Introduction and Outline

Abstract

This book deals with the problem of biological pattern formation. What are the mechanisms according to which individual organisms develop and biological patterns form? Biological organisms are characterized by their genomes. The letters of the genetic alphabet (the nucleotides), their precise arrangement in selected organisms (the gene sequence), and the molecular structure of a large number of encoded proteins are public today. However, analysis of single gene and protein function is not sufficient to explain complex pattern formation which results from collective behavior of interacting molecules and cells. In the beginning of embryological development , all cells are identical – equipped with basically the same set of genes. Accordingly, collective phenomena brought about by the interaction of cells with themselves and their surrounding are responsible for differentiation and pattern formation characterizing subsequent developmental stages. Mathematical modeling is strongly needed to discover the self-organization principles of interacting cell systems (Deutsch et al. 2003). Still, an open question is: what are appropriate mathematical models, how can they be analyzed, and which specific biological problems can they address? In this chapter, the motivation for the book is provided. The basic problems are introduced and the connection of biological pattern formation and mathematical modeling is emphasized. Finally, an outline introduces the book structure and specific suggestions on how to read the book depending on the reader’s background.