Two Symmetries Linking Biological and Physical Branching Morphogenesis

Abstract

As the different contributions in this book show, there exist a lot of branching patterns, both in physics and biology, so it is expected that general principles might govern the ubiquity of this class of patterns. However, it is not so easy to find straightforward relationships between the physical and the biological processes, although they are dearly desired. In particular, the very complex biochemistry involved in any living tissue, which eventually supports any morphogenic event, makes it difficult to sort out what is truly relevant for morphogenesis and what provides only the general support and satisfaction of metabolic demands. For example, it is clear that a growing tissue which adopts a branching mode of growth must in the first place be able to grow. Therefore, it is not at all obvious that growth factors play any role in the morphogenesis per se, except for the mere fact that they allow the tissue to get larger. Also, it should be added in such an introduction, that it is not very easy either to find relationships between biological branching processes. For example, Leonardo da Vinci thought that vessel growth and plant growth were similar, but was not able to provide a link between their growth mechanisms, except for a purely structural or metaphorical similarity.