Protein Dielectric Constants Determined from NMR Chemical Shift Perturbations

Understanding the connection between protein structure and function requires a quantitative understanding of electrostatic effects. Structure-based electrostatic 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 (ε_eff and ε_p) required in Coulombic and Poisson–Boltzmann models. The currently used values for ε_eff and ε_p are essentially empirical parameters calibrated against thermodynamic properties that are indirect measurements of protein electric fields. We determine optimal values for ε_eff and ε_p by measuring protein electric fields in solution using direct detection of NMR chemical shift perturbations (CSPs). We measured CSPs in 14 proteins to get a broad and general characterization of electric fields. Coulomb’s law reproduces the measured CSPs optimally with a protein dielectric constant (ε_eff) 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 (ε_p) ranged from 2 to 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 ε_p of 6–20 used in models based on the Poisson–Boltzmann equation when calculating thermodynamic parameters. Because the value of ε_p = 3 is obtained by analysis of NMR chemical shift perturbations instead of thermodynamic parameters such as p<i>K</i>_a values, it is likely to describe only the electric field and thus represent a more general, intrinsic, and transferable ε_p common to most folded proteins