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Proceedings of a NATO ARW held in Leeds, UK, September 11-15, 1989
This volume contains the proceedings of the NATO ARW on 'Biological
Pattern Formation' held at Merton College, University of Oxford, on
27-31 August, 1992. The objective of the workshop was to bring
together a select group of theoreticians and experimental
biologists to present the latest results in the area of biological
pattern formation and to foster interactiqn across dis- plines. The
workshop was divided into 5 main areas: (i) limb development, (ii)
Dictyostelium discoideum, (iii) Drosophila, (iv) cell movement, (v)
g- eral pattern formation. We thank all the participants for their
contributions, enthusiasm, and willingness to collaborate. There
was a genuine, open, and extremely fru- ful interaction between the
experimentalists and theoreticians which made the workshop a
success. We also thank The Welcome Trust for providing additional
funding. The local organization fell mainly on Denise McKittrick
and Beverley Bhaskhare at the Mathematical Institute, Oxford, and
Jeanette Hudson and the staff of Merton College. We greatly
appreciate their help and patience. We also thank Jonathan
Sherratt, Wendy Brandts and Debbie Benson for helping out in the
conference and for providing a happy welcome to parti- pants on a
typically cold, wet and windy English summer day.
The formation of patterns in developing biological systems involves
the spatio-temporal coordination of growth, cell-cell signalling,
tissue movement, gene expression and cell differentiation. The
interactions of these complex processes are generally nonlinear,
and this mathematical modelling and analysis are needed to provide
the framework in which to compute the outcome of different
hypothesis on modes of interaction and to make experimentally
testable predictions. This collection contains papers exploring
several aspects of the hierarchy of processes occurring during
pattern formation. A number of papers address the modelling of cell
movement and deformation, with application to pattern formation
within a collection of cells in response to external signalling
cues. The results are considered in the context of pattern
generation in Dictyostelium discoideum and bacterial colonies. A
number of models at the macroscopic level explore the possible
mechanisms underlying spatio-temporal pattern generation in early
development, focussing on primitive streak, somitogenesis,
vertebrate limb development and pigmentation patterning.The latter
two applications consider in detail the effects of growth on
patterning. The potential of models to generate more complex
patterns are considered and models involving different modes of
cell-cell signalling are investigated. Pattern selection is
analyzed in the context of chemical Turing patterns, which serve as
a paradigm for morphogenesis and a model for vegetation patterns is
presented.
The formation of patterns in developing biological systems involves the spatio-temporal coordination of growth, cell-cell signalling, tissue movement, gene expression and cell differentiation. The interactions of these complex processes are generally nonlinear, and this mathematical modelling and analysis are needed to provide the framework in which to compute the outcome of different hypothesis on modes of interaction and to make experimentally testable predictions. This collection contains papers exploring several aspects of the hierarchy of processes occurring during pattern formation. A number of papers address the modelling of cell movement and deformation, with application to pattern formation within a collection of cells in response to external signalling cues. The results are considered in the context of pattern generation in Dictyostelium discoideum and bacterial colonies. A number of models at the macroscopic level explore the possible mechanisms underlying spatio-temporal pattern generation in early development, focussing on primitive streak, somitogenesis, vertebrate limb development and pigmentation patterning. The latter two applications consider in detail the effects of growth on patterning. The potential of models to generate more complex patterns are considered and models involving different modes of cell-cell signalling are investigated. Pattern selection is analyzed in the context of chemical Turing patterns, which serve as a paradigm for morphogenesis and a model for vegetation patterns is presented.
Researchers from North America, eastern and western Europe, and the
Soviet Union contribute 45 papers relating mathematical and
experimental results on nonlinear wave phenomena in excitable media
and related nonlinear systems. A nonlinear sampling of topics
reveals such findings as sustained reactio
This volume contains the proceedings of a meeting entitled
'Nonlinear Oscillations in Biology and Chemistry', which was held
at the University of Utah May 9-11,1985. The papers fall into four
major categories: (i) those that deal with biological problems,
particularly problems arising in cell biology, (ii) those that deal
with chemical systems, (iii) those that treat problems which arise
in neurophysiology, and (iv), those whose primary emphasis is on
more general models and the mathematical techniques involved in
their analysis. Except for the paper by Auchmuty, all are based on
talks given at the meeting. The diversity of papers gives some
indication of the scope of the meeting, but the printed word
conveys neither the degree of interaction between the participants
nor the intellectual sparks generated by that interaction. The
meeting was made possible by the financial support of the
Department of Mathe matics of the University of Utah. I am indebted
to Ms. Toni Bunker of the Department of Mathematics for her very
able assistance on all manner of details associated with the
organization of the meeting. Finally, a word of thanks to all
participants for their con tributions to the success of the
meeting, and to the contributors to this volume for their efforts
in preparing their manuscripts."
General Modes of Pattern Formation; J.D. Murray. Process and
Outcome; P. Alberch, M.J. Blanco. Retinoic Acid Cannot be the
Morphogen in Reaction Diffusion Models for the Formation of the
Chick Wing Bud; Y. Almirantis, S. Papageorgiou. Pattern Formation
in Heterogeneous Domains; D.L. Benson, et al. A Field Model of
Symmetry Reversals in the Pattern Regulation of a Cell; W.A.M.
Brandts. Patterning in Limbs; S.V. Bryant, et al. The Development
of a Spatial Pattern in a Model for Cancer Growth; M.A.J. Chaplain.
Sequential and Synchronous Skin Pattern Formation; G.C. Cruywagen,
et al. Control of Gap Junction Permeability Can Control Pattern
Formation in Limb Development; R. Dillon, H.G. Othmer. Mapping Gene
Activities into Morphological Patterns in Drosophila; B. Goodwin,
S. Kauffman. Trajectories of Swimming Microorganisms and Continuum
Models of Bioconvection; N.A. Hill. The Chicken and the Egg; T.J.
Horder. 20 additional articles. Index.
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