Parallel replica dynamics method for bistable stochastic reaction networks: Simulation and sensitivity analysis

Wang, Ting; Plecháč, Petr

doi:10.1063/1.5017955

Title: Parallel replica dynamics method for bistable stochastic reaction networks: Simulation and sensitivity analysis

Abstract

Stochastic reaction networks that exhibit bistable behavior are common in systems biology, materials science, and catalysis. Sampling of stationary distributions is crucial for understanding and characterizing the long-time dynamics of bistable stochastic dynamical systems. However, simulations are often hindered by the insufficient sampling of rare transitions between the two metastable regions. In this paper, we apply the parallel replica method for a continuous time Markov chain in order to improve sampling of the stationary distribution in bistable stochastic reaction networks. The proposed method uses parallel computing to accelerate the sampling of rare transitions. Furthermore, it can be combined with the path-space information bounds for parametric sensitivity analysis. With the proposed methodology, we study three bistable biological networks: the Schlögl model, the genetic switch network, and the enzymatic futile cycle network. We demonstrate the algorithmic speedup achieved in these numerical benchmarks. More significant acceleration is expected when multi-core or graphics processing unit computer architectures and programming tools such as CUDA are employed

Authors:

Wang, Ting ^[1]; Plecháč, Petr ^[1]

Univ. of Delaware, Newark, DE (United States)

Publication Date:: Thu Dec 21 00:00:00 EST 2017

Research Org.:: Univ. of Delaware, Newark, DE (United States)

Sponsoring Org.:: USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR)

OSTI Identifier:: 1512929

Alternate Identifier(s):: OSTI ID: 1414491

Grant/Contract Number:: SC0010549

Resource Type:: Accepted Manuscript

Journal Name:: Journal of Chemical Physics

Additional Journal Information:: Journal Volume: 147; Journal Issue: 23; Journal ID: ISSN 0021-9606

Publisher:: American Institute of Physics (AIP)

Country of Publication:: United States

Language:: English

Subject:: 97 MATHEMATICS AND COMPUTING

Citation Formats


                    Wang, Ting, and Plecháč, Petr. Parallel replica dynamics method for bistable stochastic reaction networks: Simulation and sensitivity analysis.  United States: N. p., 2017. 
Web.  doi:10.1063/1.5017955.

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                    Wang, Ting, & Plecháč, Petr. Parallel replica dynamics method for bistable stochastic reaction networks: Simulation and sensitivity analysis.  United States.  https://doi.org/10.1063/1.5017955

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                    Wang, Ting, and Plecháč, Petr. Thu .  
"Parallel replica dynamics method for bistable stochastic reaction networks: Simulation and sensitivity analysis".  United States.  https://doi.org/10.1063/1.5017955.  https://www.osti.gov/servlets/purl/1512929.

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@article{osti_1512929,

  title        = {Parallel replica dynamics method for bistable stochastic reaction networks: Simulation and sensitivity analysis},

  author       = {Wang, Ting and Plecháč, Petr},

  abstractNote = {Stochastic reaction networks that exhibit bistable behavior are common in systems biology, materials science, and catalysis. Sampling of stationary distributions is crucial for understanding and characterizing the long-time dynamics of bistable stochastic dynamical systems. However, simulations are often hindered by the insufficient sampling of rare transitions between the two metastable regions. In this paper, we apply the parallel replica method for a continuous time Markov chain in order to improve sampling of the stationary distribution in bistable stochastic reaction networks. The proposed method uses parallel computing to accelerate the sampling of rare transitions. Furthermore, it can be combined with the path-space information bounds for parametric sensitivity analysis. With the proposed methodology, we study three bistable biological networks: the Schlögl model, the genetic switch network, and the enzymatic futile cycle network. We demonstrate the algorithmic speedup achieved in these numerical benchmarks. More significant acceleration is expected when multi-core or graphics processing unit computer architectures and programming tools such as CUDA are employed},

  doi          = {10.1063/1.5017955},

  journal      = {Journal of Chemical Physics},

  number       = 23,

  volume       = 147,

  place        = {United States},

  year         = {Thu Dec 21 00:00:00 EST 2017},

  month        = {Thu Dec 21 00:00:00 EST 2017}

}

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Cited by: 3 works

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Algorithm 1: Parallel replica algorithm.

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Works referenced in this record:

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Works referencing / citing this record:

Generalizing Parallel Replica Dynamics: Trajectory Fragments, Asynchronous Computing, and PDMPs
text, January 2018

Aristoff, David
arXiv
DOI: 10.48550/arxiv.1802.09444

Figures / Tables found in this record:

Figures/Tables have been extracted from DOE-funded journal article accepted manuscripts.

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Similar Records

Title: Parallel replica dynamics method for bistable stochastic reaction networks: Simulation and sensitivity analysis

Abstract

Citation Formats

Figures / Tables:

Stochastic dynamics and non-equilibrium thermodynamics of a bistable chemical system: the Schlögl model revisited journal, December 2008

Adaptively biased sequential importance sampling for rare events in reaction networks with comparison to exact solutions from finite buffer dCME method journal, July 2013

A generalized parallel replica dynamics journal, March 2015

Constructing the Energy Landscape for Genetic Switching System Driven by Intrinsic Noise journal, February 2014

Separation of time-scales and model reduction for stochastic reaction networks journal, April 2013

Accelerated Sensitivity Analysis in High-Dimensional Stochastic Reaction Networks journal, July 2015

State Space Truncation with Quantified Errors for Accurate Solutions to Discrete Chemical Master Equation journal, April 2016

The parallel replica method for computing equilibrium averages of Markov chains journal, January 2015

The finite state projection algorithm for the solution of the chemical master equation journal, January 2006

