Exact Stochastic Sşmulation Algorithms and Impulses in Biological Systems

Year 2018, , 41 - 47, 02.07.2018

Derya Altıntan , Vilda Purutçuoğlu

https://doi.org/10.22399/ijcesen.405778

Cited By: 1

Abstract

The
stochastic model is the only sort of expressions which can capture the
randomness of biological systems under different reactions. There are mainly
three methods;  Gillespie, first reaction
and next reaction algorithms; for implementing exact stochastic simulations in
these systems. Although these algorithms are successful in explaining the
natural behaviors of the systems’ activation, they cannot describe the absurd
changes, i.e.,  impulses. Moreover, the
source codes in R are not available and open for all users. In this study, we
produce these R codes and insert two major scenarios inside. In the
application, we use distinct dimensional systems and compare their
computational demands.

Keywords

Stochastic simulations, Impulses, Chemical master equations, Biological systems, Bioinformatics

References

• [1] J. M. Bower, H. Bolouri, “Computational Modelling of Genetic and Biochemical Networks”, MIT Press, 2000.
• [2] Y. Cao, H. Li, L. Petzold. “Efficient formulation of the stochastic simulation algorithm for chemically reacting systems”, Journal of Chemical Physics, 121 (9) (2004) 4059-4067. DOI: 10.1063/1.1778376
• 3] A. d'Onofrio, “Stability properties of pulse vaccination strategy in SEIR epidemic model”, Mathematical Biosciences, 179 (2002) 52-72.
• [4] M. A. Gibson and J. Bruck, “Efficient exact stochastic simulation of chemical systems with many species and many channels”, Journal of Physical Chemistry A, 104 (9) (2000) 1876-1889. DOI: 10.1021/ jp993732q
• [5] D. T. Gillespie, “Exact stochastic simulation of coupled chemical reactions”, Journal of Physical Chemistry, 81 (1977) 2340-2361. DOI: 10.1021/j100540a008
• [6] D. T. Gillespie, “A rigorous derivation of the chemical master equation”, Physica A, 188 (1992) 404-425.
• [7] S. A. Isaacson, “The reaction diffusion master equation as an asymptotic approximation of diffusion to a small target”, SIAM Journal of Applied Mathematics, 70 (1) (2009) 77-111.
• [8] N. G. Van Kampen, “Stochastic processes in physics and chemistry”, Amsterdam; New York, Elsevier North-Holland, 1981.
• [9] Z. Lu, X. Chi, L. Chen, “The effect of constant and pulse vaccination on SIR epidemic model with horizontal and vertical transmission”, Mathematical and Computer Modelling, 36 (2002) 1039-1057.
• [10] T. Mailwald, A. Schneider, H. Busch, S. Sahle, N. Gretz, T. S. Weiss, U. Kummer, U. Klinqmüller, “Combining theoretical analysis and experimental data generation reveals irf9 as a crucial factor for accelerating interferon-induced early antiviral signaling”, FEBS Journal 277 (22) (2010) 4741-4754. DOI: 10.1111/ j.1742 - 4658.2010.07880.x
• [11] T. Manninen, E. Makiraatikka, A. Ylipaa, A. Pettinen, K. Leinonen, M. L. Linne, “Discrete stochastic simulation of cell signalling: comparison of computational tools”, 28th IEEE EMBS Annual International Conference, New York City-USA pp. 2013-2016 (2006). DOI: 10.1109/IEMBS.2006. 260023
• [12] J. M. McCollum, G. D. Peterson, C. D. Cox, M. L. Simpson, N. F. Samatova, “The sorting direct method for stochastic simulation of biochemical systems with varying reaction execution behavior”, Computational Biology and Chemistry, 30 (1) (2006) 39-49. DOI: 10.1016/j.compbiolchem. 2005.10. 007
• [13] M. Pineda-Krch, “GillespieSSA: implementing the stochastic simulation algorithm in R”, Journal of Statistical Software, 25 (12) (2008) 1-18. DOI: 10.18637/jss.v025.i12
• [14] V. Purutçuoğlu, E. Wit, “Bayesian inference for the MAPK/ERK pathway by considering the dependency of the kinetic parameters”, Bayesian Analysis, 3 (2008) 851-886. DOI:10.1214/08-BA332
• [15] J. V. Rodriguez, J. A. Kaandorp, M. Dobrzynski, and J. G. Blom, “Spatial stochastic modelling of the phosphoenolpyruvate-dependent phosphotrans ferase (PTS) pathway in Escherichia coli”, Bioinformatics, 22 (15) (2006) 1895-1901. DOI:10.1093/bioinformatics/btl271
• [16] T.E. Turner, S. Schnell, K. Burrage, “Stochastic approaches for modelling in vivo reactions”, Computational Biology and Chemistry, 28 (2004) 165-178. DOI: 10.1016/j.compbiolchem. 2004.05. 001
• [17] D. J. Wilkinson, “Stochastic modelling for systems biology”, Chapman & Hall/CRC Mathematical and computational biology series. Boca Raton, FL: Taylor & Francis, 2006