Erlang-delayed stochastic chemical kinetic formalism for efficient analysis of biological systems with non-elementary reaction effects
Pages 425 - 429
Abstract
Stochastic chemical kinetics (SCK) has become an important formalism for modeling and analysis of complex biological systems as it can capture the discreteness and the randomness of underlying biochemical reactions. One of the assumptions made by SCK is that each reaction be an elementary step which cannot be broken down into smaller steps. As such, transition events of the SCK model occur spontaneously in that there is no time lag between the reaction initiation and completion. In practice, however, it is very difficult to experimentally determine if an observed state change is a result of an elementary reaction or a sequence of several reaction steps. To test various hypotheses on such time-delays through the use of the SCK, all of the intermediate reactions and species need to be explicitly specified, which can quickly become cumbersome. To more efficiently model and analyze potential effects of such intermediate reaction steps, this paper proposes a new formalism for higher-level discrete-stochastic treatment of biological systems with reaction delays. Our new formalism can represent a time delay caused by intermediate reaction steps as an Erlang random variable, allowing a model's size to be reduced substantially. This paper illustrates an application of this formalism for analysis of the effect of different transcription elongation steps and rates on the distribution of RNA molecules.
References
[1]
D. Anderson. A modified next reaction method for simulating chemical systems with time dependent propensities and delays. J Chem Phys, 127:214107, 2007.
[2]
A. Arkin, J. Ross, and H. McAdams. Stochastic kinetic analysis of developmental pathway bifurcation in phage lambda-infected escherichia coli cells. Genetics, 149:1633--1648, 1998.
[3]
M. Barrio, K. Burrage, A. Leier, and T. Tian. Oscillatory regulation of Hes1: discrete stochastic delay modelling and simulation. PLoS Comput Biol, 2(9):1017--1030, 2006.
[4]
D. Bratsun, D. Volfson, L. Tsimring, and J. Hasty. Delay-induced stochastic oscillations in gene regulation. Proc. Nat. Acad. Sci. USA, 102(41):14593, 2005.
[5]
Y. Cao, D. Gillespie, and L. Petzold. The slow-scale stochastic simulation algorithm. J Chem Phys, 122, 2005.
[6]
M. Gibson and J. Bruck. Efficient exact stochastic simulation of chemical systems with many species and many channels. J Phys Chem, A 104:1876--1889, 2000.
[7]
D. T. Gillespie. Exact stochastic simulation of coupled chemical reactions. J Phys Chem, 81(25):2340--2361, 1977.
[8]
D. T. Gillespie. Markov Processes An Introduction for Physical Scientists. Academic Press, Inc., 1992.
[9]
D. T. Gillespie. Approximate accelerated stochastic simulation of chemically reacting systems. J Chem Phys, 115(4):1716--1733, 2001.
[10]
D. T. Gillespie. Stochastic simulation of chemical kinetics. Annu Rev Phys Chem, 58(1):35--55, 2007.
[11]
H. Kuwahara and C. Myers. Production-passage-time approximation: A new approximation method to accelerate the simulation process of enzymatic reactions. J Comput Biol, 15(7):779--792, 2008.
[12]
H. Kuwahara, C. J. Myers, and M. S. Samoilov. Temperature control of fimbriation circuit switch in uropathogenic Escherichia coli: Quantitative analysis via automated model abstraction. PLoS Comput Biol, 6(3):e1000723, 03 2010.
[13]
R. Losick and C. Desplan. Stochasticity and cell fate. Science, 320(5872):65, 2008.
[14]
I. Mura, D. Prandi, C. Priami, and A. Romanel. Exploiting non-Markovian Bio-Processes. ENTCS, 253(3):83--98, 2009.
[15]
W. H. Press, B. P. Flannery, S. A. Teukolsky, and W. T. Vetterling. Numerical Recipes in C: The art of Scientific Computing. Cambridge University Press, 2nd edition, 1992.
[16]
A. Raj and A. van Oudenaarden. Single-molecule approaches to stochastic gene expression. Ann Rev Biophys, 38:255--270, 2009.
[17]
M. S. Samoilov, G. Price, and A. P. Arkin. From Fluctuations to Phenotypes: The Physiology of Noise. Sci. STKE, 2006(366):re17--, 2006.
[18]
Y. Taniguchi, P. Choi, G. Li, H. Chen, M. Babu, J. Hearn, A. Emili, and X. Xie. Quantifying E. coli proteome and transcriptome with single-molecule sensitivity in single cells. Science, 329(5991):533, 2010.
Index Terms
- Erlang-delayed stochastic chemical kinetic formalism for efficient analysis of biological systems with non-elementary reaction effects
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Published In
August 2011
688 pages
ISBN:9781450307963
DOI:10.1145/2147805
- General Chairs:
- Robert Grossman,
- Andrey Rzhetsky,
- Program Chairs:
- Sun Kim,
- Wei Wang
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Published: 01 August 2011
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