Special Issue: Membrane ComputingNo Access

P SYSTEMS WITH REACTION MAPS

LUCA BIANCO

Department of Computer Science, University of Verona, 15 Strada Le Grazie, Verona 37134, Italy

Search for more papers by this author

FEDERICO FONTANA

Department of Computer Science, University of Verona, 15 Strada Le Grazie, Verona 37134, Italy

Search for more papers by this author

, and

VINCENZO MANCA

Department of Computer Science, University of Verona, 15 Strada Le Grazie, Verona 37134, Italy

Search for more papers by this author

https://doi.org/10.1142/S0129054106003681Cited by:36 (Source: Crossref)

Abstract

Some recent types of membrane systems have shown their potential in the modelling of specific processes governing biological cell behavior. These models represent the cell as a huge and complex dynamical system in which quantitative aspects, such as biochemical concentrations, must be related to the discrete informational nature of the DNA and to the function of the organelles living in the cytosol. In an effort to compute dynamical (especially oscillatory) phenomena—so far mostly treated using differential mathematical tools—by means of rewriting rules, we have enriched a known family of membrane systems (P systems), with rules that are applied proportionally to the values expressed by real functions called reaction maps. Such maps are designed to model the dynamic behavior of a biochemical phenomenon and their formalization is best worked out inside a family of P systems called PB systems. The overall rule activity is controlled by an algorithm that guarantees the system to evolve consistently with the available resources (i.e., objects). Though radically different, PB systems with reaction maps exhibit very interesting, often similar dynamic behavior as compared to systems of differential equations. Successful simulations of the Lotka-Volterra population dynamics, the Brusselator, and the Protein Kinase C activation foster potential applications of these systems in computational systems biology.

Keywords:

AMSC: 68Q10, 68Q85, 92-08, 37N25

References

F. Bernardini and V. Manca, BioSystems 70, 85 (2002). Crossref, Web of Science, Google Scholar
F. Bernardini and V. Manca, P systems with boundary rules, LNCS 2597, Membrane Computing. International Workshop, WMC-CdeA 2002 (2002), eds. G. Păunet al. (Springer-Verlag, Berlin, 2002) pp. 107–118. Google Scholar
D. Besozzi and G. Ciobanu, A P system description of the sodium-potassium pump, LNCS 3365, Membrane Computing, 5th International Workshop, WMC 2004 (2004), eds. G. Mauriet al. (Springer-Verlag, Berlin, 2005) pp. 210–223. Google Scholar
U. S. Bhalla and R. Iyengar, Science 283(5400), 381 (1999). Crossref, Web of Science, Google Scholar
L. Bianco, F. Fontana, G. France, V. Manta, P systems for biological dynamics. In [8], 81–126 . Google Scholar
L. Bianco, F. Fontana and V. Manca, Metabolic algorithm with time-varying reaction maps, Proc. of the Third Brainstorming Week on Membrane Computing (BWMC 2005) pp. 43–62. Google Scholar
L. Bianco and V. Manca, Encoding/decoding classes of P systems, Pre-proceedings of 6th Workshop on Membrane Computing (WMC6) pp. 226–234. Google Scholar
G. Ciobanu , G. Păun and M. J. Pérez-Jiménez (eds.) , Applications of Membrane Computing ( Springer-Verlag , Berlin , 2006 ) . Google Scholar
I. R. Epstein and K. Showalter, J. Phys. Chem. 100(31), 13132 (1996). Crossref, Web of Science, Google Scholar
A. Goldbeter, Nature 420, 238 (2002). Crossref, Web of Science, Google Scholar
H. Kitano, Nature 420, 206 (2002). Crossref, Web of Science, Google Scholar
J.-C. Leloup and A. Goldbeter, J. of Biological Rhythms 13(1), 70 (1998). Crossref, Web of Science, Google Scholar
A. Lindenmayer, J. of Theoretical Biology 18, 280 (1968). Crossref, Web of Science, Google Scholar
A. J. Lotka, J. Am. Chem. Soc. 42, 1595 (1920). Crossref, Google Scholar
V. Manca, L. Bianco and F. Fontana, Evolutions and oscillations of P systems: Applications to biological phenomena, LNCS 3365, Membrane Computing, 5th International Workshop, WMC 2004 (2004), eds. G. Mauriet al. (Springer-Verlag, Berlin, 2005) pp. 63–84. Google Scholar
A. C. Newton, J. Biol. Chem. 270, 28495 (1995). Crossref, Web of Science, Google Scholar
K. Ohkusu, Eur. J. Immunol. 25, 3180 (1995). Crossref, Web of Science, Google Scholar
G. Păun, J. Comput. System Sci. 61(1), 108 (2000). Crossref, Web of Science, Google Scholar
M. J. Pérez-Jiménez and F. J. Romero-Campero , Modelling EGFR signalling network using continuous membrane systems , Third Workshop on Computational Methods in Systems Biology ( 2005 ) . Google Scholar
P. Prusinkiewiczet al., Handbook of Formal Languages III, eds. G. Rozenberg and A. Salomaa (Beyond Words, Springer-Verlag, Berlin, 1997) pp. 535–597. Crossref, Google Scholar
C. V. Rao, D. N. Wolf and A. P. Arkin, Nature 420, 231 (2002). Crossref, Web of Science, Google Scholar
G. Rozenberg and A. Salomaa (eds.) , Handbook of Formal Languages ( Springer-Verlag , Berlin , 1997 ) . Crossref, Google Scholar
I. Stamatopoulou, M. Gheorghe and P. Kefalas, Modelling dynamic organization of biology-inspired multi-agent systems with communicating x-machines and population P systems, LNCS 3365, Membrane Computing, 5th International Workshop, WMC 2004 (2004), eds. G. Mauriet al. (Springer-Verlag, Berlin, 2005) pp. 389–403. Google Scholar
Y. Suzuki and H. Tanaka , Chemical oscillation in symbolic chemical systems and its behavioral pattern , Proc. International Conference on Complex Systems , ed. Y. Bar-Yam . Google Scholar
V. Volterra, Nature 118, 558 (1926). Crossref, Google Scholar