A mathematical problem related to the deformation of membranes, bounding the intracellular tubules, at the initial stage of macropinocytosis

Despite the intensive studying of endocytosis from biochemical and morphological points of view its general physical nature remains unstudied. The main goal of this work is to study an abstract problem, the solution of which resembles the characteristic morphological feature of the initial stage of the macropinocytosis. It is the free boundary diffusion problem, which models the disturbance of osmotic equilibrium due to the interaction of lysosomal hydrolase with the large liquid drop, adsorbed at the external side of the pinocyte plasmalemma and treats this as the unique cause of appearance of the force triggering the motion of the drop toward the cell interior. Its solution imitates the initial stage of macropinocytosis in the case of generation of pinocytosic vacuoles inside the intracellulare tubular systems, that are either the endoplasmatic net, microtube system or system of cytoskeletal tubes. This work must be considered as continuation of ny effort to model phagocytosis, made in [12-14]. In particular I use here estimates of duration of all subprocesses involved there. No proof of any assertion is presented. Such a manner of the material presentation is chosen to make the paper more lucid for biologists.