The Intersection of Theory and Application in Elucidating Pattern Formation in Developmental Biology.

We discuss theoretical and experimental approaches to three distinct developmental systems that illustrate how theory can influence experimental work and vice-versa. The chosen systems - Drosophila melanogaster, bacterial pattern formation, and pigmentation patterns - illustrate the fundamental physical processes of signaling, growth and cell division, and cell movement involved in pattern formation and development. These systems exemplify the current state of theoretical and experimental understanding of how these processes produce the observed patterns, and illustrate how theoretical and experimental approaches can interact to lead to a better understanding of development. As John Bonner said long ago'We have arrived at the stage where models are useful to suggest experiments, and the facts of the experiments in turn lead to new and improved models that suggest new experiments. By this rocking back and forth between the reality of experimental facts and the dream world of hypotheses, we can move slowly toward a satisfactory solution of the major problems of developmental biology.'

[1]  G. G. Stokes "J." , 1890, The New Yale Book of Quotations.

[2]  C. M. Child Patterns and problems of development [by] C.M. Child ... , 1941 .

[3]  C. Patlak Random walk with persistence and external bias , 1953 .

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

[5]  J. Claxton THE DETERMINATION OF PATTERNS WITH SPECIAL REFERENCE TO THAT OF THE CENTRAL PRIMARY SKIN FOLLICLES IN SHEEP. , 1964, Journal of theoretical biology.

[6]  J. Adler Chemotaxis in Bacteria , 1966, Science.

[7]  J. Bonner,et al.  Differentiation , 1968, Nature.

[8]  L. Wolpert Positional information and the spatial pattern of cellular differentiation. , 1969, Journal of theoretical biology.

[9]  L. E. Scriven,et al.  Interactions of reaction and diffusion in open systems , 1969 .

[10]  L. Segel,et al.  Initiation of slime mold aggregation viewed as an instability. , 1970, Journal of theoretical biology.

[11]  F. Crick Diffusion in Embryogenesis , 1970, Nature.

[12]  L. Segel,et al.  Traveling bands of chemotactic bacteria: a theoretical analysis. , 1971, Journal of theoretical biology.

[13]  Lewis Wolpert,et al.  Chapter 6 Positional Information and Pattern Formation , 1971 .

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

[15]  L. Segel,et al.  Model for chemotaxis. , 1971, Journal of theoretical biology.

[16]  H. Berg,et al.  Chemotaxis in Escherichia coli analysed by Three-dimensional Tracking , 1972, Nature.

[17]  L Glass,et al.  Stochastic Generation of Regular Distributions , 1973, Science.

[18]  Melvin Lax,et al.  Stochastic Transport in a Disordered Solid. I. Theory , 1973 .

[19]  M. Hadley,et al.  Chromatophores and color change , 1973 .

[20]  Melvin Lax,et al.  Stochastic Transport in a Disordered Solid. II. Impurity Conduction , 1973 .

[21]  D. Brown,et al.  Chemotaxis in Escherichia coli analyzed by three-dimensional tracking. , 1974, Antibiotics and chemotherapy.

[22]  Evelyn Fox Keller,et al.  Necessary and sufficient conditions for chemotactic bands , 1975 .

[23]  C. Douglas,et al.  A continuous study of morphological phase in the swarm of Proteus. , 1976, Journal of medical microbiology.

[24]  Developmental origin of even spacing between the microchaetes of Drosophila melanogaster. , 1976, Australian journal of biological sciences.

[25]  Hans G. Othmer,et al.  Spatial patterns in coupled biochemical oscillators , 1977 .

[26]  Lee A. Segel,et al.  A Theoretical Study of Receptor Mechanisms in Bacterial Chemotaxis , 1977 .

[27]  I. Lapidus,et al.  A model for traveling bands of chemotactic bacteria. , 1978, Biophysical journal.

[28]  A. D. Dingle,et al.  Dynamics of pigment pattern formation in the zebrafish, Brachydanio rerio. I. Establishment and regulation of the lateral line melanophore stripe during the first eight days of development , 1978 .

[29]  H. Nijhout,et al.  Wing pattern formation in Lepidoptera: A model , 1978 .

[30]  D. Hoff,et al.  LARGE TIME BEHAVIOR OF SOLUTIONS OF SYSTEMS OF NONLINEAR REACTION-DIFFUSION EQUATIONS* , 1978 .

[31]  H. Othmer,et al.  The effects of cell density and metabolite flux on cellular dynamics , 1978, Journal of mathematical biology.

