Cellular automata modelling of biomolecular networks dynamics

The modelling of biological systems dynamics is traditionally performed by ordinary differential equations (ODEs). When dealing with intracellular networks of genes, proteins and metabolites, however, this approach is hindered by network complexity and the lack of experimental kinetic parameters. This opened the field for other modelling techniques, such as cellular automata (CA) and agent-based modelling (ABM). This article reviews this emerging field of studies on network dynamics in molecular biology. The basics of the CA technique are discussed along with an extensive list of related software and websites. The application of CA to networks of biochemical reactions is exemplified in detail by the case studies of the mitogen-activated protein kinase (MAPK) signalling pathway, the FAS-ligand (FASL)-induced and Bcl-2-related apoptosis. The potential of the CA method to model basic pathways patterns, to identify ways to control pathway dynamics and to help in generating strategies to fight with cancer is demonstrated. The different line of CA applications presented includes the search for the best-performing network motifs, an analysis of importance for effective intracellular signalling and pathway cross-talk.

[1]  Danail Bonchev,et al.  Complexity of Protein-Protein Interaction Networks, Complexes, and Pathways , 2003 .

[2]  L. D. de Pillis,et al.  A cellular automata model of tumor-immune system interactions. , 2006, Journal of theoretical biology.

[3]  John W Cain,et al.  Cellular automata simulation of topological effects on the dynamics of feed-forward motifs , 2008, Journal of biological engineering.

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

[5]  U. Bhalla,et al.  Emergent properties of networks of biological signaling pathways. , 1999, Science.

[6]  G. Salvesen,et al.  Structure of the Fas/FADD complex: A conditional death domain complex mediating signaling by receptor clustering , 2009, Cell cycle.

[7]  Stephen Wolfram,et al.  Theory and Applications of Cellular Automata , 1986 .

[8]  Darren J. Wilkinson Stochastic Modelling for Systems Biology , 2006 .

[9]  Dewey T. Taylor,et al.  Toward a classification of isodynamic feed-forward motifs , 2010, Journal of biological dynamics.

[10]  Classical dynamics on graphs. , 2000, Physical review. E, Statistical, nonlinear, and soft matter physics.

[11]  R. Wood‐Baker,et al.  BCL-2 Expression is Prognostic for Improved Survival in Non-small Cell Lung Cancer , 2009, Journal of thoracic oncology : official publication of the International Association for the Study of Lung Cancer.

[12]  M. Haklay,et al.  Agent-Based Models and Individualism: Is the World Agent-Based? , 2000 .

[13]  Danail Bonchev,et al.  Quantitative Measures of Network Complexity , 2005 .

[14]  C K Cheng,et al.  A cellular automata model of enzyme kinetics. , 1996, Journal of molecular graphics.

[15]  Albert-László Barabási,et al.  Linked: The New Science of Networks , 2002 .

[16]  Martin Nilsson,et al.  Cellular Automata for Simulating Molecular Self-Assembly , 2003, DMCS.

[17]  Michael Wooldridge,et al.  Agent-based software engineering , 1997, IEE Proc. Softw. Eng..

[18]  Péter Gács Reliable Cellular Automata with Self-Organization , 1997, FOCS 1997.

[19]  S. Kimura,et al.  A computational model on the modulation of mitogen-activated protein kinase (MAPK) and Akt pathways in heregulin-induced ErbB signalling. , 2003, The Biochemical journal.

[20]  Margot Thome,et al.  Regulation of lymphocyte proliferation and death by flip , 2001, Nature Reviews Immunology.

[21]  J. Cohen,et al.  Modeling Biological Systems. Principles and Applications , 1997 .

[22]  Mark E. J. Newman,et al.  Structure and Dynamics of Networks , 2009 .

[23]  Bernard Testa,et al.  Cellular automata models of biochemical phenomena , 1999, Future Gener. Comput. Syst..

[24]  David McMillen,et al.  Biochemical Network Stochastic Simulator (BioNetS): software for stochastic modeling of biochemical networks , 2004, BMC Bioinformatics.

