Abstract
Stochastic models of biological networks are well-established in computational systems biology. However, models are abstractions and parameters may be inaccurate or perturbed. An important topic is thus the sensitivity of analysis results to parameter perturbations. This investigates how seriously potential parameter perturbations affect the analysis results and to which parameters the results are most sensitive. In this paper, a stochastic simulation algorithm is presented that yields results for multiple perturbed models from a single simulation experiment and that is thus able to perform comparisons of results for various parameter sets without explicitly simulating each of these separately. The algorithm essentially makes use of likelihood ratios in a similar fashion as in the Importance Sampling technique for variance reduction. With a suitable adaptation to the context of perturbed model parameters it yields substantial runtime savings compared to multiple separate simulations of the perturbed models without any loss in statistical accuracy.
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References
Arkin, A., Ross, J., McAdams, H.H.: Stochastic kinetic analysis of developmental pathway bifurcation in phage λ-infected escherichia coli cells. Genetics 149, 1633–1648 (1998)
Blake, W.J., Kaern, M., Cantor, C.R., Collins, J.J.: Noise in eukaryotic gene expression. Nature 422, 633–637 (2003)
Fedoroff, N., Fontana, W.: Small numbers of big molecules. Science 297, 1129–1131 (2002)
McAdams, H.H., Arkin, A.: Stochastic mechanisms in gene expression. Proceedings of the National Academy of Science USA 94, 814–819 (1997)
McAdams, H.H., Arkin, A.: It’s a noisy business! Trends in Genetics 15(2), 65–69 (1999)
Turner, T.E., Schnell, S., Burrage, K.: Stochastic approaches for modelling in vivo reactions. Computational Biology and Chemistry 28, 165–178 (2004)
Gillespie, D.T.: A general method for numerically simulating the time evolution of coupled chemical reactions. Journal of Computational Physics 22, 403–434 (1976)
Gillespie, D.T.: Exact stochastic simulation of coupled chemical reactions. Journal of Physical Chemistry 71(25), 2340–2361 (1977)
Gillespie, D.: Approximate accelerated stochastic simulation of chemically reacting systems. Journal of Chemical Physics 115, 1716–1732 (2001)
Gunawan, R., Cao, Y., Petzold, L.R., Doyle III, F.J.: Sensitivity analysis of discrete stochastic systems. Biophysical Journal 88, 2530–2540 (2005)
Delbrück, M.: Statistical fluctuations in autocatalytic reactions. Journal of Chemical Physics 8, 120–124 (1940)
Singer, K.: Application of the theory of stochastic processes to the study of irreproducible chemical reactions and nucleation processes. Journal of the Royal Statistical Society 15, 92–106 (1953)
Bartholomay, A.F.: A Stochastic Approach to Chemical Reaction Kinetics. Thesis, Harvard University (1957)
Bharucha-Reid, A.T.: Elements of the Theory of Markov Processes and Their Applications. McGraw-Hill, New York (1960)
McQuarrie, D.A.: Stochastic approach to chemical kinetics. Journal of Applied Probability 4, 413–478 (1967)
van Kampen, N.: Stochastic Processes in Physics and Chemistry. Elsevier, Amsterdam (1992)
Gillespie, D.T.: A rigorous derivation of the chemical master equation. Physica A 188, 404–425 (1992)
Wolkenhauer, O., Ullah, M., Kolch, W., Cho, K.H.: Modelling and simulation of intracellular dynamics: Choosing an appropriate framework. IEEE Transactions On NanoBioScience 3(3), 200–207 (2004)
Bremaud, P.: Markov Chains. Springer, Heidelberg (1999)
Bortz, A.B., Kalos, M.H., Lebowitz, J.L.: A new algorithm for Monte Carlo simulation of Ising spin systems. Journal of Computational Physics 17, 10–18 (1975)
Gibson, M.A., Bruck, J.: Efficient exact stochastic simulation of chemical systems with many species and many channels. Journal of Physical Chemistry A 104, 1876–1889 (2000)
Cao, Y., Li, H., Petzold, L.R.: Efficient formulation of the stochastic simulation algorithm for chemically reacting systems. Journal of Chemical Physics 121(9), 4059–4067 (2004)
Feller, W.: An Introduction to Probability Theory and its Applications, vol. 2. Wiley, Chichester (1971)
Shiryaev, A.N.: Probability, 2nd edn. Springer, Heidelberg (1995)
Hammersley, J.M., Handscomb, D.C.: Monte Carlo Methods. Methuen (1964)
Glynn, P.W., Iglehart, D.L.: Importance sampling for stochastic simulations. Management Science 35(11), 1367–1392 (1989)
Cao, Y., Gillespie, D., Petzold, L.: Avoiding negative populations in explicit Poisson tau-leaping. Journal of Chemical Physics 123, 54104 (2005)
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Sandmann, W. (2007). Simultaneous Stochastic Simulation of Multiple Perturbations in Biological Network Models. In: Calder, M., Gilmore, S. (eds) Computational Methods in Systems Biology. CMSB 2007. Lecture Notes in Computer Science(), vol 4695. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-75140-3_2
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DOI: https://doi.org/10.1007/978-3-540-75140-3_2
Publisher Name: Springer, Berlin, Heidelberg
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