Metabolic P systems

• Prof. Vincenzo Manca, Dipartimento di Informatica

Prof. Vincenzo Manca accepted the invitation on 16 March 2009 (self-imposed deadline: 16 September 2009).

\( \) Metabolism is one of the basic phenomenon on which life is based. Any living organism has to maintain processes which: i) introduce matter of some kinds from the external environment, ii) transform internal matter by changing the molecule distribution of a number of biochemical species, and iii) expel outside matter which is not useful or dangerous for the organism. Molecule distribution identifies, in a first approximation, the state of the system in question, and can be represented as multiset of type \(n_A A + n_B B + \ldots n_Z Z\) giving the numbers \(n_A, n_B, \ldots , n_Z\) of molecules for each of molecule species \(A, B, \ldots , Z\). Of course, life cannot be reduced to metabolism, but no life can exist without such a kind of basic mechanism. Metabolic P systems (shortly MP systems) represent metabolic processes in a discrete mathematical framework. A metabolic P system is essentially a multiset grammar where multiset transformation rules are regulated by functions. Namely, a rule like \(A+B \to C\) means that a number \(n\) of molecules of kind \(A\) and the same number \(n\) of molecules \(B\) are replaced by \(n\) molecules of type \(C\). The value of \(n\) is given by a function, called regulator of the rule, which computes it according to the state of the system. The letter P of MP systems comes from the theoretical framework of P systems introduced by Gheorhe Paun, in the context of membrane computing. In fact, MP systems are a special class of P systems introduced for expressing metabolism in a discrete mathematical setting.

Multiset rewriting: vector notation and molar perspective

P systems provide the right conceptual framework for MP systems development. They were introduced in the context of Formal Language Theory for defining a computation model inspired by biological cells. A crucial aspect of P systems is the passage from the classical notion of string rewriting rule, to that one of multiset rewriting rule. This new perspective changes completely the typical mathematical setting of languages, grammars and automa, based on strings, and opens a new perspective where rewriting rules become a natural representation of (bio)chemical reactions. If a rule transforms a multiset of symbols/molecules, then when a conventional order, for example the alphabetic order, is fixed over a set \(X\) of \(n\) substances (molecule types), then a rule such as \(2A+B \to C\) is easily represented by two vectors of \(\bold{N}^n\), that is, a left vector \((2, 1, 0, \ldots , 0)\), and a right vector \((0, 0, 1, \ldots , 0)\). This vector reading of rules is very useful not only from the notation point of view, but for applying basic concept of linear algebra to the analysis of MP systems. Another important aspect of multiset rewriting is its natural reading according to the usual chemistry use. In fact, if we fix a number of population size, called conventional mole, for example of \(10000\) units, then a rule \(2A+B \to C\), when it is applied with a flux of \(3.2\) moles, it transforms \(64000\) molecules \(A\) and \(32000\) molecules \(B\) into \(32000\) molecules \(C\).

Subsection b

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   (1)
   F=ma. 

Subsection c

Refer to figures and equations as Fig.1 and Eq. (1).

MP systems: graph and grammar representation

File:Mp-graph.jpg

Figure 1: An MP graph

MP systems: possible extensions and applications

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Subsection e Subsection f Citing references

Groups of authors larger than 2 can be cited with "et al.".

   * As proven in (Albero A, 1999).
   * As Albero (2009) said.
   * As proven in (Albero and Bocca, 2001)
   * As proven by Albero and Bocca (2001)
   * As proven by Albero et al. (2003)
   * As proven by Albero, Bocca and Cuoco (2003)
   * As proven by Albero et al. (2007a), confirmed by Albero et al. (2007b) and discarded by Albero et al. (2007c)
   * As proven in (Albero A, 1999).
   * As proven by Albero and Bocca (2001). 

References

• V. MANCA, L. MARCHETTI (2009). XML Representation of MP Systems, 2009 IEEE Congress on Evolutionary Computation (CEC 2009), pp. 3103-3110, Trondheim, Norway, 2009.

• A. CASTELLINI, V. MANCA (2009). Learning Regulation Functions of Metabolic Systems by Artificial Neural Networks, The Genetic and Evolutionary Computation Conference (GECCO’09), Montréal, Canada, 2009

• V. MANCA et. al. (2009). MetaPlab 1.1 official guide, http://mplab.sci.univr.it (Tutorials).

