Geometrical model of spiral-cyclical self-organization of morphofunctional modules with two-dimensional (2D) transfer channels

The general model of spiral-cyclic self-organization of morphofunctional modules has been studied with the help of elliptic Riemannian geometry. Depending on the level of hierarchy cells, groups of cells, macromolecules or subcellular components can function as separate biological units. The hierarchically coordinated morphofunctional modules of biological pattern with two-dimensional (2D) channels of morphogenes transfer are formed in the process of geometric transformation. The width of 2D channel is regulated by module parameters, whereas the direction of transport is controlled by vector of module electrostatic field. The disturbance of morphogenesis in the model is regarded as a change of reciprocal hierarchically coordinated arrangement of morphofunctional modules that causes branching of 2D channels without general power- and mass transfer. The model can be used for constructing concrete analogies of self-organization of morphofunctional modules in onto- and phylogenesis.