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) = D(0)/(1 + αc), where D(0) ≈ 3.36 µm(2) 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 D(0) was interpreted using the Evans-Sackmann theory, furnishing an inter-leaflet frictional drag coefficient b(s) ≈ 1.33 × 10(8) 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.