pKa Calculations of Asp26 in Thioredoxin with Alchemical Free Energy Simulations and Hirshfeld-I Atomic Charges

Thioredoxin is a protein that has been used as model system by various computational methods to predict the pK_a of aspartate residue Asp26 which is 3.5 units higher than the solvent exposed Asp20. Here, we use extensive atomistic molecular dynamics simulations of two different protonation states of Asp26 in combination with conformational analysis based on RMSD clustering and principle component analysis to identify representative conformations of the protein in solution. For each conformation the Gibbs free energy of proton transfer between the two aspartic acid residues is calculated with the Amber99sb force field in alchemical transformation. The varying polarization of Asp20/26 in different molecular environments and protonation states is described by Hirshfeld-I (HI) atomic charges obtained from the averaged polarized electron density. Our results show that the Gibbs free energy of proton transfer is dependent on the protein conformation, the proper sampling of the neighbouring Lys57 positions and on water molecules entering the hydrophobic cavity upon deprotonating Asp26. The inclusion of polarization of both aspartate residues in the free energy cycle by the HI atomic charges improve the results from the nonpolarizable force field and reproduces the experimental reference delta pK_a value.