: 10.1139/p61-056

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

Self-Consistent Proteomic Field Theory of Stochastic Gene Switches
journal, February 2005

Optimal path to epigenetic switching
journal, January 2005

  • Roma, David Marin; O’Flanagan, Ruadhan A.; Ruckenstein, Andrei E.
  • Physical Review E, Vol. 71, Issue 1
  • DOI: 10.1103/physreve.71.011902

Chemical Models of Genetic Toggle Switches †
journal, April 2005

  • Warren, Patrick B.; ten Wolde, Pieter Rein
  • The Journal of Physical Chemistry B, Vol. 109, Issue 14
  • DOI: 10.1021/jp045523y

Determining the Stability of Genetic Switches: Explicitly Accounting for mRNA Noise
journal, June 2011

Stability and Multiattractor Dynamics of a Toggle Switch Based on a Two-Stage Model of Stochastic Gene Expression
journal, January 2012

Tristability in Cancer-Associated MicroRNA-TF Chimera Toggle Switch
journal, May 2013

  • Lu, Mingyang; Jolly, Mohit Kumar; Gomoto, Ryan
  • The Journal of Physical Chemistry B, Vol. 117, Issue 42
  • DOI: 10.1021/jp403156m

Automatic generation of cellular reaction networks with Moleculizer 1.0
journal, January 2005

  • Lok, Larry; Brent, Roger
  • Nature Biotechnology, Vol. 23, Issue 1
  • DOI: 10.1038/nbt1054

Rule-based modeling of biochemical networks
journal, January 2005

  • Faeder, James R.; Blinov, Michael L.; Goldstein, Byron
  • Complexity, Vol. 10, Issue 4
  • DOI: 10.1002/cplx.20074

The Systems Biology Markup Language (SBML): Language Specification for Level 3 Version 2 Core
journal, March 2018

  • Hucka, Michael; Bergmann, Frank T.; Dräger, Andreas
  • Journal of Integrative Bioinformatics, Vol. 15, Issue 1
  • DOI: 10.1515/jib-2017-0081

Probability-Weighted Dynamic Monte Carlo Method for Reaction Kinetics Simulations
journal, November 2001

  • Resat, Haluk; Wiley, H. Steven; Dixon, David A.
  • The Journal of Physical Chemistry B, Vol. 105, Issue 44
  • DOI: 10.1021/jp011404w

Using Equation-Free Computation to Accelerate Network-Free Stochastic Simulation of Chemical Kinetics
journal, May 2018

  • Lin, Yen Ting; Chylek, Lily A.; Lemons, Nathan W.
  • The Journal of Physical Chemistry B, Vol. 122, Issue 24
  • DOI: 10.1021/acs.jpcb.8b02960

BioNetFit: a fitting tool compatible with BioNetGen, NFsim and distributed computing environments
journal, November 2015

Phosphorylation Site Dynamics of Early T-cell Receptor Signaling
journal, August 2014

Multistate modeling and simulation for regulatory networks
conference, December 2010

  • Liu, Zhen; Mobassera, Umme Juka; Shaffer, Clifford A.
  • 2010 Winter Simulation Conference - (WSC 2010), Proceedings of the 2010 Winter Simulation Conference
  • DOI: 10.1109/WSC.2010.5679123

Multivariate structural statistics in natural history
journal, May 1974

Fokker-Planck Equation
journal, April 1963

  • Desloge, Edward A.
  • American Journal of Physics, Vol. 31, Issue 4
  • DOI: 10.1119/1.1969424

Determining the stability of genetic switches: explicitly accounting for mRNA noise
text, January 2011

Breakdown of fast-slow analysis in an excitable system with channel noise
text, January 2013

Optimal Path to Epigenetic Switching
text, January 2004

Phosphorylation Site Dynamics of Early T-cell Receptor Signaling
journal, August 2014

    Sort by:
    [ × clear filter / sort ]

    Figures / Tables found in this record:

    FIG. 1 (p. 10)figure
    FIG. 2 (p. 12)figure
    Algorithm 1 (p. 18)figure
    FIG. 3 (p. 22)figure
    FIG. 4 (p. 24)figure
    FIG. 5 (p. 25)figure
    TABLE I (p. 27)table
    FIG. 6 (p. 39)figure
    FIG. 7 (p. 40)figure
      [ × clear filter / sort ]
      Figures/Tables have been extracted from DOE-funded journal article accepted manuscripts.

      Similar Records in DOE PAGES and OSTI.GOV collections: