Mathematical Description of the Functioning of the Pulsatory Liposome

Abstract

We consider a liposome filled with the aqueous solution of an osmotic solute enclosed in a large water bath. Due to osmotic pressure, it works according to a sequence of cycles with two stages. In the first stage, the lipid vesicle with a certain input concentration of the osmotic substance is swelling up in an osmotic process until it reaches a size, when one pore is formed on its surface. The second stage follows, where the vesicle content is partially eliminated through the pore to induce a decrease in the vesicle volume up to its original size. If we take into account that the pore has two stages in its evolution, then the relaxing stage may be divided into two new stages. The swelling of the liposome is described by a differential equation. All the processes which contribute to the vesicle relaxing and its return to the initial size are described by three differential equations.