[32]  Hans G. Othmer,et al.  Synchronized and Differentiated Modes of Cellular Dynamics , 1980 .

[33]  H G Othmer,et al.  Scale-invariance in reaction-diffusion models of spatial pattern formation. , 1980, Proceedings of the National Academy of Sciences of the United States of America.

[34]  H. Fricke Juvenile‐adult Colour Patterns and Coexistence in the Territorial Coral Reef Fish Pomacanthus imperator , 1980 .

[35]  James D. Murray,et al.  A Pattern Formation Mechanism and Its Application to Mammalian Coat Markings , 1980 .

[36]  J. Bard,et al.  A model for generating aspects of zebra and other mammalian coat patterns. , 1981, Journal of theoretical biology.

[37]  Jerome Percus,et al.  Nonlinear aspects of chemotaxis , 1981 .

[38]  J. Murray A Pre-pattern formation mechanism for animal coat markings , 1981 .

[39]  E. Hertzberg,et al.  Gap junctional communication. , 1981, Annual review of physiology.

[40]  L. Wolpert Positional information and pattern formation. , 1981, Philosophical transactions of the Royal Society of London. Series B, Biological sciences.

[41]  J. Murray,et al.  On pattern formation mechanisms for lepidopteran wing patterns and mammalian coat markings. , 1981, Philosophical transactions of the Royal Society of London. Series B, Biological sciences.

[42]  H. Meinhardt Models of biological pattern formation , 1982 .

[43]  J. Bonner CHAPTER 1 – Comparative Biology of Cellular Slime Molds , 1982 .

[44]  B. Nagorcka,et al.  The role of a reaction--diffusion system in the formation of hair fibres. , 1982, Journal of theoretical biology.

[45]  H. Berg Random Walks in Biology , 2018 .

[46]  A. D. Dingle,et al.  Dynamics of pigment pattern formation in the zebrafish, Brachydanio rerio. III. Effect of anteroposterior location of three-day lateral line melanophores on colonization by the second wave of melanophores. , 1983, The Journal of experimental zoology.

[47]  Butterfly wing patterns: how good a determining mechanism is the simple diffusion of a single morphogen? , 1984, Journal of embryology and experimental morphology.

[48]  Douglas A. Lauffenburger,et al.  Traveling bands of chemotactic bacteria in the context of population growth , 1984 .

[49]  D. A. Young A local activator-inhibitor model of vertebrate skin patterns , 1984 .

[50]  M. Weir,et al.  Gap-junctional communication compartments in the Drosophila wing imaginal disk. , 1984, Developmental biology.

[51]  T. Naitoh,et al.  Adaptation of a common freshwater goby, yoshinobori, Rhinogobius brunneus Temminck et Schlegel to various backgrounds including those containing different sizes of black and white checkerboard squares , 1985 .

[52]  B. Nagorcka,et al.  The role of a reaction-diffusion system in the initiation of primary hair follicles. , 1985, Journal of theoretical biology.

[53]  B. Nagorcka,et al.  Spatial patterns produced by a reaction-diffusion system in primary hair follicles. , 1985, Journal of theoretical biology.

[54]  J. Murray,et al.  Pattern sensitivity to boundary and initial conditions in reaction-diffusion models , 1986, Journal of mathematical biology.

[55]  H. Berg,et al.  Temporal comparisons in bacterial chemotaxis. , 1986, Proceedings of the National Academy of Sciences of the United States of America.

[56]  H G Othmer,et al.  Differentiation, cell sorting and proportion regulation in the slug stage of Dictyostelium discoideum. , 1986, Journal of theoretical biology.

[57]  D R Soll,et al.  Frequency and orientation of pseudopod formation of Dictyostelium discoideum amebae chemotaxing in a spatial gradient: further evidence for a temporal mechanism. , 1987, Cell motility and the cytoskeleton.

[58]  H. Othmer,et al.  Models of dispersal in biological systems , 1988, Journal of mathematical biology.

[59]  C. Nüsslein-Volhard,et al.  The bicoid protein determines position in the Drosophila embryo in a concentration-dependent manner , 1988, Cell.

[60]  C. Nüsslein-Volhard,et al.  A gradient of bicoid protein in Drosophila embryos , 1988, Cell.

[61]  H. Meinhardt Models for positional signalling with application to the dorsoventral patterning of insects and segregation into different cell types. , 1989, Development.

[62]  J. Pearson,et al.  Turing instabilities with nearly equal diffusion coefficients , 1989 .

