Coupling Constant pH Molecular Dynamics with Accelerated Molecular Dynamics.
ABSTRACT: An extension of the constant pH method originally implemented by Mongan et al. (J. Comput. Chem.2004, 25, 2038-2048) is proposed in this study. This adapted version of the method couples the constant pH methodology with the enhanced sampling technique of accelerated molecular dynamics, in an attempt to overcome the sampling issues encountered with current standard constant pH molecular dynamics methods. Although good results were reported by Mongan et al. on application of the standard method to the hen egg-white lysozyme (HEWL) system, residues which possess strong interactions with neighboring groups tend to converge slowly, resulting in the reported inconsistencies for predicted pK(a) values, as highlighted by the authors. The application of the coupled method described in this study to the HEWL system displays improvements over the standard version of the method, with the improved sampling leading to faster convergence and producing pK(a) values in closer agreement to those obtained experimentally for the more slowly converging residues.
Project description: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 pKa 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 pKa values for HEWL over hundreds of nanoseconds of simulation relative to corresponding predicted values from simulations run in implicit solvent.
Project description:We propose a new algorithm for obtaining proton titration curves of ionizable residues. The algorithm is a pH replica-exchange method (PHREM), which is based on the constant pH algorithm of Mongan et al. (J Comput Chem 2004;25:2038-2048). In the original replica-exchange method, simulations of different replicas are performed at different temperatures, and the temperatures are exchanged between the replicas. In our PHREM, simulations of different replicas are performed at different pH values, and the pHs are exchanged between the replicas. The PHREM was applied to a blocked amino acid and to two protein systems (snake cardiotoxin and turkey ovomucoid third domain), in conjunction with a generalized Born implicit solvent. The performance and accuracy of this algorithm and the original constant pH method (PHMD) were compared. For a single set of simulations at different pHs, the use of PHREM yields more accurate Hill coefficients of titratable residues. By performing multiple sets of constant pH simulations started with different initial states, the accuracy of predicted pK(a) values and Hill coefficients obtained with PHREM and PHMD methods becomes comparable. However, the PHREM algorithm exhibits better samplings of the protonation states of titratable residues and less scatter of the titration points and thus better precision of measured pK(a) values and Hill coefficients. In addition, PHREM exhibits faster convergence of individual simulations than the original constant pH algorithm.
Project description:The majority of pK(a) values in protein unfolded states are close to the amino acid model pK(a) values, thus reflecting the weak intramolecular interactions present in the unfolded ensemble of most proteins. We have carried out thermal denaturation measurements on the WT and eight mutants of HEWL from pH 1.5 to pH 11.0 to examine the unfolded state pK(a) values and the pH dependence of protein stability for this enzyme. The availability of accurate pK(a) values for the folded state of HEWL and separate measurements of mutant-induced effects on the folded state pK(a) values, allows us to estimate the pK(a) values of seven acidic residues in the unfolded state of HEWL. Asp-48 and Asp-66 display pK(a) values of 2.9 and 3.1 in our analysis, thus representing the most depressed unfolded state pK(a) values observed to date. We observe a strong correlation between the folded state pK(a) values and the unfolded state pK(a) values of HEWL, thus suggesting that the unfolded state of HEWL possesses a large degree of native state characteristics.
Project description: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.
Project description:Development of a pH stat to properly control solution pH in biomolecular simulations has been a long-standing goal in the community. Toward 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.
Project description:The hen (chicken) egg-white lysozyme (HEWL) epitope for the monoclonal antibody HyHEL-10 Fab (Fab-10) was investigated by alanine scan mutagenesis. The association rate constants (k(on)) for the HEWL Fab-10 complexes were obtained from the homogenous solution method described in the preceding paper (Taylor et al., 1998). A new method for determining the dissociation rate constant (k(off)) for the complex, by trapping nascent free antibody with an inactive HEWL mutant is described. The values of k(on) fall within a factor of 2 of the wild-type (WT) HEWL value (1.43+/-0.13 X 10(6)M(-1)s(-1)), while the increases in k(off)more nearly reflect the total change in free energies of the complex (deltadeltaG(D)). The dissociation constants (K(D)) were measured directly in those cases where satisfactory kinetic data could not be obtained. The Y20A, K96A, and K97A HEWL.Fab-10 complexes are destabilized by more than 4 kcal/mol compared to the WT complex. The R21A, L75A, and D101A antibody complexes are moderately destabilized (0.7 < deltadeltaG(D)< or = 1.0 kcal/mol). Additional mutations of the "hotspot" residues (Tyr20, Lys96, Lys97) were constructed to probe, more precisely, the nature of their contributions to complex formation. The results show that the entire hydrocarbon side chains of Tyr20 and Lys97, and only the epsilon-amino group of Lys96, contribute to the stability of the complex. The value of deltadeltaG(D) for the R21A mutant complex is a distinct outlier in the Arg21 replacement series demonstrating the importance of supplementing alanine scan mutagenesis with additional mutations.
