Protein dimerization in 2D vs 3D: Geometric allostery enhances binding affinity.

Dimerization underpins all macromolecular assembly processes, both on and off the membrane. While the strength of dimerization, KD, is commonly quantified in solution (3D), many proteins, such as the soluble BAR (Bin/Amphiphysin/Rvs) proteins, also reversibly dimerize while bound to a membrane surface (2D). The ratio of dissociation constants, h=KD2DKD3D, defines a lengthscale that is essential for determining whether dimerization is more favorable in solution or on the membrane surface, particularly for these proteins that reversibly transition between 3D and 2D. While purely entropic rigid-body estimates of h (hRIGID apply well to transmembrane adhesion proteins, we show here using MD simulations that even moderate flexibility in BAR domains dramatically alters the free energy landscape, driving enhanced stability of the native dimer in 2D. By simulating BAR homodimerization in three environments, (1) solution (3D), (2) bound to a lipid bilayer (2D), and (3) fully solvated but restrained to a pseudo membrane (2D), we show that both 2D environments induce backbone configurations that produce more enthalpically favorable dimer states. Comparing with theory, we show that this surface-induced or geometric allostery violates the rigid-body estimates to drive h ≪ hRIGID. Remarkably, contact with an explicit lipid bilayer is not necessary to drive these changes, as the solvated pseudo membrane induces this same result. This outcome depends on the stability of the protein interaction, as a parameterization with exceptionally stable binding in 3D does not improve in 2D. Our approach provides simple metrics to move beyond rigid-body estimates of 2D affinities and fully assess whether allosteric effects stabilize dimerization on membranes.