[25]  D. Fell,et al.  Differential feedback regulation of the MAPK cascade underlies the quantitative differences in EGF and NGF signalling in PC12 cells , 2000, FEBS letters.

[26]  D. Vaux,et al.  Inhibitor of apoptosis proteins and their relatives: IAPs and other BIRPs , 2001, Genome Biology.

[27]  Glazier,et al.  Simulation of the differential adhesion driven rearrangement of biological cells. , 1993, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[28]  D. Hancock,et al.  Identification of Novel Isoforms of the BH3 Domain Protein Bim Which Directly Activate Bax To Trigger Apoptosis , 2002, Molecular and Cellular Biology.

[29]  John R. Koza,et al.  Hidden Order: How Adaptation Builds Complexity. , 1995, Artificial Life.

[30]  Stanley Wasserman,et al.  Social Network Analysis: Methods and Applications , 1994, Structural analysis in the social sciences.

[31]  Walter Nadler,et al.  Network analysis of the state space of discrete dynamical systems. , 2007, Physical review letters.

[32]  C. Duckett,et al.  Inhibitor of apoptosis proteins in eukaryotic evolution and development: a model of thematic conservation. , 2008, Developmental cell.

[33]  Chi-Ying F. Huang,et al.  Ultrasensitivity in the mitogen-activated protein kinase cascade. , 1996, Proceedings of the National Academy of Sciences of the United States of America.

[34]  Vipul Periwal,et al.  System Modeling in Cellular Biology: From Concepts to Nuts and Bolts , 2006 .

[35]  E. Gilles,et al.  Computational modeling of the dynamics of the MAP kinase cascade activated by surface and internalized EGF receptors , 2002, Nature Biotechnology.

[36]  S. V. Aksenov,et al.  A spatially extended stochastic model of the bacterial chemotaxis signalling pathway. , 2003, Journal of molecular biology.

[37]  Tecnica Conway's Game of Life , 2010 .

[38]  T. Vicsek,et al.  Generic modelling of cooperative growth patterns in bacterial colonies , 1994, Nature.

[39]  J Devillers,et al.  Internet resources for agent-based modelling , 2010, SAR and QSAR in environmental research.

[40]  Hiroaki Kitano,et al.  Foundations of systems biology , 2001 .

[41]  G. Tortora,et al.  Inhibition of bcl-2 as cancer therapy. , 2002, Annals of oncology : official journal of the European Society for Medical Oncology.

[42]  Dennis Bray,et al.  10 Computational Cell Biology - The Stochastic Approach , 2002 .

[43]  Andreas Deutsch,et al.  Modelling interacting cell systems in biology and medicine with cellular automata , 2001, German Conference on Bioinformatics.

[44]  V. Pantesco,et al.  Gene expression of anti‐ and pro‐apoptotic proteins in malignant and normal plasma cells , 2009, British journal of haematology.

[45]  Peter J Woolf,et al.  Self organization of membrane proteins via dimerization. , 2003, Biophysical chemistry.

[46]  Michael Jaye,et al.  Modeling Differential Equations in Biology , 2001 .

[47]  Jörg R. Weimar Cellular Automata Approaches to Enzymatic Reaction Networks , 2002, ACRI.

[48]  M. Piotrowska,et al.  A quantitative cellular automaton model of in vitro multicellular spheroid tumour growth. , 2009, Journal of theoretical biology.

[49]  O Mason,et al.  Graph theory and networks in Biology. , 2006, IET systems biology.

[50]  B. Kholodenko,et al.  Negative feedback and ultrasensitivity can bring about oscillations in the mitogen-activated protein kinase cascades. , 2000, European journal of biochemistry.

[51]  A. Petros,et al.  Solution structure of the antiapoptotic protein bcl-2 , 2001, Proceedings of the National Academy of Sciences of the United States of America.

[52]  Liang-yan Xue,et al.  Photodamage to multiple Bcl-xL isoforms by photodynamic therapy with the phthalocyanine photosensitizer Pc 4 , 2003, Oncogene.

[53]  James W. Haefner,et al.  Modeling Biological Systems , 1996, Springer US.

