Simulation of osmotic swelling and osmotic pumping by the stochastic immersed boundary method

Abstract

We investigate through simulation studies the osmotic swelling of microscopic vesicles that contain solute molecules. A general understanding at the microscopic level of osmotic swelling and transport phenomena is relevant to many biological systems since water movement and hydrostatic pressures within cells are primarily the result of osmotic effects. From a macroscopic point of view, osmotic pressure is described often by the van't Hoff theory which states that the pressure depends only upon the number of solute particles per unit volume. In the van't Hoff theory, the osmotic pressure does not depend on the nature or mass of the solute particles, nor upon the number of degrees of freedom within each solute particle. However, for microscopic systems, interesting violations of these principles can arise when the solute particles are of a size comparable to the vesicle radius. In this regime an important role is played by fluctuations, hydrodynamic coupling, and solute-solute interactions.

We perform simulation studies in this regime based on a stochastic immersed boundary method (SIBM) in which a special slip term has been introduced to account for the semi-permeable porosity of the vesicle membrane wall to fluid. Our SIBM model also accounts for thermal fluctuations, the elastic deformations of the vesicle membrane wall, and hydrodynamic as well as direct coupling between solutes and wall. The vesicle membrane wall is modeled as a material having a Helfrich bending energy density proportional to the square of the local mean curvature of the surface, a neo-Hookean response that resists shear, and a constant surface tension.

We find that such a microscopic vesicle containing solute molecule swells or shrinks (depending on its initial size) and eventually fluctuates about an average equilibrium size. We develop a statistical-mechanical theory that agrees well with our simulation studies to predict the vesicle size and osmotic pressure. A fundamental question we investigate, both computationally and theoretically, is the extent to which the macroscopic theory of osmosis is applicable when the solutes are elastic extended molecules of a size comparable to that of the vesicle that contains them. In particular, when the solute consists of elastic dimers, we find that the osmotic effect of the solute depends not only on the number of dimers but also on the stiffness of the bond that connects the two monomers that comprise each dimer. The stiffness dependence that is found computationally is well predicted by the statistical-mechanical theory.

Closely related to the simulation of osmotic swelling, we explore another simulation with a pumping mechanism in which a fluid flow is driven by a non-equilibrium osmotic effect. This kind of pump has been studied before [20], but here we employ a new simulation methodology in which solutes are explicitly tracked. Also, we develop a new version of a previous one-dimensional theory of the pump [20]. This new version takes into account the hydraulic resistivity of the membranes at the ends of the pump, An interesting feature of the pump is that flow can be driven in either direction, with the direction depending on the ratio of the diffusivities of the solute species. Predictions of the one-dimensional theory are compared to results of our three-dimensional numerical simulations of the pump.