Efficient sampling of puckering states of monosaccharides through replica exchange with solute tempering and bond softening

A molecular-level understanding of the structure, dynamics, and reactivity of carbohydrates is fundamental to the understanding of a range of key biological processes. The six-membered pyranose ring, a central component of biological monosaccharides and carbohydrates, has many different puckering conformations, and the conformational free energy landscape of these biologically important monosaccharides remains elusive. The puckering conformations of monosaccharides are separated by high energy barriers, which pose a great challenge for the complete sampling of these important conformations and accurate modeling of these systems. While metadynamics or umbrella sampling methods have been used to study the conformational space of monosaccharides, these methods might be difficult to generalize to other complex ring systems with more degrees of freedom. In this paper, we introduce a new enhanced sampling method for the rapid sampling over high energy barriers that combines our previously developed enhanced sampling method REST (replica exchange with solute tempering) with a bond softening (BOS) scheme that makes a chemical bond in the ring weaker as one ascends the replica ladder. We call this new method replica exchange with solute tempering and bond softening (REST/BOS). We demonstrate the superior sampling efficiency of REST/BOS over other commonly used enhanced sampling methods, including temperature replica exchange method and REST. The conformational free energy landscape of four biologically important monosaccharides, namely, α-glucose, β-glucose, β-mannose, and β-xylose, is studied using REST/BOS, and results are compared with previous experimental and theoretical studies.

Predicting reaction coordinates in energy landscapes with diffusion anisotropy

We consider a range of model potentials with metastable states undergoing molecular dynamics coupled to a thermal bath in the high friction regime and consider how the optimal reaction coordinate depends on the diffusion anisotropy. For this we use our recently proposed method "spectral gap optimization of order parameters (SGOOP)" [P. Tiwary and B. J. Berne, Proc. Natl. Acad. Sci. U. S. A. 113, 2839 (2016)]. We show how available information about dynamical observables in addition to static information can be incorporated into SGOOP, which can then be used to accurately determine the "best" reaction coordinate for arbitrary anisotropies. We compare our results with transmission coefficient calculations and published benchmarks wherever applicable or available, respectively.

Simulated Force Quench Dynamics Shows GB1 Protein Is Not a Two State Folder

Single molecule force spectroscopy is a useful technique for investigating mechanically induced protein unfolding and refolding under reduced forces by monitoring the end-to-end distance of the protein. The data is often interpreted via a "two-state" model based on the assumption that the end-to-end distance alone is a good reaction coordinate and the thermodynamic behavior is then ascribed to the free energy as a function of this one reaction coordinate. In this paper, we determined the free energy surface (PMF) of GB1 protein from atomistic simulations in explicit solvent under different applied forces as a function of two collective variables (the end-to-end-distance, and the fraction of native contacts ρ). The calculated 2-d free energy surfaces exhibited several distinct states, or basins, mostly visible along the ρ coordinate. Brownian dynamics (BD) simulations on the smoothed free energy surface show that the protein visits a metastable molten globule state and is thus a three state folder, not the two state folder inferred using the end-to-end distance as the sole reaction coordinate. This study lends support to recent experiments that suggest that GB1 is not a two-state folder.

How wet should be the reaction coordinate for ligand unbinding?

We use a recently proposed method called Spectral Gap Optimization of Order Parameters (SGOOP) [P. Tiwary and B. J. Berne, Proc. Natl. Acad. Sci. U. S. A. 113, 2839 (2016)], to determine an optimal 1-dimensional reaction coordinate (RC) for the unbinding of a bucky-ball from a pocket in explicit water. This RC is estimated as a linear combination of the multiple available order parameters that collectively can be used to distinguish the various stable states relevant for unbinding. We pay special attention to determining and quantifying the degree to which water molecules should be included in the RC. Using SGOOP with under-sampled biased simulations, we predict that water plays a distinct role in the reaction coordinate for unbinding in the case when the ligand is sterically constrained to move along an axis of symmetry. This prediction is validated through extensive calculations of the unbinding times through metadynamics and by comparison through detailed balance with unbiased molecular dynamics estimate of the binding time. However when the steric constraint is removed, we find that the role of water in the reaction coordinate diminishes. Here instead SGOOP identifies a good one-dimensional RC involving various motional degrees of freedom.

Kramers turnover: From energy diffusion to spatial diffusion using metadynamics

We consider the rate of transition for a particle between two metastable states coupled to a thermal environment for various magnitudes of the coupling strength using the recently proposed infrequent metadynamics approach [P. Tiwary and M. Parrinello, Phys. Rev. Lett. 111, 230602 (2013)]. We are interested in understanding how this approach for obtaining rate constants performs as the dynamics regime changes from energy diffusion to spatial diffusion. Reassuringly, we find that the approach works remarkably well for various coupling strengths in the strong coupling regime, and to some extent even in the weak coupling regime.

