A model-free method for measuring dimerization free energies of CLC-ec1 in lipid bilayers

The thermodynamic reasons why membrane proteins form stable complexes inside the hydrophobic lipid bilayer remain poorly understood. This is largely because of a lack of membrane-protein systems amenable for equilibrium studies and a limited number of methods for measuring these reactions. Recently, we reported the equilibrium dimerization of the CLC-ec1 Cl^-/H⁺ transporter in lipid bilayers (Chadda et al. 2016. eLife https://doi.org/10.7554/eLife.17438), which provided a new type of model system for studying protein association in membranes. The measurement was conducted using the subunit-capture approach, involving passive dilution of the protein in large multilamellar vesicles, followed by single-molecule photobleaching analysis of the Poisson distribution describing protein encapsulation into extruded liposomes. To estimate the fraction of dimers (F ) as a function of protein density, the photobleaching distributions for the nonreactive, ideal monomer and dimer species must be known so that random co-capture probabilities can be accounted for. Previously, this was done by simulating the Poisson process of protein reconstitution into a known size distribution of liposomes composed of Escherichia coli polar lipids (EPLs). In the present study, we investigate the dependency of F and ΔG° on the modeling through a comparison of different liposome size distributions (EPL versus 2:1 POPE/POPG). The results show that the estimated F values are comparable, except at higher densities when liposomes become saturated with protein. We then develop empirical controls to directly measure the photobleaching distributions of the nonreactive monomer (CLC-ec1 I201W/I422W) and ideal dimer (WT CLC-ec1 cross-linked by glutaraldehyde or CLC-ec1 R230C/L249C cross-linked by a disulfide bond). The measured equilibrium constants do not depend on the correction method used, indicating the robustness of the subunit-capture approach. This strategy therefore presents a model-free way to quantify protein dimerization in lipid bilayers, offering a simplified strategy in the ongoing effort to characterize equilibrium membrane-protein reactions in membranes.