Journal of Computational Physics, ISSN 0021-9991, 12/2018, Volume 374, pp. 954 - 983

The convergent reaction–diffusion master equation (CRDME) was recently developed to provide a lattice particle-based stochastic reaction–diffusion model that...

Doi model | Stochastic chemical kinetics | Volume reactivity model | Stochastic reaction–diffusion | Reaction–diffusion master equation | Stochastic reaction-diffusion | PATHWAYS | EUKARYOTIC GENE-EXPRESSION | CHROMATIN | Reaction-diffusion master equation | TIME | MECHANISMS | SIMULATION | PHYSICS, MATHEMATICAL | TRANSPORT | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | MODELS | DNA-BINDING SITES | STOCHASTIC CHEMICAL-KINETICS | Chemical reaction, Rate of | Analysis | Mathematics - Numerical Analysis

Doi model | Stochastic chemical kinetics | Volume reactivity model | Stochastic reaction–diffusion | Reaction–diffusion master equation | Stochastic reaction-diffusion | PATHWAYS | EUKARYOTIC GENE-EXPRESSION | CHROMATIN | Reaction-diffusion master equation | TIME | MECHANISMS | SIMULATION | PHYSICS, MATHEMATICAL | TRANSPORT | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | MODELS | DNA-BINDING SITES | STOCHASTIC CHEMICAL-KINETICS | Chemical reaction, Rate of | Analysis | Mathematics - Numerical Analysis

Journal Article

Journal of Computational Chemistry, ISSN 0192-8651, 01/2013, Volume 34, Issue 3, pp. 245 - 255

Spatial stochastic simulation is a valuable technique for studying reactions in biological systems. With the availability of high‐performance computing (HPC),...

chemical master equation | reaction‐diffusion master equation | stochastic simulation | graphics processing unit computing | Gillespie algorithm | NOISE | CHEMISTRY, MULTIDISCIPLINARY | SOFTWARE | reaction-diffusion master equation | PATHWAY | CHEMICAL-KINETICS | GENE-EXPRESSION | SYSTEMS | LIVING CELLS | Transcription Factors - metabolism | Algorithms | Stochastic Processes | Models, Biological | Computer Simulation | Gene Expression Regulation | Protein Binding | Software | DNA - metabolism | Escherichia coli - cytology | Diffusion | Microorganisms | Computer-generated environments | Computer simulation | Analysis | Methods | GPU computing

chemical master equation | reaction‐diffusion master equation | stochastic simulation | graphics processing unit computing | Gillespie algorithm | NOISE | CHEMISTRY, MULTIDISCIPLINARY | SOFTWARE | reaction-diffusion master equation | PATHWAY | CHEMICAL-KINETICS | GENE-EXPRESSION | SYSTEMS | LIVING CELLS | Transcription Factors - metabolism | Algorithms | Stochastic Processes | Models, Biological | Computer Simulation | Gene Expression Regulation | Protein Binding | Software | DNA - metabolism | Escherichia coli - cytology | Diffusion | Microorganisms | Computer-generated environments | Computer simulation | Analysis | Methods | GPU computing

Journal Article

Reports on Progress in Physics, ISSN 0034-4885, 03/2017, Volume 80, Issue 4, p. 046601

This review provides a pedagogic and self-contained introduction to master equations and to their representation by path integrals. Since the 1930s, master...

rare event probabilities | path summation | Markov processes | spectral analysis | master equations | stochastic processes | path integrals | FOKKER-PLANCK EQUATION | RENORMALIZATION-GROUP | BIRTH-DEATH PROCESSES | PHYSICS, MULTIDISCIPLINARY | REACTION-DIFFUSION PROCESSES | ASYMMETRIC EXCLUSION MODEL | NON-MARKOV PROCESSES | NEAR-CRITICAL POINT | RELATIVE SPECIES ABUNDANCE | ANNIHILATING RANDOM-WALKS | ONSAGER-MACHLUP FUNCTION

rare event probabilities | path summation | Markov processes | spectral analysis | master equations | stochastic processes | path integrals | FOKKER-PLANCK EQUATION | RENORMALIZATION-GROUP | BIRTH-DEATH PROCESSES | PHYSICS, MULTIDISCIPLINARY | REACTION-DIFFUSION PROCESSES | ASYMMETRIC EXCLUSION MODEL | NON-MARKOV PROCESSES | NEAR-CRITICAL POINT | RELATIVE SPECIES ABUNDANCE | ANNIHILATING RANDOM-WALKS | ONSAGER-MACHLUP FUNCTION

Journal Article

Journal of Computational Physics, ISSN 0021-9991, 06/2014, Volume 266, pp. 89 - 100

The efficiency of exact simulation methods for the reaction–diffusion master equation (RDME) is severely limited by the large number of diffusion events if the...