[54]  Stephen Wolfram,et al.  A New Kind of Science , 2003, Artificial Life.

[55]  D. Bonchev,et al.  Cellular Automata (CA) As a Basic Method for Studying Network Dynamics , 2006 .

[56]  J. Holland,et al.  Artificial Adaptive Agents in Economic Theory , 1991 .

[57]  G B Ermentrout,et al.  Cellular automata approaches to biological modeling. , 1993, Journal of theoretical biology.

[58]  Lemont B. Kier,et al.  Cellular Automata Modeling of Complex Biochemical Systems , 2009, Encyclopedia of Complexity and Systems Science.

[59]  Arthur W. Burks,et al.  Essays on cellular automata , 1970 .

[60]  Maurice Demarty,et al.  Modelling Bacterial Hyperstructures with Cellular Automata , 2006 .

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

[62]  Yoav Shoham,et al.  Multiagent Systems - Algorithmic, Game-Theoretic, and Logical Foundations , 2009 .

[63]  G. Casari,et al.  From molecular networks to qualitative cell behavior , 2005, FEBS letters.

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

[65]  Tommaso Toffoli Cellular automata , 1998 .

[66]  W. Marsden I and J , 2012 .

[67]  Yi Li Yang,et al.  The IAP family: endogenous caspase inhibitors with multiple biological activities , 2000, Cell Research.

[68]  S. Shen-Orr,et al.  Network motifs: simple building blocks of complex networks. , 2002, Science.

[69]  Arno Lukas,et al.  Discrete simulation of regulatory homo- and heterodimerization in the apoptosis effector phase , 2002, Bioinform..

[70]  W. Park,et al.  Increased expression of FLIP, an inhibitor of Fas‐mediated apoptosis, in stomach cancer , 2003, APMIS : acta pathologica, microbiologica, et immunologica Scandinavica.

[71]  Boguslaw Stec,et al.  The Fas/FADD death domain complex structure unravels signaling by receptor clustering , 2008, Nature.

[72]  Rudy Rucker,et al.  The Lifebox, the Seashell, and the Soul: What Gnarly Computation Taught Me About Ultimate Reality, the Meaning of Life, and How to Be Happy , 2005 .

[73]  Uta Berger,et al.  Pattern-Oriented Modeling of Agent-Based Complex Systems: Lessons from Ecology , 2005, Science.

[74]  J. Timothy Wootton,et al.  Local interactions predict large-scale pattern in empirically derived cellular automata , 2001, Nature.

[75]  Xiaolu Yang,et al.  c‐FLIPL is a dual function regulator for caspase‐8 activation and CD95‐mediated apoptosis , 2002, The EMBO journal.

[76]  Eric Bonabeau,et al.  Agent-based modeling: Methods and techniques for simulating human systems , 2002, Proceedings of the National Academy of Sciences of the United States of America.

[77]  Andreas Bender,et al.  Evolved Cellular Automata for Protein Secondary Structure Prediction Imitate the Determinants for Folding Observed in Nature , 2007, Silico Biol..

[78]  Y. Zhang,et al.  IntAct—open source resource for molecular interaction data , 2006, Nucleic Acids Res..

[79]  J. Hilke,et al.  A modified cellular automata model of nucleotide interactions and non-enzymatic transcription of DNA , 1995, Proceedings First International Symposium on Intelligence in Neural and Biological Systems. INBS'95.

[80]  John Calvin Reed,et al.  Distinct BIR Domains of cIAP1 Mediate Binding to and Ubiquitination of Tumor Necrosis Factor Receptor-associated Factor 2 and Second Mitochondrial Activator of Caspases* , 2006, Journal of Biological Chemistry.

[81]  Michael J. North,et al.  Tutorial on Agent-Based Modeling and Simulation PART 2: How to Model with Agents , 2006, Proceedings of the 2006 Winter Simulation Conference.

[82]  Danail Bonchev,et al.  Modeling Biochemical Networks: A Cellular‐Automata Approach , 2005, Chemistry & biodiversity.

[83]  B. Rost,et al.  Prediction of protein secondary structure at better than 70% accuracy. , 1993, Journal of molecular biology.