Turing patterns in network-organized activator–inhibitor systems

Differences in diffusion constants of activator and inhibitor species can destabilize biological and chemical processes, leading to the spontaneous emergence of periodic spatial patterns. A general framework now provides the tools for studying such so-called Turing patterns in systems organized in complex networks.

[1]  Zhen Jin,et al.  Formation of spatial patterns in an epidemic model with constant removal rate of the infectives , 2006, q-bio/0610006.

[2]  A. Motter,et al.  Ensemble averageability in network spectra. , 2007, Physical review letters.

[3]  Hans Meinhardt,et al.  Molecular evidence for an activator-inhibitor mechanism in development of embryonic feather branching. , 2005, Proceedings of the National Academy of Sciences of the United States of America.

[4]  T. Geisel,et al.  Forecast and control of epidemics in a globalized world. , 2004, Proceedings of the National Academy of Sciences of the United States of America.

[5]  P. Sheng,et al.  Theory and Simulations , 2003 .

[6]  I. Prigogine,et al.  Symmetry Breaking Instabilities in Dissipative Systems. II , 1968 .

[7]  S. Kondo,et al.  A reaction–diffusion wave on the skin of the marine angelfish Pomacanthus , 1995, Nature.

[8]  Albert-László Barabási,et al.  Statistical mechanics of complex networks , 2001, ArXiv.

[9]  Alexander S. Mikhailov,et al.  Foundations of Synergetics II , 1990 .

[10]  Alessandro Vespignani,et al.  Epidemic spreading in scale-free networks. , 2000, Physical review letters.

[11]  Dulos,et al.  Experimental evidence of a sustained standing Turing-type nonequilibrium chemical pattern. , 1990, Physical review letters.

[12]  L E Scriven,et al.  Instability and dynamic pattern in cellular networks. , 1971, Journal of theoretical biology.

[13]  Dean L Urban,et al.  A Graph‐Theory Framework for Evaluating Landscape Connectivity and Conservation Planning , 2008, Conservation biology : the journal of the Society for Conservation Biology.

[14]  S. Strogatz Exploring complex networks , 2001, Nature.

[15]  T. Masaki Structure and Dynamics , 2002 .

[16]  Peter K. Moore,et al.  Localized patterns in homogeneous networks of diffusively coupled reactors , 2005 .

[17]  S. N. Dorogovtsev,et al.  Laplacian spectra of, and random walks on, complex networks: are scale-free architectures really important? , 2007, Physical review. E, Statistical, nonlinear, and soft matter physics.

[18]  Albert,et al.  Emergence of scaling in random networks , 1999, Science.

[19]  T. Ichinomiya Frequency synchronization in a random oscillator network. , 2004, Physical review. E, Statistical, nonlinear, and soft matter physics.

[20]  Timothy H. Keitt,et al.  LANDSCAPE CONNECTIVITY: A GRAPH‐THEORETIC PERSPECTIVE , 2001 .

[21]  Sano,et al.  Proportion regulation of biological cells in globally coupled nonlinear systems. , 1995, Physical review letters.

[22]  A. Mikhailov Foundations of Synergetics I: Distributed Active Systems , 1991 .

[23]  Johan van de Koppel,et al.  Regular pattern formation in real ecosystems. , 2008, Trends in ecology & evolution.

[24]  Martin Fussenegger,et al.  Synthetic ecosystems based on airborne inter- and intrakingdom communication , 2007, Proceedings of the National Academy of Sciences.

[25]  Jordi Bascompte,et al.  Spatial network structure and amphibian persistence in stochastic environments , 2006, Proceedings of the Royal Society B: Biological Sciences.

[26]  Alessandro Vespignani,et al.  Dynamical Processes on Complex Networks , 2008 .

[27]  P. Maini,et al.  The Turing Model Comes of Molecular Age , 2006, Science.

