A Hierarchical Approach to Predict Conformation-Dependent Histidine Protonation States in Stable and Flexible...

Solution acidity measured by pH is an important environmental factor that affects protein structure. It influences the protonation state of protein residues, which in turn may be coupled to protein conformational changes, unfolding, and ligand binding. It remains difficult to compute and measure the p K_a of individual residues, as well as to relate them to pH-dependent protein transitions. This paper presents a hierarchical approach to compute the p K_a of individual protonatable residues, specifically histidines, coupled with underlying structural changes of a protein. A fast and efficient free energy perturbation (FEP) algorithm has also been developed utilizing a fast implementation of standard molecular dynamics (MD) algorithms. Specifically, a CUDA version of the AMBER MD engine is used in this paper. Eight histidine p K_a's are computed in a diverse set of pH stable proteins to demonstrate the proposed approach's utility and assess the predictive quality of the AMBER FF99SB force field. A reference molecule is carefully selected and tested for convergence. A hierarchical approach is used to model p K_a's of the six histidine residues of the diphtheria toxin translocation domain (DTT), which exhibits a diverse ensemble of individual conformations and pH-dependent unfolding. The hierarchical approach consists of first sampling equilibrium conformational ensembles of a protein with protonated and neutral histidine residues via long equilibrium MD simulations (Flores-Canales, J. C.; et al. bioRxiv, 2019, 572040). A clustering method is then used to identify sampled protein conformations, and p K_a's of histidines in each protein conformation are computed. Finally, an ensemble averaging formalism is developed to compute weighted average histidine p K_a's. These can be compared with an apparent experimentally measured p K_a of the DTT protein and thus allows us to propose a mechanism of pH-dependent unfolding of the DTT protein.