Self-Consistent, Free Energy Based Approximation To Calculate pH Dependent Electrostatic Effects in Proteins

Abstract

A constrained variational approach is used to derive self-consistent equations for determining the optimal, pH dependent charge state of all the protonatable groups in a protein. The approach uses a screened Coulomb potential (SCP) with a sigmoidal, distance dependent dielectric screening function for calculating the interaction energies between the charges in a protein. In addition, a formula is derived from the integral Born equation, using radially dependent permittivities, for calculating the electrostatic free energy of transferring a charged group from pure solvent to a protein in a dilute solution. The relationship between the approach and the Lorentz−Debye−Sack theory of polar solvation is outlined, and the method has been applied to calculate the pK's of the titratable groups in bovine pancreatic trypsin inhibitor, hen egg white lysozyme, ribonuclease A, and ribonuclease T1. The results are compared to recent calculations of pH dependent properties of these proteins that used the finite differenc...