Considerations on the role of surface tension and epidermal growth factor in the mechanism of integumental pattern formation

Abstract

The formation of the posterior parietal hair whorl during normal human development is proposed as a morphogenetic problem in which the effects of surface tension and the appearance of singularities figure prominently. Surface tension is considered in the sense of "Langer's lines" which define local contours of tension in the skin of the organism. According to this view, an analysis of the organism's skin tension field is fundamental to problems of integumental pattern formation. A computational analysis of the skin tension field is proposed, potentially using methods from finite element theory applied to molecular and cellular mechanisms within the skin which resist deformation. To this end, surface tension is provisionally defined as the differential adsorption (adhesion) of molecular and supramolecular binding elements within the skin. In practical applications, it is suggested that epidermal growth factor (EGF) and similar molecules have the physicochemical features and the biological effects required to experimentally probe surface tension phenomena at supramolecular levels. In this regard, the concept of topological discontinuities is introduced as a potential theoretical bridge across levels of organization. Specific examples of these discontinuities are given and discussed in terms of the development of singularities in control surfaces. It is hoped that these considerations will be useful in the mechanistic analysis of hair whorl formation during human embryo-genesis and in other problems of integumental pattern formation and nonequilibrium surface behavior.