Developmental Biology: Mathematical Modelling of Development

Abstract

Understanding how structures (e.g. hair, teeth, feathers, limbs and pigmentation patterns) arise from the initially unstructured fertilised egg is one of the key challenges in developmental biology. Mathematical models enable us to investigate how certain biochemical and/or biophysical processes interact to produce pattern and form. They provide a unifying theme for spatio‐temporal patterning across a vast range of biological applications by suggesting a set of underlying principles for pattern formation. Such models suggest that patterns and structures must have certain properties and these predictions motivate experiments. The results of such experiments help refine models and lead to more precise predictions. In this way, modelling, combined with experiment, can be a powerful investigative tool in helping unravel the complexity of morphogenesis (the formation of structure) in biology. Key Concepts: Patterning arises due to short‐range activation, long‐range inhibition. Mathematical models suggest constraints on development. Instabilities emerge from stabilising processes. Pattern properties can be mechanism‐independent. It is the integration of biochemical and biophysical processes that lead to structure formation.

A Nonoscillatory Second-Order Time-Stepping Procedure for Reaction-Diffusion Equations

“…Some were derived from phenomenological models (Gierer-Meinhardt) while other modeled simple reaction schemes (Schnackenberg trimolecular autocatalytic reactions model [3], Gray-Scott model [4], Brusselator model [5], chlorite-iodide-malonic acid, CIMA model [6]). Recent work on RD systems demonstrates that it can be used to understand biological patterns formation [7], while [8] and [9] reviewed RD systems can be used to investigate spatial patterning in developmental systems.…”