• V. MANCA (2009). Fundamentals of Metabolic P Systems. In: Gh. Paun, G. Rozenberg, A. Salomaa (eds.), Handbook of Membrane Computing, CHAPTER 19, Oxford University Press, 2009.

• V. MANCA (2009). Metabolic P Dynamics. In: Gh. Paun, G. Rozenberg, A. Salomaa (eds.), Handbook of Membrane Computing, CHAPTER 20, Oxford University Press, 2009.

• A. CASTELLINI, G. FRANCO, V. MANCA (2009). Hybrid Functional Petri Nets as MP Systems. Natural Computing, DOI 10.1007/s11047-009-9121-4

• V. MANCA (2009), Log-Gain Principles for Metabolic P Systems, CHAPTER 28, A. Condon et al. (eds.), Algorithmic Bioprocesses, Natural Computing Series, pp. 585-605, Springer-Verlag, Berlin Heidelberg 2009.

• A. CASTELLINI, G. FRANCO, V. MANCA (2008). Toward a Representation of Hybrid Functional Petri Nets by MP Systems. Y. Suzuki et. al. (eds.), IWNC 2008, pp. 28-37, Springer.

• V. MANCA, R. PAGLIARINI, S. ZORZAN (2008). Toward an MP model of Non Photochemical Quenching. WMC9, LNCS 5391, Springer.

• A. CASTELLINI, V. MANCA (2008). MetaPlab: A Computational Framework for Metabolic P Systems. WMC9, LNCS 5391, Springer.

• V. MANCA, R. PAGLIARINI, S. ZORZAN (2008). A photosynthetic process modelled by a metabolic P system. Natural Computing, DOI 10.1007/s11047-008-9104-x

• V. MANCA (2008). The metabolic algorithm: principles and applications. THEORETICAL COMPUTER SCIENCE, 404, 142-157, 2008.

• A. CASTELLINI, V. MANCA, L. MARCHETTI. (2008). MP Systems and Hybrid Petri Nets. STUDIES IN COMPUTATIONAL INTELLIGENCE, 129, 53-62.

• G. SCOLLO, G. FRANCO, V. MANCA. (2008) Relational state transition dynamics, THE JOURNAL OF LOGIC AND ALGEBRAIC PROGRAMMING, 76. 130–144, 2008.

• V. MANCA, L. BIANCO (2008). Biological networks in metabolic P systems. BIOSYSTEMS, 91, 489–498, 2008.

• F. FONTANA, V. MANCA (2008). Predator-prey dynamics in P systems ruled by metabolic algorithm. BIOSYSTEMS, 91, 545-557, 2008.

• V. MANCA (2008). Discrete Simulations of Biochemical Dynamics. In: M.H. Garzon and H. Yan (Eds.): DNA 13, LNCS 4848, 231–235, SPRINGER, 2008.

• L. BIANCO, V. MANCA, L. MARCHETTI, M. PETTERLINI (2007). Psim: a simulator for biomolecular dynamics based on P systems. In: Congress on Evolutionary Computation. Singapore, September 25-28 2007IEEE, vol. 2007 IEEE (CEC 2007), p. 883-887

• V. MANCA (2007). Metabolic Dynamics by MP Systems. In: ERCIM May Interlink, 2007. Eze, France, May 19-12, 2007.

• L. BIANCO, V. MANCA (2006). ENCODING DECODING TRANSITIONAL SYSTEMS FOR CLASSES OF P SYSTEMS. In: R. FREUND; G. PAUN; G. ROZENBERG; M. YUNG; AND A. SALOMAA. MEMBRANE COMPUTING, WMC 2005, LNCS 3850, 134-143, SPRINGER, 2006.

• L. BIANCO, F. FONTANA, G. FRANCO, V. MANCA (2006). P systems for biological dynamics. In: CIOBANU; G.; PEREZ-JIMENEZ; M. J.; PAUN; G.. Applications of Membrane Computing. 81-126, SPRINGER, 2006.

