Hox genes regulate digit patterning by controlling the wavelength of a Turing-type mechanism

Abstract

The formation of repetitive structures (such as stripes) in nature is often consistent with a reaction-diffusion mechanism, or Turing model, of self-organizing systems. We used mouse genetics to analyze how digit patterning (an iterative digit/nondigit pattern) is generated. We showed that the progressive reduction in Hoxa13 and Hoxd11-Hoxd13 genes (hereafter referred to as distal Hox genes) from the Gli3-null background results in progressively more severe polydactyly, displaying thinner and densely packed digits. Combined with computer modeling, our results argue for a Turing-type mechanism underlying digit patterning, in which the dose of distal Hox genes modulates the digit period or wavelength. The phenotypic similarity with fish-fin endoskeleton patterns suggests that the pentadactyl state has been achieved through modification of an ancestral Turing-type mechanism.

Fig. 1

(A) Expression of Sox9 in E12.5 limbs of the Hoxa13;Gli3 allelic series. Note the delayed differentiation in the anterior mesoderm in the absence of Gli3. The curved white and yellow lines show the AP profiles used for the analysis of Sox9. The red arrowhead points to a digit bifurcation. WT, wild type. (B) Sox9 staining intensity along the yellow profile indicated by the curved arrow. AP length and the period of each digit (from minimum to minimum) are measured and shown for Hoxa13^+/−;Gli3^XtJ/XtJ. (C) Chart showing the average digit periods versus AP lengths for each profile and limb. A linear relation is observed in controls and in the Gli3^XtJ/XtJ background for either the normal or heterozygous dose of Hoxa13, whereas a flatter relation that correlates with bifurcations (red arrowhead) is observed in the Hoxa13^−/−;Gli3^XtJ/XtJ limbs (red line). The curved arrow marks the yellow point corresponding to the profile in (B). (D and E) Two simulations of the reaction-diffusion model inside an E12.5 Gli3 mutant limb shape. (D) The activator concentration obtained in the simulation with a uniform modulation of wavelength ω (shown in the graph) shows digit bifurcation (red arrowhead) similar to the Hoxa13^−/−Gli3^XtJ/XtJ mutants. (E) The simulation result when wavelength is modulated according to a suitable PD gradient (in this case, a 2D gradient of simulated FGF signaling activity) avoids bifurcations, because the wavelength increases with increasing AP length. Limbs shown in all figures are forelimbs with distal to the right and anterior to the top.

Fig. 2

Representative skeletal phenotypes of newborns of the Hoxa13;Hoxd11-13;Gli3 allelic series. Digit number (indicated for the Gli3^XtJ/XtJ condition) increases as distal Hox dose is reduced. When only one functional copy of Hoxa13 remains (right column), the tip of the digits is connected by a continuous band of ossified (red) and cartilaginous (blue) tissue rimming the distal border of the limb and becoming more conspicuous as Gli3 copies are removed.

Fig. 3

The phenotypes of triple mutants can be replicated by the Turing model. (Top) The first three rows show Sox9 expression at E12.5 and E13.5 for different combinations of the triple Hoxa13;Hoxd11-13;Gli3 allelic series. As more Hox are removed, the general trend shows an increase in digit number and a decrease in digit thickness. The trend is most strongly evident in the complete absence of Gli3 (third row). (Bottom) A similar behavior is shown by the reaction-diffusion simulations, where a decrease of the PD gradient used to modulate wavelength is correlated with reduced Hox dose (k_hox). Additionally, the model predicts a narrower digital region along the PD axis, which eventually shrinks to zero, and no pattern is formed.

Fig. 4

(A) Schematic representation of the network of a general activator-inhibitor Turing model. The four reaction kinetic parameters are shown: f_u, f_v, g_u, and g_v. Fgf promotes a PD-graded distribution of the parameter f_u to drive stripe orientation (gray dashed arrow). Hox and Fgf inhibit the parameter g_u to increase the wavelength in a PD-graded manner (bold line). U, activator; V, inhibitor. (B) Graphs of the average digit period of the triple mutants with Gli3^−/− background at four equidistant positions along the PD axis of the digital region. With the exception of Hoxa13^+/−;Hoxd^{Del11-13/Del11-13};Gli3^XtJ/XtJ, a clear trend is observed: The PD gradient of wavelength is generally shallower as distal Hox genes are removed. (C) Graphs of average digit period (wavelength) versus distal Hox gene dose in the three different Gli3 backgrounds. A smooth positive correlation between Hox gene dose and wavelength is observed in all three cases.

Fig. 5

Vertebrate limb evolution and distal Hox gene function. A phylogenetic tree of representative taxa and appendage skeletal patterns is shown, as well as corresponding distal Hox expression [in actinopterygians shown for Polyodon spathula (28)] and Gli3R gradient (when known). Genetically abrogating Shh signaling and reducing distal Hox function in mouse autopods (Hoxa13^+/−;Hoxd^{Del11-13/Del11-13};Gli3^XtJ/XtJ) reveals ancestral skeletal characteristics shared with the pectoral fins of sharks (Chiloscyllium punctatum) and primitive ray-finned fishes (Polypterus senegalus): numerous, densely packed, and iterative elements, with a distal cartilaginous band corresponding to the distal radials of fish fins (arrows). The periodic pattern of skeletal elements evident in fins and mutant limbs strongly suggests that a self-organizing Turing-type mechanism of chondrogenesis is deeply conserved in vertebrate phylogeny. Our results further indicate that distal Hox gene dose regulates the number and spacing of skeletal elements formed, implicating distal Hox gene regulatory networks as critical drivers of the evolution of the pentadactyl limb.