Effects of system net charge and electrostatic truncation on all-atom constant pH molecular dynamics.

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.

Predicting proton titration in cationic micelle and bilayer environments.

Knowledge of the protonation behavior of pH-sensitive molecules in micelles and bilayers has significant implications in consumer product development and biomedical applications. However, the calculation of pKa's in such environments proves challenging using traditional structure-based calculations. Here we apply all-atom constant pH molecular dynamics with explicit ions and titratable water to calculate the pKa of a fatty acid molecule in a micelle of dodecyl trimethylammonium chloride and liquid as well as gel-phase bilayers of diethyl ester dimethylammonium chloride. Interestingly, the pKa of the fatty acid in the gel bilayer is 5.4, 0.4 units lower than that in the analogous liquid bilayer or micelle, despite the fact that the protonated carboxylic group is significantly more desolvated in the gel bilayer. This work illustrates the capability of all-atom constant pH molecular dynamics in capturing the delicate balance in the free energies of desolvation and Coulombic interactions. It also shows the importance of the explicit treatment of ions in sampling the protonation states. The ability to model dynamics of pH-responsive substrates in a bilayer environment is useful for improving fabric care products as well as our understanding of the side effects of anti-inflammatory drugs.

Introducing titratable water to all-atom molecular dynamics at constant pH.

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.

Self-assembly and bilayer-micelle transition of fatty acids studied by replica-exchange constant pH molecular dynamics.

Recent interest in the development of surfactant-based nanodelivery systems targeting tumor sites has sparked our curiosity in understanding the detailed mechanism of the self-assembly and phase transitions of pH-sensitive surfactants. Toward this goal, we applied a state-of-the-art simulation technique, continuous constant pH molecular dynamics (CpHMD) with the hybrid-solvent scheme and pH-based replica-exchange protocol, to study the de novo self-assembly of 30 and 40 lauric acids, a simple model titratable surfactant. We observed the formation of a gel-state bilayer at low and intermediate pH and a spherical micelle at high pH, with the phase transition starting at 20-30% ionization and being completed at 50%. The degree of cooperativity for the transition increases from the 30-mer to the 40-mer. The calculated apparent or bulk pKa value is 7.0 for the 30-mer and 7.5 for the 40-mer. Congruent with experiment, these data demonstrate that CpHMD is capable of accurately modeling large conformational transitions of surfactant systems while allowing the simultaneous proton titration of constituent molecules. We suggest that CpHMD simulations may become a useful tool in aiding in the design and development of pH-sensitive nanocarriers for a variety of biomedical and technological applications.

Thermodynamic coupling of protonation and conformational equilibria in proteins: theory and simulation.

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.

Diarylcyclopentendione metabolite obtained from a Preussia typharum isolate procured using an unconventional cultivation approach.

An uncommon 2,5-diarylcyclopentenone compound, preussidone (1), and a new biphenyl compound, 1',5-dimethoxy-3,5'-dimethyl-2,3'-oxybiphenyl-1,2'-diol (4), together with two known biphenyl compounds, 5-methoxy-3,5'-dimethyl-2,3'-oxybiphenyl-1,1',2'-triol (2) and cyperin (3), were obtained from a Preussia typharum isolate that was procured using a panel of unconventional media formulations. The structures of the new compounds were established by NMR and mass spectrometry, while the absolute configuration of 1 was assigned by quantum chemical ECD and VCD calculations. The antimicrobial and DPPH radical scavenging activities of 1-4 were tested. Compounds 2 and 4 exhibited DPPH radical scavenging activities that were comparable to the positive control ascorbic acid.

Charge-leveling and proper treatment of long-range electrostatics in all-atom molecular dynamics at constant pH.

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.

Atomistic simulations of pH-dependent self-assembly of micelle and bilayer from fatty acids.

Detailed knowledge of the self-assembly and phase behavior of pH-sensitive surfactants has implications in areas such as targeted drug delivery. Here we present a study of the formation of micelle and bilayer from lauric acids using a state-of-the-art simulation technique, continuous constant pH molecular dynamics (CpHMD) with conformational sampling in explicit solvent and the pH-based replica-exchange protocol. We find that at high pH conditions a spherical micelle is formed, while at low pH conditions a bilayer is formed with a considerable degree of interdigitation. The mid-point of the phase transition is in good agreement with experiment. Preliminary investigation also reveals that the effect of counterions and salt screening shifts the transition mid-point and does not change the structure of the surfactant assembly. Based on these data we suggest that CpHMD simulations may be applied to computational design of surfactant-based nano devices in the future.

Toward accurate prediction of pKa values for internal protein residues: the importance of conformational relaxation and desolvation energy.

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.

Progress in the prediction of pKa values in proteins.