[63]  P. Fisher,et al.  Quantitative analysis of cell motility and chemotaxis in Dictyostelium discoideum by using an image processing system and a novel chemotaxis chamber providing stationary chemical gradients , 1989, The Journal of cell biology.

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

[65]  J. Murray,et al.  Size-dependent pigmentation-pattern formation in embryos of Alligator mississippiensis: time of initiation of pattern generation mechanism , 1990, Proceedings of the Royal Society of London. B. Biological Sciences.

[66]  H. Nijhout,et al.  A comprehensive model for colour pattern formation in butterflies , 1990, Proceedings of the Royal Society of London. B. Biological Sciences.

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

[68]  R. M. Ford,et al.  Measurement of bacterial random motility and chemotaxis coefficients: II. Application of single‐cell‐based mathematical model , 1991, Biotechnology and bioengineering.

[69]  M. Simon,et al.  Signal transduction pathways involving protein phosphorylation in prokaryotes. , 1991, Annual review of biochemistry.

[70]  H. Berg,et al.  Complex patterns formed by motile cells of Escherichia coli , 1991, Nature.

[71]  R. M. Ford,et al.  Measurement of bacterial random motility and chemotaxis coefficients: I. Stopped‐flow diffusion chamber assay , 1991, Biotechnology and bioengineering.

[72]  R. M. Ford,et al.  Analysis of chemotactic bacterial distributions in population migration assays using a mathematical model applicable to steep or shallow attractant gradients , 1991, Bulletin of mathematical biology.

[73]  I. Epstein,et al.  Modeling of Turing Structures in the Chlorite—Iodide—Malonic Acid—Starch Reaction System , 1991, Science.

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

[75]  J. Boissonade,et al.  Turing-type chemical patterns in the chlorite-iodide-malonic acid reaction , 1991 .

[76]  M R Myerscough,et al.  Pigmentation pattern formation on snakes. , 1991, Journal of theoretical biology.

[77]  B. Ermentrout Stripes or spots? Nonlinear effects in bifurcation of reaction—diffusion equations on the square , 1991, Proceedings of the Royal Society of London. Series A: Mathematical and Physical Sciences.

[78]  W. Jäger,et al.  On explosions of solutions to a system of partial differential equations modelling chemotaxis , 1992 .

[79]  Michael J. Lyons,et al.  Stripe selection: An intrinsic property of some pattern‐forming models with nonlinear dynamics , 1992, Developmental dynamics : an official publication of the American Association of Anatomists.

[80]  M. Cross,et al.  Pattern formation outside of equilibrium , 1993 .

[81]  G. Struhl,et al.  The torso receptor localizes as well as transduces the spatial signal specifying terminal body pattern in Drosophila , 1993, Nature.

[82]  S. Masazumi Morphological color changes in the medaka, Oryzias latipes, after prolonged background adaptation. I: Changes in the population and morphology of melanophores , 1993 .

[83]  T. Schüpbach,et al.  The drosophila dorsoventral patterning gene gurken produces a dorsally localized RNA and encodes a TGFα-like protein , 1993, Cell.

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

[85]  S. Carroll,et al.  Pattern formation and eyespot determination in butterfly wings. , 1994, Science.

[86]  Robert Dillon,et al.  Pattern formation in generalized Turing systems , 1994 .

[87]  Stephen L. Johnson,et al.  Genetic control of adult pigment stripe development in zebrafish. , 1995, Developmental biology.

[88]  Eshel Ben-Jacob,et al.  Complex bacterial patterns , 1995, Nature.

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

[90]  V. French,et al.  Eyespot development on butterfly wings: the epidermal response to damage. , 1995, Developmental biology.

[91]  W. C. Evans,et al.  Forest-killing diffuse CO2 emission at Mammoth Mountain as a sign of magmatic unrest , 1995, Nature.

[92]  W. N. Reynolds,et al.  Aggregation Patterns in Stressed Bacteria. , 1995, Physical review letters.

[93]  H. Berg,et al.  Dynamics of formation of symmetrical patterns by chemotactic bacteria , 1995, Nature.

[94]  H. Berg,et al.  Spatio-temporal patterns generated by Salmonella typhimurium. , 1995, Biophysical journal.

[95]  C. Nüsslein-Volhard,et al.  Zebrafish pigmentation mutations and the processes of neural crest development. , 1996, Development.

[96]  C J Weijer,et al.  Periodic phenomena in Proteus mirabilis swarm colony development , 1996, Journal of bacteriology.

