Calculating Acid-Dissociation Constants of Proteins Using the Boundary Element Method

The boundary element method (BEM) in combination with continuum electrostatics is employed to compute the acid-dissociation constants K a (p K a = −log K a ) of titrating sites in proteins. The boundary element method determines the electrostatic potential from the solution of two coupled integral equations, valid on a triangulated surface enclosing the macromolecule. First the intrinsic p is computed from the shift of the p K a of a model compound containing the titrating site upon its transfer from solution to the protein; during this step interactions between titrating sites are neglected. Subsequently, interactions between titrating sites are included by means of a Monte Carlo scheme to sample protonation states of the protein. A convenient vector−matrix formulation in terms of the BEM is given which allows the use of a single atom or a detailed charge model (or a combination of both) to describe the titrating sites. The method has been applied to four proteins: bovine pancreatic trypsin inhibitor, calbindin, lysozyme, and ovomucoid third-domain. Different choices for the dielectric constant of proteins ranging from 4 to 78.5 were investigated in a systematic fashion. Comparisons are made with p K a values calculated by the finite difference method and those determined experimentally for these four proteins. Our results indicate that accurate p K a values are obtained with the BEM when a dielectric constant for the protein of 20 or higher is used. For calbindin, different choices for the ionic strength were considered and comparison was made with p K a values obtained experimentally and from a simulation model using explicit ions for the solvent.