Lipopolymer electrophoresis in supported bilayer membranes

Abstract

We report theory and experiments investigating the electric-field-induced drift of poly(ethylene glycol) (PEG)-derivatized lipids in supported lipid bilayer (SLB) membranes. Based on classical continuum models, an analytical formula for the lipopolymer electrophoretic mobility is derived, drawing upon the Debye–Hückel approximation. The model is extended to the high membrane surface charge densities encountered in experiments by drawing upon the Guoy-Chapman theory to correct the surface charge-surface potential relationship. This convenient approximation is successfully tested by comparison with numerical solutions of the electrokinetic model based on the non-linear Poisson–Boltzmann equation. We use the analytical model to interpret measured electrophoretic mobilities of 1,2-distearoyl-sn-glycero-3-phosphoethanolamine-N-[poly(ethylene glycol)2000-N′-carboxyfluorescein] (DSPE-PEG2k-CF) in glass-supported 1,2-dioleoyl-sn-glycero-3-phosphocholine (DOPC) bilayers at DSPE-PEG2k-CF concentrations up to 5 mol%. By separating the frictional force on lipopolymers into separate lipid-tail and polymer-chain contributions, experimental trends are captured. Fitting the model to the data furnishes several previously unknown model parameters, namely the hydrodynamic size of a polymer segment, and a polymer-bilayer frictional coupling coefficient. We show that electro-osmotic flow plays a determinative role in the lipopolymer drift. For DSPE-PEG2k-CF in DOPC, electro-osmotic flow yields significantly lower electrophoretic mobilities than expected by balancing the total lipopolymer electrical force with the Stokes–Einstein frictional force. This is attributed to the hydrodynamic coupling of PEG chains to the oppositely directed electro-osmotic flow.