[97]  C. Nüsslein-Volhard,et al.  Mutations affecting pigmentation and shape of the adult zebrafish , 1996, Development Genes and Evolution.

[98]  M. A. Herrero,et al.  Chemotactic collapse for the Keller-Segel model , 1996, Journal of mathematical biology.

[99]  C. Nüsslein-Volhard,et al.  Mutations affecting xanthophore pigmentation in the zebrafish, Danio rerio. , 1996, Development.

[100]  Hans G. Othmer,et al.  Aggregation, Blowup, and Collapse: The ABC's of Taxis in Reinforced Random Walks , 1997, SIAM J. Appl. Math..

[101]  R. A. Barrio,et al.  Confined Turing patterns in growing systems , 1997 .

[102]  Tamás Vicsek,et al.  Chemomodulation of cellular movement, collective formation of vortices by swarming bacteria, and colonial development , 1997 .

[103]  J. S. Parkinson,et al.  A model of excitation and adaptation in bacterial chemotaxis. , 1997, Proceedings of the National Academy of Sciences of the United States of America.

[104]  P. Maini,et al.  Spatial pattern formation in chemical and biological systems , 1997 .

[105]  How the leopard got its spots: a phylogenetic view of the evolution of felid coat patterns , 1997 .

[106]  H. Othmer,et al.  Oscillatory cAMP signaling in the development of Dic-tyostelium discoideum , 1998 .

[107]  J. Shapiro Thinking about bacterial populations as multicellular organisms. , 1998, Annual review of microbiology.

[108]  L Wolpert,et al.  Local inhibitory action of BMPs and their relationships with activators in feather formation: implications for periodic patterning. , 1998, Developmental biology.

[109]  L Wolpert,et al.  Mechanisms for positional signalling by morphogen transport: a theoretical study. , 1998, Journal of theoretical biology.

[110]  S. Carroll,et al.  Regulation of dopa decarboxylase expression during colour pattern formation in wild-type and melanic tiger swallowtail butterflies. , 1998, Development.

[111]  M. Brenner,et al.  Physical mechanisms for chemotactic pattern formation by bacteria. , 1998, Biophysical journal.

[112]  R. D,et al.  A Mathematical Model for Outgrowth and Spatial Patterning of the Vertebrate Limb Bud , 1999 .

[113]  J. Murray,et al.  A minimal mechanism for bacterial pattern formation , 1999, Proceedings of the Royal Society of London. Series B: Biological Sciences.

[114]  Rihito Asai,et al.  Zebrafish Leopard gene as a component of the putative reaction-diffusion system , 1999, Mechanisms of Development.

[115]  P K Maini,et al.  A two-dimensional numerical study of spatial pattern formation in interacting Turing systems , 1999, Bulletin of mathematical biology.

[116]  J. Murray,et al.  Model and analysis of chemotactic bacterial patterns in a liquid medium , 1999, Journal of mathematical biology.

[117]  M. McClure Development and evolution of melanophore patterns in fishes of the genus Danio (Teleostei: Cyprinidae) , 1999, Journal of morphology.

[118]  B. Bassler How bacteria talk to each other: regulation of gene expression by quorum sensing. , 1999, Current opinion in microbiology.

[119]  P. Maini,et al.  Reaction and diffusion on growing domains: Scenarios for robust pattern formation , 1999, Bulletin of mathematical biology.

[120]  P K Maini,et al.  Stripe formation in juvenile Pomacanthus explained by a generalized turing mechanism with chemotaxis. , 1999, Proceedings of the National Academy of Sciences of the United States of America.

[121]  Andrew J. Wathen,et al.  A model for colour pattern formation in the butterfly wing of Papilio dardanus , 2000, Proceedings of the Royal Society of London. Series B: Biological Sciences.

[122]  Herbert Levine,et al.  Cooperative self-organization of microorganisms , 2000 .

[123]  G. Odell,et al.  The segment polarity network is a robust developmental module , 2000, Nature.

[124]  Hans G. Othmer,et al.  The Diffusion Limit of Transport Equations Derived from Velocity-Jump Processes , 2000, SIAM J. Appl. Math..

[125]  Stephen L. Johnson,et al.  An orthologue of the kit-related gene fms is required for development of neural crest-derived xanthophores and a subpopulation of adult melanocytes in the zebrafish, Danio rerio. , 2000, Development.

[126]  P. Maini,et al.  Development and applications of a model for cellular response to multiple chemotactic cues , 2000, Journal of mathematical biology.

