| Popis: |
The reaction-diffusion model constitutes one of the most influential mathematical models to study the distribution of morphogens spreading within tissues. Despite its widespread appearance, the role that the finitude of the tissue plays in the spatiotemporal morphogen distribution predicted by the model has not been unveiled so far. In this study, we investigated the spatiotemporal distribution of a morphogen predicted by a reaction-diffusion model in a 1D finite domain as a proxy to simulate a biological tissue. We analytically solved, for the first time to our knowledge, the model assuming morphogen produced de novo within a finite domain and compared it with the scenario considering an infinite domain, which was previously solved. We explored the only relevant parameter in the reduced model, the tissue length in units of a characteristic reaction-diffusion length, and fully characterized the model behavior in terms of: i) geometrical aspects of the spatial distributions and ii) kinetic features derived from the time elapsed to reach the steady state. We found a critical tissue size that we estimated as ~3.3 characteristic reaction-diffusion lengths, above which the model assuming the infinite domain could suffice as a reasonable approximation. In contrast, for tissues smaller than the critical size, the error of assuming an infinite domain could rapidly accumulate, indicating that the model assuming finite domains is a better description. This new solution could replace the one used to estimate diffusion coefficients and degradation constants during the analysis of Fluorescence Recovery After Photobleaching (FRAP) experiments and it could also help to improve the performance of multiscale computational approaches, which involve a morphogen dynamics scale, typically modeled with a reaction diffusion scheme. These findings could drive new modeling strategies to understand tissue morphogenesis as well as cancer invasion, among many other relevant problems in biology and medicine. |