Nitriles at Silica Interfaces Resemble Supported Lipid Bilayers

Nitriles are important solvents not just for bulk reactions but also for interfacial processes such as separations, heterogeneous catalysis, and electrochemistry. Although nitriles have a polar end and a lipophilic end, the cyano group is not hydrophilic enough for these substances to be thought of as prototypical amphiphiles. This picture is now changing, as research is revealing that at a silica surface nitriles can organize into structures that, in many ways, resemble lipid bilayers. This unexpected organization may be a key component of unique interfacial behavior of nitriles that make them the solvents of choice for so many applications. The first hints of this lipid-bilayer-like (LBL) organization of nitriles at silica interfaces came from optical Kerr effect (OKE) experiments on liquid acetonitrile confined in the pores of sol-gel glasses. The orientational dynamics revealed by OKE spectroscopy suggested that the confined liquid is composed of a relatively immobile sublayer of molecules that accept hydrogen bonds from the surface silanol groups and an interdigitated, antiparallel layer that is capable of exchanging into the centers of the pores. This picture of acetonitrile has been borne out by molecular dynamics simulations and vibrational sum-frequency generation (VSFG) experiments. Remarkably, these simulations further indicate that the LBL organization is repeated with increasing disorder at least 20 Å into the liquid from a flat silica surface. Simulations and VSFG and OKE experiments indicate that extending the alkyl chain to an ethyl group leads to the formation of even more tightly packed LBL organization featuring entangled alkyl tails. When the alkyl portion of the molecule is a bulky t-butyl group, packing constraints prevent well-ordered LBL organization of the liquid. In each case, the surface-induced organization of the liquid is reflected in its interfacial dynamics. Acetonitrile/water mixtures are favored solvent systems for separations technologies such as hydrophilic interaction chromatography. Simulations had suggested that although a monolayer of water partitions to the silica surface in such mixtures, acetonitrile tends to associate with this monolayer. VSFG experiments reveal that, even at high water mole fractions, patches of well-ordered acetonitrile bilayers remain at the silica surface. Due to its ability to donate and accept hydrogen bonds, methanol also partitions to a silica surface in acetonitrile/methanol mixtures and can serve to take the place of acetonitrile in the sublayer closest to the surface. These studies reveal that liquid nitriles can exhibit an unexpected wealth of new organizational and dynamic behaviors at silica surfaces, and presumably at the surfaces of other chemically important materials as well. This behavior cannot be predicted from the bulk organization of these liquids. Our new understanding of the interfacial behavior of these liquids will have important implications for optimizing a wide range of chemical processes in nitrile solvents.

Prediction of Protein-Ligand Binding Poses via a Combination of Induced Fit Docking and Metadynamics Simulations

Ligand docking is a widely used tool for lead discovery and binding mode prediction based drug discovery. The greatest challenges in docking occur when the receptor significantly reorganizes upon small molecule binding, thereby requiring an induced fit docking (IFD) approach in which the receptor is allowed to move in order to bind to the ligand optimally. IFD methods have had some success but suffer from a lack of reliability. Complementing IFD with all-atom molecular dynamics (MD) is a straightforward solution in principle but not in practice due to the severe time scale limitations of MD. Here we introduce a metadynamics plus IFD strategy for accurate and reliable prediction of the structures of protein-ligand complexes at a practically useful computational cost. Our strategy allows treating this problem in full atomistic detail and in a computationally efficient manner and enhances the predictive power of IFD methods. We significantly increase the accuracy of the underlying IFD protocol across a large data set comprising 42 different ligand-receptor systems. We expect this approach to be of significant value in computationally driven drug design.

Accurate and reliable prediction of relative ligand binding potency in prospective drug discovery by way of a modern free-energy calculation protocol and force field

Designing tight-binding ligands is a primary objective of small-molecule drug discovery. Over the past few decades, free-energy calculations have benefited from improved force fields and sampling algorithms, as well as the advent of low-cost parallel computing. However, it has proven to be challenging to reliably achieve the level of accuracy that would be needed to guide lead optimization (∼5× in binding affinity) for a wide range of ligands and protein targets. Not surprisingly, widespread commercial application of free-energy simulations has been limited due to the lack of large-scale validation coupled with the technical challenges traditionally associated with running these types of calculations. Here, we report an approach that achieves an unprecedented level of accuracy across a broad range of target classes and ligands, with retrospective results encompassing 200 ligands and a wide variety of chemical perturbations, many of which involve significant changes in ligand chemical structures. In addition, we have applied the method in prospective drug discovery projects and found a significant improvement in the quality of the compounds synthesized that have been predicted to be potent. Compounds predicted to be potent by this approach have a substantial reduction in false positives relative to compounds synthesized on the basis of other computational or medicinal chemistry approaches. Furthermore, the results are consistent with those obtained from our retrospective studies, demonstrating the robustness and broad range of applicability of this approach, which can be used to drive decisions in lead optimization.

Role of Desolvation in Thermodynamics and Kinetics of Ligand Binding to a Kinase

Computer simulations are used to determine the free energy landscape for the binding of the anticancer drug Dasatinib to its src kinase receptor and show that before settling into a free energy basin the ligand must surmount a free energy barrier. An analysis based on using both the ligand-pocket separation and the pocket-water occupancy as reaction coordinates shows that the free energy barrier is a result of the free energy cost for almost complete desolvation of the binding pocket. The simulations further show that the barrier is not a result of the reorganization free energy of the binding pocket. Although a continuum solvent model gives the location of free energy minima, it is not able to reproduce the intermediate free energy barrier. Finally, it is shown that a kinetic model for the on rate constant in which the ligand diffuses up to a doorway state and then surmounts the desolvation free energy barrier is consistent with published microsecond time-scale simulations of the ligand binding kinetics for this system [Shaw, D. E. et al. J. Am. Chem. Soc.2011, 133, 9181−918321545110].

When does trimethylamine N-oxide fold a polymer chain and urea unfold it?

Longstanding mechanistic questions about the role of protecting osmolyte trimethylamine N-oxide (TMAO) that favors protein folding and the denaturing osmolyte urea are addressed by studying their effects on the folding of uncharged polymer chains. Using atomistic molecular dynamics simulations, we show that 1 M TMAO and 7 M urea solutions act dramatically differently on these model polymer chains. Their behaviors are sensitive to the strength of the attractive dispersion interactions of the chain with its environment: when these dispersion interactions are sufficiently strong, TMAO suppresses the formation of extended conformations of the hydrophobic polymer as compared to water while urea promotes the formation of extended conformations. Similar trends are observed experimentally for real protein systems. Quite surprisingly, we find that both protecting and denaturing osmolytes strongly interact with the polymer, seemingly in contrast with existing explanations of the osmolyte effect on proteins. We show that what really matters for a protective osmolyte is its effective depletion as the polymer conformation changes, which leads to a negative change in the preferential binding coefficient. For TMAO, there is a much more favorable free energy of insertion of a single osmolyte near collapsed conformations of the polymer than near extended conformations. By contrast, urea is preferentially stabilized next to the extended conformation and thus has a denaturing effect.

