Protein Dielectric Constants Determined from NMR Chemical Shift Perturbations

Understanding the connection between protein structure and function requires a quantitative under-standing of electrostatic effects. Structure-based electrostatics calculations are essential for this purpose, but their use has been limited by a long-standing discussion on which value to use for the dielectric constants (εeff and εp) required in Coulombic models and Poisson-Boltzmann models. The currently used values for εeff and εp are essentially empirical parameters calibrated against thermodynamic properties that are indirect measurements of protein electric fields. We
determine optimal values for εeff and εp by measuring protein electric fields in solution using direct detection of NMR chemical shift perturbations (CSPs). We measured CSPs in fourteen proteins to get a broad and general characterization of electric fields. Coulomb’s law reproduces the measured CSPs optimally with a protein dielectric constant (εeff) from 3 to 13, with an optimal value across all proteins of 6.5. However, when the water-protein interface is treated with finite difference Poisson-Boltzmann calculations, the optimal protein dielectric constant (εp) rangedsfrom 2-5 with an optimum of 3. It is striking how similar this value is to the dielectric constant of 2-4 measured for protein powders, and how different it is from the εp of 6-20 used in models based on the Poisson-Boltzmann equation when calculating thermodynamic parameters. Because the value of εp = 3 is obtained by analysis of NMR chemical shift perturbations instead of thermodynamic parameters such as pKa values, it is likely to describe only the electric field and thus represent a more general, intrinsic, and transferable εp common to most folded proteins.