Stochastic P systems and the simulation of biochemical processes with dynamic compartments

We introduce a sequential rewriting strategy for P systems based on Gillespie's stochastic simulation algorithm, and show that the resulting formalism of stochastic P systems makes it possible to simulate biochemical processes in dynamically changing, nested compartments. Stochastic P systems have been implemented using the spatially explicit programming language MGS. Implementation examples include models of the Lotka-Volterra auto-catalytic system, and the life cycle of the Semliki Forest virus.

[1]  Przemyslaw Prusinkiewicz,et al.  A Look at the Visual Modeling of Plants Using L-Systems , 1996, German Conference on Bioinformatics - Selected Papers.

[2]  Wolfgang Banzhaf,et al.  Artificial ChemistriesA Review , 2001, Artificial Life.

[3]  Ioan I. Ardelean,et al.  Modelling biological processes by using a probabilistic P system software , 2004, Natural Computing.

[4]  Patrick Amar,et al.  Proceedings of the AUTRANS spring school on Modelling and simulation of biological processes in the context of genomics , 2002 .

[5]  Sheldon M. Ross.  Introduction to Probability Models. , 1995 .

[6]  D. Gillespie.  A General Method for Numerically Simulating the Stochastic Time Evolution of Coupled Chemical Reactions , 1976 .

[7]  Jean-Louis Giavitto,et al.  The Topological Structures of Membrane Computing , 2002, Fundam. Informaticae.

[8]  Sheldon M. Ross,et al.  Introduction to Probability Models (4th ed.). , 1990 .

[9]  Luca Cardelli,et al.  BioAmbients: an abstraction for biological compartments , 2004, Theor. Comput. Sci..

[10]  Brian Beckman,et al.  Time warp operating system , 1987, SOSP '87.

[11]  Luis Serrano,et al.  Space as the final frontier in stochastic simulations of biological systems , 2005, FEBS letters.

[12]  Walter J. Savitch,et al.  Growth Functions of Stochastic Lindenmayer Systems , 1980, Inf. Control..

[13]  John H. Holland,et al.  Genetic Algorithms and the Optimal Allocation of Trials , 1973, SIAM J. Comput..

[14]  Grzegorz Rozenberg,et al.  Developmental systems and languages , 1972, STOC.

[15]  Luca Cardelli,et al.  Brane Calculi , 2004, CMSB.

[16]  D. Gillespie.  The chemical Langevin equation , 2000 .

[17]  David R. Jefferson,et al.  Virtual time , 1985, ICPP.

[18]  Nicolas Le Novère,et al.  STOCHSIM: modelling of stochastic biomolecular processes , 2001, Bioinform..

[19]  Adam Obtulowicz.  Probabilistic P Systems , 2002, WMC-CdeA.

[20]  Wolfgang Kreutzer,et al.  System simulation programming styles and languages , 1986 .

[21]  G Păun,et al.  From cells to computers: computing with membranes (P systems). , 2001, Bio Systems.

[22]  Giancarlo Mauri,et al.  Tau Leaping Stochastic Simulation Method in P Systems , 2006, Workshop on Membrane Computing.

[23]  Przemyslaw Prusinkiewicz,et al.  Lindenmayer Systems, Fractals, and Plants , 1989, Lecture Notes in Biomathematics.

[24]  Giancarlo Mauri,et al.  Stochastic Approaches in P Systems for Simulating Biological Systems , 2006 .

[25]  Karl J. Niklas.  The Algorithmic Beauty of Plants. The Virtual Laboratory.Przemyslaw Prusinkiewicz , Aristid Lindenmayer , James S. Hanan , F. David Fracchia , Deborah R. Fowler , Martin J. M. de Boer, Lynn Mercer , 1996 .

[26]  Daniel Le Métayer,et al.  A new computational model and its discipline of programming , 1986 .

[27]  A. Lindenmayer.  Mathematical models for cellular interactions in development. I. Filaments with one-sided inputs. , 1968, Journal of theoretical biology.

[28]  A. Lindenmayer.  Mathematical models for cellular interactions in development. II. Simple and branching filaments with two-sided inputs. , 1968, Journal of theoretical biology.

[29]  Aristid Lindenmayer,et al.  Mathematical Models for Cellular Interactions in Development , 1968 .

