A computational tool that offers accurate pKa values and atomically detailed knowledge of protonation-coupled conformational dynamics is valuable for elucidating mechanisms of energy transduction processes in biology, such as enzyme catalysis and electron transfer as well as proton and drug transport. Toward this goal we present a new technique of embedding continuous constant pH molecular dynamics within an explicit-solvent representation. In this technique we make use of the efficiency of the generalized-Born (GB) implicit-solvent model for estimating the free energy of protein solvation while propagating conformational dynamics using the more accurate explicit-solvent model. Also, we employ a pH-based replica exchange scheme to significantly enhance both protonation and conformational state sampling. Benchmark data of five proteins including HP36, NTL9, BBL, HEWL, and SNase yield an average absolute deviation of 0.53 and a root mean squared deviation of 0.74 from experimental data. This level of accuracy is obtained with 1 ns simulations per replica. Detailed analysis reveals that explicit-solvent sampling provides increased accuracy relative to the previous GB-based method by preserving the native structure, providing a more realistic description of conformational flexibility of the hydrophobic cluster, and correctly modeling solvent mediated ion-pair interactions. Thus, we anticipate that the new technique will emerge as a practical tool to capture ionization equilibria while enabling an intimate view of ionization coupled conformational dynamics that is difficult to delineate with experimental techniques alone.

Development of a pH stat to properly control solution pH in biomolecular simulations has been a long-standing goal in the community. Towards this goal recent years have witnessed the emergence of the so-called constant pH molecular dynamics methods. However, the accuracy and generality of these methods have been hampered by the use of implicit-solvent models or truncation-based electrostatic schemes. Here we report the implementation of the particle mesh Ewald (PME) scheme into the all-atom continuous constant pH molecular dynamics (CpHMD) method, enabling CpHMD to be performed with a standard MD engine at a fractional added computational cost. We demonstrate the performance using pH replica-exchange CpHMD simulations with titratable water for a stringent test set of proteins, HP36, BBL, HEWL and SNase. With the sampling time of 10 ns per replica, most pKa’s are converged, yielding the average absolute and root-mean-square deviations of 0.61 and 0.77, respectively, from experiment. Linear regression of the calculated vs experimental pKa shifts gives a correlation coefficient of 0.79, a slope of 1 and an intercept near 0. Analysis reveals inadequate sampling of structure relaxation accompanying a protonation-state switch as a major source of the remaining errors, which are reduced as simulation prolongs. These data suggest PME-based CpHMD can be used as a general tool for pH-controlled simulations of macromolecular systems in various environments, enabling atomic insights into pH-dependent phenomena involving not only soluble proteins but also transmembrane proteins, nucleic acids, surfactants and polysaccharides.

Recent development of constant pH molecular dynamics (CpHMD) methods has offered promise for adding pH-stat in molecular dynamics simulations. However, until now the working pH molecular dynamics (pHMD) implementations are dependent in part or whole on implicit-solvent models. Here we show that proper treatment of long-range electrostatics and maintaining charge neutrality of the system are critical for extending the continuous pHMD framework to the all-atom representation. The former is achieved here by adding forces to titration coordinates due to long-range electrostatics based on the generalized reaction field method, while the latter is made possible by a charge-leveling technique that couples proton titration with simultaneous ionization or neutralization of a co-ion in solution. We test the new method using the pH-replica-exchange CpHMD simulations of a series of aliphatic dicarboxylic acids with varying carbon chain length. The average absolute deviation from the experimental pK a values is merely 0.18 units. The results show that accounting for the forces due to extended electrostatics removes the large random noise in propagating titration coordinates, while maintaining charge neutrality of the system improves the accuracy in the calculated electrostatic interaction between ionizable sites. Thus, we believe that the way is paved for realizing pH-controlled all-atom molecular dynamics in the near future.

