GPU-Accelerated Implementation of Continuous Constant pH Molecular Dynamics in Amber: pKa Predictions with Single-pH Simulations

We present a GPU implementation of the continuous constant pH molecular dynamics (CpHMD) based on the most recent generalized Born implicit-solvent model in the pmemd engine of the Amber molecular dynamics package. To test the accuracy of the tool for rapid pKa predictions, a series of 2-ns single-pH simulations were performed for over 120 titratable residues in 10 benchmark proteins that were previously used to test the various continuous CpHMD methods. The calculated pKa's showed a root-mean-square deviation of 0.80 and correlation coefficient of 0.83 with respect to experiment. 90% of the pKa's were converged with estimated errors below 0.1 pH units. Surprisingly, this level of accuracy is similar to our previous replica-exchange simulations with 2 ns per replica and an exchange attempt frequency of 2 ps-1 (Huang, Harris and Shen, J Chem Info Model, 2018). Interestingly, for the linked titration sites in two enzymes, although residue-specific protonation state sampling in the single-pH simulations was not converged within 2 ns, the protonation fraction of the linked residues appeared to be largely converged, and the experimental macroscopic {\pka} values were reproduced to within 1 pH unit. Comparison with replica-exchange simulations with different exchange attempt frequencies showed that the splitting between the two macroscopic pKa's is underestimated with frequent exchange attempts such as 2 ps$^{-1}$, while single-pH simulations overestimate the splitting. The same trend is seen for the single-pH vs. replica-exchange simulations of a hydrogen-bonded aspartyl dyad in a much larger protein. A 2-ns single-pH simulation of a 400-residue protein takes about one hour on a single NVIDIA GeForce RTX 2080 graphics card, which is over 1000 times faster than a CpHMD run on a single CPU core of a high-performance computing cluster node. Thus, we envision that GPU-accelerated continuous CpHMD may be used in routine pKa predictions for a variety of applications, from assisting MD simulations with protonation state assignment to offering pH-dependent corrections of binding free energies and identifying reactive hot spots for covalent drug design.