Electrokinetic measurement of hydrodynamic properties of grafted polymer layers on liposome surfaces

Liposomes decorated with covalently-attached neutral polymers such as poly(ethylene glycol) (PEG) are pharmaceutically useful as drug delivery vehicles due to their low immunogenicity. Protection of the liposome surface from immune-system recognition requires the end-grafting of sufficiently long PEG polymers at sufficiently high densities. The hydrodynamic properties of the surface polymer layer can be studied by electrophoretic measurement of polymer-induced hydrodynamic drag. The apparent zeta potential, calculated from the mobility by use of the Smoluchowski equation, gives the location of an apparent shear surface, assuming an electrostatic-potential profile that can be calculated from the Poisson–Boltzmann equation. The shear-surface location is a measure of the polymer-layer hydrodynamic thickness. Since PEG is neutral, the polymer-layer thickness is not expected to depend significantly on ionic strength. Electrophoretic mobilities were measured for phosphatidylglycerol:phosphatidylcholine (1:9 mol:mol) and PEG-phosphatidylethanolamine:phosphatidylcholine (1:9 mol:mol) multilamellar liposomes, with PEG ranging from 350 to 5000 Da in NaCl ranging from 0.5 to 100 mM. The apparent coat thicknesses were found to be strongly ionic-strength dependent. In a simple model, the one-dimensional Navier–Stokes equation is solved analytically in the Debye–Hückel approximation assuming a rectangular polymer-segment density profile and Stokes friction in the polymer layer. It is shown that the Smoluchowski treatment underestimates the true hydrodynamic coat thickness but approaches the correct value for low ionic strength and/or high friction in the polymer layer. The model accounts for the observed ionic-strength effects and provides a formula for extracting correct hydrodynamic thicknesses and effective frictional coefficients from the data. Fitted hydrodynamic thicknesses for the present liposomes are: 2000 PEG, 45±1 Å; 3000 PEG, 73±3 Å; 5000 PEG, 132±5 Å. These values vary linearly with the polymer index, consistent with scaling theory for polymer brushes. The fitted polymer-layer frictional shielding lengths scale with the hydrodynamic thicknesses. Valid electrophoretic determinations of hydrodynamic thicknesses of neutral polymer coats are shown to require Debye screening lengths significantly longer than the coat extensions.