Are hydrodynamic interactions important in the kinetics of hydrophobic collapse?

We study the kinetics of assembly of two plates of varying hydrophobicity, including cases where drying occurs and water strongly solvates the plate surfaces. The potential of mean force and molecular-scale hydrodynamics are computed from molecular dynamics simulations in explicit solvent as a function of particle separation. In agreement with our recent work on nanospheres [J. Phys. Chem. B 2012,116, 378-389], regions of high friction are found to be engendered by large and slow solvent fluctuations. These slow fluctuations can be due to either drying or confinement. The mean first passage times for assembly are computed by means of molecular dynamics simulations in explicit solvent and by Brownian dynamics simulations along the reaction path. Brownian dynamics makes use of the potential of mean force and hydrodynamic profile that we determined. Surprisingly, we find reasonable agreement between full-scale molecular dynamics and Brownian dynamics, despite the role of slow solvent relaxation in the assembly process. We found that molecular-scale hydrodynamic interactions are essential in describing the kinetics of assembly.

Replica exchange with solute scaling: a more efficient version of replica exchange with solute tempering (REST2)

A small change in the Hamiltonian scaling in Replica Exchange with Solute Tempering (REST) is found to improve its sampling efficiency greatly, especially for the sampling of aqueous protein solutions in which there are large-scale solute conformation changes. Like the original REST (REST1), the new version (which we call REST2) also bypasses the poor scaling with system size of the standard Temperature Replica Exchange Method (TREM), reducing the number of replicas (parallel processes) from what must be used in TREM. This reduction is accomplished by deforming the Hamiltonian function for each replica in such a way that the acceptance probability for the exchange of replica configurations does not depend on the number of explicit water molecules in the system. For proof of concept, REST2 is compared with TREM and with REST1 for the folding of the trpcage and β-hairpin in water. The comparisons confirm that REST2 greatly reduces the number of CPUs required by regular replica exchange and greatly increases the sampling efficiency over REST1. This method reduces the CPU time required for calculating thermodynamic averages and for the ab initio folding of proteins in explicit water.

First passage time distribution in stochastic processes with moving and static absorbing boundaries with application to biological rupture experiments

We develop and investigate an integral equation connecting the first passage time distribution of a stochastic process in the presence of an absorbing boundary condition and the corresponding Green's function in the absence of the absorbing boundary. Analytical solutions to the integral equations are obtained for three diffusion processes in time-independent potentials which have been previously investigated by other methods. The integral equation provides an alternative way to analytically solve the three diffusion-controlled reactive processes. In order to help analyze biological rupture experiments, we further investigate the numerical solutions of the integral equation for a diffusion process in a time-dependent potential. Our numerical procedure, based on the exact integral equation, avoids the adiabatic approximation used in previous analytical theories and is useful for fitting the rupture force distribution data from single-molecule pulling experiments or molecular dynamics simulation data, especially at larger pulling speeds, larger cantilever spring constants, and smaller reaction rates. Stochastic simulation results confirm the validity of our numerical procedure. We suggest combining a previous analytical theory with our integral equation approach to analyze the kinetics of force induced rupture of biomacromolecules.

A displaced-solvent functional analysis of model hydrophobic enclosures

Calculation of protein-ligand binding affinities continues to be a hotbed of research. Although many techniques for computing protein-ligand binding affinities have been introduced--ranging from computationally very expensive approaches, such as free energy perturbation (FEP) theory; to more approximate techniques, such as empirically derived scoring functions, which, although computationally efficient, lack a clear theoretical basis--there remains pressing need for more robust approaches. A recently introduced technique, the displaced-solvent functional (DSF) method, was developed to bridge the gap between the high accuracy of FEP and the computational efficiency of empirically derived scoring functions. In order to develop a set of reference data to test the DSF theory for calculating absolute protein-ligand binding affinities, we have pursued FEP theory calculations of the binding free energies of a methane ligand with 13 different model hydrophobic enclosures of varying hydrophobicity. The binding free energies of the methane ligand with the various hydrophobic enclosures were then recomputed by DSF theory and compared with the FEP reference data. We find that the DSF theory, which relies on no empirically tuned parameters, shows excellent quantitative agreement with the FEP. We also explored the ability of buried solvent accessible surface area and buried molecular surface area models to describe the relevant physics, and find the buried molecular surface area model to offer superior performance over this dataset.

Dewetting transitions in protein cavities

In a previous analysis of the solvation of protein active sites, a drying transition was observed in the narrow hydrophobic binding cavity of Cox-2. With the use of a crude metric that often seems able to discriminate those protein cavities that dry from those that do not, we made an extensive search of the PDB, and identified five other proteins that, in molecular dynamics simulations, undergo drying transitions in their active sites. Because such cavities need not desolvate before binding hydrophobic ligands they often exhibit very large binding affinities. This article gives evidence that drying in protein cavities is not unique to Cox-2.

Competition of electrostatic and hydrophobic interactions between small hydrophobes and model enclosures

The binding affinity between a probe hydrophobic particle and model hydrophobic plates with different charge (or dipole) densities in water was investigated through molecular dynamics simulation free-energy perturbation calculations. We observed a reduced binding affinity when the plates are charged, in agreement with previous findings. With increased charge density, the plates can change from "hydrophobic like" (pulling the particle into the interplate region) to "hydrophilic like" (ejecting the particle out of the interplate region), demonstrating the competition between hydrophobic and electrostatic interactions. The reduction of the binding affinity is quadratically dependent on the magnitude of the charge for symmetric systems, but linear and cubic terms also make a contribution for asymmetric systems. Statistical perturbation theory explains these results and shows when and why implicit solvent models fail.

