Yongjia Xu (U): Computational Mathematics in Calculating Protein pKas

A common approach to computing protein pKas uses a continuum dielectric model in which the protein is a low dielectric medium with embedded atomic point charges, the solvent is a high dielectric medium with a Boltzmann distribution of ionic charges, and the pKa is related to the electrostatic free energy which is obtained by solving the Poisson-Boltzmann equation. Starting from the model pKa for a titrating residue, the method obtains the intrinsic pKa and then computes the protonation probability for a given pH including site-site interactions. This approach assumes that acid dissociation does not affect protein conformation aside from adding or deleting charges at titratable sites. In this work we demonstrate our treecode-accelerated boundary integral (TABI) solver for the relevant electrostatic calculations. Our next step is to use machine learning to help use find patterns and better predict the pKa. We aim to make our algorithm efficient in that our protein data bank is usually very large. Careful data processing can help us filter irrelevant or less relevant features and focus more on what could potentially affect pKa values.