Adaptive conformational sampling based on replicas

Computer simulations of biomolecules such as molecular dynamics simulations are limited by the time scale of conformational rearrangements. Several sampling techniques are available to search the multi-minima free energy landscape but most efficient, time-dependent methods do generally not produce a canonical ensemble. A sampling algorithm based on a self-regulating ladder of searching copies in the dihedral subspace is developped in this paper. The learning process using short- and long-term memory functions allows an efficient search in phase space while combining a deterministic dynamics and stochastic swaps with the searching copies conserves a canonical limit. The sampling efficiency and accuracy are indicated by comparing the ansatz with conventional molecular dynamics and replica exchange simulations.     

Proton transfer in carbonic anhydrase is controlled by electrostatics rather than the orientation of the acceptor

Combined quantum mechanical/molecular mechanical (QM/MM) simulations are carried out to analyze factors that dictate the proton transfer in carbonic anhydrase II (CAII), an enzyme that has been used as a prototypical example of long-range proton transfers in biomolecules. In contrast to the long-held conjecture in the experimental literature, the computed potentials of mean force (PMF) suggest that the proton transfer in CAII is not very sensitive to the orientation of the acceptor group (His 64) and, therefore, the number of water molecules that bridge the donor (zinc-water) and acceptor groups. Perturbative analysis indicates that a series of polar and charged residues close to the transfer pathways make the dominant contribution to the barrier and exothermicity of the proton transfer reaction, thus supporting the proposal from previous studies of Warshel and co-workers using a somewhat simpler QM/MM model that electrostatic interactions play a major role in the proton transfer in CAII. The PMF results are in striking contrast to previous analysis using the same QM/MM method but an ensemble of minimum energy path (MEP) calculations, which found a steep dependence of the barrier height on the number of bridging water molecules. Analysis of the configurations sampled in the PMF and MEP simulations suggests that this difference arises because the PMF simulations sample a largely stepwise mechanism while the local MEP calculations artificially favored concerted transfers due to the specific protocol used to generate the initial configurations. Therefore, this study presents a compelling argument for carrying out proper conformational sampling in the study of long-range proton transfers. Finally, we illustrate that Phi analysis, which has been widely used in protein folding studies, can potentially generate new mechanistic information for long-range proton transfers regarding the sequence of events. The results of the perturbation analysis and the Phi analysis provide opportunities for experimentally testing the mechanistic proposals from this study and our recent work in which a stepwise "proton hole" transfer pathway has been proposed.     

Interpretation of HDX Data by Maximum-Entropy Reweighting of Simulated Structural Ensembles

Hydrogen-deuterium exchange combined with mass spectrometry (HDX-MS) is a widely applied biophysical technique that probes the structure and dynamics of biomolecules without the need for site-directed modifications or bio-orthogonal labels. The mechanistic interpretation of HDX data, however, is often qualitative and subjective, owing to a lack of quantitative methods to rigorously translate observed deuteration levels into atomistic structural information. To help address this problem, we have developed a methodology to generate structural ensembles that faithfully reproduce HDX-MS measurements. In this approach, an ensemble of protein conformations is first generated, typically using molecular dynamics simulations. A maximum-entropy bias is then applied post hoc to the resulting ensemble such that averaged peptide-deuteration levels, as predicted by an empirical model, agree with target values within a given level of uncertainty. We evaluate this approach, referred to as HDX ensemble reweighting (HDXer), for artificial target data reflecting the two major conformational states of a binding protein. We demonstrate that the information provided by HDX-MS experiments and by the model of exchange are sufficient to recover correctly weighted structural ensembles from simulations, even when the relevant conformations are rarely observed. Degrading the information content of the target data—e.g., by reducing sequence coverage, by averaging exchange levels over longer peptide segments, or by incorporating different sources of uncertainty—reduces the structural accuracy of the reweighted ensemble but still allows for useful insights into the distinctive structural features reflected by the target data. Finally, we describe a quantitative metric to rank candidate structural ensembles according to their correspondence with target data and illustrate the use of HDXer to describe changes in the conformational ensemble of the membrane protein LeuT. In summary, HDXer is designed to facilitate objective structural interpretations of HDX-MS data and to inform experimental approaches and further developments of theoretical exchange models.     

