Morphogenesis through moving membranes

We present a methodology for the modelling of spatially-aware biological phenomena, based on the description of the movement of membranes in the Euclidean space. The time evolution of the system is described by an iterative algorithm, which determines the movement of the objects according to the actions they perform, and the constraints they are subjected to. We exemplify our approach with a model of the morphogenesis of Dictyostelium discoideum, and present the results of its simulation.

[1]  Tetsuya Kominami,et al.  Gastrulation in the sea urchin embryo: A model system for analyzing the morphogenesis of a monolayered epithelium , 2004, Development, growth & differentiation.

[2]  Ivana Bozic Mathematical Models of Cancer , 2013 .

[3]  Craig W. Reynolds Flocks, herds, and schools: a distributed behavioral model , 1998 .

[4]  Paolo Milazzo,et al.  Stochastic Calculus of Looping Sequences for the Modelling and Simulation of Cellular Pathways , 2009, Trans. Comp. Sys. Biology.

[5]  D. Drasdo,et al.  Modeling the interplay of generic and genetic mechanisms in cleavage, blastulation, and gastrulation , 2000, Developmental dynamics : an official publication of the American Association of Anatomists.

[6]  Louis Y. Cheng,et al.  The mechanisms and mechanics of archenteron elongation during sea urchin gastrulation , 1986 .

[7]  Robin Milner,et al.  Communicating and mobile systems - the Pi-calculus , 1999 .

[8]  J. Schwartz,et al.  Theory of Self-Reproducing Automata , 1967 .

[9]  Giovanni Pardini,et al.  Formal Modelling and Simulation of Biological Systems with Spatiality , 2011 .

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

[11]  Johann de Jong,et al.  A cell-based model of Nematostella vectensis gastrulation including bottle cell formation, invagination and zippering. , 2011, Developmental biology.

[12]  H. Othmer,et al.  A model for individual and collective cell movement in Dictyostelium discoideum. , 2000, Proceedings of the National Academy of Sciences of the United States of America.

[13]  Paolo Milazzo,et al.  A Calculus of Looping Sequences for Modelling Microbiological Systems , 2006, Fundam. Informaticae.

[14]  Glazier,et al.  Simulation of biological cell sorting using a two-dimensional extended Potts model. , 1992, Physical review letters.

[15]  Luca Cardelli,et al.  Processes in space , 2012, Theor. Comput. Sci..

[16]  Paolo Milazzo,et al.  Simulation of Spatial P system models , 2014, Theor. Comput. Sci..

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

[18]  Roberto Barbuti,et al.  Spatial Calculus of Looping Sequences , 2009, FBTC@ICALP.

[19]  Sylvia Nagl,et al.  Mathematical models of cancer , 2006 .

[20]  P. Hogeweg,et al.  Modelling Morphogenesis: From Single Cells to Crawling Slugs. , 1997, Journal of theoretical biology.

[21]  Davide Sangiorgi,et al.  Communicating and Mobile Systems: the π-calculus, , 2000 .

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

[23]  James D. Murray Mathematical Biology: I. An Introduction , 2007 .

[24]  G. Oster,et al.  How do sea urchins invaginate? Using biomechanics to distinguish between mechanisms of primary invagination. , 1995, Development.

[25]  N. Rashevsky,et al.  Mathematical biology , 1961, Connecticut medicine.

[26]  Alan Bundy,et al.  Constructing Induction Rules for Deductive Synthesis Proofs , 2006, CLASE.

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

[28]  P. Hogeweg,et al.  How amoeboids self-organize into a fruiting body: Multicellular coordination in Dictyostelium discoideum , 2001, Proceedings of the National Academy of Sciences of the United States of America.

[29]  Sylvia Nagl,et al.  Cancer Bioinformatics: From Therapy Design to Treatment , 2006 .

[30]  Luca Cardelli,et al.  Brane Calculi Interactions of Biological Membranes , 2004 .

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

[32]  Vincenzo Manca,et al.  Infobiotics: Information in Biotic Systems , 2013 .

[33]  Paolo Milazzo,et al.  Spatial P systems , 2010, Natural Computing.

[34]  A. Turing The chemical basis of morphogenesis , 1952, Philosophical Transactions of the Royal Society of London. Series B, Biological Sciences.

[35]  James D. Murray,et al.  Spatial models and biomedical applications , 2003 .

[36]  Mathias John,et al.  A Spatial Extension to the pi Calculus , 2008, Electron. Notes Theor. Comput. Sci..