Title: Computational Methods for the Calculation of Electrochemical Properties and pKa Predictions
Description: Computational methods provide important insights in structural features and properties of many systems, which in turn, reduce the cost of drug discovery. Accurate calculations of electrochemical properties and pKa predictions are crucial for understanding and modeling of many chemical reactions and biological processes. This dissertation will present two different classes of computational methods for the calculation of electrochemical properties and pKa values in two different systems. In the first part, we demonstrate the pKa calculations of histidine residues in proteins by Free Energy Perturbation (FEP) and evaluate several protein pKa prediction methods. In the second part, we demonstrate the Density Functional Theory d-block localized orbital correction (DFT-DBLOC) methodology in calculating of redox potentials and spin state splittings for octahedral transition metal containing species. Ionizable side chains in proteins are involved in catalysis and play a key role in the pH-dependence of a variety of biological reactions.

The ability to understand and model these effects requires an accurate pKa prediction of ionizable residues. The correct assignment of protonation state at a given pH helps to determine properties including protein solubility, protein folding, catalytic activity and protein–ligand binding affinities. Several computational methods have been developed to predict the residue pKa based on protein structure. Although some methods produced accurate predictions within 1 pKa unit RMS error, the RMSE over a large data set is not necessarily a good predictor of accuracy for specific types of protein environments. Most datasets studied in the pKa predictions contain highly solvent exposed residues which exhibit minimal perturbations from the intrinsic pKa values in solution. As the fraction of exposure to the solvent of the residue decreases, the predictive power of methods diminishes. However, these buried residues are often the most important residues from the standpoint of binding, catalytic activity, and other biologically important functions.

We have applied Free Energy Perturbation (FEP) method to predict a large dataset of experimentally measured pKa values of histidines in proteins and compare the results to experimental data. Histidines are particularly crucial because the imidazole side chain of histidine can serve as both acids and bases near physiological pH values and as both hydrogen bond donors and acceptors. We explain the factors determining pKa values and improve pKa predictions using enhanced protocols. We demonstrate improved performance using the FEP methodology vs example empirical and continuum solvent-based methodologies. In Chapter 4, we have evaluated the performance of the M06 and PBE0 DFT functionals and the DFT-DBLOC methodology in their ability to calculate spin splittings and redox potentials for octahedral complexes containing a first-row transition metal series atom. These quantities play a critical role in a wide range of transition metal chemistry and physics, including catalysis, electron transfer, and conductivity.

The mean unsigned errors (MUEs) for these two functionals are similar to those obtained for B3LYP using the same data sets. We then apply our localized orbital correction approach for transition metals, DBLOC, in an effort to improve the results obtained with both functionals. The PBE0- DBLOC results are remarkably close in both MUE and parameter values to those obtained for the B3LYP-DBLOC method. The M06-DBLOC results are less accurate, but the parameter values and trends are still qualitatively very similar. These results demonstrate that DBLOC corrected methods are substantially more accurate for these systems than any of the uncorrected functionals we have tested and that the deviations between hybrid DFT methods and experiment for transition metal containing systems exhibit striking physically based regularities which are very similar for the three functionals that we have examined, despite significant differences in the details of each model.