From stripes to spots: prepatterns which can be produced in the skin by a reaction-diffusion system.

A key question in the area of spatial pattern formation in developmental biology is: how do groups of cells in a homogeneous tissue suddenly differentiate along entirely different developmental paths compared to neighbouring cells? Although experiments are now beginning to provide answers to this question, the mechanisms responsible for the development of repeated or periodic structures and spatial patterns, e.g., hair follicles and pigmentation patterns, are still unknown. Theoretical biologists and applied mathematicians have suggested various prepattern mechanisms as the primary cause of repeated or periodic spatial patterns. A class of biochemical reactions referred to here as reaction-diffusion (RD) systems, having the capacity to spontaneously generate stable stationary wavelike spatial patterns (Turing, 1952), has been suggested as a possible prepattern mechanisms, e.g., during hair follicle initiation and development (Nagorcka, 1989), and pigmentation patterns (Murray, 1989). Spatial patterns arising during development of the vertebrate skin are frequently complex. Spatial patterns in the skin can be seen to vary within an individual from one region of the skin to another. One pattern change commonly observed across the skin is from stripes to spots. An RD system is defined which is able to generate different spatial patterns depending on the value of a single parameter. The parameter varied controls the transport of the chemical components of the RD system across the basement membrane separating the epidermis and dermis. The patterns produced range from stripes to an irregular array of spots. Not only are different patterns produced, but a different time sequence of prepatterns is expected to arise in the different skin regions depending on whether the first prepattern in an array of spots or stripes. As a consequence it is possible to account for hair follicle initiation in the hair-bearing regions of the mammalian skin as well as the sequence of events required for the formation of dermatoglyphics in the volar regions.

Spatial patterns produced by a reaction-diffusion system in primary hair follicles.

This paper is the third in a series examining the role of a reaction-diffusion (RD) system as the principal mechanism providing spatial information for cell differentiation during hair follicle initiation and development and hair fibre formation. A theoretical mechanism is described by which the RD system supplies positional information during hair follicle development. Solutions of the RD system within the primordial follicle are described as well as the sequence of spatial patterns provides the follicle/epidermis boundary conditions required to account for the density and grouping of follicles during initiation. At the same time the spatial patterns are also shown to be capable of providing the positional information which determines various geometrical aspects of follicle development; in particular the development of follicles at an angle to the skin surface and the initiation and location of sweat glands and sebaceous glands on the follicle.

The role of a reaction-diffusion system in the initiation of primary hair follicles.

A mechanism based on a reaction-diffusion system is proposed for the initiation of hair follicles in the epidermis during fetal development. It is demonstrated that initiation of primary follicles in a series of waves, within the proposed mechanism, is a consequence of the size and shape dependent properties of the reaction-diffusion system without the need for the propagation of signals through the skin. The observed trio grouping of follicles and variation of primary follicle density per unit skin area during development are also correctly predicted. An explanation, based on the reaction-diffusion system and the variation of its characteristic spatial wavelength with time during development, is suggested for the termination of both primary and secondary follicle initiation as well as follicle neogenesis. The proposed initiation mechanism is basically the same as that used to explain various spatial patterns observed in hair fibre formation (Nagorcka & Mooney, 1982).