Membrane Anisotropy Reshapes Scale-Free Correlations and Directional Mechanical Susceptibility in Transmembrane Proteins

Abstract

Long-range correlated motions couple distant regions of a protein, providing a physical basis for allosteric communication, cooperative conformational change, and the balance between structural stability and sensitivity to perturbations. Yet membrane proteins operate within a strongly anisotropic lipid bilayer, and how this environment reshapes such system-spanning coordination remains unclear. Using an implicit-membrane anisotropic network model, we perform a proteome-wide analysis of more than 3,000 human transmembrane proteins. We find that long-range correlations remain scale free under membrane constraints but become strongly direction dependent. Across protein sizes and topologies, their correlation lengths continue to scale with the corresponding molecular dimensions, while increasing membrane anisotropy extends in-plane correlations and shortens those along the membrane normal. Because spontaneous correlations and perturbation responses arise from the same underlying mechanics, we further resolve residue-level responses into in-plane and normal components. The resulting directional mechanical susceptibility provides new predictions of mutation-sensitive sites in GPCRs beyond those captured by conventional scalar flexibility measures. Together, these results show how environmental symmetry breaking can organize protein mechanics across scales, linking collective dynamics to the functional sensitivity of individual residues and connecting a general physical mechanism to experimentally measurable protein function.