scholarly journals Adaptive Methods For Stochastic Simulation Of Biochemical Systems

2021 ◽  
Author(s):  
Alexandra Teslya
Keyword(s):  
Stochastic Models ◽  
Rapid Development ◽  
Adaptive Methods ◽  
Biological Processes ◽  
Step Size ◽  
Time Step ◽  
Deterministic Models ◽  
Biochemical Systems ◽  
Living Organisms ◽  
Adaptive Step

Computational and Systems Biology are recently experiencing a rapid development. Mathematical modeling is a key tool in analyzing critical biological processes in cells and living organisms. In particular, stochastic models are essential to accurately describe the biochemical processes in the cell. However, stochastic models are computationally much more challenging than the traditional deterministic models. Also, the sheer scale of biological processes makes efficiency of the simulation a key issue. In this thesis we study the numerical solution of a continuous stochastic model of biochemical systems, the Chemical Langevin Equation. We propose an adaptive step-size method for the Euler-Maruyama scheme applied to small noise problems. The adaptive technique is p-mean convergent and computes simultaneously all the trajectories, using the same time-step on all trajectories. Our adaptive algorithm is tested on several examples arising in applications and shown to perform much better than the fixed step-size schemes.

Adaptive Methods For Stochastic Simulation Of Biochemical Systems

2021 ◽  
Author(s):  
Alexandra Teslya
Keyword(s):  
Stochastic Models ◽  
Rapid Development ◽  
Adaptive Methods ◽  
Biological Processes ◽  
Step Size ◽  
Time Step ◽  
Deterministic Models ◽  
Biochemical Systems ◽  
Living Organisms ◽  
Adaptive Step

Computational and Systems Biology are recently experiencing a rapid development. Mathematical modeling is a key tool in analyzing critical biological processes in cells and living organisms. In particular, stochastic models are essential to accurately describe the biochemical processes in the cell. However, stochastic models are computationally much more challenging than the traditional deterministic models. Also, the sheer scale of biological processes makes efficiency of the simulation a key issue. In this thesis we study the numerical solution of a continuous stochastic model of biochemical systems, the Chemical Langevin Equation. We propose an adaptive step-size method for the Euler-Maruyama scheme applied to small noise problems. The adaptive technique is p-mean convergent and computes simultaneously all the trajectories, using the same time-step on all trajectories. Our adaptive algorithm is tested on several examples arising in applications and shown to perform much better than the fixed step-size schemes.

scholarly journals Adaptive time step algorithms for the simulation of marine ecosystem models using the transport matrix method implementation Metos3D (v0.5.0)

2022 ◽  
Author(s):  
Markus Pfeil ◽  
Thomas Slawig
Keyword(s):  
Marine Ecosystem ◽  
Size Control ◽  
Ecosystem Model ◽  
Computational Effort ◽  
Ecosystem Models ◽  
Step Size ◽  
Time Step ◽  
Marine Ecosystem Model ◽  
Marine Ecosystem Models ◽  
Adaptive Step

Abstract. The reduction of the computational effort is desirable for the simulation of marine ecosystem models. Using a marine ecosystem model, the assessment and the validation of annual periodic solutions (i.e., steady annual cycles) against observational data are crucial to identify biogeochemical processes, which, for example, influence the global carbon cycle. For marine ecosystem models, the transport matrix method (TMM) already lowers the runtime of the simulation significantly and enables the application of larger time steps straightforwardly. However, the selection of an appropriate time step is a challenging compromise between accuracy and shortening the runtime. Using an automatic time step adjustment during the computation of a steady annual cycle with the TMM, we present in this paper different algorithms applying either an adaptive step size control or decreasing time steps in order to use the time step always as large as possible without any manual selection. For these methods and a variety of marine ecosystem models of different complexity, the accuracy of the computed steady annual cycle achieved the same accuracy as solutions obtained with a fixed time step. Depending on the complexity of the marine ecosystem model, the application of the methods shortened the runtime significantly. Due to the certain overhead of the adaptive method, the computational effort may be higher in special cases using the adaptive step size control. The presented methods represent computational efficient methods for the simulation of marine ecosystem models using the TMM but without any manual selection of the time step.

scholarly journals Numerical studies of Implicit Tau Leaping methods for stochastic biochemical systems

2021 ◽  
Author(s):  
Fauzia Jabeen
Keyword(s):  
Stochastic Models ◽  
Practical Interest ◽  
Cellular Systems ◽  
Simulation Methods ◽  
Exact Methods ◽  
Deterministic Models ◽  
Efficient Simulation ◽  
Numerical Studies ◽  
Biochemical Systems ◽  
Population Sizes

Deterministic models of chemical reactions systems have been used successfully in studying chemical kinetics problems. However, in biochemical systems (e.g. cellular systems in biology), small molecular population sizes of some key reacting species can lead to results that cannot be predicted by the traditional deterministic models. It has been found that such processes involve intrinsic randomness that can be better modeled by stochastic models. Chemical Master Equation (CME) is an accurate stochastic model of well-stirred biochemical systems. We investigate reliable and efficient simulation methods for the CME, namely the implicit tau-leaping method. The tau-leaping algorithms were tested on several models of practical interest such as the Schl¨ogl model and the Goldbeter-Koshland switch and compared to the exact methods. We observed that, for systems not reaching steady state, the implicit tau-leaping strategy is accurate.

scholarly journals Accurate parametric sensitivity of stochastic biochemical systems

2021 ◽  
Author(s):  
Farid Gassoumov
Keyword(s):  
Stochastic Models ◽  
Rapid Development ◽  
Computational Modelling ◽  
Accurate Method ◽  
Discrete Models ◽  
Rate Equations ◽  
Parametric Sensitivity ◽  
System Behaviour ◽  
Key Species ◽  
Biochemical Systems

