Constant pH Replica Exchange Molecular Dynamics in Explicit Solvent Using Discrete Protonation States: Implementation, Testing, and Validation

Abstract

By utilizing Graphics Processing Units, we show that constant pH molecular dynamics simulations (CpHMD) run in Generalized Born (GB) implicit solvent for long time scales can yield poor pK_a predictions as a result of sampling unrealistic conformations. To address this shortcoming, we present a method for performing constant pH molecular dynamics simulations (CpHMD) in explicit solvent using a discrete protonation state model. The method involves standard molecular dynamics (MD) being propagated in explicit solvent followed by protonation state changes being attempted in GB implicit solvent at fixed intervals. Replica exchange along the pH-dimension (pH-REMD) helps to obtain acceptable titration behavior with the proposed method. We analyzed the effects of various parameters and settings on the titration behavior of CpHMD and pH-REMD in explicit solvent, including the size of the simulation unit cell and the length of the relaxation dynamics following protonation state changes. We tested the method with the amino acid model compounds, a small pentapeptide with two titratable sites, and hen egg white lysozyme (HEWL). The proposed method yields superior predicted pK_a values for HEWL over hundreds of nanoseconds of simulation relative to corresponding predicted values from simulations run in implicit solvent.

Figure 1

Workflow of the proposed discrete protonation CpHMD method in explicit solvent. Following the standard MD, the solvent, including all nonstructural ions (as determined by user-input), are stripped and the protonation state changes are evaluated in a GB potential. After that, the solvent and the original settings are restored for the remaining steps.

Figure 2

RMSD compared to the 1AKI crystal structure for the ensembles at pH 1, 4, and 7. The time series is shown on the left with the normalized histograms shown on the right.

Figure 3

RMSE of all acidic titratable residue pK_a values compared to experiment during the course of the simulation. A 10 ns window was used for the running average of the computed pK_a.

Figure 4

Radial distribution functions (RDFs) of solvent oxygen atoms (O) and hydrogen atoms (H) with different unit cell sizes. The shown measurements—10, 15, and 20 Å—represent the size of the solvent buffer surrounding the solute. RDF plots for three different pHs are shown, highlighting the pH dependence of the solvent structure around the carboxylate of the aspartate model compound and its invariance to box size.

Figure 5

The relaxation of the protonated state, starting from the protonated trajectory, is shown in blue with its autocorrelation function shown in purple. The relaxation of the deprotonated state from an equilibrated snapshot from the protonated ensemble is shown in red with its autocorrelation function shown in green. Here, PR and DR stand for Protonated-Relaxation and Deprotonated-Relaxation, respectively.

Figure 6

RDFs of water oxygen atoms (O) and hydrogen atoms (H) around the center-of-mass of the carboxylate group of the model aspartate molecule at different solution pHs.

Figure 7

Titration curves of Cys-2 and Cys-4 in the ACFCA pentapeptide. Results from CpHMD (no replica exchange attempts) and pH-REMD are shown in the plots on the left and right, respectively.

Figure 8

Backbone RMSD distributions for HEWL simulations in explicit solvent with solution pH set to 1, 4, and 7. Time series are shown on the left and histograms are shown on the right.

Figure 9

(left) Plot showing the RMSE of all acidic titratable residue pK_a values compared to experiment during the course of the simulation. A 5 ns window was used for the running average of the computed pK_a. (right) Plot showing the autocorrelation function of the RMSE time series, showing that the correlation time between statistically independent samples is roughly 25 ns.