D. POPESCU*, A.G. POPESCU**, B. AMUZESCU***

*Department of Mathematical Modeling in Life Sciences, Institute of Mathematical Statistics and Applied Mathematics, Romanian Academy, 13, 13 Septembrie Street, 050911, Bucharest, Romania
**Department of Computer Sciences, IT CORE SRL, 10, Garoafei Street, 051235, Bucharest, Romania
***Department of Animal Physiology and Biophysics, Center of Neurobiology and Molecular Physiology, Faculty of Biology, University of Bucharest, 91–95, Splaiul Independenţei, Bucharest, 050095, Romania

Abstract. In this paper we describe only the first part of the duty cycle of a pulsatory liposome. An unilamellar lipid liposome filled with an aqueous solution of an impermeant solute is introduced into a hypotonic aqueous environment. Because of the mechanical tension induced by osmotic flow, the vesicle swells up to a critical size, when suddenly a transbilayer pore appears. A part of the intracellular material leaks out through this pore, and the liposome membrane relaxes and finally recovers. The swelling begins again and the liposome experiences a periodical process. For this reason we have named it a pulsatory liposome. In this paper we have obtained the differential equation of the swelling stage. Its analytical solution is the dependence of time on vesicle radius, which is the inverse of the direct function that would be of interest. We have also computed several parameters related to the swelling process: the critical swelling time and the duration of the last cycle of vesicle activity for some initial concentrations of solute.
Key words: osmotic gradient, swelling vesicle, swelling time, stopping time.

Corresponding author’s e-mail: popescu1947@yahoo.com

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