The pK(a) -cooperative aims to provide a forum for experimental and theoretical researchers interested in protein pK(a) values and protein electrostatics in general. The first round of the pK(a) -cooperative, which challenged computational labs to carry out blind predictions against pK(a) s experimentally determined in the laboratory of Bertrand Garcia-Moreno, was completed and results discussed at the Telluride meeting (July 6-10, 2009). This article serves as an introduction to the reports submitted by the blind prediction participants that will be published in a special issue of PROTEINS: Structure, Function and Bioinformatics. Here, we briefly outline existing approaches for pK(a) calculations, emphasizing methods that were used by the participants in calculating the blind pK(a) values in the first round of the cooperative. We then point out some of the difficulties encountered by the participating groups in making their blind predictions, and finally try to provide some insights for future developments aimed at improving the accuracy of pK(a) calculations.

Molecular dynamics simulations of ionic and nonionic surfactant micelles with a generalized Born implicit-solvent model.

In recent years, all-atom and coarse-grained models have been developed and applied to simulations of micelles and biological membranes. Here, we explore the question of whether a combined all-atom representation of surfactant molecules and continuum description of solvent based on the generalized Born model can be used to study surfactant micelles. Specifically, we report the parameterization of the GBSW model with a surface-area dependent nonpolar solvation energy term for dodecyl sulfate, dodecyl tetramethylammonium, and dodecyl triethyleneglycol ether molecules. In the parameterization procedure,the atomic Born radii were derived from the radial distribution functions of solvent charge and refined targeting the potential of mean force of dimer interactions from explicit-solvent simulations. The optimized radii were then applied in molecular dynamics simulations of the ionic and nonionic micelles.We found that the micelles are stable but more compact and rigid than in explicit solvent as a consequence of the drastic reduction in solvation and mobility of surfactant monomers within the micelle. Based on these data and our previous work, we suggest that in addition to a more accurate description of the nonpolar solvation energy, the ruggedness in the short-range interactions due to solvent granularity is a critical feature that needs to be taken into account to accurately model processes such as micelle formation and protein folding in implicit solvent. Finally, the explicit-solvent data presented here offers new insights into different conformational behavior of ionic and nonionic micelles which is valuable for understanding hydrophobic assemblies and of interest to the detergent industry.

Uncovering specific electrostatic interactions in the denatured states of proteins.

The stability and folding of proteins are modulated by energetically significant interactions in the denatured state that is in equilibrium with the native state. These interactions remain largely invisible to current experimental techniques, however, due to the sparse population and conformational heterogeneity of the denatured-state ensemble under folding conditions. Molecular dynamics simulations using physics-based force fields can in principle offer atomistic details of the denatured state. However, practical applications are plagued with the lack of rigorous means to validate microscopic information and deficiencies in force fields and solvent models. This study presents a method based on coupled titration and molecular dynamics sampling of the denatured state starting from the extended sequence under native conditions. The resulting denatured-state pK(a)s allow for the prediction of experimental observables such as pH- and mutation-induced stability changes. I show the capability and use of the method by investigating the electrostatic interactions in the denatured states of wild-type and K12M mutant of NTL9 protein. This study shows that the major errors in electrostatics can be identified by validating the titration properties of the fragment peptides derived from the sequence of the intact protein. Consistent with experimental evidence, our simulations show a significantly depressed pK(a) for Asp(8) in the denatured state of wild-type, which is due to a nonnative interaction between Asp(8) and Lys(12). Interestingly, the simulation also shows a nonnative interaction between Asp(8) and Glu(48) in the denatured state of the mutant. I believe the presented method is general and can be applied to extract and validate microscopic electrostatics of the entire folding energy landscape.

Probing the strand orientation and registry alignment in the propagation of amyloid fibrils.

Detailed knowledge of the structure and growth mechanism of amyloid fibrils is important for understanding the disease process. Recently, solid-state NMR and other spectroscopic data have revealed the equilibrium organization of the tertiary structure of fibrils formed by various segments of beta-amyloid peptides. A three-step "dock-and-lock" mechanism for fibril growth has been proposed on the basis of the kinetic data. Here we use all-atom replica-exchange molecular dynamics simulations in generalized-Born implicit solvent to probe the mechanism of tertiary structure propagation in fibrils of Abeta(16-22) modeled as an oligomer consisting of two beta-sheets each having four strands. The data show that following association with the oligomer, but before being fully locked onto the existing beta-sheet, the added monomer predominantly samples states with the antiparallel strand orientation, but both in- and one-residue shifted backbone hydrogen bond alignments. The in-register state, which is the experimentally observed equilibrium alignment, is marginally more stable than the registry-shifted one. These results suggest that, following the fast docking step, the added monomer dynamically slides in the backbone registry, and stabilization of the preferential alignment must occur in the second locking step as the monomer becomes fully integrated with the fibril. We also delineate the electrostatic and hydrophobic effects in directing the registry alignment during monomer addition. Surprisingly, the in-register alignment provides both increased cross-strand electrostatic attraction and hydrophobic surface burial. Finally, our data support the notion that side chain hydrophobic burial is a major driving force for beta-sheet assembly.

