Isaeva Valeria V, Kasyanov Nickolay V, Presnov Eugene V
A.N. Severtsov Institute of Ecology and Evolution of the Russian Academy of Science, 119071 Moscow, Russia.
Biosystems. 2012 Sep;109(3):280-98. doi: 10.1016/j.biosystems.2012.05.004. Epub 2012 May 17.
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.
该综述通过运用著名的数学概念和定理，对一些形态发生事件进行了拓扑学解释。生物场的空间组织可以从拓扑学角度进行分析。在生物形态发生过程中不可避免地出现的拓扑奇点，在图案形成过程中会保留并发生转变。正是拓扑学语言能够对发育和进化转变中的各种现象提供严格且充分的描述。后生动物发育中局部和全局秩序之间的关系得以确立，即局部形态发生过程与整体发育模式之间的关系。通过使用经典拓扑概念，讨论了一些发育事件的拓扑必然性。这种方法揭示了一种拓扑必然性，它是一组约束和指导胚胎发生的拓扑规则。先前存在的图案的空间对称性的打破在发育和进化中的生物形态发生中起着关键作用。
