The chemical master equation
Approximating the solution of the chemical master equation by aggregation
... The chemical master equation is a continuous time discrete space Markov model of chemical ...The chemical master equation is derived mathematically and it is shown that ...
14
Hybrid Stochastic–Deterministic Solution of the Chemical Master Equation
... words. chemical master equation, hybrid model, multiscale analysis, partial averaging, asymp- totic approximation, WKB-ansatz AMS subject ...fundamental equation of stochastic chemical ...
31
Chemical master equation and Langevin regimes for a gene transcription model
... cal Master Equation framework is based on modelling assumptions that are highly appropriate for this context, and the Stochastic Simulation Algorithm (also known as Gillespie’s algorithm) allows for ...
19
Improved Krylov-FSP Method for Solving the Chemical Master Equation
... Improved Krylov-FSP Method for Solving the Chemical Master Equation Huy D. Vo, Roger B. Sidje Abstract—Model reduction techniques are needed to directly solve the chemical master ...
6
On the numerical solution of the chemical master equation with sums of rank one tensors
... the chemical master equation admits low rank ...the chemical master equations have a natural low rank structure we think that the tensor product approaches are more promising for some ...
16
An improved finite state projection algorithm for the numerical solution of the chemical master equation with applications S
... S. MacNamara 1 K. Burrage 2 R. B. Sidje 3 (Received 1 September 2006; revised 8 September 2007) Abstract Recently, Munsky and Khammash suggested the Finite State Pro- jection (fsp) algorithm for the numerical solution of ...
23
The total quasi-steady state assumption: its justification by singular perturbation and its application to the chemical master equation
... C. F. Khoo 1 M. Hegland 2 (Received 14 August 2008; revised 18 November 2008) Abstract Deterministic models of enzymatic reactions based on the quasi- steady state assumption (qssa) and total quasi-steady state assump- ...
15
Dimensionality Reduction of the Chemical Master Equation
... differential equation-based models is that they are deterministic, and so cannot capture the variability that often dominates the behavior of biochemical networks, especially when molecular populations are small ...
149
Automatic Simulation of the Chemical Langevin Equation
... the Chemical Langevin Equation model has a closed form ...cal Master Equation. The Chemical Langevin Equation model is an approximation of the Chemical Master Equa- ...
7
Chemical master versus chemical langevin for first-order reaction networks
... the Chemical Langevin Equation for a generic first-order reaction ...the Chemical Langevin Equation is an excellent proxy for the Chemical Master ...the Chemical Langevin ...
21
Chemical master versus chemical langevin for first-order reaction networks
... The Chemical Langevin Equation is a stochastic differential equation that can be regarded as an approximation to the underlying jump ...Langevin Equation allows simulations to be performed ...
23
Multiscale modeling of chemical kinetics via the master equation
... The Schl¨ ogl reactions were used to demonstrate work on τ -Leap methods in [28], where it was noted that estimates of the mean and variance alone do not give sufficient insight into the b[r] ...
23
The Spatial Chemical Langevin Equation and Reaction Diffusion Master Equations: moments and qualitative solutions
... each equation term-wise, we showed that the RDME and SCLE match at the leading and second-leading orders, whereas deter- ministic approaches match only at the leading ...
14
Operator Approach to the Master Equation for the One-Step Process
... physical, chemical, technical, biological, environmental, economic, and sociological ...this equation. The expansion of the equation in a formal Taylor series (the so called Kramers–Moyal’s ...
6
A hybrid moment equation approach to gas-grain chemical modeling
... the master equation prescription can be “realized” through a stochastic simulation algorithm (SSA), pro- posed by Gillespie 1976 (see also Gillespie 1977 , 2007 ...the master equation, so this ...
11
Chemical Reactions 2 The Chemical Equation
... The Chemical Equation INFORMATION Chemical equations are symbolic devices used to represent actual chemical ...the equation, called the reactants, is separated with an arrow (Æ) from ...
5
Interpreting the chemical equation
... balanced chemical equation. A chemical equation tells us what substances are added together as reactants and what substances are produced as ...a chemical reaction because atoms can not ...
11
Balancing Chemical Equation
... ➢The electrons lost (during oxidation) must equal the electrons gained (during reduction).. Balancing Oxidation-Reduction Reactions:..[r] ...
On a Fractional Master Equation and a Fractional Diffusion Equation
... *Corresponding Author: [email protected] Copyright © 2013 Horizon Research Publishing All rights reserved. Abstract In this paper , we derive the solutions of fractional master equation defined by (2.1) ...
5
Steps for balancing a chemical equation
... B. Law of Conservation of Mass - Matter cannot be gained or lost in the process of a chemical reaction. The law of conservation of mass states that we must have a balanced equation. C. List five factors ...
8