Recent development of titratable coions has paved the way for realizing all-atom molecular dynamics at constant pH. To further improve physical realism, here we describe a technique in which proton titration of the solute is directly coupled to the interconversion between water and hydroxide or hydronium. We test the new method in replica-exchange continuous constant pH molecular dynamics simulations of three proteins, HP36, BBL, and HEWL. The calculated pKa values based on 10-ns sampling per replica have the average absolute and root-mean-square errors of 0.7 and 0.9 pH units, respectively. Introducing titratable water in molecular dynamics offers a means to model proton exchange between solute and solvent, thus opening a door to gaining new insights into the intricate details of biological phenomena involving proton translocation.

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Proton uptake or release controls many important biological processes, such as energy transduction, virus replication, and catalysis. Accurate pK(a) prediction informs about proton pathways, thereby revealing detailed acid-base mechanisms. Physics-based methods in the framework of molecular dynamics simulations not only offer pK(a) predictions but also inform about the physical origins of pK(a) shifts and provide details of ionization-induced conformational relaxation and large-scale transitions. One such method is the recently developed continuous constant pH molecular dynamics (CPHMD) method, which has been shown to be an accurate and robust pK(a) prediction tool for naturally occurring titratable residues. To further examine the accuracy and limitations of CPHMD, we blindly predicted the pK(a) values for 87 titratable residues introduced in various hydrophobic regions of staphylococcal nuclease and variants. The predictions gave a root-mean-square deviation of 1.69 pK units from experiment, and there were only two pK(a)'s with errors greater than 3.5 pK units. Analysis of the conformational fluctuation of titrating side-chains in the context of the errors of calculated pK(a) values indicate that explicit treatment of conformational flexibility and the associated dielectric relaxation gives CPHMD a distinct advantage. Analysis of the sources of errors suggests that more accurate pK(a) predictions can be obtained for the most deeply buried residues by improving the accuracy in calculating desolvation energies. Furthermore, it is found that the generalized Born implicit-solvent model underlying the current CPHMD implementation slightly distorts the local conformational environment such that the inclusion of an explicit-solvent representation may offer improvement of accuracy.

Ionization-coupled conformational phenomena are ubiquitous in biology. However, quantitative characterization of the underlying thermodynamic cycle comprised of protonation and conformational equilibria has remained an elusive goal. Here we use theory and continuous constant pH molecular dynamics (CpHMD) simulations to provide a thermodynamic description for the coupling of proton titration and conformational exchange between two distinct states of a protein. CpHMD simulations with a hybrid-solvent scheme and the pH-based replica-exchange (REX) protocol are applied to obtain the equilibrium constants and atomic details of the ionization-coupled conformational exchange between open and closed states of an engineered mutant of staphylococcal nuclease. Although the coupling of protonation and conformational equilibria is not exact in the simulation, the results are encouraging. They demonstrate that REX-CpHMD simulations can be used to study thermodynamics of ionization-coupled conformational processes--which has not possible using present experimental techniques or traditional simulations based on fixed protonation states.

When the major ampulate spidroins (MaSp1) are called upon to form spider dragline silk, one of nature’s most amazing materials, a small drop in pH must occur. Using a state-of-the-art simulation technique, constant pH molecular dynamics, we discovered a few residues that respond to the pH signal in the dimerization of the N-terminal domain (NTD) of MaSp1 which is an integral step in the fiber assembly. At neutral pH the deprotonation of Glu79 and Glu119 leads to water penetration and structural changes at the monomer-monomer binding interface. At strongly acidic pH, the protonation of Asp39 and Asp40 weakens the electrostatic attraction between the monomers. Thus, we propose a “trap-and-trigger” mechanism whereby the intermolecular salt-bridges at physiologically relevant pH conditions always act as a stabilizing “trap” favoring dimerization. As pH is lowered to about 6, Glu79 and Glu119 become protonated, triggering the dimerization and subsequent silk formation. We speculate that this type of mechanism is operative in many other pH-sensitive biological processes.