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Reproducing ensemble averaged electrostatics with Super-Gaussian-based smooth dielectric function: application to electrostatic component of binding energy of protein complexes

Proteins constantly sample various conformations as they carry their biological function, including interacting with their partners, and this should be taken into account in any numerical protocol aiming at computing their thermodynamic properties. Here we report an application of previously reported Super-Gaussian-based smooth dielectric function (J Math Biol., 2019 Jul; 79(2):631– 672) to reproduce ensemble averaged electrostatics. This is an important achievement, since it dramatically reduces the computational demand for MM/PBSA applications and bypasses the necessity of long molecular dynamics simulations. Instead, a single frame, typically energy-minimized structure, in conjunction of Super-Gaussian-based smooth dielectric function, as implemented in DelPhi, can deliver ensemble averaged quantities. The approach is tested against ensemble averaged electrostatic component of binding free energy of protein-protein complexes. It is demonstrated that Super-Gaussian-based smooth dielectric function reproduces ensemble averaged quantities, resulting in correlation coefficients of about 0.8 and slope of the fitting line of 1.0.