46748-AC6
Statistical Thermodynamics of Solutions Enclosed in Fluctuating Semipermeable Capsules
In the first year of the project we have made two major advances in elucidating the statistical thermodynamics of particle-encapsulating vesicles. The first relates to actual membrane vesicles in solution, which are highly swollen, approaching their maximum volume prior to tearing (lysis). The second achievement, which is of a more theoretical interest, is the development of a scaling theory, providing a unified description of random closed manifolds being either pressurized or swollen by encapsulated particles.
We have treated a fluctuating, semipermeable vesicle, embedded in solution while enclosing a fixed number of solute particles. This is a ubiquitous scenario in various industrial applications (liposomes), as well as in many key functions of biological cells. We have shown that, under rather general conditions, the swelling of the vesicle toward its maximum volume as the number of encapsulated particles is increased (or, alternatively, the concentration of the outer solution
is decreased) exhibits a continuous phase transition from a fluctuating state to the maximum-volume configuration. Beyond the transition vesicle fluctuations are suppressed and appreciable
pressure difference and surface tension build up. This newly discovered phase transition is unique to particle-encapsulating vesicles, whose volume and inner pressure both fluctuate, and is absent when the swelling is caused by a controlled pressure difference. In practice the vesicle is expected to rupture (lyse) slightly above the transition. The criticality implies a universal swelling behavior of vesicles as they approach their limiting volume and osmotic lysis -- i.e., one should be able to rescale the measurements for different vesicles and different encapsulated solutions to fit a single master curve. We have contacted a few experimental groups in the hope to observe this critical behavior in reality.
In a different direction, we have studied the statistical mechanics of a general, closed, random manifold of fixed area and fluctuating volume, encapsulating a fixed number of noninteracting particles. A scaling analysis has been devised, which yields a unified description of such swollen manifolds, as well as those swollen by a controlled pressure difference. According to the scaling theory the mean volume of particle-encapsulating manifolds gradually increases with the number of particles, following a single scaling law. This is markedly different from the swelling under fixed pressure difference, where certain models exhibit criticality. We have thereby indicated when the swelling due to encapsulated particles is thermodynamically inequivalent to that caused by fixed pressure. The general predictions for pressurized manifolds encompass previously studied cases. The ones concerning particle-encapsulating manifolds have been further supported by Monte Carlo simulations of two model systems -- a two-dimensional self-avoiding ring and a three-dimensional self-avoiding fluid vesicle. We have demonstrated that in former case the particle-induced swelling is thermodynamically equivalent to the pressure-induced one, whereas in the latter it is not.
These two advances pave the way for the study of more specific scenarios involving vesicular capsules in the next two years of the project. The project serves as the core of a graduate student's PhD dissertation.
