From glycosylated cell surfaces to sterically stabilized liposomes, polymers attached to membranes attract biological and therapeutic interest. Can the scaling laws of polymer "brushes" describe the physical properties of these coats? We delineate conditions where the Alexander-de Gennes theory of polymer brushes successfully fits the intermembrane distance versus applied osmotic stress data of Kenworthy et al. for poly(ethylene glycol)-grafted multilamellar liposomes. We establish that the polymer density and size in the brush must be high enough that, in a bulk solution of equivalent monomer density, the polymer osmotic pressure is independent of polymer molecular weight (the des Cloizeaux semidilute regime of bulk polymer solutions). The condition that attached polymers behave as semidilute bulk solutions offers a rigorous criterion for brush scaling-law behavior. There is a deep connection between the behaviors of semidilute polymer solutions in bulk and polymers grafted to a surface at a density such that neighbors pack to form a uniform brush. In this regime, two-parameter unconstrained fits of the Alexander-de Gennes brush scaling laws to the Kenworthy et al. data yield effective monomer lengths of 3.3-3.6 A, which agree with structural predictions. The fitted distances between grafting sites are larger than expected from the nominal mole fraction of poly(ethylene glycol)-lipids; the chains apparently saturate the surface. Osmotic stress measurements can be used to estimate the actual densities of membrane-grafted polymers.

Directly measured forces between DNA helices in ordered arrays have been reduced to simple force coefficients and mathematical expressions for the interactions between pairs of molecules. The tabulated force parameters and mathematical expressions can be applied to parallel molecules or, by transformation, to skewed molecules of variable separation and mutual angle. This "toolbox" of intermolecular forces is intended for use in modelling molecular interactions, assembly, and conformation. The coefficients characterizing both the exponential hydration and the electrostatic interactions depend strongly on the univalent counterion species in solution, but are only weakly sensitive to anion type and temperature (from 5 to 50 degrees C). Interaction coefficients for the exponentially varying hydration force seen at spacings less than 10 to 15 A between surfaces are extracted directly from pressure versus interaxial distance curves. Electrostatic interactions are only observed at larger spacings and are always coupled with configurational fluctuation forces that result in observed exponential decay lengths that are twice the expected Debye-Huckel length. The extraction of electrostatic force parameters relies on a theoretical expression describing steric forces of molecules "colliding" through soft exponentially varying direct interactions.

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