Abstract
As biomedical research advances there is an increasing need to model and simulate more complicated systems to better understand them. Since biochemical processes are inherently stochastic and often contain both continuous and discrete behavior, stochastic hybrid systems are an ideal modeling paradigm for capturing their dynamics. In this paper we present a framework for modeling biochemical systems and demonstrate the approach for the sugar cataract development process including two methods of modeling drug treatment. Further, we present a simulation method that uses second-order Taylor approximations for the continuous dynamics and an improved method for detecting boundary hits. We use the sugar cataract development process to demonstrate the results of the method.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Ghosh, R., Tomlin, C.: Symbolic reachable set computation of piecewise affine hybrid automata and its application to biological modeling: Delta-notch protein signalling. Sys. Bio. 1, 170–183 (2004)
Alur, R., Belta, C., Ivanicic, F., Kumar, V., Mintz, M., Pappas, G., Rubin, H., Schug, J.: Hybrid modeling and simulation of biomolecular networks. In: Di Benedetto, M.D., Sangiovanni-Vincentelli, A.L. (eds.) HSCC 2001. LNCS, vol. 2034, pp. 19–33. Springer, Heidelberg (2001)
Hespanha, J., Singh, A.: Stochastic models for chemically reacting systems using polynomial stochastic hybrid systems. Int. J. on Robust Cont., Special Issue on Control at Small Scales 15, 669–689 (2005)
Hu, J., Wu, W., Sastry, S.: Modeling subtilin production in bacillus subtilis using stochastic hybrid systems. In: Alur, R., Pappas, G.J. (eds.) HSCC 2004. LNCS, vol. 2993, pp. 417–431. Springer, Heidelberg (2004)
Drulhe, S., Ferrari-Trecate, G., de Jong, H., Viari, A.: Reconstruction of switching thresholds in piecewise-affine models of genetic regulatory networks. In: Hespanha, J.P., Tiwari, A. (eds.) HSCC 2006. LNCS, vol. 3927, pp. 184–199. Springer, Heidelberg (2006)
Salis, H., Kaznessis, Y.: Accurate hybrid stochastic simulation of a system of coupled chemical or biochemical reactions. J. Chem. Phys. 122, 54–103 (2005)
Ramos, M., Melo, A., Henriques, E., Gomes, J., Reuter, N., Maigret, B., Floriano, W., Nascimento, M.: Modeling enzyme-inhibitor interactions in serine proteases. Int. J. Quant. Chem. 74(3), 299–314 (1999)
Marini, I., Bucchioni, L., Borella, P., Corso, A.D., Mura, U.: Sorbitol dehydrogenase from bovine lens: Purification and properties. Arch. Biochem. and Biophy. 340, 383–391 (1997)
Mannella, R.: Absorbing boundaries and optimal stopping in a stochastic differential equation. Phys. Lett. A 254, 257–262 (1999)
Lamm, G.: Extended brownian dynamics. iii. three dimensional diffusion. J. Chem. Phys. 80(6), 2845–2855 (1983)
Peters, E., Barenbrug, T.: Efficient brownian dynamics simulation of particles near walls. i. reflecting and absorbing walls. Physical Review 66, 1–7 (2002)
Elowitz, M., Levine, A., Siggia, E., Swain, P.: Stochastic gene expression in a single cell. Science 1183(297) (2002)
Bujorianu, M., Lygeros, J.: Theoretical foundations of general stochastic hybrid systems: Modeling and optimal control. In: IEEE Conf. on Dec. and Cont. (2004)
Koutsoukos, X., Riley, D.: Computational methods for reachability analysis of stochastic hybrid systems. In: Hespanha, J.P., Tiwari, A. (eds.) HSCC 2006. LNCS, vol. 3927, pp. 377–391. Springer, Heidelberg (2006)
Bernadskiy, M., Sharykin, R., Alur, R.: Structured modeling of concurrent stochastic hybrid systems. In: Lakhnech, Y., Yovine, S. (eds.) FORMATS 2004 and FTRTFT 2004. LNCS, vol. 3253, pp. 309–324. Springer, Heidelberg (2004)
Riley, D., Koutsoukos, X., Riley, K.: Safety analysis of sugar cataract development using stochastic hybrid systems. In: Bemporad, A., Bicchi, A., Buttazzo, G. (eds.) HSCC 2007. LNCS, vol. 4416, pp. 758–761. Springer, Heidelberg (2007)
Kloeden, P., Platen, E.: Numerical Solution of Stochastic Differential Equations. Springer, Heidelberg (1999)
Gobet, E.: Euler schemes and half-space approximation for the simulation of diffusion in a domain. ESAIM: Probability and Statistics 5, 261–297 (2001)
Gillespie, D.: A general method for numerically simulating the stochastic time evolution of coupled chemical reactions. J. Comp. Phys. 22, 403–434 (1976)
Auger, A., Chatelain, P., Koumoutsakos, P.: R-leaping: Accelerating the stochastic simulation algorithm by reaction leaps. J. Chem. Phys. 125, 84–103 (2006)
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 2008 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Riley, D., Koutsoukos, X., Riley, K. (2008). Modeling and Simulation of Biochemical Processes Using Stochastic Hybrid Systems: The Sugar Cataract Development Process. In: Egerstedt, M., Mishra, B. (eds) Hybrid Systems: Computation and Control. HSCC 2008. Lecture Notes in Computer Science, vol 4981. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-78929-1_31
Download citation
DOI: https://doi.org/10.1007/978-3-540-78929-1_31
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-78928-4
Online ISBN: 978-3-540-78929-1
eBook Packages: Computer ScienceComputer Science (R0)