Ben Tahar, S.; Comellas, E.; Duerr, T.; Monaghan, J. R.; Romero, J. J. M.; Shefelbine, S. J.

Skeletal patterning in limb development has historically been modeled resorting to two main approaches: positional information (PI) and reaction-diffusion (R-D) models. Although recent research has started to examine how they interact, the influence of growth in the models is still mostly ignored. In order to explicitly include growth as a key element of the patterning process, we propose a growth-reaction-diffusion framework. Our model scales the system with the characteristic timescale of growth, introducing two key parameters: (1) the reaction time relative to growth and (2) the diffusion time relative to growth. Rather than modeling specific molecular pathways, we focus on the core processes that govern differentiation into cartilage. The reaction parameter represents information processing within the domain (e.g., protein production), while the diffusion parameter describes information propagation (e.g., signaling). Positional information informs the timescales of reaction and diffusion relative to growth. To validate this framework, we simulate limb development in the mouse and axolotl. Our model reproduces established biological outcomes, including the effects of altered positional cues and morphogen distributions. We demonstrate that modulating the rate of specification processing and propagation relative to growth influences proximal-distal and anterior-posterior patterning. By explicitly incorporating growth into a reaction-diffusion framework, our approach advances previous models and offers a more comprehensive understanding of limb skeletal patterning.