Hydrophobic interactions in model enclosures from small to large length scales: non-additivity in explicit and implicit solvent models

The binding affinities between a united-atom methane and various model hydrophobic enclosures were studied through high accuracy free energy perturbation methods (FEP). We investigated the non-additivity of the hydrophobic interaction in these systems, measured by the deviation of its binding affinity from that predicted by the pairwise additivity approximation. While only small non-additivity effects were previously reported in the interactions in methane trimers, we found large cooperative effects (as large as -1.14 kcal mol(-1) or approximately a 25% increase in the binding affinity) and anti-cooperative effects (as large as 0.45 kcal mol(-1)) for these model enclosed systems. Decomposition of the total potential of mean force (PMF) into increasing orders of multi-body interactions indicates that the contributions of the higher order multi-body interactions can be either positive or negative in different systems, and increasing the order of multi-body interactions considered did not necessarily improve the accuracy. A general correlation between the sign of the non-additivity effect and the curvature of the solute molecular surface was observed. We found that implicit solvent models based on the molecular surface area (MSA) performed much better, not only in predicting binding affinities, but also in predicting the non-additivity effects, compared with models based on the solvent accessible surface area (SASA), suggesting that MSA is a better descriptor of the curvature of the solutes. We also show how the non-additivity contribution changes as the hydrophobicity of the plate is decreased from the dewetting regime to the wetting regime.

Diversity of chemical mechanisms in thioredoxin catalysis revealed by single-molecule force spectroscopy

Thioredoxins (Trxs) are oxidoreductase enzymes, present in all organisms, that catalyze the reduction of disulfide bonds in proteins. By applying a calibrated force to a substrate disulfide, the chemical mechanisms of Trx catalysis can be examined in detail at the single-molecule level. Here we use single-molecule force-clamp spectroscopy to explore the chemical evolution of Trx catalysis by probing the chemistry of eight different Trx enzymes. All Trxs show a characteristic Michaelis-Menten mechanism that is detected when the disulfide bond is stretched at low forces, but at high forces, two different chemical behaviors distinguish bacterial-origin from eukaryotic-origin Trxs. Eukaryotic-origin Trxs reduce disulfide bonds through a single-electron transfer reaction (SET), whereas bacterial-origin Trxs show both nucleophilic substitution (S(N)2) and SET reactions. A computational analysis of Trx structures identifies the evolution of the binding groove as an important factor controlling the chemistry of Trx catalysis.

Dewetting and hydrophobic interaction in physical and biological systems

Hydrophobicity manifests itself differently on large and small length scales. This review focuses on large-length-scale hydrophobicity, particularly on dewetting at single hydrophobic surfaces and drying in regions bounded on two or more sides by hydrophobic surfaces. We review applicable theories, simulations, and experiments pertaining to large-scale hydrophobicity in physical and biomolecular systems and clarify some of the critical issues pertaining to this subject. Given space constraints, we cannot review all the significant and interesting work in this active field.

Thermodynamic properties of liquid water: an application of a nonparametric approach to computing the entropy of a neat fluid

Due to its fundamental importance to molecular biology, great interest has continued to persist in developing novel techniques to efficiently characterize the thermodynamic and structural features of liquid water. A particularly fruitful approach, first applied to liquid water by Lazaridis and Karplus, is to use molecular dynamics or Monte Carlo simulations to collect the required statistics to integrate the inhomogeneous solvation theory equations for the solvation enthalpy and entropy. We here suggest several technical improvements to this approach, which may facilitate faster convergence and greater accuracy. In particular, we devise a nonparametric k'th nearest neighbors (NN) based approach to estimate the water-water correlation entropy, and suggest an alternative factorization of the water-water correlation function that appears to more robustly describe the correlation entropy of the neat fluid. It appears that the NN method offers several advantages over the more common histogram based approaches, including much faster convergence for a given amount of simulation data; an intuitive error bound that may be readily formulated without resorting to block averaging or bootstrapping; and the absence of empirically tuned parameters, which may bias the results in an uncontrolled fashion.

Scanning tunneling microscopy images of alkane derivatives on graphite: role of electronic effects

Scanning tunneling microscopy (STM) images of self-assembled monolayers of close-packed alkane chains on highly oriented pyrolitic graphite often display an alternating bright and dark spot pattern. Classical simulations suggest that a tilt of the alkane backbone is unstable and, therefore, unlikely to account for the contrast variation. First principles calculations based on density functional theory show that an electronic effect can explain the observed alternation. Furthermore, the asymmetric spot pattern associated with the minimum energy alignment is modulated depending on the registry of the alkane adsorbate relative to the graphite surface, explaining the characteristic moiré pattern that is often observed in STM images with close packed alkyl assemblies.

Role of water in mediating the assembly of Alzheimer amyloid-beta Abeta16-22 protofilaments

The role of water in promoting the formation of protofilaments (the basic building blocks of amyloid fibrils) is investigated using fully atomic molecular dynamics simulations. Our model protofilament consists of two parallel beta-sheets of Alzheimer Amyloid-beta 16-22 peptides (Ac-K(16)-L(17)-V(18)-F(19)-F(20)-A(21)-E(22)-NH2). Each sheet presents a distinct hydrophobic and hydrophilic face and together self-assemble to a stable protofilament with a core consisting of purely hydrophobic residues (L(17), F(19), A(21)), with the two charged residues (K(16), E(22)) pointing to the solvent. Our simulations reveal a subtle interplay between a water mediated assembly and one driven by favorable energetic interactions between specific residues forming the interior of the protofilament. A dewetting transition, in which water expulsion precedes hydrophobic collapse, is observed for some, but not all molecular dynamics trajectories. In the trajectories in which no dewetting is observed, water expulsion and hydrophobic collapse occur simultaneously, with protofilament assembly driven by direct interactions between the hydrophobic side chains of the peptides (particularly between F-F residues). For those same trajectories, a small increase in the temperature of the simulation (on the order of 20 K) or a modest reduction in the peptide-water van der Waals attraction (on the order of 10%) is sufficient to induce a dewetting transition, suggesting that the existence of a dewetting transition in simulation might be sensitive to the details of the force field parametrization.

