On a new mechanism of the emergence of spatial distributions in biological models

Abstract

Non-uniform distributions of various biological factors can be essential for tissue growth control, morphogenesis or tumor growth. The first model describing the emergence of such distributions was suggested by A. Turing for the explanation of cell differentiation in a growing embryo. In this model, diffusion-driven instability of the homogeneous in space solution appears due to the interaction of two or more morphogens described by a reaction–diffusion system of equations. In this work we suggest another mechanism of the emergence of spatial distributions in biological tissues based on local cell communication and global inhibition, and described by a nonlocal reaction–diffusion equation. Instability of the homogeneous in space solution leads to the emergence of stationary pulses and not of periodic solutions as in the case of Turing instability.