The Reaction-Diffusion System as a Spatial Organizer during Initiation and Development of Hair Follicles and Formation of the Fibre

Abstract

It is proposed that a reaction-diffusion (RD) system (Turing, 1952) confined to the epithelium interacts with the dermis to provide the spatial information necessary for the initiation and growth of hair follicles and fibres. The reaction and diffusion rates are chosen to be consistent with certain broad constraints (Murray, 1982) which ensure that nonhomogeneous distributions in the RD system components, denoted as X and Y, arise spontaneously. The nonhomogeneous distributions are in the form of complementary wavelike spatial patterns in both [X] and [Y]. The first pattern to arise consists of an irregular array of approximately equidistant maxima. The maxima in [X] provide the spatial signals for the initiation of the first wave of primary hair (wool) follicles. As an approximation it is possible to consider the developing primordial follicles to be separate from the epidermis. A sequence of patterns is predicted to arise at various stages in the development of the follicles. The spatial patterns may account for (i) the development of follicles at an angle to the skin surface, (ii) the initiation and location of apocrine sweat glands, and (iii) the initiation and location of sebaceous glands. At the same time the sequence of patterns expected in the primary follicles also causes several more waves of primary follicle initiation in the epidermis leading to the formation of a trio grouping of primary follicles. The same RD system continues to provide wavelike spatial information in the follicle bulb where it produces one of several spatial patterns in [X] depending on the size and shape of the follicle bulb. The pattern sequence predicted is consistent with that observed in the distribution of para- and orthocortical cells in the cross-section of wool fibres within different diameter ranges. The predicted pattern sequence may also account for a range of hair fibre cross-sectional shapes observed in mice and other species. A scheme is outlined for the differentiation of epithelial cells into various multicell layers and fibre components as they migrate out of the follicle bulb.