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A Model of Pattern Coupled to Form in Metazoans

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Mathematical Modelling of Biosystems

Part of the book series: Applied Optimization ((APOP,volume 102))

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Abstract

A model of patterning in living systems is examined, one involving the sequential interaction of a pair of signaling pathways. The model of pattern is coupled to the changing shape of a (closed, thick) epithelial shape. Focus is on patterning that couples localized cell differentiation and epithelial shape changes. Aspects of the model are discussed in turn: the pattern, the epithelial sheet geometry, and the coupling of the latter two. Changes in the pattern give rise to a changing epithelial shape, and a changing epithelial shape in turn causes a change in the pattern, and so on, as the total a area increases. The model is intended to provide a simplest example of morphogenesis. An effort is made to reduce morphogenesis to its most elemental ‘modules’: pattern, shape and their interaction. This may be seen as a reversal from the usual historical progression (e.g., as in physics), i.e., first from phenomenological modeling, then only later, to its reductionist underpinnings: first came thermodynamics and later statistical mechanics. Post DNA biology has been for the past fifty years primarily, and certainly very fruitfully, focused on the genetic and molecular basis of development. The present work attempts to work from the genetic and molecular underpinnings toward a more phenomenological model of the origin of animals, but one simpler and more comprehensible. Mathematical modeling has rarely dealt with animal form, or with its coupling to pattern, and an attempt is made in this direction. A preliminary attempt is made to uncover possible molecular and genetic foundations of the present elemental model of interacting shape and pattern.

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Author information

Authors and Affiliations

  1. University of California Riverside, 136 Calumet Ave., San Anselmo, Ca., 94960

    Frederick W. Cummings (Professor of Physics (emeritus)

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  1. Frederick W. Cummings
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Editors and Affiliations

  1. Federal University of Rio de Janeiro UFRJ-COPPE-Centre of Technology, 21.941-972-P.O. Box 68.511, Rio de Janeiro-RJ, Brazil

    Rubem P. Mondaini

  2. Center for Applied Optimization, University of Florida, 303 Weil Hall, P.O.Box 116595, Gainesville, FL, 32611-6595, USA

    Panos M. Pardalos

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Cummings, F.W. (2008). A Model of Pattern Coupled to Form in Metazoans. In: Mondaini, R.P., Pardalos, P.M. (eds) Mathematical Modelling of Biosystems. Applied Optimization, vol 102. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-76784-8_2

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