Project description:Accurate computational methods of determining protein and nucleic acid pK(a) values are vital to understanding pH-dependent processes in biological systems. In this article, we use the recently developed method constant pH molecular dynamics (CPHMD) to explore the calculation of highly perturbed pK(a) values in variants of staphylococcal nuclease (SNase). Simulations were performed using the replica exchange (REX) protocol for improved conformational sampling with eight temperature windows, and yielded converged proton populations in a total sampling time of 4 ns. Our REX-CPHMD simulations resulted in calculated pK(a) values with an average unsigned error (AUE) of 0.75 pK units for the acidic residues in ? + PHS, a hyperstable variant of SNase. For highly pK(a)-perturbed SNase mutants with known crystal structures, our calculations yielded an AUE of 1.5 pK units and for those mutants based on modeled structures an AUE of 1.4 pK units was found. Although a systematic underestimate of pK shifts was observed in most of the cases for the highly perturbed pK mutants, correlations between conformational rearrangement and plasticity associated with the mutation and error in pK(a) prediction was not evident in the data. This study further extends the scope of electrostatic environments explored using the REX-CPHMD methodology and suggests that it is a reliable tool for rapidly characterizing ionizable amino acids within proteins even when modeled structures are employed.
Project description:Constant pH molecular dynamics offers a means to rigorously study the effects of solution pH on dynamical processes. Here, we address two critical questions arising from the most recent developments of the all-atom continuous constant pH molecular dynamics (CpHMD) method: (1) What is the effect of spatial electrostatic truncation on the sampling of protonation states? (2) Is the enforcement of electrical neutrality necessary for constant pH simulations? We first examined how the generalized reaction field and force-shifting schemes modify the electrostatic forces on the titration coordinates. Free energy simulations of model compounds were then carried out to delineate the errors in the deprotonation free energy and salt-bridge stability due to electrostatic truncation and system net charge. Finally, CpHMD titration of a mini-protein HP36 was used to understand the manifestation of the two types of errors in the calculated pK(a) values. The major finding is that enforcing charge neutrality under all pH conditions and at all time via cotitrating ions significantly improves the accuracy of protonation-state sampling. We suggest that such finding is also relevant for simulations with particle mesh Ewald, considering the known artifacts due to charge-compensating background plasma.
Project description:Nanoparticle (NP) delivery to solid tumors has recently been questioned. To better understand the magnitude of NP tumor delivery, we reanalyzed published murine NP tumor pharmacokinetic (PK) data used in the Wilhelm et al. study. Studies included in their analysis reporting matched tumor and blood concentration versus time data were evaluated using classical PK endpoints and compared to the unestablished percent injected dose (%ID) in tumor metric from the Wilhelm et al. study. The %ID in tumor was poorly correlated with standard PK metrics that describe NP tumor delivery (AUCtumor/AUCblood ratio) and only moderately associated with maximal tumor concentration. The relative tumor delivery of NPs was ~100-fold greater as assessed by the standard AUCtumor/AUCblood ratio than by %ID in tumor. These results strongly suggest that PK metrics and calculations can influence the interpretation of NP tumor delivery and stress the need to properly validate novel PK metrics against traditional approaches.
Project description:The data described here supports the research article "Unraveling HIV Protease Flaps Dynamics by Constant pH Molecular Dynamics Simulations" (Soares et al., 2016) . The data involves both standard Molecular Dynamics (MD) and Constant pH Molecular Dynamics (CpHMD) to elucidate the effect of protonation states of catalytic dyad on the HIV-PR conformation. The data obtained from MD simulation demonstrate that the protonation state of the two aspartic acids (Asp25/Asp25') has a strong influence on the dynamics of the HIV-PR. Regarding the CpHMD simulation, we performed pka calculations for HIV-PR and the data indicate that only one catalytic aspartate should be protonated.