Computational and Systems Biology are experiencing a rapid development in recent years. Mathematical and computational modelling are critical tools for studying cellular dynamics. Molecular interactions in a cell may display significant random fluctuations when some key species have low amounts (RNA, DNA), making the traditional model of the deterministic reaction rate equations insufficient. Consequently, stochastic models are required to accurately represent the biochemical system behaviour. Nonetheless, stochastic models are more challenging to simulate and analyse than the deterministic ones. Parametric sensitivity is a powerful tool for exploring the system behaviour, such as system robustness with respect to perturbations in its parameters. We present an accurate method for estimating parametric sensitivities for stochastic discrete models of biochemical systems using a high order Coupled Finite Difference scheme and illustrate its advantages compared to the existing techniques

scholarly journals Accurate parametric sensitivity of stochastic biochemical systems

2021 ◽  
Author(s):  
Farid Gassoumov
Keyword(s):  
Stochastic Models ◽  
Rapid Development ◽  
Computational Modelling ◽  
Accurate Method ◽  
Discrete Models ◽  
Rate Equations ◽  
Parametric Sensitivity ◽  
System Behaviour ◽  
Key Species ◽  
Biochemical Systems

Computational and Systems Biology are experiencing a rapid development in recent years. Mathematical and computational modelling are critical tools for studying cellular dynamics. Molecular interactions in a cell may display significant random fluctuations when some key species have low amounts (RNA, DNA), making the traditional model of the deterministic reaction rate equations insufficient. Consequently, stochastic models are required to accurately represent the biochemical system behaviour. Nonetheless, stochastic models are more challenging to simulate and analyse than the deterministic ones. Parametric sensitivity is a powerful tool for exploring the system behaviour, such as system robustness with respect to perturbations in its parameters. We present an accurate method for estimating parametric sensitivities for stochastic discrete models of biochemical systems using a high order Coupled Finite Difference scheme and illustrate its advantages compared to the existing techniques

On stochastic models in biology and medicine

2020 ◽  
Vol 13 (08) ◽  
pp. 2050168
Author(s):  
Iveta Nikolova
Keyword(s):  
Probability Theory ◽  
Autoimmune Disease ◽  
Stochastic Models ◽  
Initial Conditions ◽  
Living Systems ◽  
Biological Processes ◽  
Probability Models ◽  
Deterministic Models ◽  
Classical Probability ◽  
Basic Concepts

Stochastic models along with deterministic models are successfully used for mathematical description of biological processes. They apply knowledge from probability theory and mathematical statistics to analyze specific characteristics of living systems. The paper is devoted to some stochastic models of various phenomena in biology and medicine. Basic concepts and definitions used in classical probability models are considered and illustrated by several examples with solutions. The stochastic kinetic modeling approach is described. A new kinetic model of autoimmune disease is presented. It is a system of nonlinear partial integro-differential equations supplemented by corresponding initial conditions. The modeling problem is solved computationally.

scholarly journals Numerical studies of Implicit Tau Leaping methods for stochastic biochemical systems

2021 ◽  
Author(s):  
Fauzia Jabeen
Keyword(s):  
Stochastic Models ◽  
Practical Interest ◽  
Cellular Systems ◽  
Simulation Methods ◽  
Exact Methods ◽  
Deterministic Models ◽  
Efficient Simulation ◽  
Numerical Studies ◽  
Biochemical Systems ◽  
Population Sizes

Deterministic models of chemical reactions systems have been used successfully in studying chemical kinetics problems. However, in biochemical systems (e.g. cellular systems in biology), small molecular population sizes of some key reacting species can lead to results that cannot be predicted by the traditional deterministic models. It has been found that such processes involve intrinsic randomness that can be better modeled by stochastic models. Chemical Master Equation (CME) is an accurate stochastic model of well-stirred biochemical systems. We investigate reliable and efficient simulation methods for the CME, namely the implicit tau-leaping method. The tau-leaping algorithms were tested on several models of practical interest such as the Schl¨ogl model and the Goldbeter-Koshland switch and compared to the exact methods. We observed that, for systems not reaching steady state, the implicit tau-leaping strategy is accurate.

Environmental significance of atrazine in aqueous systems and its removal by biological processes: an overview

2013 ◽  
Vol 8 (2) ◽  
pp. 159-178 ◽  
Keyword(s):  
Drinking Water ◽  
Ground Water ◽  
Water Environment ◽  
Biological Processes ◽  
Biological Degradation ◽  
Environmental Significance ◽  
Carbon And Nitrogen ◽  
Carbon Nitrogen Ratio ◽  
Nitrogen Ratio ◽  
Living Organisms

Atrazine, a chlorinated s-triazine group of herbicide is one of the most widely used pesticides in the World. Due to its extensive use, long half-life and various toxic properties, it has very high environmental significance. Up to 22 mg l-1 of atrazine was found in ground water whereas permissible limit of atrazine is in ppb level in drinking water. As per Indian standard there should not be any pesticide present in drinking water. Among many other treatment processes available, Incineration, adsorption, chemical treatment, phytoremediation and biodegradation are the most commonly used ones. Biological degradation of atrazine depends upon various factors like the operating environment, external carbon and nitrogen sources, carbon/ nitrogen ratio (C/N), water content and the bacterial strain. Although, general atrazine degradation pathways are available, the specific pathways in specific conditions are not yet clearly defined. In this paper extensive review has been made on the occurrence of atrazine in surface and ground water bodies, probable sources and causes of its occurrence in water environment, the toxicity of atrazine on various living organisms and its removal by biological processes.

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