Self-organized BMP signaling dynamics underlie the development and evolution of tetrapod digit patterns

Repeating patterns of synovial joints are a highly conserved feature of articulated digits, with variations in joint number and location giving rise to a diverse range of digit morphologies and limb functions across the tetrapod clade. During development, joints form iteratively within the growing digit ray, as a population of distal progenitors alternately specifies joint and phalanx cell fates to segment the digit into distinct elements. Whilst numerous molecular pathways have been implicated in this fate choice, it remains unclear how they give rise to a repeating pattern. Here, using single cell RNA-sequencing and spatial gene expression profiling, we investigate the transcriptional dynamics of interphalangeal joint specification in vivo. Combined with mathematical modelling, we predict that interactions within the BMP signaling pathway - between the ligand GDF5, the inhibitor NOG, and the intracellular effector pSMAD - result in a self-organizing Turing system that forms periodic joint patterns. Our model is able to recapitulate the spatiotemporal gene expression dynamics observed in vivo, as well as phenocopy digit malformations caused by BMP pathway perturbations. By contrasting in silico simulations with in vivo morphometrics of two morphologically distinct digits, we show how changes in signaling parameters and growth dynamics can result in variations in the size and number of phalanges. Together, our results reveal a self-organizing mechanism that underpins tetrapod digit patterning and its evolvability, and, more broadly, illustrate how Turing systems based on a single molecular pathway may generate complex repetitive patterns in a wide variety of organisms.