scholarly journals On the origins of approximations for stochastic chemical kinetics

2005 ◽  
Vol 123 (16) ◽  
pp. 164115 ◽  
Author(s):  
Eric L. Haseltine ◽  
James B. Rawlings
Keyword(s):  
Chemical Kinetics ◽  
Stochastic Chemical Kinetics

scholarly journals IMPLICIT SIMULATION METHODS FOR STOCHASTIC CHEMICAL KINETICS

2015 ◽  
Vol 5 (3) ◽  
pp. 420-452 ◽  
Author(s):  
Tae-Hyuk Ahn ◽  
◽  
Xiaoying Han ◽  
Adrian Sandu ◽  
◽  
...  
Keyword(s):  
Chemical Kinetics ◽  
Simulation Methods ◽  
Stochastic Chemical Kinetics

Preconditioned Bayesian Regression for Stochastic Chemical Kinetics

2013 ◽  
Vol 58 (3) ◽  
pp. 592-626 ◽  
Author(s):  
Alen Alexanderian ◽  
Francesco Rizzi ◽  
Muruhan Rathinam ◽  
Olivier P. Le Maître ◽  
Omar M. Knio
Keyword(s):  
Chemical Kinetics ◽  
Bayesian Regression ◽  
Stochastic Chemical Kinetics

scholarly journals Enhanced identification and exploitation of time scales for model reduction in stochastic chemical kinetics

2008 ◽  
Vol 129 (24) ◽  
pp. 244112 ◽  
Author(s):  
Carlos A. Gómez-Uribe ◽  
George C. Verghese ◽  
Abraham R. Tzafriri
Keyword(s):  
Model Reduction ◽  
Chemical Kinetics ◽  
Time Scales ◽  
Stochastic Chemical Kinetics

Effect of reactant size on discrete stochastic chemical kinetics

2007 ◽  
Vol 126 (3) ◽  
pp. 034302 ◽  
Author(s):  
Dan T. Gillespie ◽  
Sotiria Lampoudi ◽  
Linda R. Petzold
Keyword(s):  
Chemical Kinetics ◽  
Stochastic Chemical Kinetics

scholarly journals The subtle business of model reduction for stochastic chemical kinetics

2009 ◽  
Vol 130 (6) ◽  
pp. 064103 ◽  
Author(s):  
Dan T. Gillespie ◽  
Yang Cao ◽  
Kevin R. Sanft ◽  
Linda R. Petzold
Keyword(s):  
Model Reduction ◽  
Chemical Kinetics ◽  
Stochastic Chemical Kinetics

scholarly journals Infinite level-dependent QBD processes and matrix-analytic solutions for stochastic chemical kinetics

2011 ◽  
Vol 43 (4) ◽  
pp. 1005-1026 ◽  
Author(s):  
Tuğrul Dayar ◽  
Werner Sandmann ◽  
David Spieler ◽  
Verena Wolf
Keyword(s):  
Chemical Kinetics ◽  
Numerical Experiments ◽  
Analytic Solutions ◽  
Lyapunov Theory ◽  
Stationary Probability ◽  
Stochastic Chemical Kinetics ◽  
Stationary Probability Distribution ◽  
Qbd Processes ◽  
Level Number ◽  
Probability Mass

Systems of stochastic chemical kinetics are modeled as infinite level-dependent quasi-birth-and-death (LDQBD) processes. For these systems, in contrast to many other applications, levels have an increasing number of states as the level number increases and the probability mass may reside arbitrarily far away from lower levels. Ideas from Lyapunov theory are combined with existing matrix-analytic formulations to obtain accurate approximations to the stationary probability distribution when the infinite LDQBD process is ergodic. Results of numerical experiments on a set of problems are provided.

Modelling the dynamics of signalling pathways

2008 ◽  
Vol 45 ◽  
pp. 1-28 ◽  
Author(s):  
Sree N. Sreenath ◽  
Kwang-Hyun Cho ◽  
Peter Wellstead
Keyword(s):  
Chemical Kinetics ◽  
Transforming Growth Factor ◽  
Interleukin 1 ◽  
Transforming Growth Factor Β ◽  
Nuclear Factor Κb ◽  
Stochastic Chemical Kinetics ◽  
Discrete State ◽  
Explicit Mention ◽  
Decision Making Processes ◽  
The Right

In the present chapter we discuss methodologies for the modelling, calibration and validation of cellular signalling pathway dynamics. The discussion begins with the typical range of techniques for modelling that might be employed to go from the chemical kinetics to a mathematical model of biochemical pathways. In particular, we consider the decision-making processes involved in selecting the right mechanism and level of detail of representation of the biochemical interactions. These include the choice between (i) deterministic and stochastic chemical kinetics representations, (ii) discrete and continuous time models and (iii) representing continuous and discrete state processes. We then discuss the task of calibrating the models using information available in web-based databases. For situations in which the data are not available from existing sources we discuss model calibration based upon measured data and system identification methods. Such methods, together with mathematical modelling databases and computational tools, are often available in standard packages. We therefore make explicit mention of a range of popular and useful sites. As an example of the whole modelling and calibration process, we discuss a study of the cross-talk between the IL-1 (interleukin-1)-stimulated NF-κB (nuclear factor κB) pathway and the TGF-β (transforming growth factor β)-stimulated Smad2 pathway.

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