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 (FDimer) 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 FDimer 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 FDimer 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.