Operator splitting | Adaptivity | Hybrid methods | Local error | Reaction–diffusion master equation | Reaction-diffusion master equation | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | ESCHERICHIA-COLI | GENE-EXPRESSION | PHYSICS, MATHEMATICAL | CELL | Monte Carlo method | Errors | Operators | Splitting | Approximation | Computer simulation | Mathematical analysis | Diffusion | Estimates | Biological Sciences | Naturvetenskap | Computational Mathematics | Biokemi och molekylärbiologi | Biologiska vetenskaper | Biochemistry and Molecular Biology | Mathematics | Natural Sciences | Beräkningsmatematik | Matematik

Operator splitting | Adaptivity | Hybrid methods | Local error | Reaction–diffusion master equation | Reaction-diffusion master equation | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | ESCHERICHIA-COLI | GENE-EXPRESSION | PHYSICS, MATHEMATICAL | CELL | Monte Carlo method | Errors | Operators | Splitting | Approximation | Computer simulation | Mathematical analysis | Diffusion | Estimates | Biological Sciences | Naturvetenskap | Computational Mathematics | Biokemi och molekylärbiologi | Biologiska vetenskaper | Biochemistry and Molecular Biology | Mathematics | Natural Sciences | Beräkningsmatematik | Matematik

Journal Article

5.
Full Text
Reaction-diffusion master equation, diffusion-limited reactions, and singular potentials

Physical Review E - Statistical, Nonlinear, and Soft Matter Physics, ISSN 1539-3755, 12/2009, Volume 80, Issue 6

To model biochemical systems in which both noise in the chemical reaction process and spatial movement of molecules is important, both the reaction-diffusion...

PHYSICS, FLUIDS & PLASMAS | reaction-diffusion systems | reaction kinetics theory | PHYSICS, MATHEMATICAL | CHEMICAL-REACTIONS | RATES | master equation | pseudopotential methods | biochemistry | noise | molecule-molecule reactions | SYSTEMS | stochastic processes | EXACT STOCHASTIC SIMULATION

PHYSICS, FLUIDS & PLASMAS | reaction-diffusion systems | reaction kinetics theory | PHYSICS, MATHEMATICAL | CHEMICAL-REACTIONS | RATES | master equation | pseudopotential methods | biochemistry | noise | molecule-molecule reactions | SYSTEMS | stochastic processes | EXACT STOCHASTIC SIMULATION

Journal Article

2007, OXFORD SCIENCE PUBLICATIONS. SER: OXFORD MATHEMATICAL MONOGRAPHS., ISBN 9780198569039, 647

The Heat Equation is one of the three classical linear partial differential equations of second order that form the basis of any elementary introduction to the...

Boundary value problems | Mathematics | mathematical and statistical physics | Boundary layer theory | Nonlinear | Heat equation | Linear partial differential equations | Fluid flow | Mathematical biology | Lubrication | Diffusion | Heat transfer

Boundary value problems | Mathematics | mathematical and statistical physics | Boundary layer theory | Nonlinear | Heat equation | Linear partial differential equations | Fluid flow | Mathematical biology | Lubrication | Diffusion | Heat transfer

Book

SIAM Journal on Applied Mathematics, ISSN 0036-1399, 1/2009, Volume 70, Issue 1, pp. 77 - 111

The reaction-diffusion master equation (RDME) has recently been used as a model for biological systems in which both noise in the chemical reaction process and...

Molecules | Error rates | Approximation | Reaction kinetics | Mathematical lattices | Chemical reactions | Mathematical models | Mathematics | Spatial models | Perceptron convergence procedure | Diffusion (limited) vacation | Master equation | Stochastic chemical kinetics | Reaction-diffusion | CELLS | MATHEMATICS, APPLIED | EUKARYOTIC GENE-EXPRESSION | stochastic chemical kinetics | INTEGRAL-EQUATIONS | NOISE | diffusion (limited) vacation | CHEMICAL-REACTIONS | reaction-diffusion | master equation | NUMERICAL-SOLUTION | STOCHASTIC SIMULATION | KINETICS | DOUBLE-EXPONENTIAL TRANSFORMATION | DYNAMICS | Studies | Diffusion | Asymptotic methods | Differential equations | Approximations

