ZI-Closure Scheme: A Method to Solve and Study Stochastic Reaction Networks
We use an example to present in exhaustive detail the algorithmic steps of the zero-information (ZI) closure scheme (Smadbeck and Kaznessis, Proc Natl Acad Sci USA 110:14261–14265, 2013). ZI-closure is a method for solving the chemical master equation (CME) of stochastic chemical reaction networks.
This work was supported by a grant from the National Institutes of Health (GM111358) and a grant from the National Science Foundation (CBET-1412283). This work utilized the high-performance computational resources of the Extreme Science and Engineering Discovery Environment (XSEDE), which is supported by National Science Foundation grant number ACI-1053575. Support from the University of Minnesota Digital Technology Center, from the Minnesota Supercomputing Institute (MSI), and from CAPES—Coordenaçäo de Aperfeiçoamento de Pessoal de Nível Superior—Brazil is gratefully acknowledged. This work was partially completed Spring 2016, when YNK was Visiting Scholar at the Isaac Newton Institute of Mathematical Sciences at the University of Cambridge, attending the programme Stochastic Dynamical Systems in Biology.
- 2.K.R. Popper, The Open Universe: An Argument for Indeterminism (Cambridge, Routledge, 1982), p. xixGoogle Scholar
- 3.W. James, The Dilemma of Determinism. The Will to Believe (New York, Dover, 1956)Google Scholar
- 4.I. Prigogine, The End of Certainty: Time, Chaos, and the New Laws of Nature (Free Press, New York, 1997)Google Scholar
- 7.N.G. Van Kampen, Stochastic Processes in Physics and Chemistry, Revised and enlarged edition (Elsevier, Amsterdam, 2004)Google Scholar
- 10.D.T Gillespie, A general method for numerically simulating the stochastic time evolution of coupled reactions. J. Comput. Phys. 22, 403–434 (1976)Google Scholar
- 20.M.H. DeGroot, M.H. Schervish, Probability and Statistics, 4th edn. (Pearson, Cambridge, 2012)Google Scholar