Lipid-Shell PARCH: A Physically Motivated Scale for Transmembrane Residue Hydropathy.

Understanding how amino acid residues partition from water into lipid bilayers is fundamental to membrane protein folding, stability, and function. Existing hydrophobicity scales derive from isolated protein systems, organic solvent approximations, or computationally expensive free energy methods, each with significant limitations in capturing the full thermodynamic and topographic complexity of membrane protein environments. Here we present a lipid-shell modification to the protocol for assigning a residue's character on a hydropathy (PARCH) scale, in which the protein's first hydration shell is enclosed by a lipid boundary layer during thermal annealing. This modification preserves the core PARCH methodology─evaluating water retention around residues as a function of temperature─while imposing the chemical potential boundary condition appropriate for membrane-embedded proteins. Using the OmpLA host-guest system, we compute PARCH values (PVs) that align with the experimental water-to-bilayer transfer free energy scale of Moon and Fleming (PNAS, 108, 10174-10177, 2011) without calibration to that data. We further demonstrate that depth-dependent PV profiles for arginine and leucine mirror experimentally measured partition energies across six membrane positions. Finally, PVs for a tandem arginine double mutant reveal a per-residue cooperative hydration redistribution that provides microscopic insight into thermodynamic cooperativity previously measured experimentally. Together, these results establish the lipid-shell PARCH modification as a computationally affordable and physically meaningful approach to quantifying membrane hydropathy that is sensitive to residue identity, membrane depth, and cooperative hydration among tandem charged residues.