Molecules | Error rates | Approximation | Reaction kinetics | Mathematical lattices | Chemical reactions | Mathematical models | Mathematics | Spatial models | Perceptron convergence procedure | Diffusion (limited) vacation | Master equation | Stochastic chemical kinetics | Reaction-diffusion | CELLS | MATHEMATICS, APPLIED | EUKARYOTIC GENE-EXPRESSION | stochastic chemical kinetics | INTEGRAL-EQUATIONS | NOISE | diffusion (limited) vacation | CHEMICAL-REACTIONS | reaction-diffusion | master equation | NUMERICAL-SOLUTION | STOCHASTIC SIMULATION | KINETICS | DOUBLE-EXPONENTIAL TRANSFORMATION | DYNAMICS | Studies | Diffusion | Asymptotic methods | Differential equations | Approximations

Journal Article

Journal of Chemical Physics, ISSN 0021-9606, 2010, Volume 132, Issue 7, p. 074101

We have developed a computational framework for accurate and efficient simulation of stochastic spatially inhomogeneous biochemical systems. The new...

reaction-diffusion systems | ESCHERICHIA-COLI | PHYSICS, ATOMIC, MOLECULAR & CHEMICAL | CHEMISTRY, PHYSICAL | biodiffusion | CHEMICAL-REACTIONS | proteins | biochemistry | GENE-EXPRESSION | SYSTEMS | molecular biophysics | stochastic processes | CELL | Markov Chains | Algorithms | Models, Chemical | Models, Biological | Computer Simulation | Kinetics | Diffusion | Theoretical Methods and Algorithms

reaction-diffusion systems | ESCHERICHIA-COLI | PHYSICS, ATOMIC, MOLECULAR & CHEMICAL | CHEMISTRY, PHYSICAL | biodiffusion | CHEMICAL-REACTIONS | proteins | biochemistry | GENE-EXPRESSION | SYSTEMS | molecular biophysics | stochastic processes | CELL | Markov Chains | Algorithms | Models, Chemical | Models, Biological | Computer Simulation | Kinetics | Diffusion | Theoretical Methods and Algorithms

Journal Article

Theoretical Biology and Medical Modelling, ISSN 1742-4682, 02/2015, Volume 12, Issue 1, pp. 5 - 5

Background: It has been established that stochastic effects play an important role in spatio-temporal biochemical networks. A popular method of representing...

Reaction Diffusion Master Equation | Spatial Chemical Langevin Equation | Noise-induced phenomena | Turing patterns | FIELD-THEORY | DIFFERENTIAL-EQUATIONS | MODEL | SIMULATION | PATTERN-FORMATION | BIOLOGY | MATHEMATICAL & COMPUTATIONAL BIOLOGY | SYSTEMS | OSCILLATIONS | Predatory Behavior | Algorithms | Animals | Diffusion | Models, Biological | Computer Simulation | Differential equations

Reaction Diffusion Master Equation | Spatial Chemical Langevin Equation | Noise-induced phenomena | Turing patterns | FIELD-THEORY | DIFFERENTIAL-EQUATIONS | MODEL | SIMULATION | PATTERN-FORMATION | BIOLOGY | MATHEMATICAL & COMPUTATIONAL BIOLOGY | SYSTEMS | OSCILLATIONS | Predatory Behavior | Algorithms | Animals | Diffusion | Models, Biological | Computer Simulation | Differential equations

Journal Article

Bulletin of Mathematical Biology, ISSN 0092-8240, 8/2019, Volume 81, Issue 8, pp. 2960 - 3009

Models of chemical kinetics that incorporate both stochasticity and diffusion are an increasingly common tool for studying biology. The variety of competing...

