### Abstract

The dynamical solution of a well-mixed, nonlinear stochastic chemical kinetic system, described by the Master equation, may be exactly computed using the stochastic simulation algorithm. However, because the computational cost scales with the number of reaction occurrences, systems with one or more "fast" reactions become costly to simulate. This paper describes a hybrid stochastic method that partitions the system into subsets of fast and slow reactions, approximates the fast reactions as a continuous Markov process, using a chemical Langevin equation, and accurately describes the slow dynamics using the integral form of the "Next Reaction" variant of the stochastic simulation algorithm. The key innovation of this method is its mechanism of efficiently monitoring the occurrences of slow, discrete events while simultaneously simulating the dynamics of a continuous, stochastic or deterministic process. In addition, by introducing an approximation in which multiple slow reactions may occur within a time step of the numerical integration of the chemical Langevin equation, the hybrid stochastic method performs much faster with only a marginal decrease in accuracy. Multiple examples, including a biological pulse generator and a large-scale system benchmark, are simulated using the exact and proposed hybrid methods as well as, for comparison, a previous hybrid stochastic method. Probability distributions of the solutions are compared and the weak errors of the first two moments are computed. In general, these hybrid methods may be applied to the simulation of the dynamics of a system described by stochastic differential, ordinary differential, and Master equations.

Original language | English (US) |
---|---|

Article number | 054103 |

Journal | Journal of Chemical Physics |

Volume | 122 |

Issue number | 5 |

DOIs | |

State | Published - Jan 1 2005 |

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### All Science Journal Classification (ASJC) codes

- Physics and Astronomy(all)
- Physical and Theoretical Chemistry

### Cite this

*Journal of Chemical Physics*,

*122*(5), [054103]. https://doi.org/10.1063/1.1835951

}

*Journal of Chemical Physics*, vol. 122, no. 5, 054103. https://doi.org/10.1063/1.1835951

**Accurate hybrid stochastic simulation of a system of coupled chemical or biochemical reactions.** / Salis, Howard M.; Kaznessis, Yiannis.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Accurate hybrid stochastic simulation of a system of coupled chemical or biochemical reactions

AU - Salis, Howard M.

AU - Kaznessis, Yiannis

PY - 2005/1/1

Y1 - 2005/1/1

N2 - The dynamical solution of a well-mixed, nonlinear stochastic chemical kinetic system, described by the Master equation, may be exactly computed using the stochastic simulation algorithm. However, because the computational cost scales with the number of reaction occurrences, systems with one or more "fast" reactions become costly to simulate. This paper describes a hybrid stochastic method that partitions the system into subsets of fast and slow reactions, approximates the fast reactions as a continuous Markov process, using a chemical Langevin equation, and accurately describes the slow dynamics using the integral form of the "Next Reaction" variant of the stochastic simulation algorithm. The key innovation of this method is its mechanism of efficiently monitoring the occurrences of slow, discrete events while simultaneously simulating the dynamics of a continuous, stochastic or deterministic process. In addition, by introducing an approximation in which multiple slow reactions may occur within a time step of the numerical integration of the chemical Langevin equation, the hybrid stochastic method performs much faster with only a marginal decrease in accuracy. Multiple examples, including a biological pulse generator and a large-scale system benchmark, are simulated using the exact and proposed hybrid methods as well as, for comparison, a previous hybrid stochastic method. Probability distributions of the solutions are compared and the weak errors of the first two moments are computed. In general, these hybrid methods may be applied to the simulation of the dynamics of a system described by stochastic differential, ordinary differential, and Master equations.

AB - The dynamical solution of a well-mixed, nonlinear stochastic chemical kinetic system, described by the Master equation, may be exactly computed using the stochastic simulation algorithm. However, because the computational cost scales with the number of reaction occurrences, systems with one or more "fast" reactions become costly to simulate. This paper describes a hybrid stochastic method that partitions the system into subsets of fast and slow reactions, approximates the fast reactions as a continuous Markov process, using a chemical Langevin equation, and accurately describes the slow dynamics using the integral form of the "Next Reaction" variant of the stochastic simulation algorithm. The key innovation of this method is its mechanism of efficiently monitoring the occurrences of slow, discrete events while simultaneously simulating the dynamics of a continuous, stochastic or deterministic process. In addition, by introducing an approximation in which multiple slow reactions may occur within a time step of the numerical integration of the chemical Langevin equation, the hybrid stochastic method performs much faster with only a marginal decrease in accuracy. Multiple examples, including a biological pulse generator and a large-scale system benchmark, are simulated using the exact and proposed hybrid methods as well as, for comparison, a previous hybrid stochastic method. Probability distributions of the solutions are compared and the weak errors of the first two moments are computed. In general, these hybrid methods may be applied to the simulation of the dynamics of a system described by stochastic differential, ordinary differential, and Master equations.

UR - http://www.scopus.com/inward/record.url?scp=22944451159&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=22944451159&partnerID=8YFLogxK

U2 - 10.1063/1.1835951

DO - 10.1063/1.1835951

M3 - Article

C2 - 15740306

AN - SCOPUS:22944451159

VL - 122

JO - Journal of Chemical Physics

JF - Journal of Chemical Physics

SN - 0021-9606

IS - 5

M1 - 054103

ER -