Inter-dependent tissue growth and Turing patterning in a model for long bone development.

The development of long bones requires a sophisticated spatial organization of cellular signalling, proliferation, and differentiation programs. How such spatial organization emerges on the growing long bone domain is still unresolved. Based on the reported biochemical interactions we developed a regulatory model for the core signalling factors IHH, PTCH1, and PTHrP and included two cell types, proliferating/resting chondrocytes and (pre-)hypertrophic chondrocytes. We show that the reported IHH-PTCH1 interaction gives rise to a Schnakenberg-type Turing kinetics, and that inclusion of PTHrP is important to achieve robust patterning when coupling patterning and tissue dynamics. The model reproduces relevant spatiotemporal gene expression patterns, as well as a number of relevant mutant phenotypes. In summary, we propose that a ligand-receptor based Turing mechanism may control the emergence of patterns during long bone development, with PTHrP as an important mediator to confer patterning robustness when the sensitive Turing system is coupled to the dynamics of a growing and differentiating tissue. We have previously shown that ligand-receptor based Turing mechanisms can also result from BMP-receptor, SHH-receptor, and GDNF-receptor interactions, and that these reproduce the wildtype and mutant patterns during digit formation in limbs and branching morphogenesis in lung and kidneys. Receptor-ligand interactions may thus constitute a general mechanism to generate Turing patterns in nature.