Protein Dielectric Constants Determined from NMR Chemical Shift Perturbations

• Published in: Journal of the American Chemical Society Vol. 135; no. 45; pp. 16968 - 16976
• Main Authors: Kukic, Predrag, Farrell, Damien, McIntosh, Lawrence P, García-Moreno E, Bertrand, Jensen, Kristine Steen, Toleikis, Zigmantas, Teilum, Kaare, Nielsen, Jens Erik
• Format: Journal Article
• Language: English
• Published: United States American Chemical Society 13.11.2013
• Subjects: Animals; Cattle; Humans; Models, Molecular; Nuclear Magnetic Resonance, Biomolecular - methods; Protein Conformation; Proteins - chemistry; Static Electricity
• ISSN: 0002-7863; 1520-5126
• DOI: 10.1021/ja406995j

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 (εeff and εp) required in Coulombic 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 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 (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) 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 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 pK a 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.