Modeling of stochastic biological processes with non-polynomial propensities using non-central conditional moment equation

IFAC Proceedings Volumes (IFAC-PapersOnline)

Volumn 19, Issue , 2014, Pages 1729-1735

  Kazeroonian, Atefeh ^a,b   Theis, Fabian J ^a,b   Hasenauer, Jan ^a,b  

^a INSTITUTE OF EPIDEMIOLOGY   (Germany)

^b TECHNICAL UNIVERSITY OF MUNICH   (Germany)

Author keywords

Chemical master equation; Moment equations; Stochastic modeling

Indexed keywords

AUTOMATION; RATIONAL FUNCTIONS; STOCHASTIC CONTROL SYSTEMS; STOCHASTIC MODELS;

BIOLOGICAL PROCESS; CHEMICAL MASTER EQUATION; CONDITIONAL MOMENTS; DIRECT SIMULATION; HIGHER ORDER REACTION; METHOD OF CONDITIONAL MOMENTS; MOMENT EQUATIONS; STOCHASTIC FLUCTUATION;

STOCHASTIC SYSTEMS;

EID: 84929714133     PISSN: 14746670     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.3182/20140824-6-za-1003.02298     Document Type: Conference Paper

References (24)

1. A. Eldar and M. B. Elowitz. Functional roles for noise in genetic circuits. Nature, 467(9):1-7, Sept. 2010. doi:10.1038/nature09326.
2. S. Engblom. Computing the moments of high dimensional solutions of the master equation. Appl. Math. Comp., 180:498-515, 2006.
3. W. Feller. On the integro-differential equation of purely discontinous Markoff processes. Trans. of the American Mathematical Society, 48:4885-4915, 1940.
4. C. W. Gardiner. Handbook of stochastic methods: For physics, chemistry and natural sciences. Springer Series in Synergetics. Springer Berlin / Heidelberg, 4th edition, 2011.
5. C. S. Gillespie. Moment-closure approximations for mass-action models. IET Syst. Biol., 3(1):52-58, 2009.
6. E. L. Haseltine and J. B. Rawlings. Approximate simulation of coupled fast and slow reactions for stochastic chemical kinetics. J. Chem. Phys., 117(15):6959-6969, 2002.
7. E. L. Haseltine and J. B. Rawlings. On the origins of approximations for stochastic chemical kinetics. J. Chem. Phys., 123(164115), 2005.
8. J. Hasenauer, V. Wolf, A. Kazeroonian, and F. J. Theis. Method of conditional moments (MCM) for the chemical master equation. J. Math. Biol., pages 1-49, 2013.
9. A. Hellander and P. Lötstedt. Hybrid method for the Chemical Master Equation. J. Comput. Phys., 227:100-122, 2007.
10. T. A. Henzinger, L. Mikeev, M. Mateescu, and V. Wolf. Hybrid numerical solution of the chemical master equation. In Proceedings of the 8th International Conference on Computational Methods in Systems Biology, pages 55-65, New York, NY, USA, 2010. ACM.
11. T. Jahnke. On reduced models for the chemical master equation. Multiscale Model. Simul., 9(4):1646-1676, 2011.
12. T. Jahnke and W. Huisinga. Solving the chemical master equation for monomolecular reaction systems analytically. J. Math. Biol., 54(1):1-26, 2007.
13. I. Lestas, G. Vinnicombe, and J. Paulsson. Fundamental limits on the suppression of molecular fluctuations. Nat., 467:174-178, Sept. 2010.
14. S. Menz, J. C. Latorre, C. Schütte, and W. Huisinga. Hybrid stochastic deterministic solution of the Chemical Master Equation. SIAM J. on Multiscale Model. Simul., 10(4):1232-1262, 2012.
15. P. Milner, C. S. Gillespie, and D. J. Wilkinson. Moment closure approximations for stochastic kinetic models with rational rate laws. Mathematical Biosciences, 231 (2):99-104, 2011.
16. B. Munsky and M. Khammash. The finite state projection algorithm for the solution of the chemical master equation. J. Chem. Phys., 124(4):044104, 2006.
17. B. Munsky, B. Trinh, and M. Khammash. Listening to the noise: random fluctuations reveal gene network parameters. Mol. Syst. Biol., 5(318), 2009.
18. B. Munsky, G. Neuert, and A. von Oudenaarden. Using gene expression noise to understand gene regulation. Science, 336 (6078):183-187, 2012.
19. J. M. Raser and E. K. O'Shea. Control of stochasticity in eukaryotic gene expression. Science, 304 (5678):1811-1814, 2004.
20. R. Sidje, K. Burrage, and S. MacNamara. Inexact uniformization method for computing transient distributions of Markov chains. SIAM J. Sci. Comput., 29(6): 2562-2580, 2007.
21. A. Singh and J. P. Hespanha. Approximate moment dynamics for chemically reacting systems. IEEE Trans. Autom. Control, 56(2):414-418, 2011.
22. Y. Taniguchi, P. J. Choi, G.-W. Li, H. Chen, M. Babu, J. Hearn, A. Emili, and X.S. Xie. Quantifying E. coli proteome and transcriptome with single-molecule sensitivity in single cells. Science, 329 (5991):533-538, 2010.
23. N. G. van Kampen. Stochastic processes in physics and chemistry. North-Holland, Amsterdam, 3rd revised edition, 2007.
24. C. Zechner, J. Ruess, P. Krenn, S. Pelet, M. Peter, J. Lygeros, and H. Koeppl. Moment-based inference predicts bimodality in transient gene expression. Proc. Nati. Acad. Sci. USA, 109(21):8340-8345, 2012.