[127]  L. G. Stern,et al.  Fractional step methods applied to a chemotaxis model , 2000, Journal of mathematical biology.

[128]  S. Leibler,et al.  An ultrasensitive bacterial motor revealed by monitoring signaling proteins in single cells. , 2000, Science.

[129]  H. Berg Motile Behavior of Bacteria , 2000 .

[130]  S. Carroll,et al.  The generation and diversification of butterfly eyespot color patterns , 2001, Current Biology.

[131]  The role of EGF and TGF-b signaling in specifying the polarity of the Drosophila egg and embryo , 2001 .

[132]  Collapsing bacterial cylinders. , 1999, Physical review. E, Statistical, nonlinear, and soft matter physics.

[133]  N. A. Whitehead,et al.  Quorum-sensing in Gram-negative bacteria. , 2001, FEMS microbiology reviews.

[134]  V. French,et al.  Butterfly Eyespot Patterns: Evidence for Specification by a Morphogen Diffusion Gradient , 2001, Acta biotheoretica.

[135]  K. Painter Models for pigment pattern formation in the skin of fishes , 2001 .

[136]  S. Liaw,et al.  Turing model for the patterns of lady beetles. , 2001, Physical review. E, Statistical, nonlinear, and soft matter physics.

[137]  P. Maini,et al.  Mathematical Models for Biological Pattern Formation , 2001 .

[138]  G. Ruxton The possible fitness benefits of striped coat coloration for zebra , 2002 .

[139]  Qing Nie,et al.  Do morphogen gradients arise by diffusion? , 2002, Developmental cell.

[140]  A. Wathen,et al.  A predictive model for color pattern formation in the butterfly wing of {\it Papilio dardanus} , 2002 .

[141]  S. Leibler,et al.  Establishment of developmental precision and proportions in the early Drosophila embryo , 2002, Nature.

[142]  Douglas A Lauffenburger,et al.  Modeling and computational analysis of EGF receptor-mediated cell communication in Drosophila oogenesis. , 2002, Development.

[143]  P. Maini,et al.  Pattern formation in reaction-diffusion models with nonuniform domain growth , 2002, Bulletin of mathematical biology.

[144]  N. Barkai,et al.  Robustness of the BMP morphogen gradient in Drosophila embryonic patterning , 2022 .

[145]  R. Prum,et al.  Reaction–diffusion models of within-feather pigmentation patterning , 2002, Proceedings of the Royal Society of London. Series B: Biological Sciences.

[146]  Yoh Iwasa,et al.  Directionality of stripes formed by anisotropic reaction-diffusion models. , 2002, Journal of theoretical biology.

[147]  M. Sugimoto Morphological color changes in fish: Regulation of pigment cell density and morphology , 2002, Microscopy research and technique.

[148]  Hans G. Othmer,et al.  The Diffusion Limit of Transport Equations II: Chemotaxis Equations , 2002, SIAM J. Appl. Math..

[149]  J. Eisen,et al.  Headwaters of the zebrafish — emergence of a new model vertebrate , 2002, Nature Reviews Genetics.

[150]  Y. Iwasa,et al.  Origin of directionality in the fish stripe pattern , 2003, Developmental dynamics : an official publication of the American Association of Anatomists.

[151]  Dirk Horstmann,et al.  F ¨ Ur Mathematik in Den Naturwissenschaften Leipzig from 1970 until Present: the Keller-segel Model in Chemotaxis and Its Consequences from 1970 until Present: the Keller-segel Model in Chemotaxis and Its Consequences , 2022 .

[152]  M. Brenner,et al.  Motility of Escherichia coli cells in clusters formed by chemotactic aggregation , 2003, Proceedings of the National Academy of Sciences of the United States of America.

[153]  A. Filloux,et al.  [Biofilm: set-up and organization of a bacterial community]. , 2003, Medecine sciences : M/S.

[154]  J. M. Turner,et al.  Zebrafish puma mutant decouples pigment pattern and somatic metamorphosis. , 2003, Developmental biology.

[155]  J. M. Turner,et al.  Temporal and cellular requirements for Fms signaling during zebrafish adult pigment pattern development , 2003, Development.

[156]  A. ADoefaa,et al.  ? ? ? ? f ? ? ? ? ? , 2003 .

[157]  Hans Meinhardt,et al.  The Algorithmic Beauty of Sea Shells , 2003, The Virtual Laboratory.

[158]  Shigeru Kondo,et al.  Pigment cell organization in the hypodermis of zebrafish , 2003, Developmental dynamics : an official publication of the American Association of Anatomists.