Role of the active-site solvent in the thermodynamics of factor Xa ligand binding

Understanding the underlying physics of the binding of small-molecule ligands to protein active sites is a key objective of computational chemistry and biology. It is widely believed that displacement of water molecules from the active site by the ligand is a principal (if not the dominant) source of binding free energy. Although continuum theories of hydration are routinely used to describe the contributions of the solvent to the binding affinity of the complex, it is still an unsettled question as to whether or not these continuum solvation theories describe the underlying molecular physics with sufficient accuracy to reliably rank the binding affinities of a set of ligands for a given protein. Here we develop a novel, computationally efficient descriptor of the contribution of the solvent to the binding free energy of a small molecule and its associated receptor that captures the effects of the ligand displacing the solvent from the protein active site with atomic detail. This descriptor quantitatively predicts (R(2) = 0.81) the binding free energy differences between congeneric ligand pairs for the test system factor Xa, elucidates physical properties of the active-site solvent that appear to be missing in most continuum theories of hydration, and identifies several features of the hydration of the factor Xa active site relevant to the structure-activity relationship of its inhibitors.

Probing the chemistry of thioredoxin catalysis with force

Thioredoxins are enzymes that catalyse disulphide bond reduction in all living organisms. Although catalysis is thought to proceed through a substitution nucleophilic bimolecular (S(N)2) reaction, the role of the enzyme in modulating this chemical reaction is unknown. Here, using single-molecule force-clamp spectroscopy, we investigate the catalytic mechanism of Escherichia coli thioredoxin (Trx). We applied mechanical force in the range of 25-600 pN to a disulphide bond substrate and monitored the reduction of these bonds by individual enzymes. We detected two alternative forms of the catalytic reaction, the first requiring a reorientation of the substrate disulphide bond, causing a shortening of the substrate polypeptide by 0.79 +/- 0.09 A (+/- s.e.m.), and the second elongating the substrate disulphide bond by 0.17 +/- 0.02 A (+/- s.e.m.). These results support the view that the Trx active site regulates the geometry of the participating sulphur atoms with sub-ångström precision to achieve efficient catalysis. Our results indicate that substrate conformational changes may be important in the regulation of Trx activity under conditions of oxidative stress and mechanical injury, such as those experienced in cardiovascular disease. Furthermore, single-molecule atomic force microscopy techniques, as shown here, can probe dynamic rearrangements within an enzyme's active site during catalysis that cannot be resolved with any other current structural biological technique.

Hydrophobic aided replica exchange: an efficient algorithm for protein folding in explicit solvent

A hydrophobic aided replica exchange method (HAREM) is introduced to accelerate the simulation of all-atom protein folding in explicit solvent. This method is based on exaggerating the hydrophobic effect of various protein amino acids in water by attenuating the protein-water attractive interactions (mimicking the Chaperon effect) while leaving other interactions among protein atoms and water molecules unchanged. The method is applied to a small representative protein, the alpha-helix 3K(I), and it is found that the HAREM method successfully folds the protein within 4 ns, while the regular replica exchange method does not fold the same protein within 5 ns, even with many more replicas.

Nanoscale dewetting transition in protein complex folding

In a previous study, a surprising drying transition was observed to take place inside the nanoscale hydrophobic channel in the tetramer of the protein melittin. The goal of this paper is to determine if there are other protein complexes capable of displaying a dewetting transition during their final stage of folding. We searched the entire protein data bank (PDB) for all possible candidates, including protein tetramers, dimers, and two-domain proteins, and then performed the molecular dynamics (MD) simulations on the top candidates identified by a simple hydrophobic scoring function based on aligned hydrophobic surface areas. Our large scale MD simulations found several more proteins, including three tetramers, six dimers, and two two-domain proteins, which display a nanoscale dewetting transition in their final stage of folding. Even though the scoring function alone is not sufficient (i.e., a high score is necessary but not sufficient) in identifying the dewetting candidates, it does provide useful insights into the features of complex interfaces needed for dewetting. All top candidates have two features in common: (1) large aligned (matched) hydrophobic areas between two corresponding surfaces, and (2) large connected hydrophobic areas on the same surface. We have also studied the effect on dewetting of different water models and different treatments of the long-range electrostatic interactions (cutoff vs PME), and found the dewetting phenomena is fairly robust. This work presents a few proteins other than melittin tetramer for further experimental studies of the role of dewetting in the end stages of protein folding.

Elastic bag model for molecular dynamics simulations of solvated systems: application to liquid water and solvated peptides

The fluctuating elastic boundary (FEB) model for molecular dynamics has recently been developed and validated through simulations of liquid argon. In the FEB model, a flexible boundary which consists of particles connected by springs is used to confine the solvated system, thereby eliminating the need for periodic boundary conditions. In this study, we extend this model to the simulation of bulk water and solvated alanine dipeptide. Both the confining potential and boundary particle interaction functions are modified to preserve the structural integrity of the boundary and prevent the leakage of the solute-solvent system through the boundary. A broad spectrum of structural and dynamic properties of liquid water are computed and compared with those obtained from conventional periodic boundary condition simulations. The applicability of the model to biomolecular simulations is investigated through the analysis of conformational population distribution of solvated alanine dipeptide. In most cases we find remarkable agreement between the two simulation approaches.

Signatures of hydrophobic collapse in extended proteins captured with force spectroscopy

We unfold and extend single proteins at a high force and then linearly relax the force to probe their collapse mechanisms. We observe a large variability in the extent of their recoil. Although chain entropy makes a small contribution, we show that the observed variability results from hydrophobic interactions with randomly varying magnitude from protein to protein. This collapse mechanism is common to highly extended proteins, including nonfolding elastomeric proteins like PEVK from titin. Our observations explain the puzzling differences between the folding behavior of highly extended proteins, from those folding after chemical or thermal denaturation. Probing the collapse of highly extended proteins with force spectroscopy allows separation of the different driving forces in protein folding.

