Size matters: tissue size as a marker for a transition between reaction-diffusion regimes in spatio-temporal distribution of morphogens.

The reaction-diffusion model constitutes one of the most influential mathematical models to study distribution of morphogens in tissues. Despite its widespread use, the effect of finite tissue size on model-predicted spatio-temporal morphogen distributions has not been completely elucidated. In this study, we analytically investigated the spatio-temporal distributions of morphogens predicted by a reaction-diffusion model in a finite one-dimensional domain, as a proxy for a biological tissue, and compared it with the solution of the infinite-domain model. We explored the reduced parameter, the tissue length in units of a characteristic reaction-diffusion length, and identified two reaction-diffusion regimes separated by a crossover tissue size estimated in approximately three characteristic reaction-diffusion lengths. While above this crossover the infinite-domain model constitutes a good approximation, it breaks below this crossover, whereas the finite-domain model faithfully describes the entire parameter space. We evaluated whether the infinite-domain model renders accurate estimations of diffusion coefficients when fitted to finite spatial profiles, a procedure typically followed in fluorescence recovery after photobleaching (FRAP) experiments. We found that the infinite-domain model overestimates diffusion coefficients when the domain is smaller than the crossover tissue size. Thus, the crossover tissue size may be instrumental in selecting the suitable reaction-diffusion model to study tissue morphogenesis.

Postembryonic development and aging of the appendicular skeleton in Ambystoma mexicanum.

BACKGROUND: The axolotl is a key model to study appendicular regeneration. The limb complexity resembles that of humans in structure and tissue components; however, axolotl limbs develop postembryonically. In this work, we evaluated the postembryonic development of the appendicular skeleton and its changes with aging. RESULTS: The juvenile limb skeleton is formed mostly by Sox9/Col1a2 cartilage cells. Ossification of the appendicular skeleton starts when animals reach a length of 10 cm, and cartilage cells are replaced by a primary ossification center, consisting of cortical bone and an adipocyte-filled marrow cavity. Vascularization is associated with the ossification center and the marrow cavity formation. We identified the contribution of Col1a2-descendants to bone and adipocytes. Moreover, ossification progresses with age toward the epiphyses of long bones. Axolotls are neotenic salamanders, and still ossification remains responsive to l-thyroxine, increasing the rate of bone formation. CONCLUSIONS: In axolotls, bone maturation is a continuous process that extends throughout their life. Ossification of the appendicular bones is slow and continues until the complete element is ossified. The cellular components of the appendicular skeleton change accordingly during ossification, creating a heterogenous landscape in each element. The continuous maturation of the bone is accompanied by a continuous body growth.