The Intersection of Theory and Application in Elucidating Pattern Formation in Developmental Biology

¹ School of Mathematics and Digital Technology Center, University of Minnesota, Minneapolis, MN 55455 USA
² Department of Mathematics, Department of Mathematics and Maxwell, Institute for Mathematical Sciences, Heriot-Watt University, Edinburgh, EH14 4AS, UK
³ Agricultural & Biological Engineering, Purdue University, West Lafayette, IN USA 47907 USA
⁴ Mathematical Biosciences Institute, Ohio State University, Columbus, OH 43210 USA

Corresponding author: othmer@math.umn.edu

Abstract

We discuss theoretical and experimental approaches to three distinct developmental systems that illustrate how theory can influence experimental work and vice-versa. The chosen systems – Drosophila melanogaster, bacterial pattern formation, and pigmentation patterns – illustrate the fundamental physical processes of signaling, growth and cell division, and cell movement involved in pattern formation and development. These systems exemplify the current state of theoretical and experimental understanding of how these processes produce the observed patterns, and illustrate how theoretical and experimental approaches can interact to lead to a better understanding of development. As John Bonner said long ago
`We have arrived at the stage where models are useful to suggest experiments, and the facts of the experiments in turn lead to new and improved models that suggest new experiments. By this rocking back and forth between the reality of experimental facts and the dream world of hypotheses, we can move slowly toward a satisfactory solution of the major problems of developmental biology.'