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

[160]  A. Graham,et al.  The neural crest , 2003, Current Biology.

[161]  J. M. Turner,et al.  Essential role for puma in development of postembryonic neural crest-derived cell lineages in zebrafish. , 2003, Developmental biology.

[162]  C. Nüsslein-Volhard,et al.  Formation of the adult pigment pattern in zebrafish requires leopard and obelix dependent cell interactions , 2003, Development.

[163]  Dale Kaiser,et al.  Coupling cell movement to multicellular development in myxobacteria , 2003, Nature Reviews Microbiology.

[164]  I. Vallet Biofilm: mise en place et organisation d'une communaut , 2003 .

[165]  Anotida Madzvamuse,et al.  Pigmentation pattern formation in butterflies: experiments and models. , 2003, Comptes rendus biologies.

[166]  Y. Tu,et al.  Quantitative modeling of sensitivity in bacterial chemotaxis: The role of coupling among different chemoreceptor species , 2003, Proceedings of the National Academy of Sciences of the United States of America.

[167]  E. Peter Greenberg,et al.  Bacterial communication: Tiny teamwork , 2003, Nature.

[168]  Radek Erban,et al.  From Individual to Collective Behavior in Bacterial Chemotaxis , 2004, SIAM J. Appl. Math..

[169]  F. Süffert Die ausbildung des imaginalen flügelschnittes in der schmetterlingspuppe , 2004, Zeitschrift für Morphologie und Ökologie der Tiere.

[170]  W. Shi,et al.  Chemotaxis-guided movements in bacteria. , 2004, Critical reviews in oral biology and medicine : an official publication of the American Association of Oral Biologists.

[171]  Kathryn W. Tosney Long‐distance cue from emerging dermis stimulates neural crest melanoblast migration , 2004, Developmental dynamics : an official publication of the American Association of Anatomists.

[172]  H. Meinhardt,et al.  A theory of biological pattern formation , 1972, Kybernetik.

[173]  Dirk Horstmann,et al.  A Constructive Approach to Traveling Waves in Chemotaxis , 2004, J. Nonlinear Sci..

[174]  Rafael Lahoz-Beltra,et al.  EVOLVING MORPHOGENETIC FIELDS IN THE ZEBRA SKIN PATTERN BASED ON TURING'S MORPHOGEN HYPOTHESIS , 2004 .

[175]  J. Michiels,et al.  Quorum sensing and swarming migration in bacteria. , 2004, FEMS microbiology reviews.

[176]  G. Barlow,et al.  Fishes of the world , 2004, Environmental Biology of Fishes.

[177]  Adam P Arkin,et al.  Design and Diversity in Bacterial Chemotaxis: A Comparative Study in Escherichia coli and Bacillus subtilis , 2004, PLoS biology.

[178]  David H. Sharp,et al.  Dynamic control of positional information in the early Drosophila embryo , 2004, Nature.

[179]  R. Dilão,et al.  Modelling butterfly wing eyespot patterns , 2004, Proceedings of the Royal Society of London. Series B: Biological Sciences.

[180]  D L S McElwain,et al.  A history of the study of solid tumour growth: The contribution of mathematical modelling , 2004, Bulletin of mathematical biology.

[181]  H. Othmer,et al.  Mathematical modeling of tumor-induced angiogenesis , 2004, Journal of mathematical biology.

[182]  Rodolfo H. Torres,et al.  Structural colouration of mammalian skin: convergent evolution of coherently scattering dermal collagen arrays , 2004, Journal of Experimental Biology.

[183]  G. Wadhams,et al.  Making sense of it all: bacterial chemotaxis , 2004, Nature Reviews Molecular Cell Biology.

[184]  Qing Nie,et al.  Formation of the BMP activity gradient in the Drosophila embryo. , 2005, Developmental cell.

[185]  Radek Erban,et al.  From Signal Transduction to Spatial Pattern Formation in E. coli: A Paradigm for Multiscale Modeling in Biology , 2005 .

[186]  W. Bialek,et al.  Diffusion and scaling during early embryonic pattern formation. , 2005, Proceedings of the National Academy of Sciences of the United States of America.

[187]  Manu , 2005, Chasing Neotropical Birds.

[188]  P. Trainor Specification of neural crest cell formation and migration in mouse embryos. , 2005, Seminars in cell & developmental biology.

[189]  Andreas Deutsch,et al.  Pigment pattern formation in zebrafish during late larval stages: A model based on local interactions , 2005, Developmental dynamics : an official publication of the American Association of Anatomists.

