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On Morphogenesis in Living Systems

  • F. W. Cummings

Abstract

A proposal is given for a description of single-cell-thickness surfaces that are undergoing morphogenetic movements such as in the early development of living systems. A two-dimensional “middle” surface must obey an equation which is independent of the coordinates, a fact which is useful in its determination as the Gauss curvature, a second-order partial nonlinear equation for the metric coefficient in conformal coordinates. This equation is thought of as coupled to a “pattern”-determining equation, which describes a combination of a set of biochemicals in terms of a single dominant one. A suggestion is made that this master pattern biochemical may be the ubiquitous calmodulin, a suggestion independent of the formalism given. The coupled system of two equations for pattern and form is then discussed as a model for gastrulation, the movement of the single-cell-thick sheets observed in numerous organisms. It is seen that a simple assumption for the Gauss curvature as a function of pattern, having one minimum, suffices to describe interesting aspects of early growth movements.

Keywords

Fundamental Form Gauss Curvature Imaginal Disc North Pole Middle Surface 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 1987

Authors and Affiliations

  • F. W. Cummings

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