Ligands mounted to surfaces via extensible tethers are present in nature and represent a growing class of molecules used to engineer adhesion in drug targeting, biosensing, self-assembling nanostructures, and in other biophysical research. Using a continuum approach with geometric and thermodynamic arguments, we derive a number of analytical expressions that relate key properties of single-tethered ligand-receptor interactions to multiple bond formation between curved surfaces. The theoretical predictions are in good agreement with measurements made with the surface forces apparatus. We establish that, when ligated, many tethers commonly used in biophysical research exhibit a discrete binding range that can be accurately measured with force spectroscopy. The distribution of bound ligated tethers is independent of the surfaces' interaction radius, R. The bridging force scales linearly with R, the tether's effective spring constant and grafting density, and with the ligand-receptor bond energy when the surfaces are in direct contact. These results are contrasted to bridging forces that evolve between plane-parallel geometries. Last, we show how our simple analytical reductions can be used to predict adhesive forces for STEALTH liposomes and other targeted and self-assembled nanoparticles.

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End-grafted poly(ethylene glycol) (or PEG) polymer chains are used to extend the in vivo circulation time of targeted liposomes and nanoparticles; however, the most efficacious structure for also imparting high target specificity remains unknown. Using the surface force apparatus, we have measured the specific and nonspecific forces between bimodal mixtures of grafted polymer mushrooms and model receptor surfaces. Specifically, supported lipid membranes anchoring 2000 or 5000 Da PEG with a controlled fraction of PEG(2000) bearing biotin ligands were compressed against opposing streptavidin surfaces. The presence of the longer 5000 Da chain increased the steric repulsion of the bimodal mushroom layer and thus decreased the net adhesive force when shorter chains were ligated. However, the 5000 Da chain did not detectably alter the distance where ligand-receptor binding occurs and adhesion begins. This latter result is in good agreement with theoretical predictions based on summing the repulsive steric and attractive bridging forces. Further, all ligated structures adhered to receptors under both static and dynamic fluid flow conditions. The dynamic movement of the flexible PEG tethers permitted ligand-receptor bonds to form far beyond the equilibrium edge of the bimodal mushroom layer. This work demonstrates that liposome targeting should be enhanced by grafting ligands to liposomes with a tether that has a contour length longer than the equilibrium height of the bimodal mushroom layer.

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Superplastic nanowires were formed by touching the NaCl(100) surface with a Au tip in a transmission electron microscope. The nanowires were stretched < or =2.2 microm, or 280%, and bent >90 degrees upon compression, when showered with the electron beam. More surprisingly, no dislocations were observable during the elongation due to fast diffusion. Mechanical measurements in humid atmospheres suggest that salt nanowires also form in ambient environments.