An Experimental and Theoretical Study of the Formation of Nanostructures of Self-Assembled Cyanuric Acid through Hydrogen Bond Networks on Graphite

The self-assembly of cyanuric acid into ordered nanostructures on a crystalline substrate, highly ordered pyrolytic graphite (HOPG), has been investigated at low temperature under ultrahigh vacuum (UHV) conditions by means of scanning tunneling microscopy in conjunction with theoretical simulations. Many domains with different self-assembly patterns were observed. One such domain represents the formation of an open 2D rosette (cyclic) structure from the self-assembly process, the first observation of this type of structure for pure cyanuric acid on a graphite substrate. Each self-assembled domain exhibits characteristic superstructures formed through different hydrogen bond networks at low coverage and low deposition rate. Experimental observation of coexistent, two-dimensional crystalline structures with distinct hydrogen bond patterns is supported by energy minimizations and molecular dynamics calculations, which show multiple stable structures for this molecule when self-assembled on graphite.

Destruction of long-range interactions by a single mutation in lysozyme

We propose a mechanism, based on a > or =10-micros molecular dynamics simulation, for the surprising misfolding of hen egg-white lysozyme caused by a single mutation (W62G). Our simulations of the wild-type and mutant lysozymes in 8 M urea solution at biological temperature (with both pH 2 and 7) reveal that the mutant structure is much less stable than that of the wild type, with the mutant showing larger fluctuations and less native-like contacts. Analysis of local contacts reveals that the Trp-62 residue is the key to a cooperative long-range interaction within the wild type, where it acts like a bridge between two neighboring basic residues. Thus, a native-like cluster or nucleation site can form near these residues in the wild type but not in the mutant. The time evolution of the secondary structure also exhibits a quicker loss of the beta-sheets in the mutant than in the wild type, whereas some of the alpha-helices persist during the entire simulation in both the wild type and the mutant in 8 M urea (even though the tertiary structures are basically all gone). These findings, while supporting the general conclusions of a recent experimental study by Dobson and coworkers [Klein-Seetharam J, Oikama M, Grimshaw SB, Wirmer J, Duchardt E, Ueda T, Imoto T, Smith LJ, Dobson CM, Schwalbe H (2002) Science 295:1719-1722], provide a detailed but different molecular picture of the misfolding mechanism.

Effect of ions on the hydrophobic interaction between two plates

We use molecular dynamics simulations to investigate the solvent mediated attraction and drying between two nanoscale hydrophobic surfaces in aqueous salt solutions. We study these effects as a function of the ionic charge density, that is, the ionic charge per unit ionic volume, while keeping the ionic diameter fixed. The attraction is expressed by a negative change in the free energy as the plates are brought together, with enthalpy and entropy changes that both promote aggregation. We find a strong correlation between the strength of the hydrophobic interaction and the degree of preferential binding/exclusion of the ions relative to the surfaces. The results show that amplification of the hydrophobic interaction, a phenomenon analogous to salting-out, is a purely entropic effect and is induced by high-charge-density ions that exhibit preferential exclusion. In contrast, a reduction of the hydrophobic interaction, analogous to salting-in, is induced by low-charge-density ions that exhibit preferential binding, the effect being either entropic or enthalpic. Our findings are relevant to phenomena long studied in solution chemistry, as we demonstrate the significant, yet subtle, effects of electrolytes on hydrophobic aggregation and collapse.

Aggregation and dispersion of small hydrophobic particles in aqueous electrolyte solutions

The effect of salts on the solvent-induced interactions between hydrophobic particles dispersed in explicit aqueous solution is investigated as a function of the salt's ionic charge density by molecular dynamics simulations. We demonstrate that aggregates of the hydrophobic particles can be formed or dissolved in response to changes in the charge density of the ions. Ions with high charge density increase the propensity of the hydrophobic particles to aggregate. This corresponds to stronger hydrophobic interactions and a decrease in the solubility (salting-out) of the hydrophobic particles. Ions with low charge density can either increase or decrease the propensity for aggregation depending on whether the concentration of the salt is low or high, respectively. At low concentrations of low charge density ions, the aggregate forms a "micelle-like" structure in which the ions are preferentially adsorbed at the surface of the aggregate. These "micelle-like" structures can be soluble in water so that the electrolyte can both increase the solubility and increase aggregation at the same time. We also find, that at the concentration of the hydrophobic particles studied (approximately 0.75 m), the aggregation process resembles a first-order transition in finite systems.

Motifs for molecular recognition exploiting hydrophobic enclosure in protein-ligand binding

The thermodynamic properties and phase behavior of water in confined regions can vary significantly from that observed in the bulk. This is particularly true for systems in which the confinement is on the molecular-length scale. In this study, we use molecular dynamics simulations and a powerful solvent analysis technique based on inhomogenous solvation theory to investigate the properties of water molecules that solvate the confined regions of protein active sites. Our simulations and analysis indicate that the solvation of protein active sites that are characterized by hydrophobic enclosure and correlated hydrogen bonds induce atypical entropic and enthalpic penalties of hydration. These penalties apparently stabilize the protein-ligand complex with respect to the independently solvated ligand and protein, which leads to enhanced binding affinities. Our analysis elucidates several challenging cases, including the super affinity of the streptavidin-biotin system.

Frustrated ostwald ripening in self-assembled monolayers of cruciform pi-systems

This study details a scanning tunneling microscopy investigation into the mechanism of chiral grain growth in highly ordered, self-assembled monolayer films composed of cruciform pi-systems. Although the molecules themselves are achiral, when they adsorb from solution onto graphite, they adopt a gear-like conformation that, by virtue of the surface, is chiral. These handed subunits arrange themselves into enantiomeric two-dimensional domains. The unique finding from this study is that Ostwald ripening is frustrated between domain boundaries that are of opposite chirality because direct interconversion between the chiral units on the surface is energetically inhibited.

