A Primer on Reaction-Diffusion Models in Embryonic Development

Matthew J Thompson, Hans Othmer, David Umulis

Abstract: A fundamental problem in developmental biology is understanding how complex patterns and organised tissues develop from a small group of nearly identical cells. A wealth of experimental data has exposed the complexity of the molecular networks guiding cellular decisions of organisation and patterning – networks whose output evolves over space and time as development progresses. Integrating this data into reaction–diffusion (RD) mathematical models that describe the spatiotemporal dynamics of molecular species during development provides a rigorous approach to test the plausibility of hypothesised mechanisms guiding pattern formation, to understand how the complexity is regulated and to optimise experimental design. RD modelling provides a complementary mode of inquiry that both depends on and informs experimental research. RD systems are used in developmental biology to model morphogen-mediated pattern formation.