Adapting rule-based model descriptions for simulating in continuous and hybrid space

Space plays an ever increasing role in cell biological modeling and simulation. This ranges from compartmental dynamics, via mesh-based approaches, to individuals moving in continuous space. An attributed, multi-level, rule-based language, ML-Space, is presented that allows to integrate these different types of spatial dynamics within one model. The associated simulator combines Gillespie's method, the Next Subvolume method, and Brownian dynamics. This allows the simulation of reaction diffusion systems as well as taking excluded volume effects into account. A small example illuminates the potential of the approach in dealing with complex spatial dynamics like those involved in studying the dynamics of lipid rafts and their role in receptor co-localization.

[1]  Adelinde M. Uhrmacher,et al.  Spatial modeling in cell biology at multiple levels , 2010, Proceedings of the 2010 Winter Simulation Conference.

[2]  Andreas Hellander,et al.  An adaptive algorithm for simulation of stochastic reaction-diffusion processes , 2010, J. Comput. Phys..

[3]  J. Elf,et al.  Stochastic reaction-diffusion kinetics in the microscopic limit , 2010, Proceedings of the National Academy of Sciences.

[4]  Stefan Leye,et al.  Flexible experimentation in the modeling and simulation framework JAMES II - implications for computational systems biology , 2010, Briefings Bioinform..

[5]  Adelinde M. Uhrmacher,et al.  Exploring the performance of spatial stochastic simulation algorithms , 2011, J. Comput. Phys..

[6]  J. Hancock,et al.  Lipid rafts: contentious only from simplistic standpoints , 2006, Nature Reviews Molecular Cell Biology.

[7]  James R. Faeder,et al.  Compartmental rule-based modeling of biochemical systems , 2009, Proceedings of the 2009 Winter Simulation Conference (WSC).

[8]  Dan V. Nicolau,et al.  Identifying Optimal Lipid Raft Characteristics Required To Promote Nanoscale Protein-Protein Interactions on the Plasma Membrane , 2006, Molecular and Cellular Biology.

[9]  Kai Simons,et al.  Lipid Rafts As a Membrane-Organizing Principle , 2010, Science.

[10]  Ezio Bartocci,et al.  Shape Calculus. A Spatial Mobile Calculus for 3D Shapes , 2010, Sci. Ann. Comput. Sci..

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

[12]  Joachim Niehren,et al.  Author manuscript, published in "Computational Methods in Systems Biology, 6th International Conference CMSB (2008) 83-102" The Attributed Pi-Calculus with Priorities , 2009 .

[13]  B. Kholodenko.  Cell-signalling dynamics in time and space , 2006, Nature Reviews Molecular Cell Biology.

[14]  Mathias John,et al.  A Spatial Extension to the π Calculus , 2007 .

[15]  P. R. ten Wolde,et al.  Spatio-temporal correlations can drastically change the response of a MAPK pathway , 2009, Proceedings of the National Academy of Sciences.

[16]  Antoine Lejay,et al.  Simulation of exit times and positions for Brownian motions and Diffusions , 2007 .

[17]  Adelinde M. Uhrmacher,et al.  Multi-resolution spatial simulation for molecular crowding , 2008, 2008 Winter Simulation Conference.

[18]  Thomas Hinze,et al.  Rule-based spatial modeling with diffusing, geometrically constrained molecules , 2010, BMC Bioinformatics.

[19]  Peter Tang,et al.  Dynamic cellular automata : an alternative approach to cellular simulation , 2007 .

[20]  Corrado Priami,et al.  Beta Binders for Biological Interactions , 2004, CMSB.

[21]  Andreas Hellander,et al.  Simulation of Stochastic Reaction-Diffusion Processes on Unstructured Meshes , 2008, SIAM J. Sci. Comput..

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

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

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

[25]  Adelinde M. Uhrmacher,et al.  Experiments with Single Core, Multi-core, and GPU Based Computation of Cellular Automata , 2009, 2009 First International Conference on Advances in System Simulation.

[26]  Adelinde M. Uhrmacher,et al.  Rule-based multi-level modeling of cell biological systems , 2011, BMC Systems Biology.

[27]  Muffy Calder,et al.  Some Investigations Concerning the CTMC and the ODE Model Derived From Bio-PEPA , 2009, FBTC@ICALP.

[28]  J. Edwards,et al.  Quantitative understanding of cell signaling: the importance of membrane organization. , 2010, Current opinion in biotechnology.

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

[30]  Joachim Niehren,et al.  Biochemical Reaction Rules with Constraints , 2011, ESOP.