Aggregation and dispersion of small hydrophobic particles in aqueous electrolyte solutions

The effect of salts on the solvent-induced interactions between hydrophobic particles dispersed in explicit aqueous solution is investigated as a function of the salt's ionic charge density by molecular dynamics simulations. We demonstrate that aggregates of the hydrophobic particles can be formed or dissolved in response to changes in the charge density of the ions. Ions with high charge density increase the propensity of the hydrophobic particles to aggregate. This corresponds to stronger hydrophobic interactions and a decrease in the solubility (salting-out) of the hydrophobic particles. Ions with low charge density can either increase or decrease the propensity for aggregation depending on whether the concentration of the salt is low or high, respectively. At low concentrations of low charge density ions, the aggregate forms a "micelle-like" structure in which the ions are preferentially adsorbed at the surface of the aggregate. These "micelle-like" structures can be soluble in water so that the electrolyte can both increase the solubility and increase aggregation at the same time. We also find, that at the concentration of the hydrophobic particles studied (approximately 0.75 m), the aggregation process resembles a first-order transition in finite systems.

Dynamics of Water Confined in the Interdomain Region of a Multidomain Protein

Molecular dynamics simulations are performed to study the dynamics of interfacial water confined in the interdomain region of a two-domain protein, BphC enzyme. The results show that near the protein surface the water diffusion constant is much smaller and the water-water hydrogen bond lifetime is much longer than that in bulk. The diffusion constant and hydrogen bond lifetime can vary by a factor of as much as 2 in going from the region near the hydrophobic domain surface to the bulk. Water molecules in the first solvation shell persist for a much longer time near local concave sites than near convex sites. Also, the water layer survival correlation time shows that on average water molecules near the extended hydrophilic surfaces have longer residence times than those near hydrophobic surfaces. These results indicate that local surface curvature and hydrophobicity have a significant influence on water dynamics.

Integrated Modeling Program, Applied Chemical Theory (IMPACT)

We provide an overview of the IMPACT molecular mechanics program with an emphasis on recent developments and a description of its current functionality. With respect to core molecular mechanics technologies we include a status report for the fixed charge and polarizable force fields that can be used with the program and illustrate how the force fields, when used together with new atom typing and parameter assignment modules, have greatly expanded the coverage of organic compounds and medicinally relevant ligands. As we discuss in this review, explicit solvent simulations have been used to guide our design of implicit solvent models based on the generalized Born framework and a novel nonpolar estimator that have recently been incorporated into the program. With IMPACT it is possible to use several different advanced conformational sampling algorithms based on combining features of molecular dynamics and Monte Carlo simulations. The program includes two specialized molecular mechanics modules: Glide, a high-throughput docking program, and QSite, a mixed quantum mechanics/molecular mechanics module. These modules employ the IMPACT infrastructure as a starting point for the construction of the protein model and assignment of molecular mechanics parameters, but have then been developed to meet specialized objectives with respect to sampling and the energy function.

Why Is the Partial Molar Volume of CO2 So Small When Dissolved in a Room Temperature Ionic Liquid? Structure and Dynamics of CO2 Dissolved in [Bmim+] [PF6-]

When supercritical CO2 is dissolved in an ionic liquid, its partial molar volume is much smaller than that observed in most other solvents. In this article we explore in atomistic detail and explain in an intuitive way the peculiar volumetric behavior experimentally observed when supercritical CO2 is dissolved in 1-butyl-3-methylimidazolium hexafluorophosphate ([Bmim+] [PF6(-)]). We also provide physical insight into the structure and dynamics occurring across the boundary of the CO2 ionic liquid interface. We find that the liquid structure of [Bmim+] [PF6(-)] in the presence of CO2 is nearly identical to that in the neat ionic liquid (IL) even at fairly large mole fractions of CO2. Our simulations indicate, in agreement with experiments, that partial miscibilities of one fluid into the other are very unsymmetrical, CO2 being highly soluble in the ionic liquid phase while the ionic liquid is highly insoluble in the CO2 phase. We interpret our results in terms of the size and shape of spontaneously forming cavities in the ionic liquid phase, and we propose that CO2 occupies extremely well-defined locations in the IL. Even though our accurate prediction of cavity sizes in the neat IL indicates that these cavities are small compared with the van der Waals radius of a single carbon or oxygen atom, CO2 appears to occupy a space that was for the most part a priori "empty".

Transport properties of normal liquid helium: Comparison of various methodologies

We revisit the problem of self-diffusion in normal liquid helium above the lambda transition. Several different methods are applied to compute the velocity autocorrelation function. Since it is still impossible to determine the exact result for the velocity autocorrelation function from simulation, we appeal to the computation of short-time moments to determine the accuracy of the different approaches at short times. The main conclusion reached from our study is that both the quantum mode-coupling theory and the numerical analytic continuation approach must be regarded as a viable and competitive methods for the computation of dynamical properties of quantum systems.

Replica exchange with solute tempering: a method for sampling biological systems in explicit water

An innovative replica exchange (parallel tempering) method called replica exchange with solute tempering (REST) for the efficient sampling of aqueous protein solutions is presented here. The method bypasses the poor scaling with system size of standard replica exchange and thus reduces the number of replicas (parallel processes) that must be used. This reduction is accomplished by deforming the Hamiltonian function for each replica in such a way that the acceptance probability for the exchange of replica configurations does not depend on the number of explicit water molecules in the system. For proof of concept, REST is compared with standard replica exchange for an alanine dipeptide molecule in water. The comparisons confirm that REST greatly reduces the number of CPUs required by regular replica exchange and increases the sampling efficiency. This method reduces the CPU time required for calculating thermodynamic averages and for the ab initio folding of proteins in explicit water.

