Efficient method to characterize the context-dependent hydrophobicity of proteins.

Characterizing the hydrophobicity of a protein surface is relevant to understanding and quantifying its interactions with ligands, other proteins, and extended interfaces. However, the hydrophobicity of a complex, heterogeneous protein surface depends not only on the chemistry of the underlying amino acids but also on the precise chemical pattern and topographical context presented by the surface. Characterization of such context-dependent hydrophobicity at nanoscale resolution is a nontrivial task. The free energy, μ(v)(ex), of forming a cavity near a surface has been shown to be a robust measure of context-dependent hydrophobicity, with more favorable μ(v)(ex) values suggesting hydrophobic regions. However, estimating μ(v)(ex) for cavities significantly larger than the size of a methane molecule in a spatially resolved manner near proteins is a computationally daunting task. Here, we present a new method for estimating μ(v)(ex) that is 2 orders of magnitude more efficient than conventional techniques. Our method envisions cavity creation as the emptying of a volume of interest, v, by applying an external potential that is proportional to the number of water molecules, N(v), in v. We show that the "force" to be integrated to obtain μ(v)(ex) is simply the average of N(v) in the presence of the potential, and can be sampled accurately using short simulations (50-100 ps), making our method very efficient. By leveraging the efficiency of the method to calculate μ(v)(ex) at various locations in the hydration shell of the protein, hydrophobin II, we are able to construct a hydrophobicity map of the protein that accounts for topographical and chemical context. Interestingly, we find that the map is also dependent on the shape and size of v, suggesting an "observer context" in mapping the hydrophobicity of protein surfaces.