Kinetic Monte Carlo
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Contents |
Seminal Papers
- Bortz, A.B., Kalos, M.H. and Lebowitz, J.L. (1975) Journal of Computational Physics 17 10-18. (pdf)
This paper is usually cited as the basis for KMC in the physics literature, although there are older simulations using null event type algorithms.
- D. T. Gillespie (1976) A general method for numerically simulating the stochastic time evolution of coupled chemical reactions. J. Comput. Phys. 22, 403. [1]
- D.T. Gillespie (1977) Exact stochastic simulation of coupled chemical reactions. J. Phys. Chem. 81, 2340-61. [2]
Reviews
- H. Li, Y. Cao, L. R. Petzold, and D. T. Gillespie. Algorithms and Software for Stochastic Simulation of Biochemical Reacting Systems. Biotechnol. Prog. Epub ahead of print. PMID 17894470
Recent review of available software. Looks like it might be incomplete, but I haven't read it so anyone who does please fill in here. --Faeder 18:39, 16 November 2007 (EST)
- D. T. Gillespie (2007) Stochastic simulation of chemical kinetics. Annu. Rev. Phys. Chem. 58 35-55. PMID 17037977.
- A. F. Voter (2007) Introduction to the kinetic Monte Carlo method. In Radiation Effects in Solids (K. E. Sickafus, E. A. Kotomin and B. P. Uberuaga., Eds.) Springer, Berlin, Ch. 1. ISBN: 978-1-4020-5293-4
- A. Chatterjee and D. G. Vlachos (2007) An overview of spatial microscopic and accelerated kinetic Monte Carlo methods. J. Computer-Aided Mater. Des. 14 253-308. [3]
Algorithmic Refinements
- M. A. Gibson and J. Bruck, "Efficient Exact Stochastic Simulation of Chemical Systems with Many Species and Many Channels," J. Phys. Chem. A 104 (2000) 1876-1889.
- Y. Cao, H. Li and L. Petzold, "Efficient formulation of the stochastic simulation algorithm for chemically reacting systems," J. Chem. Phys. 121 (2004) 4059-4067.
- J. M. McCollum, G. D. Peterson, C. D. Cox, M. L. Simpson and N. F. Samatova, "The sorting direct method for stochastic simulation of biochemical systems with varying reaction execution behavior," Comput. Biol. Chem. 30 (2006) 39-49.
- T. P. Schulze (2002) Kinetic Monte Carlo simulations with minimal searching. Phys. Rev. E 65, [4]
- J. L. Blue, I. Beichl and F. Sullivan (1994) Phys. Rev. E 51, R867.
Rule-Based Extensions
- J. Yang, M. Monine, J. R. Faeder, and W. S. Hlavacek (2007) Kinetic Monte Carlo Method for Rule-based Modeling of Biochemical Networks. Submitted. (preprint)
This short paper presents a rule-based KMC method based on simulation of individual particles rather than populations. The Gillespie method is used for event sampling, but the scaling is independent of the feasible network size.
- V. Danos, J. Feret, W. Fontana, and J. Krivine (2007) Scalable simulation of cellular signalling networks. Lecture Notes in Computer Science 4807, 139. (preprint)
This paper provides a formal description of a method for doing KMC of rule-based models using the Gillespie method for event selection. Method is applied to a network model of EGFR signaling with about 70 rules that has a feasible state space of 1023 species.
- V. Danos, J. Feret, W. Fontana, R. Harmer and J. Krivine (2007) Rule-based modelling of cellular signalling. Lecture Notes in Computer Science 4703, 17-41. [5] (preprint)
The primary focus of this paper is to show how concurrent languages, such as kappa and BNGL, can be used to model signal transduction. The paper does, however, introduce the idea of rule-based Gillespie simulations in Section 2.3. Here is the relevant section, which nicely summarizes the idea of using rules rather than reactions as the basis for KMC:
The trajectories are obtained using an entirely rule-based version of Gillespie’s kinetics which generates a continuous time Markov chain [34]. At any given time a rule can apply to a given state in a number of ways. That number is multiplied by the rate of the rule and defines the rule’s activity or flux in that state of the system. It determines the likelihood that this rule will fire next, while the total activity of the system determines probabilistically the associated time advance. This simulation principle can be implemented within with rather nice complexity properties, since the cost of a simulation event (triggering a rule) can be made independent on the size of the agent population and depends only logarithmically in the number of rules. This is very useful when it comes to larger systems.
