Reaction Cycles in Membrane Systems and Molecular Dynamics

1 Leiden University, Mathematical Institute Niels Bohrweg 1, 2333 CA Leiden, The Netherlands muskulus@math.leidenuniv.nl 2 Vrije Universiteit Amsterdam, Faculteit der Bewegingswetenschappen Van der Boechorststraat 9, 1081 BT Amsterdam, The Netherlands s.houweling@fbw.vu.nl 3 Leiden University, Leiden Institute of Advanced Computer Science Niels Bohrweg 1, 2333 CA Leiden, The Netherlands {rbrijder,rozenber}@liacs.nl 4 Universita degli Studi di Milano Dipartimento di Informatica e Comunicazione Via Comelico 39, 20135 Milano, Italy besozzi@dico.unimi.it 5 Universita degli Studi di Milano Dipartimento di Informatica, Sistemistica e Comunicazione Via Bicocca degli Arcimboldi 8, 20126 Milano, Italy {pescini,cazzaniga}@disco.unimib.it

[1]  John Odentrantz,et al.  Markov Chains: Gibbs Fields, Monte Carlo Simulation, and Queues , 2000, Technometrics.

[2]  D. Vere-Jones Markov Chains , 1972, Nature.

[3]  David Parker,et al.  Symbolic Representations and Analysis of Large Probabilistic Systems , 2004, Validation of Stochastic Systems.

[4]  D. Gillespie Approximate accelerated stochastic simulation of chemically reacting systems , 2001 .

[5]  Peter Dittrich,et al.  Chemical Organisation Theory , 2007, Bulletin of mathematical biology.

[6]  Peter Buchholz,et al.  Hierarchical Reachability Graph Generation for Petri Nets , 2002, Formal Methods Syst. Des..

[7]  Peter F. Stadler,et al.  Relevant cycles in Chemical reaction Networks , 2001, Adv. Complex Syst..

[8]  J. Bauer,et al.  Chemical reaction network theory for in-silico biologists , 2003 .

[9]  Evelyne Contejean,et al.  An Efficient Incremental Algorithm for Solving Systems of Linear Diophantine Equations , 1994, Inf. Comput..

[10]  Gheorghe Paun,et al.  Membrane Computing , 2002, Natural Computing Series.

[11]  Gregory Gutin,et al.  Digraphs - theory, algorithms and applications , 2002 .

[12]  James Lyle Peterson,et al.  Petri net theory and the modeling of systems , 1981 .

[13]  D. Gillespie Exact Stochastic Simulation of Coupled Chemical Reactions , 1977 .

[14]  Reinhard Diestel,et al.  Graph Theory , 1997 .

[15]  Michael Muskulus,et al.  Complexity of bio-computation: symbolic dynamics in membrane systems , 2006, Int. J. Found. Comput. Sci..

[16]  Christophe Reutenauer,et al.  Aspects mathématiques des réseaux de pétri , 1988 .

[17]  K. Burrage,et al.  Binomial leap methods for simulating stochastic chemical kinetics. , 2004, The Journal of chemical physics.

[18]  Giancarlo Mauri,et al.  Dynamical probabilistic P systems , 2006, Int. J. Found. Comput. Sci..

[19]  Gheorghe Paun,et al.  Computing with Membranes , 2000, J. Comput. Syst. Sci..

[20]  Michael Clausen,et al.  Efficient Solution of Linear Diophantine Equations , 1989, J. Symb. Comput..

[21]  Michael Muskulus,et al.  First Steps Towards a Geometry of Computation , 2005 .

[22]  Ernst W. Mayr An Algorithm for the General Petri Net Reachability Problem , 1984, SIAM J. Comput..

[23]  Giancarlo Mauri,et al.  Quantum Sequential P Systems with Unit Rules and Energy Assigned to Membranes , 2005, Workshop on Membrane Computing.

[24]  Michael A. Gibson,et al.  Efficient Exact Stochastic Simulation of Chemical Systems with Many Species and Many Channels , 2000 .

[25]  B. Palsson,et al.  The underlying pathway structure of biochemical reaction networks. , 1998, Proceedings of the National Academy of Sciences of the United States of America.

[26]  Tadao Murata,et al.  Petri nets: Properties, analysis and applications , 1989, Proc. IEEE.

[27]  Pietro Speroni di Fenizio,et al.  Chemical Organisation Theory , 2005, Bulletin of mathematical biology.

[28]  Martín Matamala,et al.  Some remarks on cycles in graphs and digraphs , 2001, Discret. Math..

[29]  Giancarlo Mauri,et al.  Analysis and Simulation of Dynamics in Probabilistic P Systems , 2005, DNA.

[30]  B. M. Schmitt,et al.  The Concept of “Buffering” in Systems and Control Theory: From Metaphor to Math , 2004, Chembiochem : a European journal of chemical biology.