Abstract
P systems have clear structural analogies with the cell. However, certain difficulties arise when one attempts to represent a biomolecular process using these systems. This chapter suggests some ways to overcome such difficulties and to provide P systems with further functionalities aimed at increasing their versatility in the modeling of biomolecular processes. Concepts from state transition dynamics are taken to put P systems in a general analysis framework for dynamical discrete systems. An explicit notion of environment is proposed to provide P systems with a regulatory and constraining agent, as real biomolecular processes must deal with. The chapter focuses on a new rewriting strategy inspired by biochemistry, in which reactivities play a central role in driving the rules as happens during biochemical reactions. Tests on an algorithm implementing rewriting with reactivities, realized on a simulator called Psim, show the capability of this algorithm to express several processes with precision, particularly those presenting oscillatory phenomena. Finally, an analysis of the process of leukocyte recruitment is also performed using Psim.
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
I.I. Ardelean, D. Besozzi: New Proposals for the Formalization of Membrane Proteins. In Proc. Second Brainstorming Week on Membrane Computing, Seville, Spain, February 2004 (Gh. Păun, A. Riscos-Núñez, A. Romero-Jiménez, F. Sancho-Caparrini, eds.), 53–59.
G. Bellin, G. Boudol: The Chemical Abstract Machine. Theoretical Computer Science, 96 (1992), 217–248.
F. Bernardini, M. Gheorghe: Cell Communication in Tissue P Systems and Cell Division in Population P Systems. In Proc. Second Brainstorming Week on Membrane Computing, Seville, Spain, February 2004 (Gh. Păun, A. Riscos-Núñez, A. Romero-Jiménez, F. Sancho-Caparrini, eds.), 74–91.
F. Bernardini, V. Manca: Dynamical Aspects of P Systems. BioSystems, 70 (2002), 85–93.
F. Bernardini, V. Manca: P Systems with Boundary Rules. In Membrane Computing, International Workshop, WMC-CdeA 2002, Curtea de Argeş, Romania, August 2002, Revised Papers (Gh. Păun, G. Rozenberg, A. Salomaa, C. Zandron, eds.), LNCS 2597, Springer, Berlin, 2003, 107–118.
D. Besozzi, I.I. Ardelean, G. Mauri: The Potential of P Systems for Modeling the Activity of Mechanosensitive Channels in E. Coli. In Pre-Proceedings of Workshop on Membrane Computing, WMC2003, Tarragona, GRLMC Report 28/03, 84–102.
C. Bonanno, V. Manca: Discrete Dynamics in Biological Models. Romanian Journal of Information Scicnce and Technology, 5,1–2 (2002), 45–67.
G. Ciobanu, D. Paraschiv: Membrane Software. A P System Simulator. Fundamenta Informaticae, 49,1–3 (2002),61–66.
R.L. Devaney: Introduction to Chaotic Dynamical Systems. Addison-Wesley, Reading, MA, 1989.
G. Franco, V. Manca: Modeling Some Biological Phenomena by P Systems. In Proc. of the 2nd Annual Meeting of CE MolCoNet Project, Wien, Austria, November 2003, 1–3.
G. Franco, V. Manca: A Membrane System for the Leukocyte Selective Recruitment. In Membrane Computing, International Workshop, WMC2003, Tarragona, Spain, July 2003, Revised Papers (C. MartÃn-Vide, Gh. Păun, G. Rozenberg, A. Salomaa, eds.), LNCS 2933, Springer, Berlin, 2004, 181–190.
R. Freund: Energy-Controlled P Systems. In Membrane Computing, International Workshop, WMC-CdeA 2002, Curtea de Argeş, Romania, August 2002, Revised Papers (Gh. Păun, G. Rozenberg, A. Salomaa, C. Zandron, eds.), LNCS 2597, Springer, Berlin, 2003, 247–260.
T. Head: Formal Language Theory and DNA: An Analysis of the Generative Capacity of Specific Recombinant Behaviours. Bull. Mathematical Biology, 49 (1987), 737–759.
R.C. Hilborn: Chaos and Nonlinear Dynamics. Oxford University Press, Oxford, UK, 2000.
