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 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 Numerical studies of higher order tau-leaping methods

2021 ◽  
Author(s):  
Anuj Dhoj Thapa
Keyword(s):  
Stochastic Simulation ◽  
Computational Cost ◽  
Practical Interest ◽  
Stochastic Simulation Algorithm ◽  
Simulation Method ◽  
Equation Model ◽  
Fast Reactions ◽  
Biochemical Systems ◽  
Computationally Intensive ◽  
Reacting Systems

Gillespie's algorithm, also known as the Stochastic Simulation Algorithm (SSA), is an exact simulation method for the Chemical Master Equation model of well-stirred biochemical systems. However, this method is computationally intensive when some fast reactions are present in the system. The tau-leap scheme developed by Gillespie can speed up the stochastic simulation of these biochemically reacting systems with negligible loss in accuracy. A number of tau-leaping methods were proposed, including the explicit tau-leaping and the implicit tau-leaping strategies. Nonetheless, these schemes have low order of accuracy. In this thesis, we investigate tau-leap strategies which achieve high accuracy at reduced computational cost. These strategies are tested on several biochemical systems of practical interest.

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 Numerical studies of higher order tau-leaping methods

2021 ◽  
Author(s):  
Anuj Dhoj Thapa
Keyword(s):  
Stochastic Simulation ◽  
Computational Cost ◽  
Practical Interest ◽  
Stochastic Simulation Algorithm ◽  
Simulation Method ◽  
Equation Model ◽  
Fast Reactions ◽  
Biochemical Systems ◽  
Computationally Intensive ◽  
Reacting Systems

Gillespie's algorithm, also known as the Stochastic Simulation Algorithm (SSA), is an exact simulation method for the Chemical Master Equation model of well-stirred biochemical systems. However, this method is computationally intensive when some fast reactions are present in the system. The tau-leap scheme developed by Gillespie can speed up the stochastic simulation of these biochemically reacting systems with negligible loss in accuracy. A number of tau-leaping methods were proposed, including the explicit tau-leaping and the implicit tau-leaping strategies. Nonetheless, these schemes have low order of accuracy. In this thesis, we investigate tau-leap strategies which achieve high accuracy at reduced computational cost. These strategies are tested on several biochemical systems of practical interest.

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.

Methodology of Research in Micropollutants – Heavy Metals

1982 ◽  
Vol 14 (12) ◽  
pp. 107-125 ◽  
Author(s):  
Roland Wollast
Keyword(s):  
Heavy Metals ◽  
Mathematical Models ◽  
Aqueous Phase ◽  
Suspended Matter ◽  
Solid Phase ◽  
Aquatic Organisms ◽  
Biological Processes ◽  
Particulate Phase ◽  
Sources Of Pollution ◽  
Adsorption Desorption

A comparison of the concentration of dissolved and of particulate heavy metals in the aquatic system indicates that these elements are strongly enriched in the suspended matter. The transfer between the aqueous phase and the solid phase may be due to dissolution-precipitation reactions, adsorption-desorption processes or biological processes. When these processes are identified, it is further possible to develop mathematical models which describe the behaviour of these elements. The enrichment of heavy metals in the particulate phase suspended or deposited and in aquatic organisms constitutes a powerful tool in order to evaluate sources of pollution.

scholarly journals Design of a biochemical circuit motif for learning linear functions

2014 ◽  
Vol 11 (101) ◽  
pp. 20140902 ◽  
Author(s):  
Matthew R. Lakin ◽  
Amanda Minnich ◽  
Terran Lane ◽  
Darko Stefanovic
Keyword(s):  
Internal State ◽  
Linear Functions ◽  
Learning Performance ◽  
Adaptive Behaviour ◽  
Biological Processes ◽  
Biochemical System ◽  
Biochemical Systems ◽  
Robustness To Noise ◽  
Novel Design

Learning and adaptive behaviour are fundamental biological processes. A key goal in the field of bioengineering is to develop biochemical circuit architectures with the ability to adapt to dynamic chemical environments. Here, we present a novel design for a biomolecular circuit capable of supervised learning of linear functions, using a model based on chemical reactions catalysed by DNAzymes. To achieve this, we propose a novel mechanism of maintaining and modifying internal state in biochemical systems, thereby advancing the state of the art in biomolecular circuit architecture. We use simulations to demonstrate that the circuit is capable of learning behaviour and assess its asymptotic learning performance, scalability and robustness to noise. Such circuits show great potential for building autonomous in vivo nanomedical devices. While such a biochemical system can tell us a great deal about the fundamentals of learning in living systems and may have broad applications in biomedicine (e.g. autonomous and adaptive drugs), it also offers some intriguing challenges and surprising behaviours from a machine learning perspective.

The sorting direct method for stochastic simulation of biochemical systems with varying reaction execution behavior

2006 ◽  
Vol 30 (1) ◽  
pp. 39-49 ◽  
Author(s):  
James M. McCollum ◽  
Gregory D. Peterson ◽  
Chris D. Cox ◽  
Michael L. Simpson ◽  
Nagiza F. Samatova
Keyword(s):  
Stochastic Simulation ◽  
Direct Method ◽  
Biochemical Systems

scholarly journals Accurate Stochastic Simulation Methods for Homogeneous Biochemical Networks

2021 ◽  
Author(s):  
Farida Ansari
Keyword(s):  
Master Equation ◽  
Stochastic Simulation ◽  
Growth Factor Receptor ◽  
Stochastic Simulation Algorithm ◽  
Chemical Master Equation ◽  
Biochemical Networks ◽  
Random Time Change ◽  
Simulation Strategy ◽  
Epidermal Growth ◽  
Exact Stochastic Simulation

Stochastic models of intracellular processes are subject of intense research today. For homogeneous systems, these models are based on the Chemical Master Equation, which is a discrete stochastic model. The Chemical Master Equation is often solved numerically using Gillespie’s exact stochastic simulation algorithm. This thesis studies the performance of another exact stochastic simulation strategy, which is based on the Random Time Change representation, and is more efficient for sensitivity analysis, compared to Gillespie’s algorithm. This method is tested on several models of biological interest, including an epidermal growth factor receptor model.

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