Abstract
In this paper we discuss the role that P systems have in the description of oscillatory biochemical processes once the membrane system evolution depends on the process parameters. This discussion focuses on a specific application example, meanwhile it includes a general definition of oscillation based on which we want to explore the meaning of oscillatory behaviors more deeply. The symbolic-based approach to biochemical processes such as that provided by P systems has recently resulted in insightful model descriptions. For this reason we expect it to turn useful in computational systems biology, whose models must deal with the twofold nature of the cell that is a continuous biochemical reactor ruled by discrete information contained in the DNA.
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.
Similar content being viewed by others
References
Bianco, L., Fontana, F., Franco, G., Manca, V.: P systems for biological dynamics. In: Ciobanu, G., Păun, G., Pérez-Jiménez, M.J. (eds.) Applications of Membrane Computing, pp. 81–126. Springer, Berlin (2006)
Bianco, L., Fontana, F., Manca, V.: Metabolic algorithm with time-varying reaction maps. In: Proc. of the Third Brainstorming Week on Membrane Computing, Sevilla, Spain, pp. 43–62 (2005)
Bianco, L., Fontana, F., Manca, V.: Reaction-driven membrane systems. In: Wang, L., Chen, K., S. Ong, Y. (eds.) ICNC 2005. LNCS, vol. 3611, pp. 1155–1158. Springer, Heidelberg (2005)
Gillespie, D.T.: Exact stochastic simulation of coupled chemical reactions. J. of Phys. Chem. 81, 2340–2361 (1977)
Goldbeter, A.: Computational approaches to cellular rhythms. Nature 420, 238–244 (2002)
Goldbeter, A.: Biochemical Oscillations and Cellular Rhythms. The Molecular Bases of Periodic and Chaotic Behaviour. Cambridge University Press, New York (2004)
Gonze, D., Halloy, J., Goldbeter, A.: Stochastic model for circadian oscillations: Emergence of a biological rhythm. Int. J. of Quantum Chemistry 98, 228–238 (2004)
Hilborn, R.C.: Chaos and Nonlinear Dynamics. Oxford University Press, Oxford (2000)
Jones, D.S., Sleeman, B.D.: Differential Equations and Mathematical Biology. Chapman & Hall/CRC, London (2003)
Kailath, T.: Linear Systems. Prentice-Hall, Englewood Cliffs (1980)
Kitano, H.: Computational systems biology. Nature 420, 206–210 (2002)
Leloup, J.C., Goldbeter, A.: A model for circadian rhythms in Drosophila incorporating the formation of a complex between the PER and TIM proteins. J. of Biological Rhythms 13, 70–87 (1998)
Lindenmayer, A.: Mathematical models for cellular interaction in development. J. of Theoretical Biology 18, 280–315, Part I and II (1968)
Manca, V., Bianco, L., Fontana, F.: Evolutions and oscillations of P systems: Applications to biological phenomena. In: [16], pp. 63–84
Manca, V., Franco, G., Scollo, G.: State transition dynamics: Basic concepts and molecular computing perspectives. In: Gheorghe, M. (ed.) Molecular Computational Models - Unconventional Approaches. Idea Group, USA (2004)
Mauri, G., Păun, G., Pérez-Jiménez, M.J., Rozenberg, G., Salomaa, A. (eds.) WMC 2004. LNCS, vol. 3365. Springer, Heidelberg (2005)
Păun, G.: Computing with membranes. J. Comput. System Sci. 61, 108–143 (2000)
Păun, G.: Membrane Computing. An Introduction. Springer, Berlin (2002)
Pérez-Jiménez, M.J., Romero-Campero, F.J.: Modelling EGFR signalling network using continuous membrane systems. In: Plotkin, G. (ed.) Proceedings of the Third International Workshop on Computational Methods in Systems Biology 2005 (CMSB 2005), University of Edinburgh, UK (2005)
Prusinkiewicz, P., Hammel, M., Hanan, J., Mech, R.: Visual models of plant development. In: [21], Beyond Words, vol. III, pp. 535–597
Rozenberg, G., Salomaa, A. (eds.): Handbook of Formal Languages. Springer, Berlin (1997)
Stamatopoulou, I., Gheorghe, M., Kefalas, P.: Modelling dynamic organization of biology-inspired multi-agent systems with communicating X-machines and population P systems. In: [16], pp. 389–403
Suzuki, Y., Tanaka, H.: Chemical oscillation in symbolic chemical systems and its behavioral pattern. In: Bar-Yam, Y. (ed.) Proc. International Conference on Complex Systems, Nashua, NH (1997)
Vincent, T.L., Grantham, W.J.: Nonlinear and Optimal Control Systems. Wiley, New York (1997)
Volterra, V.: Fluctuations in the abundance of a species considered mathematically. Nature 118, 558–560 (1926)
Zeng, H.: Constitutive overexpression of the drosophila period protein inhibits period mRNA cycling. The EMBO Journal 13, 3590–3598 (1994)
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
Fontana, F., Bianco, L., Manca, V. (2006). P Systems and the Modeling of Biochemical Oscillations. In: Freund, R., Păun, G., Rozenberg, G., Salomaa, A. (eds) Membrane Computing. WMC 2005. Lecture Notes in Computer Science, vol 3850. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11603047_14
Download citation
DOI: https://doi.org/10.1007/11603047_14
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-30948-2
Online ISBN: 978-3-540-32340-2
eBook Packages: Computer ScienceComputer Science (R0)