Identification of potential small molecule binding pockets on Rho family GTPases

Rho GTPases are conformational switches that control a wide variety of signaling pathways critical for eukaryotic cell development and proliferation. They represent attractive targets for drug design as their aberrant function and deregulated activity is associated with many human diseases including cancer. Extensive high-resolution structures (>100) and recent mutagenesis studies have laid the foundation for the design of new structure-based chemotherapeutic strategies. Although the inhibition of Rho signaling with drug-like compounds is an active area of current research, very little attention has been devoted to directly inhibiting Rho by targeting potential allosteric non-nucleotide binding sites. By avoiding the nucleotide binding site, compounds may minimize the potential for undesirable off-target interactions with other ubiquitous GTP and ATP binding proteins. Here we describe the application of molecular dynamics simulations, principal component analysis, sequence conservation analysis, and ensemble small-molecule fragment mapping to provide an extensive mapping of potential small-molecule binding pockets on Rho family members. Characterized sites include novel pockets in the vicinity of the conformationaly responsive switch regions as well as distal sites that appear to be related to the conformations of the nucleotide binding region. Furthermore the use of accelerated molecular dynamics simulation, an advanced sampling method that extends the accessible time-scale of conventional simulations, is found to enhance the characterization of novel binding sites when conformational changes are important for the protein mechanism.     

Homogeneous and heterogeneous tertiary structure ensembles of amyloid-β peptides

The interplay of modern molecular simulation and high-quality nuclear magnetic resonance (NMR) experiments has reached a fruitful stage for quantitative characterization of structural ensembles of disordered peptides. Amyloid-β 1-42 (Aβ42), the primary peptide associated with Alzheimer's disease, and fragments such as Aβ21-30 are both classified as intrinsically disordered peptides (IDPs). We use a variety of NMR observables to validate de novo molecular dynamics simulations in explicit water to characterize the tertiary structure ensemble of Aβ42 and Aβ21-30 from the perspective of their classification as IDPs. Unlike the Aβ21-30 fragment that conforms to expectations of an IDP that is primarily extended, we find that Aβ42 samples conformations reflecting all possible secondary structure categories and spans the range of IDP classifications from collapsed structured states to highly extended conformations, making it an IDP with a far more heterogeneous tertiary ensemble.     

Experimental verification of lipid bilayer structure through multi-scale modeling

Great progress has been made in applying coarse-grain molecular dynamics (CGMD) simulations to the investigation of membrane biophysics. In order to validate the accuracy of CGMD simulations of membranes, atomistic scale detail is necessary for direct comparison to structural experiments. Here, we present our strategy for verifying CGMD lipid bilayer simulations. Through reverse coarse graining and subsequent calculation of the bilayer electron density profile, we are able to compare the simulations to our experimental low angle X-ray scattering (LAXS) data. In order to determine the best match to the experimental data, atomistic simulations are run at a range of areas (in the NP_NAT ensemble), starting from distinct configurations extracted from the CGMD simulation (run in the NPT ensemble). We demonstrate the effectiveness of this procedure with two small, single-component bilayers, and suggest that the greater utility of our algorithm will be for CGMD simulations of more complex structures.     

