A solver for the stochastic master equation applied to gene regulatory networks

Hegland, Markus; Burden, Conrad J.; Santoso, Lucia Maria; MacNamara, Shev; Booth, Hilary

doi:10.1016/j.cam.2006.02.053

Cited by 98 publications

(108 citation statements)

References 11 publications

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“…5.1. For M = 10 6 SSA consumes more than 90 % of the CPU time when K = 2 15 and the quotient between the CPU time for SSA, T SSA , and the CPU time for the hybrid algorithm, T HY B , is greater than one for M ≥ 10 4 . For the larger value of K in Table 5, relatively more time is spent on the calculations of the sums.…”

Section: Circadian Rhythm Modelmentioning

confidence: 98%

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Hybrid method for the chemical master equation

Hellander

Lötstedt

2007

Journal of Computational Physics

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The chemical master equation is solved by a hybrid method coupling a macroscopic, deterministic description with a mesoscopic, stochastic model. The molecular species are divided into one subset where the expected values of the number of molecules are computed and one subset with species with a stochastic variation in the number of molecules. The macroscopic equations resemble the reaction rate equations and the probability distribution for the stochastic variables satisfy a master equation. The probability distribution is obtained by the Stochastic Simulation Algorithm due to Gillespie. The equations are coupled via a summation over the mesoscale variables. This summation is approximated by Monte Carlo and Quasi Monte Carlo methods. The error in the approximations is analyzed. The hybrid method is applied to three chemical systems from molecular cell biology.

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Section: Circadian Rhythm Modelmentioning

confidence: 98%

“…While this can result in a considerable reduction of the complexity, a profound knowledge of the biological system is required to introduce some simplifying assumptions. For moderate numbers of reacting species, sparse grid methods are an alternative [15].…”

Section: Introductionmentioning

confidence: 99%

Hybrid method for the chemical master equation

Hellander

Lötstedt

2007

Journal of Computational Physics

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“…. , β η of the current approximation p n = η i=1 β i v j i Galerkin matrix A defined by (16) Output:…”

Section: Inputmentioning

confidence: 99%

Solving Chemical Master Equations by an Adaptive Wavelet Method

Jahnke¹,

Galan²

2008

AIP Conference Proceedings

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Solving chemical master equations numerically on a large state space is known to be a difficult problem because the huge number of unknowns is far beyond the capacity of traditional methods. We present an adaptive method which compresses the problem very efficiently by representing the solution in a sparse wavelet basis that is updated in each step. The step-size is chosen adaptively according to estimates of the temporal and spatial approximation errors. Numerical examples demonstrate the reliability of the error estimation and show that the method can solve large problems with bimodal solution profiles.

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“…The finite state projection ( fsp) method [8] is based on a truncation of the state space combined with an interpolation using piecewise polynomials on the space partitions. The aggregation approach [6] uses a finite volume method and local polynomial approximation for state space approximation and the expokit method [9] for the solution of the resulting ode. This method has been extended by an adaptive sparse grid approximation in order to solve large systems.…”

Section: C377mentioning

confidence: 99%

Approximating the solution of the chemical master equation by aggregation

Hegland¹

2008

ANZIAMJ

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The chemical master equation is a continuous time discrete space Markov model of chemical reactions. The chemical master equation is derived mathematically and it is shown that the corresponding initial value problem has a unique solution. Conditions are given under which this solution is a probability distribution. We present finite state and aggregation-disaggregation approximations and provide error bounds for the case of piecewise constant disaggregation. The aggregation-disaggregation approximation allows the solution of the chemical master equation for larger state spaces and is also an important tool for the solution of multidimensional problems.

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A solver for the stochastic master equation applied to gene regulatory networks

Cited by 98 publications

References 11 publications

Hybrid method for the chemical master equation

Hybrid method for the chemical master equation

Solving Chemical Master Equations by an Adaptive Wavelet Method

Approximating the solution of the chemical master equation by aggregation

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