Towards an integrated experimental-theoretical approach for assessing the mechanistic basis of hair and feather morphogenesis

Abstract

In his seminal 1952 paper, 'The Chemical Basis of Morphogenesis', Alan Turing lays down a milestone in the application of theoretical approaches to understand complex biological processes. His deceptively simple demonstration that a system of reacting and diffusing chemicals could, under certain conditions, generate spatial patterning out of homogeneity provided an elegant solution to the problem of how one of nature's most intricate events occurs: the emergence of structure and form in the developing embryo. The molecular revolution that has taken place during the six decades following this landmark publication has now placed this generation of theoreticians and biologists in an excellent position to rigorously test the theory and, encouragingly, a number of systems have emerged that appear to conform to some of Turing's fundamental ideas. In this paper, we describe the history and more recent integration between experiment and theory in one of the key models for understanding pattern formation: the emergence of feathers and hair in the skins of birds and mammals.

Keywords: Turing patterns; activator–inhibitor; feather buds and hair follicles; morphogenesis; reaction–diffusion; skin patterning.

Figure 1.

Biological pattern formation. (a–c) Self-organization at various spatial scales: (a) aggregation of Dictyostelium discoideum; (b) flocking; (c) patchy vegetation in Nigeria. (d–f) Pigmentation patterns: (d) swallowtail butterfly; (e) zebra; (f) sailfish tang. (g–j) Feathers, hairs and scales: (g) peacock; (h) Vladimir the cat; (i) three-banded armadillo; (j) central bearded dragon. Image information: (d–j) K.J.P.; (a) http://en.wikipedia.org/wiki/File:Dictyostelium_Aggregation.JPG, released into public domain, accessed 21/01/2012; (b) http://en.wikipedia.org/wiki/File:Fugle,_%C3%B8rns%C3%B8_073.jpg, released into public domain by C. Rasmussen, accessed 21 January 2012; (c) http://en.wikipedia.org/wiki/File:Gapped_Bush_Niger_Nicolas_Barbier.jpg, released into public domain by Nicolas Barbier, accessed 21 January 2012.

Figure 2.

(a(i)) Schematic of the underlying interactions in a pure activator (u)–inhibitor (v) system. (a(ii)–a(vi)) Simulation of a pure AI system showing the spatial pattern for (top) u and (bottom) v at (a(ii)) t = 0, (a(iii)) t = 20, (a(iv)) t = 40 (a(v)) t = 100, at (a(vi)) t = 1000. Peaks of u and v concentration lie in phase. Simulations performed using the Gierer–Meinhardt [15] system, and with d = 0.025, a = 0.5. (b(i)) Schematic of the underlying interactions in a cross activator–inhibitor system. (b(ii)–b(vi)) Simulation of a cross AI system showing the spatial pattern for (top) u and (bottom) v at (b(ii)) t = 0, (b(iii)) t = 10, (b(iv)) t = 20, (b(v)) t = 50, at (b(vi)) t = 1000. Peaks of u and v concentration lie out of phase. Simulations were performed using Schnakenberg [43] kinetics, and , with d = 0.025, a = 1.0. For both sets of simulations, initial conditions were set at a small perturbation of the uniform steady state and zero-flux conditions were employed at the boundaries of a square field of dimensions 10 × 10.

Figure 3.

Developmental patterning of hairs and feathers. (a) Spatio-temporal sequence of feather development in the chicken embryo (stages shown range from a third to midway through the incubation period). Feather buds initially develop along two lines either side of the midline and subsequently spread into lateral regions. Note that significant growth occurs during the patterning process. (b) Naked neck chickens, conspicuous by their absence of neck feathering. (c) Mid to late gestation of the mouse embryo, stained for a marker of developing follicles (purple foci). (d) Schematic of the molecular network underpinning mouse follicle formation. The dashed region encloses a specific loop with the features of a pure activator–inhibitor system.

Figure 4.

Turing patterns for the reaction–diffusion system (4.1) to (4.4). Parameters fixed according to set 1 in table 1 except S_I and k₂ (varied as indicated). For each plot, equations (4.1) to (4.4) were solved until a fixed time and activator concentration was plotted using a black (high > 3) to white (low = 0) scale. Patterns develop along a central band, with regions left and right generating ubiquitously high and low activator levels, respectively. Notably, we observe a broad spectrum of patterning, ranging between spots, fusions, stripes and holes. Points marked B and N refer to prospective body and neck parameter sets (see text for details). For all simulations, initial conditions were set at a small perturbation of the uniform steady-state and zero-flux conditions were employed at the boundaries of a square field of dimension 2 × 2.

