Chemical Langevin Equation for Complex Reactions

2020 ◽  
Vol 124 (5) ◽  
pp. 810-816 ◽  
Author(s):  
Tao Li
Keyword(s):  
Langevin Equation ◽  
Chemical Langevin Equation

scholarly journals Adaptive time-stepping using control theory for the Chemical Langevin Equation

2021 ◽  
Author(s):  
Silvana Ilie ◽  
Monjur Morshed
Keyword(s):  
Control Theory ◽  
Time Scales ◽  
Langevin Equation ◽  
Multiple Time Scales ◽  
Multiple Time ◽  
Time Stepping ◽  
Chemical Langevin Equation ◽  
Biochemical Systems ◽  
Adaptive Time ◽  
Adaptive Time Stepping

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.

scholarly journals Adaptive time-stepping using control theory for the Chemical Langevin Equation

2021 ◽  
Author(s):  
Silvana Ilie ◽  
Monjur Morshed
Keyword(s):  
Control Theory ◽  
Time Scales ◽  
Langevin Equation ◽  
Multiple Time Scales ◽  
Multiple Time ◽  
Time Stepping ◽  
Chemical Langevin Equation ◽  
Biochemical Systems ◽  
Adaptive Time ◽  
Adaptive Time Stepping

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.

scholarly journals The chemical Langevin equation for biochemical systems in dynamic environments

2021 ◽  
Author(s):  
Lucy Ham ◽  
Megan Coomer ◽  
Michael P.H. Stumpf
Keyword(s):  
Langevin Equation ◽  
Stochastic Dynamics ◽  
Computational Simulation ◽  
Intrinsic Noise ◽  
Simulation Method ◽  
Reaction Networks ◽  
Biochemical Reaction Networks ◽  
Extrinsic Noise ◽  
Chemical Langevin Equation ◽  
Biochemical Systems

Modelling and simulation of complex biochemical reaction networks form cornerstones of modern biophysics. Many of the approaches developed so far capture temporal fluctuations due to the inherent stochasticity of the biophysical processes, referred to as intrinsic noise. Stochastic fluctuations, however, predominantly stem from the interplay of the network with many other - and mostly unknown - fluctuating processes, as well as with various random signals arising from the extracellular world; these sources contribute extrinsic noise. Here we provide a computational simulation method to probe the stochastic dynamics of biochemical systems subject to both intrinsic and extrinsic noise. We develop an extrinsic chemical Langevin equation - a physically motivated extension of the chemical Langevin equation - to model intrinsically noisy reaction networks embedded in a stochastically fluctuating environment. The extrinsic CLE is a continuous approximation to the Chemical Master Equation (CME) with time-varying propensities. In our approach, noise is incorporated at the level of the CME, and can account for the full dynamics of the exogenous noise process, irrespective of timescales and their mismatches. We show that our method accurately captures the first two moments of the stationary probability density when compared with exact stochastic simulation methods, while reducing the computational runtime by several orders of magnitude. Our approach provides a method that is practical, computationally efficient and physically accurate to study systems that are simultaneously subject to a variety of noise sources.

scholarly journals The complex chemical Langevin equation

2014 ◽  
Vol 141 (2) ◽  
pp. 024103 ◽  
Author(s):  
David Schnoerr ◽  
Guido Sanguinetti ◽  
Ramon Grima
Keyword(s):  
Langevin Equation ◽  
Complex Chemical ◽  
Chemical Langevin Equation
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