Abstract
Starting from a biochemical signalling pathway model expressed in a process algebra enriched with quantitative information we automatically derive both continuous-space and discrete-state representations suitable for numerical evaluation. We compare results obtained using implicit numerical differentiation formulae to those obtained using approximate stochastic simulation thereby exposing a flaw in the use of the differentiation procedure producing misleading results.
This is a preview of subscription content, log in via an institution to check access.
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
Schoeberl, B., Eichler-Jonsson, C., Gilles, E.D., Muller, G.: Computational modeling of the dynamics of the MAP kinase cascade activated by surface and internalized EGF receptors. Nature Biotechnology 20, 370–375 (2002)
Hillston, J.: A Compositional Approach to Performance Modelling. Cambridge University Press, Cambridge (1996)
Calder, M., Gilmore, S., Hillston, J.: Modelling the influence of RKIP on the ERK signalling pathway using the stochastic process algebra PEPA. In: Ingolfsdottir, A., Nielson, H.R. (eds.) Proceedings of the BioConcur Workshop on Concurrent Models in Molecular Biology, London, England (August 2004)
Calder, M., Gilmore, S., Hillston, J.: Automatically deriving ODEs from process algebra models of signalling pathways. In: Plotkin, G. (ed.) Proceedings of Computational Methods in Systems Biology (CMSB 2005), Edinburgh, Scotland, pp. 204–215 (April 2005)
Cho, K.-H., Shin, S.-Y., Kim, H.-W., Wolkenhauer, O., McFerran, B., Kolch, W.: Mathematical modeling of the influence of RKIP on the ERK signaling pathway. In: Priami, C. (ed.) CMSB 2003. LNCS, vol. 2602, pp. 127–141. Springer, Heidelberg (2003)
Calder, M., Gilmore, S., Hillston, J.: Modelling the influence of RKIP on the ERK signalling pathway using the stochastic process algebra PEPA. Transactions on Computational Systems Biology (2006); Extended version of [3] (to appear)
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)
Gillespie, D.T.: Exact stochastic simulation of coupled chemical reactions. Journal of Physical Chemistry 81(25), 2340–2361 (1977)
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., Petzold, L.R.: Improved leap-size selection for accelerated stochastic simulation. J. Comp. Phys. 119, 8229–8234 (2003)
Rathinam, M., Petzold, L.R., Cao, Y., Gillespie, D.T.: Stiffness in stochastic chemically reacting systems: The implicit tau-leaping method. Journal of Chemical Physics 119(24), 12784–12794 (2003)
Cao, Y., Gillespie, D.T., Petzold, L.: Accelerated stochastic simulation of the stiff enzyme-substrate reaction. Journal of Chemical Physics 123, 144917–1 – 144917–12 (2005)
Gillespie, D., Petzold, L.: System Modelling in Cellular Biology. In: Szallasi, Z., Stelling, J., Periwal, V. (eds.) Numerical Simulation for Biochemical Kinetics. MIT Press, Cambridge (2006)
Chatterjee, A., Mayawala, K., Edwards, J.S., Vlachos, D.G.: Time accelerated Monte Carlo simulations of biological networks using the binomial τ-leap method. Bioinformatics 21(9), 2136–2137 (2005)
Calder, M., Vyshemirsky, V., Gilbert, D., Orton, R.: Analysis of signalling pathways using the PRISM model checker. In: Plotkin, G. (ed.) Proceedings of Computational Methods in Systems Biology (CMSB 2005), Edinburgh, Scotland (April 2005)
Kwiatkowska, M., Norman, G., Parker, D.: PRISM: Probabilistic symbolic model checker. In: Field, T., Harrison, P.G., Bradley, J., Harder, U. (eds.) TOOLS 2002. LNCS, vol. 2324, pp. 200–204. Springer, Heidelberg (2002)
Aziz, A., Sanwal, K., Singhal, V., Brayton, R.: Model checking continuous time Markov chains. ACM Transactions on Computational Logic 1, 162–170 (2000)
Cardelli, L.: Mapk cascade. Microsoft Research Cambridge UK technical note (July 2005), Available on-line at: http://research.microsoft.com/Users/luca/Notes/MapkCascade.pdf
Chi-Ying, F.H., Ferrell Jr., J.E.: Ultrasensitivity in the mitogen-activated protein kinase cascade. Biochemistry 93(19), 10078–10083 (1996)
Hillston, J.: Process algebras for quantitative analysis. In: Proceedings of the 20th Annual IEEE Symposium on Logic in Computer Science (LICS 2005), Chicago, pp. 239–248. IEEE Computer Society Press, Los Alamitos (2005)
Hillston, J.: Fluid flow approximation of PEPA models. In: Proceedings of the Second International Conference on the Quantitative Evaluation of Systems, Torino, Italy, pp. 33–43. IEEE Computer Society Press, Los Alamitos (2005)
Priami, C., Regev, A., Silverman, W., Shapiro, E.: Application of a stochastic name passing calculus to representation and simulation of molecular processes. Information Processing Letters 80, 25–31 (2001)
Shampine, L.F., Reichelt, M.W.: The Matlab ODE suite. SIAM J. Sci. Comput. 18(1), 1–22 (1997)
Buchholtz, M., Gilmore, S., Haenel, V., Montangero, C.: End-to-end integrated security and performance analysis on the DEGAS Choreographer platform. In: Fitzgerald, J.S., Hayes, I.J., Tarlecki, A. (eds.) FM 2005. LNCS, vol. 3582, pp. 286–301. Springer, Heidelberg (2005)
Ramsey, S., Orrell, D., Bolouri, H.: Dizzy: stochastic simulation of large-scale genetic regulatory networks. J. Bioinf. Comp. Biol. 3(2), 415–436 (2005)
Hucka, M., Finney, A., Sauro, H.M., Bolouri, H., Doyle, J.C., Kitano, H., et al.: The systems biology markup language (SBML): a medium for representation and exchange of biochemical network models. Bioinformatics 19(4) (2003)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2006 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Calder, M., Duguid, A., Gilmore, S., Hillston, J. (2006). Stronger Computational Modelling of Signalling Pathways Using Both Continuous and Discrete-State Methods. In: Priami, C. (eds) Computational Methods in Systems Biology. CMSB 2006. Lecture Notes in Computer Science(), vol 4210. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11885191_5
Download citation
DOI: https://doi.org/10.1007/11885191_5
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-46166-1
Online ISBN: 978-3-540-46167-8
eBook Packages: Computer ScienceComputer Science (R0)