On Morphogenesis in Living Systems

  • F. W. Cummings


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.


Fundamental Form Gauss Curvature Imaginal Disc North Pole Middle Surface 
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© Springer-Verlag Berlin Heidelberg 1987

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  • F. W. Cummings

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