Life Sciences, general | Brownian dynamics | Mathematical and Computational Biology | Reaction–diffusion master equation | Mathematics | Spatial models | Cell Biology | MOLECULAR-DYNAMICS | APPROXIMATIONS | RESOLUTION | Reaction-diffusion master equation | SIMULATION | DIFFUSION MASTER EQUATION | ANOMALOUS DIFFUSION | CHEMICAL-REACTIONS | BIOLOGY | MATHEMATICAL & COMPUTATIONAL BIOLOGY | CYTOPLASM | COEFFICIENTS | Brownian motion | Molecular modelling | Reviews | Chemical kinetics | Reaction kinetics | Molecular dynamics | Modelling | Mathematical models | Stochasticity | Kinetics | Diffusion | Molecular chains | Organic chemistry | Special Issue | Gillespie and his Algorithms

Life Sciences, general | Brownian dynamics | Mathematical and Computational Biology | Reaction–diffusion master equation | Mathematics | Spatial models | Cell Biology | MOLECULAR-DYNAMICS | APPROXIMATIONS | RESOLUTION | Reaction-diffusion master equation | SIMULATION | DIFFUSION MASTER EQUATION | ANOMALOUS DIFFUSION | CHEMICAL-REACTIONS | BIOLOGY | MATHEMATICAL & COMPUTATIONAL BIOLOGY | CYTOPLASM | COEFFICIENTS | Brownian motion | Molecular modelling | Reviews | Chemical kinetics | Reaction kinetics | Molecular dynamics | Modelling | Mathematical models | Stochasticity | Kinetics | Diffusion | Molecular chains | Organic chemistry | Special Issue | Gillespie and his Algorithms

Journal Article

Journal of Computational Physics, ISSN 0021-9991, 02/2019, Volume 378, pp. 1 - 17

We have developed a new algorithm which merges discrete stochastic simulation, using the spatial stochastic simulation algorithm (sSSA), with the particle...

Discrete stochastic simulation | Reaction–diffusion master equation | Particle based fluid dynamics | CONCENTRIC ANNULUS | COMPLEX FLUIDS | NATURAL-CONVECTION | SQUARE | HYDRODYNAMICS | Reaction-diffusion master equation | PHYSICS, MATHEMATICAL | HORIZONTAL CYLINDER | FREE-SURFACE FLOWS | SPH METHOD | TRANSPORT | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | THERMODYNAMICS | Fluid mechanics | Yeast | Fluid dynamics | Computational fluid dynamics | Computer simulation | Fluid flow | Finite element method | Organic chemistry | Algorithms | Energy dissipation | Meshless methods | Smooth particle hydrodynamics | Reaction-diffusion equations | Diffusion | Microfluidics | Particle Based Fluid Dynamics | Discrete Stochastic Simulation | Reaction-Diffusion Master Equation

Discrete stochastic simulation | Reaction–diffusion master equation | Particle based fluid dynamics | CONCENTRIC ANNULUS | COMPLEX FLUIDS | NATURAL-CONVECTION | SQUARE | HYDRODYNAMICS | Reaction-diffusion master equation | PHYSICS, MATHEMATICAL | HORIZONTAL CYLINDER | FREE-SURFACE FLOWS | SPH METHOD | TRANSPORT | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | THERMODYNAMICS | Fluid mechanics | Yeast | Fluid dynamics | Computational fluid dynamics | Computer simulation | Fluid flow | Finite element method | Organic chemistry | Algorithms | Energy dissipation | Meshless methods | Smooth particle hydrodynamics | Reaction-diffusion equations | Diffusion | Microfluidics | Particle Based Fluid Dynamics | Discrete Stochastic Simulation | Reaction-Diffusion Master Equation

Journal Article

12.
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Accuracy of the Michaelis - Menten approximation when analysing effects of molecular noise

Journal of the Royal Society Interface, ISSN 1742-5689, 05/2015, Volume 12, Issue 106, p. 20150054

Quantitative biology relies on the construction of accurate mathematical models, yet the effectiveness of these models is often predicated on making...

Reaction-diffusion master equation | Michaelis-Menten | Stochastic models | reaction-diffusion master equation | stochastic models | STEADY-STATE ASSUMPTION | MULTIDISCIPLINARY SCIENCES | MASTER EQUATION | Enzymes - chemistry | Reproducibility of Results | Algorithms | Models, Chemical | Stochastic Processes | Computer Simulation | Sensitivity and Specificity | Signal-To-Noise Ratio | Substrate Specificity | Enzyme Activation | Kinetics | Models, Statistical |

Reaction-diffusion master equation | Michaelis-Menten | Stochastic models | reaction-diffusion master equation | stochastic models | STEADY-STATE ASSUMPTION | MULTIDISCIPLINARY SCIENCES | MASTER EQUATION | Enzymes - chemistry | Reproducibility of Results | Algorithms | Models, Chemical | Stochastic Processes | Computer Simulation | Sensitivity and Specificity | Signal-To-Noise Ratio | Substrate Specificity | Enzyme Activation | Kinetics | Models, Statistical |