We calculate the membrane-induced interaction between inclusions, in terms of the membrane stretching and bending moduli and the spontaneous curvature. We find that the membrane-induced interaction between inclusions varies nonmonotonically as a function of the inclusion spacing. The location of the energy minimum depends on the spontaneous curvature and the membrane perturbation decay length, where the latter is set by the membrane moduli. The membrane perturbation energy increases with the inclusion radius. The Ornstein-Zernike theory, with the Percus-Yevick closure, is used to calculate the radial distribution function of inclusions. We find that when the spontaneous curvature is zero, the interaction between inclusions due to the membrane deformation is qualitatively similar to the hard-core interaction. However, in the case of finite spontaneous curvature, the effective interaction is dramatically modified.

Although polyethylene glycol (PEG) is widely used for aggregating or fusing cells, the forces responsible for these interactions have remained elusive. Through a variety of techniques including quasi-elastic light scattering, surface force measurements, and 31P-NMR, we have established that while PEG of molecular weight 8000−10000 is effective in causing the aggregation of vesicles, PEG of lower or higher molecular weight (1000 and 18 500, respectively) is ineffective. For the first time, direct force measurements between lipid bilayers in solutions of 8000−10000 molecular weight reveal the existence of an attractive osmotic force due to a polymer depleted layer near the bilayer surface. Lower molecular weight PEG does not have a large enough size (Flory radius, R F) to generate a significant depletion force, while higher molecular weight PEG adsorbs sufficiently on the bilayer surfaces to eliminate the depletion attraction and produces a repulsive steric barrier to aggregation. The measured forces can be quantitatively described in terms of current theories of colloidal and polymer interactions. These findings suggest that the differential osmotic pressure produced by the depletion layer is responsible for vesicle aggregation and that fusion is promoted when the depletion pressure is strong enough to locally destabilize two membranes by possibly thinning them at their point of closest approach. The results provide a physicochemical basis for using PEG of certain molecular weights as fusogens for cells, liposomes, and vesicles.

Mechanical parts often move, not smoothly, but in jerks known as stick−slip. Stick−slip motion may be regular (repetitive or periodic) or irregular (erratic or intermittent). In the case of frictional sliding, stick−slip can have serious and often undesirable consequencesresulting in noise (chatter), high energy loss (friction), surface damage (wear), and component failure. We review the origins of stick−slip friction and present new experimental results on model surfaces that clarify its different origins, its dependence on experimental conditions or “system parameters”, and how stick−slip can be controlled in practical situations.

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