D.S. Jones, B.D. Sleeman: Differential Equations and Mathematical Biology. Chapman & Hall/CRC, London, UK, 2003.
T. Kailath: Linear Systems. Prentice-Hall, Englewood Cliffs, 1980.
S.A. Kauffman: The Origins of Order. Oxford University Press, New York, NY, 1993.
J.D. Lambert: Computational Methods in Ordinary Differential Equations. J. Wiley & Sons, New York, NY, 1973.
C.G. Langton: Computation at the Edge of Chaos: Phase Transitions and Emergent Computation. Physica D, 42,12 (1990).
A. Lindenmayer: Mathematical Models for Cellular Interaction in Development. J. of Theoretical Biology, 18 (1968), 280–315.
B.H. Mahan: University Chemistry. Addison Wesley, Reading, MA, 1967.
M. Malita: Membrane Computing in Prolog. In Pre-Proceedings of the Workshop on Multiset Processing, Curtea de Argeş, Romania, 2000, 159–175.
V. Manca, G. Franco, G. Scollo: String Transition Dynamics — Basic Concepts and Molecular Computing Perspectives. In Molecular Computational Models — Unconventional Approaches (M. Gheorghe, ed.), Idea Group, London, 2004, 32–55.
G. Nicolis, I. Prigogine: Exploring Complexity. An Introduction. Freeman and Company, San Francisco, CA, 1989.
A. Păun: On P Systems with Membrane Division. In Unconventional Models of Computation (I. Antoniou, C.S. Calude, M.J. Dinneen, eds.), Springer, London, UK, 2000, 187–201.
A. Păun, Gh. Păun: The Power of Communication: P Systems with Symport/Antiport. New Generation Computing, 20,3 (2002), 295–306.
Gh. Păun: Computing with Membranes. J. Comput. System Sci., 61,1 (2000), 108–143.
Gh. Păun: Membrane Computing. An Introduction. Springer, Berlin, 2002.
Gh. Păun, G. Rozenberg: A Guide to Membrane Computing. Theoretical Computer Science, 287 (2002), 73–100.
Gh. Păun, G. Rozenberg, A. Salomaa: DNA Computing — New Computing Paradigms. Springer, Berlin, 1998.
Gh. Păun, Y. Suzuki, H. Tanaka: P Systems with Energy Accounting. Int. J. Computer Math., 78,3 (2001), 343–364.
G. Rozenberg, A. Salomaa: Handbook of Formal Languages. Springer, Berlin, Germany, 1997.
K.S. Scott: Chemical Chaos. Oxford University Press, Oxford, UK, 1991.
L.A. Segel, I.R. Cohen: Design Principles for the Immune System and Other Distributed Autonomous System. Oxford University Press, Oxford, UK, 2001.
Y. Suzuki, H. Tanaka: Chemical Oscillation in Symbolic Chemical Systems and Its Behavioral Pattern. In Proc. International Conference on Complex Systems (Y. Bar-Yam, ed.), Nashua, NH, September 1997.
Y. Suzuki, H. Tanaka: On a Lisp Implementation of a Class of P Systems. Romanian Journal of Information Science and Technology, 3,2 (2000), 173–186.
Y. Suzuki, H. Tanaka: Abstract Rewriting Systems on Multisets and Their Application for Modeling Complex Behaviours. In Proc. of Brainstorming Week on Membrane Computing, Tarragona, Spain, February 2003, 313–331.
S. Wolfram: Theory and Application of Cellular Automata. Addison-Wesley, Reading, MA, 1986.
A. Wuensche: Basins of Attraction in Network Dynamics: A Conceptual Framework for Biomolecular Networks. In Modularity in Development and Evolution (G. Schlosser, G.P. Wagner, eds.), Chicago University Press, Chicago, MA, 2003.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2006 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Bianco, L., Fontana, F., Franco, G., Manca, V. (2006). P Systems for Biological Dynamics. In: Ciobanu, G., Păun, G., Pérez-Jiménez, M.J. (eds) Applications of Membrane Computing. Natural Computing Series. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-29937-8_3
Download citation
DOI: https://doi.org/10.1007/3-540-29937-8_3
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-25017-3
Online ISBN: 978-3-540-29937-0
eBook Packages: Computer ScienceComputer Science (R0)