[30]  Olivier Bournez,et al.  Rewriting Logic and Probabilities , 2003, RTA.

[31]  A. Lindenmayer,et al.  Grammars of Development: Discrete-State Models for Growth, Differentiation, and Gene Expression in Modular Organisms , 1992 .

[32]  M. Cieslak.  Stochastic Simulation of Pattern Formation: An Application of L-systems , 2006 .

[33]  Grzegorz Rozenberg,et al.  Automata, languages, development , 1976 .

[34]  Przemyslaw Prusinkiewicz,et al.  Applications of L-systems to computer imagery , 1986, Graph-Grammars and Their Application to Computer Science.

[35]  Madhu Mutyam.  Probabilistic Rewriting P Systems , 2003, Int. J. Found. Comput. Sci..

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

[37]  Jean-Louis Giavitto,et al.  Rewriting and Simulation Application to the Modeling of the Lambda Phage Switch , 2007 .

[38]  J. Ziegler,et al.  Artificial Chemistries-A Review , 2001 .

[39]  G. Agha,et al.  Probabilistic Rewrite Theories , 2003 .

[40]  Jose Marques Henriques,et al.  FRACTALS IN THE FUNDAMENTAL AND APPLIED SCIENCES , 2007 .

[41]  Anne Auger,et al.  R-leaping: accelerating the stochastic simulation algorithm by reaction leaps. , 2006, The Journal of chemical physics.

[42]  Leah Edelstein-Keshet,et al.  Mathematical models in biology , 2005, Classics in applied mathematics.

[43]  J. Trempe.  Molecular biology of the cell, 3rd edition Bruce Alberts, Dennis Bray, Julian Lewis, Martin Raff, Keith Roberts and James D. Watson, Garland Publishing, 1994, 559.95 (xiii + 1294 pages), ISBN 0-815-31619-4 , 1995, Trends in Endocrinology & Metabolism.

[44]  Masaru Tomita,et al.  Space in systems biology of signaling pathways – towards intracellular molecular crowding in silico , 2005, FEBS letters.

[45]  G. Rozenberg,et al.  Lindenmayer Systems: Impacts on Theoretical Computer Science, Computer Graphics, and Developmental Biology , 2001 .

[46]  John von Neumann,et al.  Theory Of Self Reproducing Automata , 1967 .

[47]  J. Davies,et al.  Molecular Biology of the Cell , 1983, Bristol Medico-Chirurgical Journal.

[48]  Marian Gheorghe,et al.  On P Systems as a Modelling Tool for Biological Systems , 2005, Workshop on Membrane Computing.

[49]  Francesco Bernardini,et al.  Membrane systems for molecular computing and biological modelling , 2005 .

[50]  Takashi Yokomori,et al.  Stochastic Characterizations of EOL Languages , 1980, Inf. Control..

[51]  P. Haccou.  Mathematical Models of Biology , 2022 .

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

[53]  T. Mexia,et al.  Author ' s personal copy , 2009 .

[54]  Colin Smith,et al.  L-System Description of Subdivision Curves , 2003, Int. J. Shape Model..

[55]  Olivier Michel,et al.  Computational models for integrative and developmental biology , 2002 .

[56]  Jean-Louis Giavitto,et al.  MGS: a Rule-Based Programming Language for Complex Objects and Collections , 2001, Electron. Notes Theor. Comput. Sci..

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

[58]  Phil Hontalas,et al.  Distributed Simulation and the Time Wrap Operating System. , 1987, SOSP 1987.

[59]  Claude Kirchner,et al.  Probabilistic Rewrite Strategies. Applications to ELAN , 2002, RTA.

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

[61]  W. Pitts,et al.  A Logical Calculus of the Ideas Immanent in Nervous Activity (1943) , 2021, Ideas That Created the Future.

[62]  Grzegorz Rozenberg,et al.  The mathematical theory of L systems , 1980 .

[63]  W S McCulloch,et al.  A logical calculus of the ideas immanent in nervous activity , 1990, The Philosophy of Artificial Intelligence.

[64]  Masaru Tomita,et al.  E-CELL: software environment for whole-cell simulation , 1999, Bioinform..

[65]  Przemyslaw Prusinkiewicz,et al.  The Algorithmic Beauty of Plants , 1990, The Virtual Laboratory.