Figure 5.

Comparison between experimental and model patterns. (a) Cultured embryonic mouse skin, stained for a marker of developing follicles (purple foci). Note the clear lines of foci aligned parallel to the cut tissue edge. (b) Blow-up of the dashed square in (a). (c) Simulation of equations (4.1) to (4.4). The right-hand side boundary is set to be ‘lossy’, with components of the reaction–diffusion model assumed to flow across the tissue edge boundary, with zero-flux conditions on the remaining three. Simulations were performed using parameters drawn from set 1 of table 1, except and solved on a square field of dimension 3 × 3. For experimental details, see the study of Mou et al. [26].

Figure 6.

Figure illustrating the test–predict–refine cycle for modelling. Experimental data are reproduced from the study of Mou et al. [86] and we refer there for full details. Modelling in (b) and (d) is similar to that produced earlier [86], however performed for equations (4.1) to (4.4). Modelling in parts (e–g) is new. (a) Recreation of a ‘naked-neck’ in wild-type skin through application of exogenous BMP12. From left to right: control (no exogenous inhibitor); +20 ng ml^–1; +40 ng ml^–1. (b) In silico hypothesis testing through simulating equations (4.1) to (4.4) with k₂ varying smoothly from neck to body to replicate the hypothesized variation in inhibitor sensitivity. Exogenous inhibitor is increased from left to right: control, S_I = 1; S_I = 1.5; S_I = 2. (c) A model prediction showing the impact of uniformly reducing inhibitor sensitivity. From left to right: control, . (d) An experimental reproduction shows the same qualitative behaviour. From left to right: control; +8 μM DM, +5 μM SB; +10 μM DM, +5 μM SB. DM, Dorsomorphin; SB, SB203580. (e) RA, which is normally only produced by neck skin, sensitizes the skin to the inhibitor. From left to right: control (no exogenous RA); +0.2 μM RA; +1.0 μM RA; +5.0 μM RA. (f) A refinement of the model in which k₂ saturates according to equation (4.5) and recapitulates the experiment. We set k_max = 4, K = 5 and set varying RA levels for neck (RAⁿ = 20 + RA^e) and body (RA^b = 10 + RA^e) regions. From left to right: control, RA^e = 0 ; RA^e = 20; RA^e = 100; RA^e = 500. (g) Demonstration of saturability of RA signalling in cultured chicken skin. Each data point show the response of the skin to increasing concentrations of RA, measured through the relative expression of the RA response gene Dhrs3. Each point shows the mean expression and error bars, respectively. The RA dose–response curve was generated by quantitative PCR method using FastStart Universal SYBR Green Master Mix (Roche). The primer sequences used were: for Dhrs3, 5′-CTCTGCTGCCACCCAAAC-3′ and 5′-TGGTCTCCTTCAGGCATTTC-3; and for Gapdh, 5′-ATCTTTAACCACTGCTCCTTG-3′ and 5′-CATGCTGAGCCTATTCACTG-3′. The dashed line plots the saturating form of the function given by equation (4.5), with k_max = 2000, K = 0.175.

Figure 7.

(a) Experimental timecourse of Edar expression on a portion of treated mouse skin of field dimension 1 × 1 mm; data originally published in Mou et al. [26]. Note that each time point has been drawn from a distinct experimental dataset. (b) Simulations of equations (4.1) to (4.4) on a square field of dimension 1 × 1 mm showing pattern evolution over 48 h and based on the dimensional parameters drawn from set 2 in table 1. Each frame plots the activator expression, using a white (low)–blue (medium)–black (high) colour scale. Parameters are illustrative and chosen to yield a comparable density to the primary hair follicle pattern shown in (a). For each row, the parameters marked with an asterisk (*) as in table 1 have been scaled by the same constant γ, to produce the same spot density at each parameter set. We also label the corresponding molecular half lives for each value of γ. Initial conditions were set as a small (1%) random perturbation of the uniform steady state, with zero-flux conditions imposed at the domain boundaries.