Switching and diffusion models for gene regulation networks

Somkid Intep, Desmond J. Higham, X. Mao

Research output: Contribution to journalArticle

6 Citations (Scopus)

Abstract

We analyze a hierarchy of three regimes for modeling gene regulation. The most complete model is a continuous time, discrete state space, Markov jump process. An intermediate 'switch plus diffusion' model takes the form of a stochastic differential equation driven by an independent continuous time Markov switch. In the third 'switch plus ODE' model the switch remains but the diffusion is removed. The latter two models allow for multi-scale simulation where, for the sake of computational efficiency, system components are treated differently according to their abundance. The 'switch plus ODE' regime was proposed by Paszek (Modeling stochasticity in gene regulation: characterization in the terms of the underlying distribution function, Bulletin of Mathematical Biology, 2007), who analyzed the steady state behavior, showing that the mean was preserved but the variance only approximated that of the full model. Here, we show that the tools of stochastic calculus can be used to analyze first and second moments for all time. A technical issue to be addressed is that the state space for the discrete-valued switch is infinite. We show that the new 'switch plus diffusion' regime preserves the biologically relevant measures of mean and variance, whereas the 'switch plus ODE' model uniformly underestimates the variance in the protein level. We also show that, for biologically relevant parameters, the transient behaviour can differ significantly from the steady state, justifying our time-dependent analysis. Extra computational results are also given for a protein dimerization model that is beyond the scope of the current analysis.
LanguageEnglish
Pages30-45
Number of pages16
JournalMultiscale Modeling and Simulation: A SIAM Interdisciplinary Journal
Volume8
Issue number1
Early online date2 Sep 2009
DOIs
Publication statusPublished - 2009

Fingerprint

Gene Regulation
gene expression
Diffusion Model
Gene expression
Switch
switches
Switches
gene
State Space
Model
protein
Mathematical Biology
Markov Jump Processes
proteins
Proteins
Protein
Multiscale Simulation
Stochastic Calculus
Markov processes
stochasticity

Keywords

  • diffusion
  • hybrid model
  • Gillespie’s algorithm
  • Ito lemma
  • Markov chain
  • slow scale simulation
  • stochastic simulation algorithm
  • transcription
  • tran-sition rate
  • translation

Cite this

@article{68d415decca54c53b1231ad555706511,
title = "Switching and diffusion models for gene regulation networks",
abstract = "We analyze a hierarchy of three regimes for modeling gene regulation. The most complete model is a continuous time, discrete state space, Markov jump process. An intermediate 'switch plus diffusion' model takes the form of a stochastic differential equation driven by an independent continuous time Markov switch. In the third 'switch plus ODE' model the switch remains but the diffusion is removed. The latter two models allow for multi-scale simulation where, for the sake of computational efficiency, system components are treated differently according to their abundance. The 'switch plus ODE' regime was proposed by Paszek (Modeling stochasticity in gene regulation: characterization in the terms of the underlying distribution function, Bulletin of Mathematical Biology, 2007), who analyzed the steady state behavior, showing that the mean was preserved but the variance only approximated that of the full model. Here, we show that the tools of stochastic calculus can be used to analyze first and second moments for all time. A technical issue to be addressed is that the state space for the discrete-valued switch is infinite. We show that the new 'switch plus diffusion' regime preserves the biologically relevant measures of mean and variance, whereas the 'switch plus ODE' model uniformly underestimates the variance in the protein level. We also show that, for biologically relevant parameters, the transient behaviour can differ significantly from the steady state, justifying our time-dependent analysis. Extra computational results are also given for a protein dimerization model that is beyond the scope of the current analysis.",
keywords = "diffusion, hybrid model, Gillespie’s algorithm, Ito lemma, Markov chain, slow scale simulation, stochastic simulation algorithm, transcription, tran-sition rate, translation",
author = "Somkid Intep and Higham, {Desmond J.} and X. Mao",
year = "2009",
doi = "10.1137/080735412",
language = "English",
volume = "8",
pages = "30--45",
journal = "Multiscale Modeling and Simulation: A SIAM Interdisciplinary Journal",
issn = "1540-3459",
number = "1",

}

Switching and diffusion models for gene regulation networks. / Intep, Somkid; Higham, Desmond J.; Mao, X.