A coupling of homology modeling with multiple molecular dynamics simulation for identifying representative conformation of GPCR structures: a case study on human bombesin receptor subtype-3

In this study, a computational pipeline was therefore devised to overcome homology modeling (HM) bottlenecks. The coupling of HM with molecular dynamics (MD) simulation is useful in that it tackles the sampling deficiency of dynamics simulations by providing good-quality initial guesses for the native structure. Indeed, HM also relaxes the severe requirement of force fields to explore the huge conformational space of protein structures. In this study, the interaction between the human bombesin receptor subtype-3 and MK-5046 was investigated integrating HM, molecular docking, and MD simulations. To improve conformational sampling in typical MD simulations of GPCRs, as in other biomolecules, multiple trajectories with different initial conditions can be employed rather than a single long trajectory. Multiple MD simulations of human bombesin receptor subtype-3 with different initial atomic velocities are applied to sample conformations in the vicinity of the structure generated by HM. The backbone atom conformational space distribution of replicates is analyzed employing principal components analysis. As a result, the averages of structural and dynamic properties over the twenty-one trajectories differ significantly from those obtained from individual trajectories.     

Calculation and Visualization of Atomistic Mechanical Stresses in Nanomaterials and Biomolecules

Many biomolecules have machine-like functions, and accordingly are discussed in terms of mechanical properties like force and motion. However, the concept of stress, a mechanical property that is of fundamental importance in the study of macroscopic mechanics, is not commonly applied in the biomolecular context. We anticipate that microscopical stress analyses of biomolecules and nanomaterials will provide useful mechanistic insights and help guide molecular design. To enable such applications, we have developed Calculator of Atomistic Mechanical Stress (CAMS), an open-source software package for computing atomic resolution stresses from molecular dynamics (MD) simulations. The software also enables decomposition of stress into contributions from bonded, nonbonded and Generalized Born potential terms. CAMS reads GROMACS topology and trajectory files, which are easily generated from AMBER files as well; and time-varying stresses may be animated and visualized in the VMD viewer. Here, we review relevant theory and present illustrative applications.     

The Folding Transition-State Ensemble of a Four-Helix Bundle Protein: Helix Propensity as a Determinant and Macromolecular Crowding as a Probe

The four-helix bundle protein Rd-apocyt b₅₆₂, a redesigned stable variant of apocytochrome b₅₆₂, exhibits two-state folding kinetics. Its transition-state ensemble has been characterized by Φ-value analysis. To elucidate the molecular basis of the transition-state ensemble, we have carried out high-temperature molecular dynamics simulations of the unfolding process. In six parallel simulations, unfolding started with the melting of helix I and the C-terminal half of helix IV, and followed by helix III, the N-terminal half of helix IV and helix II. This ordered melting of the helices is consistent with the conclusion from native-state hydrogen exchange, and can be rationalized by differences in intrinsic helix propensity. Guided by experimental Φ-values, a putative transition-state ensemble was extracted from the simulations. The residue helical probabilities of this transition-state ensemble show good correlation with the Φ-values. To further validate the putative transition-state ensemble, the effect of macromolecular crowding on the relative stability between the unfolded ensemble and the transition-state ensemble was calculated. The resulting effect of crowding on the folding kinetics agrees well with experimental observations. This study shows that molecular dynamics simulations combined with calculation of crowding effects provide an avenue for characterize the transition-state ensemble in atomic details.     

A preformed binding interface in the unbound ensemble of an intrinsically disordered protein: evidence from molecular simulations

Intrinsically disordered proteins play an important role in cellular signalling, mediated by their interactions with other biomolecules. A key question concerns the nature of their binding mechanism, and whether the bound structure is induced only by proximity to the binding partner. This is difficult to answer through experiment alone because of the very heterogeneous nature of the unbound ensemble, and the probable rapid interconversion of the various unbound structures. Here we report the most extensive set of simulations on NCBD to date: we use large-scale replica exchange molecular dynamics to explore the unbound state. An important feature of the study is the use of an atomistic force field that has been parametrised against experimental data for weakly structured peptides, together with an accurate explicit water model. Neither the force field nor the starting conformations are biased towards a particular structure. The regions of NCBD that have high helical propensity in the simulations correspond closely to helices in the 'core' unbound conformation determined by NMR, although no single member of the simulated unbound ensemble closely resembles the core conformation, or either of the two known bound conformations. We have validated the results against NMR spectroscopy and SAXS measurements, obtaining reasonable agreement. The two helices which most stabilise the binding of NCBD with ACTR are formed readily; the third helix, which is less important for binding but is involved in most of the intraprotein contacts of NCBD in the bound conformation, is formed more rarely, and tends not to coexist with the other helices. These results support a mechanism by which NCBD gains the advantages of disorder, while forming binding-competent structures in the unbound state. We obtain support for this mechanism from coarse-grained simulations of NCBD with, and without, its binding partner.     

