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Catastrophe theory and cellular determination, transdetermination and differentiation

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Abstract

Catastrophe theory can be used to illustrate the results of some of the events that occur during embryogenesis. Trajectories over the surface of catastrophe manifolds provide an extension of Waddington's concept of a description of embryogenesis based on chreodic paths on an epigenetic landscape. The development of Elementary Catastrophe Theory to describe time- and spece-equivalent events provides a rich qualitative “language” that seems well suited for the description of cellular behavior. Space-equivalent catastrophes have been used to illustrate the processes of cellular determination, differentiation, and transdetermination with initial success. This use should be tested further, for example, by experimental manipulation of embryonic tissue at well defined intervals of time during its development. The relationship of this approach to some others and to possible future theoretical developments has been discussed.

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  1. Biology Department, Williams College, 01267, Williamstown, MA, U.S.A.

    A. E. R. Woodcock

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Woodcock, A.E.R. Catastrophe theory and cellular determination, transdetermination and differentiation. Bltn Mathcal Biology 41, 101–117 (1979). https://doi.org/10.1007/BF02547928

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