[190]  C. Tomlin,et al.  Mathematical Modeling of Planar Cell Polarity to Understand Domineering Nonautonomy , 2005, Science.

[191]  Stanislav Y Shvartsman,et al.  Computational analysis of EGFR inhibition by Argos. , 2005, Developmental biology.

[192]  S. Shvartsman,et al.  Systems-level questions in Drosophila oogenesis. , 2005, Systems biology.

[193]  N. Dostatni,et al.  Bicoid Determines Sharp and Precise Target Gene Expression in the Drosophila Embryo , 2005, Current Biology.

[194]  Yu-Chiun Wang,et al.  Spatial bistability of Dpp–receptor interactions during Drosophila dorsal–ventral patterning , 2005, Nature.

[195]  Osamu Shimmi,et al.  Facilitated Transport of a Dpp/Scw Heterodimer by Sog/Tsg Leads to Robust Patterning of the Drosophila Blastoderm Embryo , 2005, Cell.

[196]  Travis M. Evans,et al.  A simulation study of the genetic regulatory hierarchy for butterfly eyespot focus determination , 2006, Evolution & development.

[197]  A. Goryachev,et al.  Systems analysis of a quorum sensing network: design constraints imposed by the functional requirements, network topology and kinetic constants. , 2006, Bio Systems.

[198]  P. Williams,et al.  Quorum Sensing in Yersinia enterocolitica Controls Swimming and Swarming Motility , 2006, Journal of bacteriology.

[199]  Charless C. Fowlkes,et al.  Three-dimensional morphology and gene expression in the Drosophila blastoderm at cellular resolution II: dynamics , 2006, Genome Biology.

[200]  Luigi Martinelli,et al.  Quantifying the Gurken morphogen gradient in Drosophila oogenesis. , 2006, Developmental cell.

[201]  David M. Umulis,et al.  Shaping BMP morphogen gradients in the Drosophila embryo and pupal wing , 2005, Development.

[202]  David G Míguez,et al.  On the orientation of stripes in fish skin patterning. , 2006, Biophysical chemistry.

[203]  R. Kolter,et al.  Microbial sciences: The superficial life of microbes , 2006, Nature.

[204]  Leon Glass,et al.  Reverse Engineering the Gap Gene Network of Drosophila melanogaster , 2006, PLoS Comput. Biol..

[205]  Rajbir Singh,et al.  Biofilms: implications in bioremediation. , 2006, Trends in microbiology.

[206]  Johannes Jaeger,et al.  On the dynamic nature of positional information. , 2006, BioEssays : news and reviews in molecular, cellular and developmental biology.

[207]  P. Maini,et al.  Two-stage Turing model for generating pigment patterns on the leopard and the jaguar. , 2006, Physical review. E, Statistical, nonlinear, and soft matter physics.

[208]  Gregory T. Reeves,et al.  Quantitative models of developmental pattern formation. , 2006, Developmental cell.

[209]  Pascal Schneider,et al.  Generation of the primary hair follicle pattern. , 2006, Proceedings of the National Academy of Sciences of the United States of America.

[210]  W. Pavan,et al.  The genetic regulation of pigment cell development. , 2006, Advances in experimental medicine and biology.

[211]  J. Timmer,et al.  Supporting Online Material Material and Methods , 2022 .

[212]  A. Polezhaev,et al.  Spatial patterns formed by chemotactic bacteria Escherichia coli. , 2006, The International journal of developmental biology.

[213]  Stephen J Eglen,et al.  Development of regular cellular spacing in the retina: theoretical models. , 2006, Mathematical medicine and biology : a journal of the IMA.

[214]  V. Sperandio,et al.  Quorum sensing in Escherichia coli and Salmonella. , 2006, International journal of medical microbiology : IJMM.

[215]  David M. Umulis,et al.  Robust, bistable patterning of the dorsal surface of the Drosophila embryo. , 2006, Proceedings of the National Academy of Sciences of the United States of America.

[216]  Stanislav Y Shvartsman,et al.  Modeling the bicoid gradient: diffusion and reversible nuclear trapping of a stable protein. , 2007, Developmental biology.

[217]  H. Othmer,et al.  Taxis equations for amoeboid cells , 2006, Journal of mathematical biology.

[218]  Lars Hufnagel,et al.  On the mechanism of wing size determination in fly development , 2007, Proceedings of the National Academy of Sciences.