[28]  K. Shiota,et al.  TGFβ2 acts as an “Activator” molecule in reaction‐diffusion model and is involved in cell sorting phenomenon in mouse limb micromass culture , 2000, Developmental dynamics : an official publication of the American Association of Anatomists.

[29]  Shigeru Kondo,et al.  Interactions between zebrafish pigment cells responsible for the generation of Turing patterns , 2009, Proceedings of the National Academy of Sciences.

[30]  Alessandro Vespignani,et al.  Reaction–diffusion processes and metapopulation models in heterogeneous networks , 2007, cond-mat/0703129.

[31]  K. Kaneko,et al.  Regulative differentiation as bifurcation of interacting cell population. , 2007, Journal of theoretical biology.

[32]  S. Havlin,et al.  Scale-free networks are ultrasmall. , 2002, Physical review letters.

[33]  Daniel Walgraef,et al.  Spatio-temporal pattern formation , 1996 .

[34]  Stuart A Newman,et al.  Activator-inhibitor dynamics of vertebrate limb pattern formation. , 2007, Birth defects research. Part C, Embryo today : reviews.

[35]  Alessandro Vespignani,et al.  The role of the airline transportation network in the prediction and predictability of global epidemics , 2006, Proceedings of the National Academy of Sciences of the United States of America.

[36]  Michael Menzinger,et al.  Laplacian spectra as a diagnostic tool for network structure and dynamics. , 2007, Physical review. E, Statistical, nonlinear, and soft matter physics.

[37]  Owe Orwar,et al.  Molecular engineering: Networks of nanotubes and containers , 2001, Nature.

[38]  V. Latora,et al.  Complex networks: Structure and dynamics , 2006 .

[39]  B. Mohar THE LAPLACIAN SPECTRUM OF GRAPHS y , 1991 .

[40]  H. Meinhardt,et al.  Pattern formation by local self-activation and lateral inhibition. , 2000, BioEssays : news and reviews in molecular, cellular and developmental biology.

[41]  Alexander S Mikhailov,et al.  Diffusion-induced instability and chaos in random oscillator networks. , 2009, Physical review. E, Statistical, nonlinear, and soft matter physics.

[42]  H. Swinney,et al.  Transition from a uniform state to hexagonal and striped Turing patterns , 1991, Nature.

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

[44]  Hans Meinhardt,et al.  Global cell sorting in the C. elegans embryo defines a new mechanism for pattern formation. , 2006, Developmental biology.

[45]  A. Hastings,et al.  Strong effect of dispersal network structure on ecological dynamics , 2008, Nature.

[46]  Mat E. Barnet,et al.  A synthetic Escherichia coli predator–prey ecosystem , 2008, Molecular systems biology.

[47]  Jurgen Kurths,et al.  Synchronization in complex networks , 2008, 0805.2976.

[48]  M. Mimura,et al.  On a diffusive prey--predator model which exhibits patchiness. , 1978, Journal of theoretical biology.

[49]  L E Scriven,et al.  Non-linear aspects of dynamic pattern in cellular networks. , 1974, Journal of theoretical biology.

[50]  S. N. Dorogovtsev,et al.  Spectra of complex networks. , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.

[51]  Thilo Gross,et al.  Instabilities in spatially extended predator-prey systems: spatio-temporal patterns in the neighborhood of Turing-Hopf bifurcations. , 2007, Journal of theoretical biology.

[52]  F. Bignone Structural Complexity of Early Embryos: A Study on the Nematode Caenorhabditis elegans , 2001, Journal of biological physics.

[53]  Alessandro Vespignani,et al.  Epidemic modeling in metapopulation systems with heterogeneous coupling pattern: theory and simulations. , 2007, Journal of theoretical biology.

[54]  Maron,et al.  Spatial pattern formation in an insect host-parasitoid system , 1997, Science.

[55]  Peter K. Moore,et al.  Network topology and Turing instabilities in small arrays of diffusively coupled reactors , 2004 .