Mathematical Modeling of the Pulsatory Lipid Vesicle Dynamics under Osmotic Stress

I consider a great lipid vesicle filled with an aqueous solution of a solute, for which its membrane is impermeable. Because of the mechanical tension induced by the osmotic flow, the vesicle swells up to a critical size, triggering a transient lipidic pore when it is introduced into a hypotonic aqueous medium. In this paper, we will obtain the differential equations of the vesicle dynamics, which is in fact a periodic process due to osmotic gradient and transbilayer pore appearance. We will also analyse the characteristic parameters of this process: swelling time, pore lifetime, number of cycles, the length time of vesicle activity, material quantity leaked out during a cycle. In the end, we present the condition to design a n-cycles working vesicle and propose some biotechnological applications.