Observation of a dewetting transition in the collapse of the melittin tetramer

Marked hydration changes occur during the self-assembly of the melittin protein tetramer in water. Hydrophobicity induces a drying transition in the gap between simple sufficiently large (more than 1 nm(2)) strongly hydrophobic surfaces as they approach each other, resulting in the subsequent collapse of the system, as well as a depletion of water next to single surfaces. Here we investigate whether the hydrophobic induced collapse of multidomain proteins or the formation of protein oligimers exhibits a similar drying transition. We performed computer simulations to study the collapse of the tetramer of melittin in water, and observed a marked water drying transition inside a nanoscale channel of the tetramer (with a channel size of up to two or three water-molecule diameters). This transition, although occurring on a microscopic length scale, is analogous to a first-order phase transition from liquid to vapour. We find that this drying is very sensitive to single mutations of the three isoleucines to less hydrophobic residues and that such mutations in the right locations can switch the channel from being dry to being wet. Thus, quite subtle changes in hydrophobic surface topology can profoundly influence the drying transition. We show that, even in the presence of the polar protein backbone, sufficiently hydrophobic protein surfaces can induce a liquid-vapour transition providing an enormous driving force towards further collapse. This behaviour was unexpected because of the absence of drying in the collapse of the multidomain protein 2,3-dihydroxybiphenyl dioxygenase (BphC).

Polarizable molecules in the vibrational spectroscopy of water

We examine the role of electronic polarizability in water on short (tens of femtoseconds), intermediate (hundreds of femtoseconds), and long (approximately 1 ps) time scales by comparing molecular dynamics results to experimental data for vibrational spectroscopy of HOD in liquid D2O. Because the OH absorption frequency is sensitive to the details of the atomic forces experienced in the liquid, our results provide important quantitative comparisons for several popular empirical water potentials. When compared with their fixed-charge counterparts, the polarizable models give similar slower long time constants for the decay of vibrational correlations and re-orientational motion that is in better agreement with experiments. Polarizable potentials yield qualitatively dissimilar predictions for frequency fluctuations and transition dipole moment fluctuations at equilibrium. Models that confine the polarizability to the plane of the molecule (i.e., TIP4P-FQ) overestimate the width of the distribution describing frequency fluctuations by more than a factor of two. These models also underestimate the amplitude of the hydrogen-bond stretch at 170 cm(-1). A potential that has both an out-of-plane polarization and fluctuating charges, POL5-TZ, compares best with experiments. We interpret our findings in terms of microscopic dynamics and make suggestions that may improve the quality of emerging polarizable force fields for water.

Importance of accurate charges in molecular docking: quantum mechanical/molecular mechanical (QM/MM) approach

The extent to which accuracy of electric charges plays a role in protein-ligand docking is investigated through development of a docking algorithm, which incorporates quantum mechanical/molecular mechanical (QM/MM) calculations. In this algorithm, fixed charges of ligands obtained from force field parameterization are replaced by QM/MM calculations in the protein environment, treating only the ligands as the quantum region. The algorithm is tested on a set of 40 cocrystallized structures taken from the Protein Data Bank (PDB) and provides strong evidence that use of nonfixed charges is important. An algorithm, dubbed "Survival of the Fittest" (SOF) algorithm, is implemented to incorporate QM/MM charge calculations without any prior knowledge of native structures of the complexes. Using an iterative protocol, this algorithm is able in many cases to converge to a nativelike structure in systems where redocking of the ligand using a standard fixed charge force field exhibits nontrivial errors. The results demonstrate that polarization effects can play a significant role in determining the structures of protein-ligand complexes, and provide a promising start towards the development of more accurate docking methods for lead optimization applications.

Ultra-high vacuum scanning tunneling microscopy and theoretical studies of 1-halohexane monolayers on graphite

A simple model system for the 2D self-assembly of functionalized organic molecules on surfaces was examined in a concerted experimental and theoretical effort. Monolayers of 1-halohexanes were formed through vapor deposition onto graphite surfaces in ultrahigh vacuum. Low-temperature scanning tunneling microscopy allowed the molecular conformation, orientation, and monolayer crystallographic parameters to be determined. Essentially identical noncommensurate monolayer structures were found for all 1-halohexanes, with differences in image contrast ascribed mainly to electronic factors. Energy minimizations and molecular dynamics simulations reproduced structural parameters of 1-bromohexane monolayers quantitatively. An analysis of interactions driving the self-assembly process revealed the crucial role played by small but anisotropic electrostatic forces associated with the halogen substituent. While alkyl chain dispersion interactions drive the formation of a close-packed adsorbate monolayer, electrostatic headgroup forces are found to compete successfully in the control of both the angle between lamella and backbone axes and the angle between surface and backbone planes. This competition is consistent with energetic tradeoffs apparent in adsorption energies measured in earlier temperature-programmed desorption studies. In accordance with the higher degree of disorder observed in scanning tunneling microscopy images of 1-fluorohexane, theoretical simulations show that electrostatic forces associated with the fluorine substituent are sufficiently strong to upset the delicate balance of interactions required for the formation of an ordered monolayer. The detailed dissection of the driving forces for self-assembly of these simple model systems is expected to aid in the understanding of the more complex self-assembly processes taking place in the presence of solvent.

Self-Assembly of Small Polycyclic Aromatic Hydrocarbons on Graphite: A Combined Scanning Tunneling Microscopy and Theoretical Approach

Self-assembled monolayers of chrysene and indene on graphite have been observed and characterized individually with scanning tunneling microscopy (STM) at 80 K under low-temperature, ultrahigh vacuum conditions. These molecules are small, polycyclic aromatic hydrocarbons (PAHs) containing no alkyl chains or functional groups that are known to promote two-dimensional self-assembly. Energy minimization and molecular dynamics simulations performed for small groups of the molecules physisorbed on graphite provide insight into the monolayer structure and forces that drive the self-assembly. The adsorption energy for a single chrysene molecule on a model graphite substrate is calculated to be 32 kcal/mol, while that for indene is 17 kcal/mol. Two distinct monolayer structures have been observed for chrysene, corresponding to high- and low-density assemblies. High-resolution STM images taken of chrysene with different bias polarities reveal distinct nodal structure that is characteristic of the molecular electronic state(s) mediating the tunneling process. Density functional theory calculations are utilized in the assignment of the observed electronic states and possible tunneling mechanism. These results are discussed within the context of PAH and soot particle formation, because both chrysene and indene are known reaction products from the combustion of small hydrocarbons. They are also of fundamental interest in the fields of nanotechnology and molecular electronics.