Computation of elastic constants of solids using molecular simulation: comparison of constant volume and constant pressure ensemble methods

We compute the elastic stiffness tensor of fcc argon at 60 K and 1 bar using molecular simulation tools. Three different methods are investigated: explicit deformations of the simulation box, strain fluctuations at constant pressure and stress fluctuations at constant volume. Statistical ensemble sampling is done using molecular dynamics and Monte Carlo simulations. We observe a good agreement between the different methods and sampling algorithms excepted with molecular dynamics simulations in the (NpT) ensemble. There, we notice a strong dependence of the computed elastic constants with the barostat parameter, whereas molecular dynamics simulations in the (NVT) ensemble are not affected by the thermostat parameter.     

Structural Characterization of N-WASP Domain V Using MD Simulations with NMR and SAXS Data

Because of their large conformational heterogeneity, structural characterization of intrinsically disordered proteins (IDPs) is very challenging using classical experimental methods alone. In this study, we use NMR and small-angle x-ray scattering (SAXS) data with multiple molecular dynamics (MD) simulations to describe the conformational ensemble of the fully disordered verprolin homology domain of the neural Aldrich syndrome protein involved in the regulation of actin polymerization. First, we studied several back-calculation software of SAXS scattering intensity and optimized the adjustable parameters to accurately calculate the SAXS intensity from an atomic structure. We also identified the most appropriate force fields for MD simulations of this IDP. Then, we analyzed four conformational ensembles of neural Aldrich syndrome protein verprolin homology domain, two generated with the program flexible-meccano with or without NMR-derived information as input and two others generated by MD simulations with two different force fields. These four conformational ensembles were compared to available NMR and SAXS data for validation. We found that MD simulations with the AMBER-03w force field and the TIP4P/2005s water model are able to correctly describe the conformational ensemble of this 67-residue IDP at both local and global level.     

Open-Boundary Molecular Dynamics of a DNA Molecule in a Hybrid Explicit/Implicit Salt Solution

The composition and electrolyte concentration of the aqueous bathing environment have important consequences for many biological processes and can profoundly affect the behavior of biomolecules. Nevertheless, because of computational limitations, many molecular simulations of biophysical systems can be performed only at specific ionic conditions: either at nominally zero salt concentration, i.e., including only counterions enforcing the system’s electroneutrality, or at excessive salt concentrations. Here, we introduce an efficient molecular dynamics simulation approach for an atomistic DNA molecule at realistic physiological ionic conditions. The simulations are performed by employing the open-boundary molecular dynamics method that allows for simulation of open systems that can exchange mass and linear momentum with the environment. In our open-boundary molecular dynamics approach, the computational burden is drastically alleviated by embedding the DNA molecule in a mixed explicit/implicit salt-bathing solution. In the explicit domain, the water molecules and ions are both overtly present in the system, whereas in the implicit water domain, only the ions are explicitly present and the water is described as a continuous dielectric medium. Water molecules are inserted and deleted into/from the system in the intermediate buffer domain that acts as a water reservoir to the explicit domain, with both water molecules and ions free to enter or leave the explicit domain. Our approach is general and allows for efficient molecular simulations of biomolecules solvated in bathing salt solutions at any ionic strength condition.     