A method to determine residue-specific unfolded-state pKa values from analysis of stability changes in single mutant cycles.

It is now widely recognized that the unfolded state of a protein in equilibrium with the native state under folding conditions may contain significant residual structures. However, due to technical difficulties residue-specific interactions in the unfolded state remain elusive. Here we introduce a method derived from the Wyman-Tanford theory to determine residue-specific pK(a)'s in the unfolded state. This method requires equilibrium stability measurements of the wild type and single-point mutants in which titrable residues are replaced with charge-neutral ones under two pH conditions. Application of the proposed approach reveals a highly depressed pK(a) for Asp8 in the unfolded state of the NTL9 protein. Knowledge of unfolded-state pK(a)'s enables quantitative estimation of the unfolded-state electrostatic effects on protein stability. It also provides valuable benchmarks for the improvement of force fields and validation of microscopic information from molecular dynamics simulations.

Recent development and application of constant pH molecular dynamics.

Solution pH is a critical environmental factor for chemical and biological processes. Over the last decade, significant efforts have been made in the development of constant pH molecular dynamics (pHMD) techniques for gaining detailed insights into pH-coupled dynamical phenomena. In this article we review the advancement of this field in the past five years, placing a special emphasis on the development of the all-atom continuous pHMD technique. We discuss various applications, including the prediction of pKa shifts for proteins, nucleic acids and surfactant assemblies, elucidation of pH-dependent population shifts, protein-protein and protein-RNA binding, as well as the mechanisms of pH-dependent self-assembly and phase transitions of surfactants and peptides. We also discuss future directions for the further improvement of the pHMD techniques.

Mechanism of the pH-Controlled Self-Assembly of Nanofibers from Peptide Amphiphiles.

Stimuli-responsive, self-assembling nanomaterials hold a great promise to revolutionize medicine and technology. However, current discovery is slow and often serendipitous. Here we report a multiscale modeling study to elucidate the pH-controlled self-assembly of nanofibers from the peptide amphiphiles, palmitoyl-I-A3E4-NH2. The coarse-grained simulations revealed the formation of random-coil based spherical micelles at strong electrostatic repulsion. However, at weak or no electrostatic repulsion, the micelles merge into a nanofiber driven by the ß-sheet formation between the peptide segments. The all-atom constant pH molecular dynamics revealed a cooperative transition between random coil and ß-sheet in the pH range 6-7, matching the CD data. Interestingly, although the bulk pKa is more than one unit below the transition pH, consistent with the titration data, the highest pKa's coincide with the transition pH, suggesting that the latter may be tuned by modulating the pKa's of a few solvent-buried Glu side chains. Together, these data offer, to our best knowledge, the first multiresolution and quantitative view of the pH-dependent self-assembly of nanofibers. The novel protocols and insights gained are expected to advance the computer-aided design and discovery of pH-responsive nanomaterials.

Unraveling A Trap-and-Trigger Mechanism in the pH-Sensitive Self-Assembly of Spider Silk Proteins.

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.

Nucleotide Dynamics at the A-Site Cleft in the Peptidyltransferase Center of H. marismortui 50S Ribosomal Subunits.

Resistance mutations to antibiotics targeting rRNA can be far from the drug-binding site. Crystallography studies revealed that the antibiotic resistance mutation G2482A (G2447A in E. coli ) in Haloarcula marismortui 50S ribosomes does not directly contact the drug or introduce changes to the ribosomal structure except for losing a potassium ion coordinated to a base triple at the drug-binding site. Using molecular dynamics simulations, we tested hypotheses regarding the effects of the G2482A mutation and ion coordination on the conformational dynamics of the 50S ribosome. Simulations show that the mutation enhances conformational fluctuation at the antibiotic binding site, weakens the hydrogen-bonding network, and increases flexibility at the 50S peptidyl transferase center (PTC). Our data supports the view that distant mutations can perturb the dynamic network in the ribosomal PTC, thereby raising the entropic cost of antibiotic binding. These results underscore the importance of considering conformational dynamics in rational drug design.

Nitric oxide coupling mediated by iron porphyrins: the N-N bond formation step is facilitated by electrons and a proton.

The coupling of two NO molecules catalyzed by iron porphyrins is of biological importance. We use density functional theory calculations to examine the factors that control the fundamental N-N bond formation step mediated by a single iron porphyrin. The presence of an axial Im ligand, extra electrons, and most importantly a proton, enhance the N-N bond formation step in our model.

Continuous Constant pH Molecular Dynamics in Explicit Solvent with pH-Based Replica Exchange.

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.