scholarly journals An Efficient Tau-Leaping Simulation Method for Stochastic Biochemical Kinetics

2021 ◽  
Author(s):  
Serguei Rousskikh
Keyword(s):  
Simulation Method ◽  
Biochemical Networks ◽  
Multiple Time Scales ◽  
Multiple Time ◽  
Simulation Methods ◽  
Cellular Processes ◽  
Biochemical Kinetics ◽  
Numerical Tests ◽  
Biochemical Systems ◽  
Explicit Simulation

Stochastic modeling and simulation of biochemical systems are topics of high interest in Computational Biology. Stochastic mathematical models are critical in accurately capturing the variability observed experimentally in cellular processes, in particular when some species have low molecular numbers. Many, realistic biochemical networks exhibit stiffness, due to the presence of multiple time-scales. For such networks explicit simulation methods are computationally quite intensive. In this thesis, we introduce an improved implicit tau-leaping strategy for the simulation of stochastic biochemical kinetic models. Numerical tests on various biochemical systems of interest in applications show the efficiency of our method.

scholarly journals An Efficient Tau-Leaping Simulation Method for Stochastic Biochemical Kinetics

2021 ◽  
Author(s):  
Serguei Rousskikh
Keyword(s):  
Simulation Method ◽  
Biochemical Networks ◽  
Multiple Time Scales ◽  
Multiple Time ◽  
Simulation Methods ◽  
Cellular Processes ◽  
Biochemical Kinetics ◽  
Numerical Tests ◽  
Biochemical Systems ◽  
Explicit Simulation

Stochastic modeling and simulation of biochemical systems are topics of high interest in Computational Biology. Stochastic mathematical models are critical in accurately capturing the variability observed experimentally in cellular processes, in particular when some species have low molecular numbers. Many, realistic biochemical networks exhibit stiffness, due to the presence of multiple time-scales. For such networks explicit simulation methods are computationally quite intensive. In this thesis, we introduce an improved implicit tau-leaping strategy for the simulation of stochastic biochemical kinetic models. Numerical tests on various biochemical systems of interest in applications show the efficiency of our method.

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 Effective Time-Stepping For The Tau-Leaping Method for Stochastic Simulation Of Well-Stirred Biochemical Networks

2021 ◽  
Author(s):  
Mahmuda Binte Mostofa Ruma
Keyword(s):  
Mathematical Models ◽  
Stochastic Simulation ◽  
Practical Interest ◽  
Cellular Level ◽  
Biochemical Networks ◽  
Biological Processes ◽  
Time Stepping ◽  
Effective Time ◽  
Numerical Tests ◽  
Biochemical Systems

Biological processes at the cellular level are noisy. The noise arises due to random molecular collisions, and may be substantial in systems with low molecular counts in some species. This thesis introduces a variable tau-leaping method for the simulation of stochastic discrete mathematical models of well-stirred biochemical systems which is theoretically justified. Numerical tests on several models of biochemical systems of practical interest illustrate the advantages of the adaptive tau-leap method over the existing schemes.

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 Exact model reduction with delays: closed-form distributions and extensions to fully bi-directional monomolecular reactions

2014 ◽  
Vol 11 (95) ◽  
pp. 20140108 ◽  
Author(s):  
Andre Leier ◽  
Manuel Barrio ◽  
Tatiana T. Marquez-Lago
Keyword(s):  
Closed Form ◽  
Biological Research ◽  
Multiple Time Scales ◽  
Multiple Time ◽  
Pharmaceutical Chemical ◽  
Computational Costs ◽  
Qualitative And Quantitative ◽  
Linear Chains ◽  
Biochemical Systems ◽  
Monomolecular Reactions

In order to systematically understand the qualitative and quantitative behaviour of chemical reaction networks, scientists must derive and analyse associated mathematical models. However, biochemical systems are often very large, with reactions occurring at multiple time scales, as evidenced by signalling pathways and gene expression kinetics. Owing to the associated computational costs, it is then many times impractical, if not impossible, to solve or simulate these systems with an appropriate level of detail. By consequence, there is a growing interest in developing techniques for the simplification or reduction of complex biochemical systems. Here, we extend our recently presented methodology on exact reduction of linear chains of reactions with delay distributions in two ways. First, we report that it is now possible to deal with fully bi-directional monomolecular systems, including degradations, synthesis and generalized bypass reactions. Second, we provide all derivations of associated delays in analytical, closed form. Both advances have a major impact on further reducing computational costs, while still retaining full accuracy. Thus, we expect our new methodology to respond to current simulation needs in pharmaceutical, chemical and biological research.

scholarly journals Effective Time-Stepping For The Tau-Leaping Method for Stochastic Simulation Of Well-Stirred Biochemical Networks

2021 ◽  
Author(s):  
Mahmuda Binte Mostofa Ruma
Keyword(s):  
Mathematical Models ◽  
Stochastic Simulation ◽  
Practical Interest ◽  
Cellular Level ◽  
Biochemical Networks ◽  
Biological Processes ◽  
Time Stepping ◽  
Effective Time ◽  
Numerical Tests ◽  
Biochemical Systems

Biological processes at the cellular level are noisy. The noise arises due to random molecular collisions, and may be substantial in systems with low molecular counts in some species. This thesis introduces a variable tau-leaping method for the simulation of stochastic discrete mathematical models of well-stirred biochemical systems which is theoretically justified. Numerical tests on several models of biochemical systems of practical interest illustrate the advantages of the adaptive tau-leap method over the existing schemes.

scholarly journals Adaptive Time-Stepping Using Control Theory for the Chemical Langevin Equation

2015 ◽  
Vol 2015 ◽  
pp. 1-10 ◽  
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.

SOME REMARKS ON THE MULTIPLE TIME SCALES OF DIFFUSION IN MINERALS AND MELTS

2018 ◽  
Author(s):  
Yan Liang ◽  
◽  
Daniele J. Cherniak ◽  
Chenguang Sun
Keyword(s):  
Time Scales ◽  
Multiple Time Scales ◽  
Multiple Time

scholarly journals Odor response adaptation in Drosophila—a continuous individualization process

2021 ◽  
Vol 383 (1) ◽  
pp. 143-148
Author(s):  
Shadi Jafari ◽  
Mattias Alenius
Keyword(s):  
Sensory Neurons ◽  
Olfactory System ◽  
Multiple Time Scales ◽  
Multiple Time ◽  
Olfactory Perception ◽  
Adaptation Mechanisms ◽  
Metabolic States ◽  
The Central Nervous System ◽  
Olfactory Adaptation ◽  
Central Adaptation

AbstractOlfactory perception is very individualized in humans and also in Drosophila. The process that individualize olfaction is adaptation that across multiple time scales and mechanisms shape perception and olfactory-guided behaviors. Olfactory adaptation occurs both in the central nervous system and in the periphery. Central adaptation occurs at the level of the circuits that process olfactory inputs from the periphery where it can integrate inputs from other senses, metabolic states, and stress. We will here focus on the periphery and how the fast, slow, and persistent (lifelong) adaptation mechanisms in the olfactory sensory neurons individualize the Drosophila olfactory system.

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