Topological singularities and symmetry breaking in development

The review presents a topological interpretation of some morphogenetic events through the use of well-known mathematical concepts and theorems. Spatial organization of the biological fields is analyzable in topological terms. Topological singularities inevitably emerging in biological morphogenesis are retained and transformed during pattern formation. It is the topological language that can provide strict and adequate description of various phenomena in developmental and evolutionary transformations. The relationship between local and global orders in metazoan development, i.e., between local morphogenetic processes and integral developmental patterns, is established. A topological inevitability of some developmental events through the use of classical topological concepts is discussed. This methodology reveals a topological imperative as a certain set of topological rules that constrains and directs embryogenesis. A breaking of spatial symmetry of preexisting pattern plays a critical role in biological morphogenesis in development and evolution.