[219]  Arthur D Lander,et al.  Morpheus Unbound: Reimagining the Morphogen Gradient , 2007, Cell.

[220]  Y. Kalaidzidis,et al.  Kinetics of Morphogen Gradient Formation , 2007, Science.

[221]  Victoria Bolós,et al.  Notch signaling in development and cancer. , 2007, Endocrine reviews.

[222]  Michael J Saxton,et al.  A biological interpretation of transient anomalous subdiffusion. I. Qualitative model. , 2007, Biophysical journal.

[223]  W. Bialek,et al.  Probing the Limits to Positional Information , 2007, Cell.

[224]  Shigeru Kondo,et al.  Pattern regulation in the stripe of zebrafish suggests an underlying dynamic and autonomous mechanism , 2007, Proceedings of the National Academy of Sciences.

[225]  W. Bialek,et al.  Stability and Nuclear Dynamics of the Bicoid Morphogen Gradient , 2007, Cell.

[226]  D. Parichy Homology and the evolution of novelty during Danio adult pigment pattern development. , 2007, Journal of experimental zoology. Part B, Molecular and developmental evolution.

[227]  M. S. Steinberg,et al.  Differential adhesion in morphogenesis: a modern view. , 2007, Current opinion in genetics & development.

[228]  Qing Nie,et al.  Computational analysis of BMP gradients in dorsal-ventral patterning of the zebrafish embryo. , 2007, Journal of theoretical biology.

[229]  P K Maini,et al.  A mechanism for morphogen-controlled domain growth , 2007, Journal of mathematical biology.

[230]  S. Jonathan Chapman,et al.  Mathematical Models of Avascular Tumor Growth , 2007, SIAM Rev..

[231]  Charless C. Fowlkes,et al.  A Quantitative Spatiotemporal Atlas of Gene Expression in the Drosophila Blastoderm , 2008, Cell.

[232]  David M. Umulis,et al.  The BMP-binding protein Crossveinless 2 is a short-range, concentration-dependent, biphasic modulator of BMP signaling in Drosophila. , 2008, Developmental cell.

[233]  Jeffrey M. Marcus,et al.  A simulation study of mutations in the genetic regulatory hierarchy for butterfly eyespot focus determination , 2008, Biosyst..

[234]  J. M. Otaki Physiologically induced color-pattern changes in butterfly wings: mechanistic and evolutionary implications. , 2008, Journal of insect physiology.

[235]  Chuan Xue Mathematical models of taxis-driven bacterial pattern formation , 2008 .

[236]  N. Barkai,et al.  Scaling of the BMP activation gradient in Xenopus embryos , 2008, Nature.

[237]  Hilary L. Ashe,et al.  Type IV collagens regulate BMP signalling in Drosophila , 2008, Nature.

[238]  P. Maini,et al.  Partial differential equations for self-organization in cellular and developmental biology , 2008 .

[239]  S. Shvartsman,et al.  Nuclear Trapping Shapes the Terminal Gradient in the Drosophila Embryo , 2008, Current Biology.

[240]  M. Saxton A biological interpretation of transient anomalous subdiffusion. II. Reaction kinetics. , 2008, Biophysical journal.

[241]  T. Shinbrot,et al.  In silico zebrafish pattern formation. , 2008, Developmental biology.

[242]  D. Kaiser Myxococcus-from single-cell polarity to complex multicellular patterns. , 2008, Annual review of genetics.

[243]  David M. Umulis,et al.  Robustness of embryonic spatial patterning in Drosophila melanogaster. , 2008, Current topics in developmental biology.

[244]  K. Painter,et al.  A User's Guide to Pde Models for Chemotaxis , 2022 .

[245]  Alexander Spirov,et al.  Formation of the bicoid morphogen gradient: an mRNA gradient dictates the protein gradient , 2009, Development.

[246]  B. L. Bard Jonathan,et al.  A unity underlying the different zebra striping patterns , 2009 .

[247]  B. N. Schwanwitsch 21. On the Ground‐plan of Wing‐pattern in Nymphalids and certain other Families of the Rhopaloeerous Lepidoptera. , 2009 .

[248]  Chuan Xue,et al.  Multiscale Models of Taxis-Driven Patterning in Bacterial Populations , 2009, SIAM J. Appl. Math..

[249]  K. Painter,et al.  Stippling the Skin: Generation of Anatomical Periodicity by Reaction-Diffusion Mechanisms , 2009 .

[250]  Li S-R,et al.  On a Model Mechanism for the Spatial Patterning of Teeth Primordia in the Alligator , 2022 .