• F. FONTANA; L. BIANCO; V. MANCA V. (2006). P systems and the modeling of biochemical oscillations. In: R. FREUND; G. PAUN; G. ROZENBERG; M. YUNG; AND A. SALOMAA;. Membrane Computing, WMC 2005, LNCS 3850, 200-2009, SPRINGER, 2006.

• G. FRANCO; P. H. GUZZI; V. MANCA, T. MAZZA (2006). Mitotic Oscillators as MP Graphs. In: H.J. HOOGEBOOM ET AL. EDS.. Membrane Computing, LNCS 4361, 382-394, SPRINGER, 2006.

• V. MANCA (2006). MP Systems Approaches to Biochemical Dynamics: Biological Rhythms and Oscillations. In: H.J. HOOGEBOOM ET AL. EDS.. Membrane Computing. vol. LNCS 4361, 86-99, SPRINGER, 2006.

• V. MANCA, L. BIANCO, F. FONTANA (2006). Evolutions and Oscillations of P Systems: Theorethical Considerations and Applications to Biochemical Phenomena. In: G. MAURI; G. PAUN. G. ROZENBERG. Membrane Computing - WMC2004.LNCS 3365, 63-84, SPRINGER, 2006.

• G. SCOLLO, V. MANCA, (2006). A Relational View of Recurrence and Attractors in State Transition Dynamics. In: R.A. SCHMIDT ED.. RELMICS /AKA 2006, LNCS 4136, 358-372, SPRINGER, 2006.

• L. BIANCO, F. FONTANA, V. MANCA (2005). Reaction-driven membrane systems. In: L. WUNG; K. CHEN; Y.S. ONG. Advances in Natural Computation, 3611, 1150-1153, SPRINGER, 2005.

• V. MANCA, G. FRANCO, G. SCOLLO (2005). State Transition Dynamics: basic concepts and molecular computing perspectives,. In Molecular Computational Models: Unconventional Approaches, IDEA GROUP INC., 32-55, 2005.

• F. BERNARDINI, M. GHEORGHE, V. MANCA (2005). On P systems and Almost Periodicity. FUNDAMENTA INFORMATICAE, 64(1-4), 29-42, 2005.

• V. MANCA (2004). String Models and String Theories. In: CARLOS MARTIN-VIDE; VICTOR MITRANA; GHEORGHE PAUN. Formal Languages and Applications, Studies in Fuzziness and Soft Computing. vol. 148, p. 439-456, BERLIN: Springer, ISBN/ISSN: 3-540-209007-7

• F. BERNARDINI, V. MANCA (2003). P Systems with boundary rules. In: G. Paun, G. Rozenberg, A. Salomaa, C. Zandron. Membrane Computing WMC 2002. vol. 2597, p. 107-118, BERLIN: Springer

• G. FRANCO, V. MANCA (2003). A membrane system for selective leukocyte recruitment. In: ALHAZOV A.; MARTIN-VIDE C.; PAUN G.. Membrane Computing WMC 2003. vol. 2933, p. 181-190, BERLIN: Springer

• F. BERNARDINI, V. MANCA (2003). Dynamical aspects of P systems. BIOSYSTEMS; p. 85-93, ISSN: 0303-2647

• C. BONANNO, V. MANCA (2002). Discrete dynamics in biological models. ROMANIAN JOURNAL OF INFORMATION SCIENCE AND TECHNOLOGY, vol. 5; p. 45-67, ISSN: 1453-8245

• V. MANCA, M.D. MARTINO (1999). From String Rewriting to Logical Metabolic Systems. In: PAUN G.; SALOMAA A.. Grammatical Models of Multiagent Systems. vol. 8, p. 297-315, London: Gordon and Breach Science Publishers.

• V. MANCA (1998). String Rewriting and Metabolism: A logical perspective. Springer Series in Discrete Mathematics and Theoretical Computer Science, Vol. 7, Computing with Bio-Molecules. p. 361-60, Singapore: Springer-Verlag

External links

Eugene M. Izhikevich website See also

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Categories: Scholarpedia

Sponsored by: Dr. Pierluigi Frisco, Heriot-Watt University, School of Mathematical and Computer Sciences, Edinburgh, UK

Reviewed by: Anonymous

Accepted on: 2010-03-08 10:23:40 GMT