No abstract

Onsager's irreversible thermodynamics is used to perform a systematic deduction of the kinetic equations governing the opening and collapse of transient pores in spherical vesicles. We show that the edge tension has to be determined from the initial stage of the pore relaxation and that in the final state the vesicle membrane is not completely relaxed, since the surface tension and the pressure difference are about 25% of its initial value. We also show that the pore life-time is controlled by the solution viscosity and its opening is driven by the solution leak-out and the surface tension drop. The final collapse is due to a non-linear interplay between the edge and the surface tensions together with the pressure difference. Also, we discuss the connection with previous models.

We propose a free energy expression accounting for the formation of spherical vesicles from planar lipid membranes and derive a Fokker-Planck equation for the probability distribution describing the dynamics of vesicle formation. We find that formation may occur as an activated process for small membranes and as a transport process for sufficiently large membranes. We give explicit expressions for the transition rates and the characteristic time of vesicle formation in terms of the relevant physical parameters.

This study is devoted to reveal a simple self-healing, diffusive-dissolution-like mechanism of transient pore's closing in a model spherical vesicle. It is based on a novel thermodynamic mechanism invented in terms of structural flux-force relations, with Onsager's coefficients reflecting the mainand cross-effects of nearly one-micrometer-in-diameter pore formation (of linear cross sectional size r) immersed within the membrane of a spherical vesicle of at least several tens of micrometer in its radius (R). The closing nanoscopic limit is given by r → 0. The pore's formation is envisaged as a kind of bending and excess-area bearing (randomly occurring) failure, contrasting with a homogenizing action of the surface tension, trying to recover an even distribution of the elastic energy accumulated in the membrane. The failure yields at random the subsequent transient pore of a certain (1341) 1342A. Gadomski et al.characteristic length along which the solution leaks out, with some appreciable speed, until the passage is ultimately closed within a suitable time interval. Inside such a time span, the system relaxes back toward its local equilibrium and uncompressed state until which the pore dissolves, and the before mentioned excess area vanishes. The (slow and non-exponential) relaxation-dissolution behavior bears a diffusion fingerprint, and it can be related with varying osmotic-pressure conditions. Useful connotations with a qualitatively similar biolubrication mechanism in articulating (micellescontaining) systems, down to the nanoscale, have also been pointed out.

In this work, we present in detail, in an accessible manner for undergraduate and graduate physics students, the model of spontaneous curvature, due to Helfrich, that quantitatively explains why the red blood cells in their natural state adopt a biconcave shape. The main hypothesis is that the equilibrium cell shape satisfies the principle of minimum free energy. Therefore, in the model, an expression for the membrane free energy is postulated based on the Helfrich theory. In that approximation, the membrane is modelled as a two-dimensional surface and the energy is written as a function of the surface principal curvatures and three parameters, including the spontaneous curvature, c0, which is associated with the chemical composition of the membrane. The negative values for c0 induce invaginations in the cell membrane. The model predicts the discocyte-spherocyte transition for the red blood cell. In the article, the concepts involved in the theory are developed in detail, and an algorithm that allows obtaining the contour of the cell is presented in detail as supplementary material.