Topological determination of early morphogenesis in Metazoa

This paper presents a topological interpretation of some developmental events through the use of well-known concepts and theorems of combinatorial geometry. The organization of early embryo using a simulation of cleavage considering only blastomere contacts is examined. Each blastomere is modeled as a topological cell and whole embryo—as cell packing. The egg cleavage results in a pattern of cellular contacts on the surface of each blastomere and whole embryo, a discrete morphogenetic field. We find topological distinctions between different types of early egg cleavage and suggest a topological classification of cleavage. Blastulation and gastrulation may be related to an inevitable emergence of discrete curvature that directs development in three-dimensional space. The relationship between local and global orders in metazoan development, i.e., between local morphogenetic processes and integral developmental patterns, is established. Thus, this methodology reveals a topological imperative: a certain set of topological rules that constrains and directs biological morphogenesis.     

Comparative analysis of topological organization in Metazoa

Topological patterns in Metazoa, using previously elaborated methodology with employment of the genus of the surface (p) as topological invariant are considered. The term "density of the genus of the surface" is introduced. In sponges and in a lesser degree among Cnidaria and, Ctenophoria an increase of genus p up to indefinite high values and the shaping of topologically complicated quasifractal systems (irrigation system in sponges and gastro-vascular system in Radiata) are evident. In most Bilateria a stable topological pattern with open digestive tube is formed and subsequent topological complications of other systems may occur. Complicated topological patterns increasing the genus of the surface are evolved on the base of quasifractal systems: gut pockets in turbellaria, tracheal system in arthropods, bronchial system in birds, gills in bivalve mollusks, etc. Peculiarities of ordered and disordered topological patterns as well as topological origin of the increase of the genus of the surface are considered.     

Topological Patterns in Metazoan Evolution and Development

Topological patterns in the development and evolution of metazoa, from sponges to chordates, are considered by means of previously elaborated methodology, with the genus of the surface used as a topological invariant. By this means metazoan morphogenesis may be represented as topological modification(s) of the epithelial surfaces of an animal body. The animal body surface is an interface between an organism and its environment, and topological transformations of the body surface during metazoan development and evolution results in better distribution of flows to and from the external medium, regarded as the source of nutrients and oxygen and the sink of excreta, so ensuring greater metabolic intensity. In sponges and some Cnidaria, the increase of this genus up to high values and the shaping of topologically complicated fractal-like systems are evident. In most Bilateria, a stable topological pattern with a through digestive tube is formed, and the subsequent topological complications of other systems can also appear. The present paper provides a topological interpretation of some developmental events through the use of well-known mathematical concepts and theorems; the relationship between local and global orders in metazoan development, i.e., between local morphogenetic processes and integral developmental patterns, is established. Thus, this methodology reveals a “topological imperative”: A certain set of topological rules that constrains and directs biological morphogenesis.     

Minimal mixture principle as a method of choosing the form of a dynamic model]

The extremality principle for molecular processes in biological systems is considered. The principle is based on an assumption that the main function of biological processes is the separation of the "product" from the "scheme". The form of the dynamical model of the process is determined from the requirement of the "minimum mixture". As an example Selkov's model of glycolysis is considered.     

Larvae of related Diptera species from thermally contrasting habitats exhibit continuous up-regulation of heat shock proteins and high thermotolerance

A population of Stratiomys japonica, a species belonging to the family Stratiomyidae (Diptera), common name ‘soldier flies’, occurs in a hot volcanic spring, which is apparently among the most inhospitable environments for animals because of chemical and thermal conditions. Larvae of this species, which naturally often experience temperatures more than 40 °C, have constitutively high concentrations of the normally inducible heat-shock protein Hsp70, but very low level of corresponding mRNA. Larvae of three other species of the same family, Stratiomys singularior, Nemotelus bipunctatus and Oxycera pardalina, are confined to different type semi-aquatic habitats with contrasting thermal regime. However, all of them shared the same pattern of Hsp70 expression. Interestingly, heat-shock treatment of S. japonica larvae activates heat-shock factor and significantly induces Hsp70 synthesis, whereas larvae of O. pardalina, a species from constant cold environment, produce significantly less Hsp70 in response to heat shock. Adults of the four species also exhibit lower, but detectable levels of Hsp70 without heat shock. Larvae of all species studied have very high tolerance to temperature stress in comparison with other Diptera species investigated, probably representing an inherent adaptive feature of all Stratiomyidae enabling successful colonization of highly variable and extreme habitats.