Membrane-bound KRAS approximates an entropic ensemble of configurations

KRAS4B is a membrane-anchored signaling protein and a primary target in cancer research. Predictions from molecular dynamics simulations that have previously shaped our mechanistic understanding of KRAS signaling disagree with recent experimental results from neutron reflectometry, NMR, and thermodynamic binding studies. To gain insight into these discrepancies, we compare this body of biophysical data to back-calculated experimental results from a series of molecular simulations that implement different subsets of molecular interactions. Our results show that KRAS4B approximates an entropic ensemble of configurations at model membranes containing 30% phosphatidylserine lipids, which is not significantly shaped by interactions between the globular G-domain of KRAS4B and the lipid membrane. These findings revise our understanding of KRAS signaling and promote a model in which the protein samples the accessible conformational space in a near-uniform manner while being available to bind to effector proteins.     

Solid-State NMR-Restrained Ensemble Dynamics of a Membrane Protein in Explicit Membranes

Solid-state NMR has been used to determine the structures of membrane proteins in native-like lipid bilayer environments. Most structure calculations based on solid-state NMR observables are performed using simulated annealing with restrained molecular dynamics and an energy function, where all nonbonded interactions are represented by a single, purely repulsive term with no contributions from van der Waals attractive, electrostatic, or solvation energy. To our knowledge, this is the first application of an ensemble dynamics technique performed in explicit membranes that uses experimental solid-state NMR observables to obtain the refined structure of a membrane protein together with information about its dynamics and its interactions with lipids. Using the membrane-bound form of the fd coat protein as a model membrane protein and its experimental solid-state NMR data, we performed restrained ensemble dynamics simulations with different ensemble sizes in explicit membranes. For comparison, a molecular dynamics simulation of fd coat protein was also performed without any restraints. The average orientation of each protein helix is similar to a structure determined by traditional single-conformer approaches. However, their variations are limited in the resulting ensemble of structures with one or two replicas, as they are under the strong influence of solid-state NMR restraints. Although highly consistent with all solid-state NMR observables, the ensembles of more than two replicas show larger orientational variations similar to those observed in the molecular dynamics simulation without restraints. In particular, in these explicit membrane simulations, Lys⁴⁰, residing at the C-terminal side of the transmembrane helix, is observed to cause local membrane curvature. Therefore, compared to traditional single-conformer approaches in implicit environments, solid-state NMR restrained ensemble simulations in explicit membranes readily characterize not only protein dynamics but also protein-lipid interactions in detail.     

Highly Disordered Amyloid-β Monomer Probed by Single-Molecule FRET and MD Simulation

Monomers of amyloid-β (Aβ) protein are known to be disordered, but there is considerable controversy over the existence of residual or transient conformations that can potentially promote oligomerization and fibril formation. We employed single-molecule Förster resonance energy transfer (FRET) spectroscopy with site-specific dye labeling using an unnatural amino acid and molecular dynamics simulations to investigate conformations and dynamics of Aβ isoforms with 40 (Aβ40) and 42 residues (Aβ42). The FRET efficiency distributions of both proteins measured in phosphate-buffered saline at room temperature show a single peak with very similar FRET efficiencies, indicating there is apparently only one state. 2D FRET efficiency-donor lifetime analysis reveals, however, that there is a broad distribution of rapidly interconverting conformations. Using nanosecond fluorescence correlation spectroscopy, we measured the timescale of the fluctuations between these conformations to be ～35 ns, similar to that of disordered proteins. These results suggest that both Aβ40 and Aβ42 populate an ensemble of rapidly reconfiguring unfolded states, with no long-lived conformational state distinguishable from that of the disordered ensemble. To gain molecular-level insights into these observations, we performed molecular dynamics simulations with a force field optimized to describe disordered proteins. We find, as in experiments, that both peptides populate configurations consistent with random polymer chains, with the vast majority of conformations lacking significant secondary structure, giving rise to very similar ensemble-averaged FRET efficiencies.