Tanford–Kirkwood electrostatics for protein modeling

Solvent plays a significant role in determining the electrostatic potential energy of proteins, most notably through its favorable interactions with charged residues and its screening of electrostatic interactions. These energetic contributions are frequently ignored in computational protein design and protein modeling methodologies because they are difficult to evaluate rapidly and accurately. To address this deficiency, we report a revised form of the original Tanford–Kirkwood continuum electrostatic model [Tanford, C. & Kirkwood, J. G. (1957) J. Am. Chem. Soc. 79, 5333–5339], which accounts for the effects of solvent polarization on charged atoms in proteins. The Tanford–Kirkwood model was modified to increase its speed and to improve its sensitivity to the details of protein structure. For the 37 electrostatic self-energies of the polar side-chains in bovine pancreatic trypsin inhibitor, and their 666 interaction energies, the modified Tanford–Kirkwood potential of mean force differs from a computationally intensive numerical potential (DelPhi) by root-mean-square errors of 0.6 kcal/mol and 0.08 kcal/mol, respectively. The Tanford–Kirkwood approach makes possible a realistic treatment of electrostatics in computationally demanding protein modeling calculations. For example, pH titration calculations for ovomucoid third domain that model polar side-chain relaxation (including >2 × 10(23) rotamer conformations of the protein) provide pKa values of unprecedented accuracy.