Stochastic amplification and signaling in enzymatic futile cycles through noise-induced bistability with oscillations journal, February 2005

Efficient computation of parameter sensitivities of discrete stochastic chemical reaction networks journal, January 2010

Detection of multistability, bifurcations, and hysteresis in a large class of biological positive-feedback systems journal, February 2004

Large fluctuations and optimal paths in chemical kinetics journal, April 1994

A mathematical formalization of the parallel replica dynamics journal, January 2012

A pathwise derivative approach to the computation of parameter sensitivities in discrete stochastic chemical systems journal, January 2012

Efficient stochastic sensitivity analysis of discrete event systems journal, February 2007

Path-Space Information Bounds for Uncertainty Quantification and Sensitivity Analysis of Stochastic Dynamics journal, January 2016

Exact stochastic simulation of coupled chemical reactions journal, December 1977

Optimal enumeration of state space of finitely buffered stochastic molecular networks and exact computation of steady state landscape probability journal, March 2008

Solutions of ordinary differential equations as limits of pure jump markov processes journal, April 1970

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

Accurate Chemical Master Equation Solution Using Multi-Finite Buffers journal, January 2016

Construction of a genetic toggle switch in Escherichia coli journal, January 2000

Efficiency of the Girsanov Transformation Approach for Parametric Sensitivity Analysis of Stochastic Chemical Kinetics journal, January 2016

An Efficient Finite Difference Method for Parameter Sensitivities of Continuous Time Markov Chains journal, January 2012

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

Noise-induced multistability in chemical systems: Discrete versus continuum modeling journal, April 2015

A relative entropy rate method for path space sensitivity analysis of stationary complex stochastic dynamics journal, February 2013

Robust, bistable patterning of the dorsal surface of the Drosophila embryo journal, July 2006

Exponential sensitivity of noise-driven switching in genetic networks journal, June 2008

The Parallel Replica Method for Simulating Long Trajectories of Markov Chains journal, August 2014

Large deviations for two-scale chemical kinetic processes journal, January 2017

The geometric minimum action method: A least action principle on the space of curves journal, January 2008

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

Robust, bistable patterning of the dorsal surface of the Drosophila embryo journal, July 2006

Accelerated Sensitivity Analysis in High-Dimensional Stochastic Reaction Networks text, January 2014

Generalizing Parallel Replica Dynamics: Trajectory Fragments, Asynchronous Computing, and PDMPs text, January 2018

Stochastic dynamics and non-equilibrium thermodynamics of a bistable chemical system: the Schlögl model revisited
journal, December 2008

Adaptively biased sequential importance sampling for rare events in reaction networks with comparison to exact solutions from finite buffer dCME method
journal, July 2013

A generalized parallel replica dynamics
journal, March 2015

Constructing the Energy Landscape for Genetic Switching System Driven by Intrinsic Noise
journal, February 2014

Separation of time-scales and model reduction for stochastic reaction networks
journal, April 2013

Accelerated Sensitivity Analysis in High-Dimensional Stochastic Reaction Networks
journal, July 2015

State Space Truncation with Quantified Errors for Accurate Solutions to Discrete Chemical Master Equation
journal, April 2016

The parallel replica method for computing equilibrium averages of Markov chains
journal, January 2015

The finite state projection algorithm for the solution of the chemical master equation
journal, January 2006

Stochastic amplification and signaling in enzymatic futile cycles through noise-induced bistability with oscillations
journal, February 2005

Efficient computation of parameter sensitivities of discrete stochastic chemical reaction networks
journal, January 2010

Detection of multistability, bifurcations, and hysteresis in a large class of biological positive-feedback systems
journal, February 2004

Large fluctuations and optimal paths in chemical kinetics
journal, April 1994

A mathematical formalization of the parallel replica dynamics
journal, January 2012

A pathwise derivative approach to the computation of parameter sensitivities in discrete stochastic chemical systems
journal, January 2012

Efficient stochastic sensitivity analysis of discrete event systems
journal, February 2007

Path-Space Information Bounds for Uncertainty Quantification and Sensitivity Analysis of Stochastic Dynamics
journal, January 2016

Exact stochastic simulation of coupled chemical reactions
journal, December 1977

Optimal enumeration of state space of finitely buffered stochastic molecular networks and exact computation of steady state landscape probability
journal, March 2008

Solutions of ordinary differential equations as limits of pure jump markov processes
journal, April 1970

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

Accurate Chemical Master Equation Solution Using Multi-Finite Buffers
journal, January 2016

Construction of a genetic toggle switch in Escherichia coli
journal, January 2000

Efficiency of the Girsanov Transformation Approach for Parametric Sensitivity Analysis of Stochastic Chemical Kinetics
journal, January 2016

An Efficient Finite Difference Method for Parameter Sensitivities of Continuous Time Markov Chains
journal, January 2012

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

Noise-induced multistability in chemical systems: Discrete versus continuum modeling
journal, April 2015

A relative entropy rate method for path space sensitivity analysis of stationary complex stochastic dynamics
journal, February 2013

Robust, bistable patterning of the dorsal surface of the Drosophila embryo
journal, July 2006

Exponential sensitivity of noise-driven switching in genetic networks
journal, June 2008

The Parallel Replica Method for Simulating Long Trajectories of Markov Chains
journal, August 2014

Large deviations for two-scale chemical kinetic processes
journal, January 2017

The geometric minimum action method: A least action principle on the space of curves
journal, January 2008

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

Robust, bistable patterning of the dorsal surface of the Drosophila embryo
journal, July 2006

Accelerated Sensitivity Analysis in High-Dimensional Stochastic Reaction Networks
text, January 2014

Generalizing Parallel Replica Dynamics: Trajectory Fragments, Asynchronous Computing, and PDMPs
text, January 2018