Concentration dependence of lipopolymer self-diffusion in supported bilayer membranes

Self-diffusion coefficients of poly(ethylene glycol)2k-derivatized lipids (DSPE-PEG2k-CF) in glass-supported DOPC phospholipid bilayers are ascertained from quantitative fluorescence recovery after photobleaching (FRAP). We developed a first-order reaction–diffusion model to ascertain the bleaching constant, mobile fraction and lipopolymer self-diffusion coefficient D_s at concentrations in the range c ≈ 0.5–5 mol%. In contrast to control experiments with 1,2-dioleoyl-sn-glycero-3-phosphoethanolamine-N-(7-nitro-2-1,3-benzoxadiazol-4-yl) (ammonium salt) (DOPE-NBD) in 1,2-dioleoyl-sn-glycero-3-phosphocholine (DOPC), the lipopolymer self-diffusion coefficient decreases monotonically with increasing concentration, without a distinguishing mushroom-to-brush transition. Our data yield a correlation D_s = D₀/(1 + αc), where D₀ ≈ 3.36 µm² s⁻¹ and α ≈ 0.56 (with c expressed as a mole percent). Interpreting the dilute limit with the Scalettar–Abney–Owicki statistical mechanical theory for transmembrane proteins yields an effective disc radius a_e ≈ 2.41 nm. On the other hand, the Bussell–Koch–Hammer theory, which includes hydrodynamic interactions, yields a_e ≈ 2.92 nm. As expected, both measures are smaller than the Flory radius of the 2 kDa poly(ethylene glycol) (PEG) chains, R_F ≈ 3.83 nm, and significantly larger than the nominal radius of the phospholipid heads, a_l ≈ 0.46 nm. The diffusion coefficient at infinite dilution D₀ was interpreted using the Evans–Sackmann theory, furnishing an inter-leaflet frictional drag coefficient b_s ≈ 1.33 × 10⁸ N s m⁻³. Our results suggest that lipopolymer interactions are dominated by the excluded volume of the PEG-chain segments, with frictional drag dominated by the two-dimensional bilayer hydrodynamics.