Geometric-Chemical Distance Between Protein Surfaces

Proteins recognize, bind, and catalyze through molecular surfaces, where geometry and chemical patterning determine interaction. Comparing these surfaces requires both a geometric--chemical distance and a correspondence that relates one complete surface to another. Here we introduce IFACE (Intrinsic Field--Aligned Coupled Embedding). IFACE derives a symmetric geometric--chemical distance by optimizing a probabilistic coupling over intrinsic geometry, mean curvature, electrostatics, hydrophobicity, and hydrogen-bond propensity. The same coupling provides an explicit surface map. For molecular-dynamics conformers, IFACE distinguishes the same protein from distinct proteins more accurately than TM-distance and Laplace--Beltrami spectral distance. A Jensen--Shannon distribution distance performs best in this binary identity test, because aggregate surface-feature distributions already identify each protein. A distance must also satisfy a global requirement: its pairwise values must place many distinct protein surfaces consistently in one space. We therefore tested IFACE across six protein families. It produces the strongest family classification and clustering among the distributional, spectral, MaSIF, and SurfaceID comparisons. The inferred maps preserve geodesic neighborhoods and transfer heme-centered pocket regions across cytochrome P450 proteins. IFACE therefore provides, from one construction, both a distance between complete protein surfaces and the local map that explains that distance.