The effect of chain length on protein solubilization in polymer-based vesicles (polymersomes)

Abstract

Using a mean-field analysis we derive a consistent model for the perturbation of a symmetric polymeric bilayer due to the incorporation of transmembrane proteins, as a function of the polymer molecular weight and the protein dimensions. We find that the mechanism for the inhibition of protein incorporation in polymeric bilayers differs from that of their inclusion in polymer-carrying lipid vesicles; in polymersomes, the equilibrium concentration of transmembrane proteins decreases as a function of the thickness mismatch between the protein and the bilayer core, whereas in liposomes the presence of polymer chains affects the protein adsorption kinetics. Despite the increased stiffness of polymer bilayers (when compared to lipid ones), their perturbation decay length and range of protein-protein interaction is found to be relatively long. The energetic penalty due to protein adsorption increases relatively slowly as a function of the polymer chain length due to the self-assembled nature of the polymer bilayer. As a result, we predict that transmembrane proteins may be incorporated in significant numbers even in bilayers where the thickness mismatch is large.

FIGURE 1

Conformation of polymer chains near an inclusion in a polymeric bilayer: 2L_m in the thickness of a flat bilayer, 2L_p the inclusion thickness and z is the distance from the inclusion boundary. The chains in the unperturbed bilayer are highly stretched (L_maN^2/3, where N is the number of segments and a the segment length). As a result, the requirement to match the thickness of much shorter proteins can be achieved without undergoing significant compression when compared to the free chain radius of gyration. For example, a polymer chain with N = 1000 will have an unperturbed radius of gyration that scales as 30a, but can stretch to order 100a in the bilayer. Thus, matching a protein whose thickness is half that of the bilayer (50a) is easily obtained.

FIGURE 2

Bilayer thickness profile, (Eq. 6) as a function of the distance from the inclusion boundary, z. All length scales are in units of a, the segment size. The flat monolayer thickness, L_m = 2 and the protein thickness, L_p = 8, 4 and 1.5 when L_p ≫ L_m, L_p = 2L_m and L_p < L_m respectively.

FIGURE 3

Protein-induced membrane perturbation energy, (Eq. 5) as a function of chain molecular weight.

FIGURE 4

Perturbation energy of a given membrane, as a function of protein size, (Eq. 7). The membrane thickness is L_m = 2 and (γa²) is taken to be 0.1 kT. Note that higher values of γ will lead to an even more significant shift in the minimum toward larger proteins.

FIGURE 5

A schematic of bilayer perturbation by nonincorporated transmembrane proteins. As is shown, partial embedding of the protein, although reducing the membrane perturbation, involves an energetic penalty due to the surface tension between hydrophobic and hydrophilic regions.