Determining the long-term behavior of cell populations: A new procedure for detecting ergodicity in large stochastic reaction networks

IFAC Proceedings Volumes (IFAC-PapersOnline)

Volumn 19, Issue , 2014, Pages 1711-1716

  Gupta, Ankit ^a   Khammash, Mustafa ^a  

^a ETH ZURICH   (Switzerland)

Author keywords

Ergodicity; Markov models; Reaction networks; Stationarity; Stochastic systems

Indexed keywords

AUTOMATION; CELL CULTURE; CELL PROLIFERATION; CONSTRAINT SATISFACTION PROBLEMS; MARKOV PROCESSES; ORDINARY DIFFERENTIAL EQUATIONS; PROBABILITY DISTRIBUTIONS; STOCHASTIC CONTROL SYSTEMS; STOCHASTIC SYSTEMS;

CHEMICAL MASTER EQUATION; ERGODICITY; FEASIBILITY PROBLEM; MACROSCOPIC PROPERTIES; MARKOV MODEL; REACTION NETWORK; STATIONARITY; UNDERLYING DYNAMICS;

STOCHASTIC MODELS;

EID: 84923807226     PISSN: 14746670     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.3182/20140824-6-za-1003.00291     Document Type: Conference Paper

References (9)

1. Briat, C., Gupta, A., and Khammash, M. (2013). A scalable computational framework for establishing longterm behavior of stochastic reaction networks. Unpublished. Available on arXiv:1304.5404.
2. Cohen, H. (1993). A course in computational algebraic number theory, Volume 138 of Graduate Texts in Mathematics. Springer-Verlag, Berlin.
3. Davis, C. (1954). Theory of positive linear dependence. Amer. J. Math., 76, 733-746.
4. Elowitz, M.B., Levine, A.J., Siggia, E.D., and Swain, P.S. (2002). Stochastic gene expression in a single cell. Science, 297(5584), 1183-1186.
5. Gillespie, D.T. (1977). Exact stochastic simulation of coupled chemical reactions. The Journal of Physical Chemistry, 81(25), 2340-2361.
6. Meyn, S.P. and Tweedie, R.L. (1993). Stability of Markovian processes. III. Foster-Lyapunov criteria for continuous-time processes. Adv. in Appl. Probab., 25(3), 518-548.
7. Norris, J.R. (1998). Markov chains, Volume 2 of Cambridge Series in Statistical and Probabilistic Mathematics. Cambridge University Press, Cambridge. Reprint of 1997 original.
8. Pauleve, L., Craciun, G., and Koeppl, H. (2013). Dynamical properties of discrete reaction networks. Unpublished. Available on arXiv:1302.3363.
9. Vilar, J.M.G., Kueh, H.Y., Barkai, N., and Leibler, S. (2002). Mechanisms of noise-resistance in genetic oscillator. Proc. Natl. Acad. Sci., 99(9), 5988-5992.