General Models of Pattern Formation: Some Uses, Problems and Successes

  • J. D. Murray
Part of the NATO ASI Series book series (NSSA, volume 259)

Abstract

Understanding the evolution of spatial patterns and the mechanisms which create them are among the most crucial issues in developmental biology. Whether the process is the generation of cartilage patterns in the developing limb, the formation of feathers and scales, the myriad of colour patterns on butterfly wings, regeneration in Hydra, the segmentation in the egg of a developing Drosophila, the patterns on the coats of animals, the formation of the grex in Dictyostelium and so on, a key question is “How are these patterns formed and what is the mechanism (or mechanisms) that creates them?” Enormous progress has been made in understanding some of the basic principles that any mechanism must possess to be able to generate spatial patterns. In spite of this we still do not know, with any certainty, definitive details of a single pattern formation mechanism which is involved in development. Model mechanisms — morphogenetic models — for biological pattern generation can suggest to the embryologist possible scenarios as to how, and sometimes when, pattern is laid down and how the embryonic form might be created. Although genes control pattern formation, genetics says nothing about the actual mechanisms involved nor how the vast range of pattern and form that we see evolves from a homogeneous mass of dividing cells. However, with the enormous strides made in our understanding of a wide variety of developmental situations there is room for optimism that in the not too distant future we shall have isolated not only the biochemical and physical elements involved but also have discovered some of the actual mechanisms. There has, in the past few years, been an increasing recognition among experimentalists and theoreticians that the most dramatic progress in biology will come about through a genuine interdisciplinary approach in which biomedical scientists, mathematicians and physical scientists all play a role. The book by Murray (1989) discusses in detail many successful case studies of such an interdisciplinary approach.

Keywords

Convection Colchicine Proteus 

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Copyright information

© Springer Science+Business Media New York 1993

Authors and Affiliations

  • J. D. Murray
    • 1
  1. 1.Applied Mathematics FS-20University of WashingtonSeattleUSA

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