The Geometry of Morphogenesis and the Morphogenetic Field Concept

Abstract

The process of morphogenesis, which can be defined as an evolution of the form of an organism, is one of the most intriguing mysteries in the life sciences. The discovery and description of the spatial–temporal distribution of the gene expression pattern during morphogenesis, together with its key regulators, is one of the main recent achievements in developmental biology. Nevertheless, gene expression patterns cannot explain the development of the precise geometry of an organism and its parts in space. Here, we suggest a set of postulates and possible approaches for discovering the correspondence between molecular biological information and its realization in a given geometry of an organism in space–time.

First, we suggest that the geometry of the organism and its parts is coded by a molecular code located on the cell surfaces in such a way that, with each cell, there can be associated a corresponding matrix, containing this code. As a particular model, we propose coding by several types of oligosaccharide residues of glycoconjugates.

Second, we provide a notion of cell event, and suggest a description of development as a tree of cell events, where by cell event we understand the changing of cell state, e.g. the processes of cell division, cell growth/death, cell shifting or cell differentiation.

Next we suggest describing cell motion laws using the notion of a “morphogenetic field”, meaning an object in an “event space” over a “cell space”, which governs the transformation of the coded biological information into an instructive signal for a cell event for a given cell, depending on the position of the cell in the developing embryo. The matrix on a cell surface will be changed after each cell event according to the rule(s) dictated by the morphogenetic field of an organism.

Finally, we provide some ideas about the connections between the morphogenetic code on the cell surface, cell motion law(s), and the geometry of an embryo.

This paper presents a set of ideas concerning the connection between biological information, encoded in the cells, and the realization of the geometrical form of a developing organism. Some suggestions are made for mathematical formalization of this connection. The active discussion of this and similar questions at the IHES Workshop (2010) indicated a strong interest in the subject. Therefore, we believe that, although this work is still far from finalized, it is worthwhile publishing this paper in order to stimulate further discussion. Hence, we strongly encourage the reader to independently consider the ideas, concepts and statements presented here in the framework of an integrated model, as it is possible that some of them may turn out to be unviable, while others may be of some interest and importance.