Morphogen distribution in a growing tissue

ALBERTO SEBASTIÁN CECCARELLI; AUGUSTO BORGES; OSVALDO CHARA

Buenos Aires

Workshop; A Systems Approach to Biology; 2018

Centro Latinoamericano de Formación Interdisciplinaria (CELFI) del Ministerio de Ciencia, Tecnología e Innovación Productiva

Morphogens are chemical substances that are instrumental for cell signaling during tissue development and regeneration. Classical studies beautifully described spatiotemporal distribution of morphogen concentration in terms of models involving mechanisms of reaction and diffusion in infinite domains. Since during these processes tissues expand, an important question would be how the expansion of the tissue would influence spatiotemporal morphogen distribution. To tackle this question, we study mathematical models given by one-dimension partial differential equations (PDEs). In particular, we investigate a model encoding a mechanism of reaction, diffusion and advection that incorporates the tissue expansion in a finite domain and compare it with a model involving only reaction, diffusion in a finite domain and the classical model in an infinite domain. We here show the results obtained from an analytical solution for the reaction-diffusion-advection and for the reaction-diffusion model models in finite domains and compare them with classical reaction-diffusion model in the infinite domain. In addition, we compare analytical with numerical results of the models in finite domains.