Adaptive Time-Stepping Using Control Theory for the Chemical Langevin Equation
Stochastic modeling of biochemical systems has been the subject of intense research in recent years due to the large number of important applications of these systems. A critical stochastic model of well-stirred biochemical systems in the regime of relatively large molecular numbers, far from the th...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2015-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2015/567275 |
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| Summary: | Stochastic modeling of biochemical systems has been the subject of intense research in recent years due to the large
number of important applications of these systems. A critical stochastic model of well-stirred biochemical systems in
the regime of relatively large molecular numbers, far from the thermodynamic limit, is the chemical Langevin equation.
This model is represented as a system of stochastic differential equations, with multiplicative and noncommutative
noise. Often biochemical systems in applications evolve on multiple time-scales; examples include slow transcription
and fast dimerization reactions. The existence of multiple time-scales leads to mathematical stiffness, which is a major
challenge for the numerical simulation. Consequently, there is a demand for efficient and accurate numerical methods to
approximate the solution of these models. In this paper, we design an adaptive time-stepping method, based on control
theory, for the numerical solution of the chemical Langevin equation. The underlying approximation method is the
Milstein scheme. The adaptive strategy is tested on several models of interest and is shown to have improved efficiency
and accuracy compared with the existing variable and constant-step methods. |
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| ISSN: | 1110-757X 1687-0042 |