Reaction-Diffusion Approach to Somite Formation

Pattern formation in reaction-diffusion and reaction-diffusion-convection systems

Pattern Formation by Reaction-diffusion

PROBLEM DEFINITION In biology, embryological development of the structure of an organism or limb is referred to as morphogenesis. As a result of morphogenesis, complex shapes and patterns can form starting from just a single cell. Two main mechanisms that contribute to the embryo’s development are cell movement and cell specialization based on cell position. These mechanisms are influenced by s...

The reaction-diffusion approach to morphogenesis

⎯ Morphogenesis is the ensemble of processes that determines form, shape and patterns in organisms. Based on a reactiondiffusion theoretical setting and some prototype reaction schemes, we make a review of the models and experiments that support possible mechanisms of morphogenesis. We present specific case studies from chemistry (Belousov-Zhabotinsky reaction) and biology (formation of wing ey...

Renormalisation Group Approach to Reaction-diffusion Problems

We describe how the methods of quantum field theory and the renormalisation group may be applied to classical stochastic particle systems which appear in non-equilibrium statistical mechanics. An emphasis is placed on the similarities and differences between these methods and more conventional applications of quantum field theory. Some simple applications are discussed.

Mathematical models for somite formation.

Somitogenesis is the process of division of the anterior-posterior vertebrate embryonic axis into similar morphological units known as somites. These segments generate the prepattern which guides formation of the vertebrae, ribs and other associated features of the body trunk. In this work, we review and discuss a series of mathematical models which account for different stages of somite format...