In: Multiscale Modeling and Simulation: A SIAM Interdisciplinary Journal , Vol. 8, No. 1, 2009, p. 30-45.

Research output: Contribution to journalArticle

TY - JOUR

T1 - Switching and diffusion models for gene regulation networks

AU - Intep, Somkid

AU - Higham, Desmond J.

AU - Mao, X.

PY - 2009

Y1 - 2009

N2 - We analyze a hierarchy of three regimes for modeling gene regulation. The most complete model is a continuous time, discrete state space, Markov jump process. An intermediate 'switch plus diffusion' model takes the form of a stochastic differential equation driven by an independent continuous time Markov switch. In the third 'switch plus ODE' model the switch remains but the diffusion is removed. The latter two models allow for multi-scale simulation where, for the sake of computational efficiency, system components are treated differently according to their abundance. The 'switch plus ODE' regime was proposed by Paszek (Modeling stochasticity in gene regulation: characterization in the terms of the underlying distribution function, Bulletin of Mathematical Biology, 2007), who analyzed the steady state behavior, showing that the mean was preserved but the variance only approximated that of the full model. Here, we show that the tools of stochastic calculus can be used to analyze first and second moments for all time. A technical issue to be addressed is that the state space for the discrete-valued switch is infinite. We show that the new 'switch plus diffusion' regime preserves the biologically relevant measures of mean and variance, whereas the 'switch plus ODE' model uniformly underestimates the variance in the protein level. We also show that, for biologically relevant parameters, the transient behaviour can differ significantly from the steady state, justifying our time-dependent analysis. Extra computational results are also given for a protein dimerization model that is beyond the scope of the current analysis.

AB - We analyze a hierarchy of three regimes for modeling gene regulation. The most complete model is a continuous time, discrete state space, Markov jump process. An intermediate 'switch plus diffusion' model takes the form of a stochastic differential equation driven by an independent continuous time Markov switch. In the third 'switch plus ODE' model the switch remains but the diffusion is removed. The latter two models allow for multi-scale simulation where, for the sake of computational efficiency, system components are treated differently according to their abundance. The 'switch plus ODE' regime was proposed by Paszek (Modeling stochasticity in gene regulation: characterization in the terms of the underlying distribution function, Bulletin of Mathematical Biology, 2007), who analyzed the steady state behavior, showing that the mean was preserved but the variance only approximated that of the full model. Here, we show that the tools of stochastic calculus can be used to analyze first and second moments for all time. A technical issue to be addressed is that the state space for the discrete-valued switch is infinite. We show that the new 'switch plus diffusion' regime preserves the biologically relevant measures of mean and variance, whereas the 'switch plus ODE' model uniformly underestimates the variance in the protein level. We also show that, for biologically relevant parameters, the transient behaviour can differ significantly from the steady state, justifying our time-dependent analysis. Extra computational results are also given for a protein dimerization model that is beyond the scope of the current analysis.

KW - diffusion

KW - hybrid model

KW - Gillespie’s algorithm

KW - Ito lemma

KW - Markov chain

KW - slow scale simulation

KW - stochastic simulation algorithm

KW - transcription

KW - tran-sition rate

KW - translation

U2 - 10.1137/080735412

DO - 10.1137/080735412

M3 - Article

VL - 8

SP - 30

EP - 45

JO - Multiscale Modeling and Simulation: A SIAM Interdisciplinary Journal

T2 - Multiscale Modeling and Simulation: A SIAM Interdisciplinary Journal

JF - Multiscale Modeling and Simulation: A SIAM Interdisciplinary Journal

SN - 1540-3459

IS - 1

ER -