Measurement of the nonlinear elasticity of red blood cell membranes.

The membranes of human red blood cells (RBCs) are a composite of a fluid lipid bilayer and a triangular network of semiflexible filaments (spectrin). We perform cellular microrheology using the dynamic membrane fluctuations of the RBCs to extract the elastic moduli of this composite membrane. By applying known osmotic stresses, we measure the changes in the elastic constants under imposed strain and thereby determine the nonlinear elastic properties of the membrane. We find that the elastic nonlinearities of the shear modulus in tensed RBC membranes can be well understood in terms of a simple wormlike chain model. Our results show that the elasticity of the spectrin network can mostly account for the area compression modulus at physiological osmolality, suggesting that the lipid bilayer has significant excess area. As the cell swells, the elastic contribution from the now tensed lipid membrane becomes dominant.

Hydrodynamics in curved membranes: the effect of geometry on particulate mobility.

We determine the particulate transport properties of fluid membranes with nontrivial geometries that are surrounded by viscous Newtonian solvents. Previously, this problem in membrane hydrodynamics was discussed for the case of flat membranes by Saffman and Delbrück [P. G. Saffman and M. Delbrück, Proc. Natl. Acad. Sci. U.S.A. 72, 3111 (1975)]. We review and develop the formalism necessary to consider the hydrodynamics of membranes with arbitrary curvature and show that the effect of local geometry is twofold. First, local Gaussian curvature introduces in-plane viscous stresses even for situations in which the velocity field is coordinate-independent. Secondly, even in the absence of Gaussian curvature, the geometry of the membrane modifies the momentum transport between the bulk fluids and the membrane. We illustrate these effects by examining in detail the mobilities of particles bound to spherical and cylindrical membranes. These two examples provide experimentally testable predictions for particulate mobilities and membrane velocity fields on giant unilamellar vesicles and membrane tethers. Finally, we use the examples of spherical and cylindrical membranes to demonstrate how the global geometry and topology of the membrane influences the membrane velocities and the particle mobilities.

Measurement of red blood cell mechanics during morphological changes.

The human red blood cell (RBC) membrane, a fluid lipid bilayer tethered to an elastic 2D spectrin network, provides the principal control of the cell's morphology and mechanics. These properties, in turn, influence the ability of RBCs to transport oxygen in circulation. Current mechanical measurements of RBCs rely on external loads. Here we apply a noncontact optical interferometric technique to quantify the thermal fluctuations of RBC membranes with 3 nm accuracy over a broad range of spatial and temporal frequencies. Combining this technique with a new mathematical model describing RBC membrane undulations, we measure the mechanical changes of RBCs as they undergo a transition from the normal discoid shape to the abnormal echinocyte and spherical shapes. These measurements indicate that, coincident with this morphological transition, there is a significant increase in the membrane's shear, area, and bending moduli. This mechanical transition can alter cell circulation and impede oxygen delivery.

Diffusion and binding of finite-size particles in confined geometries.

Describing the diffusion of particles through crowded, confined environments with which they can interact is of considerable biological and technological interest. Under conditions where the confinement dimensions become comparable to the particle dimensions, steric interactions between particles, as well as particle-wall interactions, will play a crucial role in determining transport properties. To elucidate the effects of these interactions on particle transport, we consider the diffusion and binding of finite-size particles within a channel whose diameter is comparable to the size of the particles. Using a simple lattice model of this process, we calculate the steady-state current and density profiles of both bound and free particles in the channel. We show that the system can exhibit qualitatively different behavior depending on the ratio of the channel width to the particle size. We also perform simulations of this system and find excellent agreement with our analytic results.

Capillary wave dynamics on supported viscoelastic films: single and double layers.

We study the capillary wave dynamics of a single viscoelastic supported film and of a double layer of immiscible viscoelastic supported films. Using both simple scaling arguments and a continuum hydrodynamic theory, we investigate the effects of viscoelasticity and interfacial slip on the relaxation dynamics of these capillary waves. Our results account for the recent observation of a wavelength-independent decay rate for capillary waves in a supported polystyrene/brominated polystyrene double layer [X. Hu, Phys. Rev. E 74, 010602(R) (2006)].

Equilibrium bundle size of rodlike polyelectrolytes with counterion-induced attractive interactions.

Multivalent counterions can induce an effective attraction between like-charged rodlike polyelectrolytes, leading to the formation of polyelectrolyte bundles. In this paper, we calculate the equilibrium bundle size using a simple model in which the attraction between polyelectrolytes (assumed to be pairwise additive) is treated phenomenologically. If the counterions are pointlike, they almost completely neutralize the charge of the bundle, and the equilibrium bundle size diverges. When the counterions are large, however, steric and short-range electrostatic interactions prevent charge neutralization of the bundle, thus forcing the equilibrium bundle size to be finite. We also show that if the attractive interactions between the rods become frustrated as the bundle grows, finite-size bundles can be obtained with pointlike counterions.