Hydrocarbon chains of biomembrane phospholipids: structural realizations of noncrystallographic symmetrical constructions

The characteristic features of the structures of the most common hydrocarbon (fatty acid) chains of phospholipid molecules that form the basis for biological membranes are considered. It has been established that the most symmetrical association of tetrahedrally coordinated chains corresponding to the hydrocarbon chains of phospholipids was found to be the four-dimensional 240-vertex diamond-like substructure of a three-dimensional sphere: the {240} polytope. The building blocks of the phospholipid hydrocarbon chain are defined as 14- and 11-vertex fragments of the tetrahedrally coordinated linear substructure of the {240} polytope and are also defined by structural realizations of a special combinatorial construction on seven symbols. It is shown that the symmetry-based requirement for the assembly only from an integer number of such building blocks makes it possible to explain the realization of a very limited number of hydrocarbon chains of biomembrane phospholipids from a huge number of combinatorially possible variants of similar chains.