Modelling Spatial Heterogeneity and Macromolecular Crowding with Membrane Systems

In biological processes, intrinsic noise, spatial heterogeneity and molecular crowding deeply affect the system dynamics. The classic stochastic methods lack of the necessary features needed for the description of these phenomena. Membrane systems are a suitable framework to embed these characteristics; in particular, the variants of τ-DPP and Sτ -DPP allow the modelling and stochastic simulations of multivolume biochemical systems, in which diffusion and size of volumes and chemicals are taken into account improving the description of these biological systems. In this paper we show, by means of two models of reactiondiffusion and crowded systems, the correctness and accuracy of our simulation methods.

[1]  Corrado Priami,et al.  Transactions on Computational Systems Biology VI , 2006, Trans. Computational Systems Biology.

[2]  S. Zimmerman,et al.  Estimation of macromolecule concentrations and excluded volume effects for the cytoplasm of Escherichia coli. , 1991, Journal of molecular biology.

[3]  Linda R Petzold,et al.  Efficient step size selection for the tau-leaping simulation method. , 2006, The Journal of chemical physics.

[4]  Cazzaniga Stochastic algorithms for biochemical processes , 2010 .

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

[6]  Giancarlo Mauri,et al.  A Novel Variant of Tissue P Systems for the Modelling of Biochemical Systems , 2009 .

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

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

[9]  Erik De Schutter,et al.  Monte Carlo Methods for Simulating Realistic Synaptic Microphysiology Using MCell , 2000 .

[10]  A. Wit,et al.  SPATIAL PATTERNS AND SPATIOTEMPORAL DYNAMICS IN CHEMICAL SYSTEMS , 2007 .

[11]  Raoul Kopelman,et al.  Fractal Reaction Kinetics , 1988, Science.

[12]  David Bernstein,et al.  Simulating mesoscopic reaction-diffusion systems using the Gillespie algorithm. , 2005, Physical review. E, Statistical, nonlinear, and soft matter physics.

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

[14]  A. Minton,et al.  Macromolecular crowding: biochemical, biophysical, and physiological consequences. , 1993, Annual review of biophysics and biomolecular structure.

[15]  P. R. ten Wolde,et al.  Green's-function reaction dynamics: a particle-based approach for simulating biochemical networks in time and space. , 2005, The Journal of chemical physics.

[16]  A. Verkman,et al.  Crowding effects on diffusion in solutions and cells. , 2008, Annual review of biophysics.

[17]  Gordon Broderick,et al.  A life-like virtual cell membrane using discrete automata , 2004, Silico Biol..

[18]  A. Minton,et al.  The Influence of Macromolecular Crowding and Macromolecular Confinement on Biochemical Reactions in Physiological Media* , 2001, The Journal of Biological Chemistry.

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

[20]  A. Fulton,et al.  How crowded is the cytoplasm? , 1982, Cell.

[21]  Daniel T Gillespie,et al.  Stochastic simulation of chemical kinetics. , 2007, Annual review of physical chemistry.

[22]  Roger Brent,et al.  Detailed Simulations of Cell Biology with Smoldyn 2.1 , 2010, PLoS Comput. Biol..

[23]  Diego Rossinelli,et al.  Accelerated stochastic and hybrid methods for spatial simulations of reaction–diffusion systems , 2008 .

[24]  J. Elf,et al.  Spontaneous separation of bi-stable biochemical systems into spatial domains of opposite phases. , 2004, Systems biology.

[25]  Allen P. Minton,et al.  The effect of volume occupancy upon the thermodynamic activity of proteins: some biochemical consequences , 2004, Molecular and Cellular Biochemistry.

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

[27]  Alfonso Rodríguez-Patón,et al.  A New Class of Symbolic Abstract Neural Nets: Tissue P Systems , 2002, COCOON.

[28]  Erik De Schutter,et al.  Computational neuroscience : realistic modeling for experimentalists , 2000 .

[29]  Judith Herzfeld,et al.  Life in a crowded world , 2004, EMBO reports.

[30]  Johan Hattne,et al.  Stochastic reaction-diffusion simulation with MesoRD , 2005, Bioinform..

[31]  M Ander,et al.  SmartCell, a framework to simulate cellular processes that combines stochastic approximation with diffusion and localisation: analysis of simple networks. , 2004, Systems biology.

[32]  Hugues Berry,et al.  Monte carlo simulations of enzyme reactions in two dimensions: fractal kinetics and spatial segregation. , 2002, Biophysical journal.

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

[34]  Giancarlo Mauri,et al.  A Novel Variant of P Systems for the Modelling and Simulation of Biochemical Systems , 2009, Workshop on Membrane Computing.

[35]  Daniel S. Banks,et al.  Anomalous diffusion of proteins due to molecular crowding. , 2005, Biophysical journal.

[36]  Tatiana T Marquez-Lago,et al.  Binomial tau-leap spatial stochastic simulation algorithm for applications in chemical kinetics. , 2007, The Journal of chemical physics.

[37]  Mario J. Pérez-Jiménez,et al.  P Systems, a New Computational Modelling Tool for Systems Biology , 2006, Trans. Comp. Sys. Biology.

[38]  Mansour,et al.  Reaction-diffusion master equation: A comparison with microscopic simulations. , 1996, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[39]  Linda R. Petzold,et al.  Improved leap-size selection for accelerated stochastic simulation , 2003 .

[40]  Arun Yethiraj,et al.  Effect of macromolecular crowding on reaction rates: a computational and theoretical study. , 2009, Biophysical journal.

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

[42]  Allen P. Minton,et al.  Cell biology: Join the crowd , 2003, Nature.