Topological analysis of the fusion process between cellular and subcellular compartments

The study presents an application of the theory of homeomorphic transformations of topological manifolds and the operation of the connected sum of manifolds for topological analysis of membrane transformations during the fusion process between cellular and subcellular compartments. The biological cell and the subcellular structures in the form of vesicles are modelled by an arrangement of two concentric spheres corresponding to the inner and outer layer of the membrane bounding the vesicles. The analysis shows eight succeeding topological stages of membrane transformations during the fusion process and these stages are characterized. It is concluded that there is a vectorial translocation of lipid molecules from the outer layers of the membranes before the fusion process to the internal layer of the membrane bounding the vesicle after the fusion process and there is no lipid translocation in the reverse direction.