We describe a fully data driven model that learns to perform a retrosynthetic reaction prediction task, which is treated as a sequence-to-sequence mapping problem. The end-to-end trained model has an encoder–decoder architecture that consists of two recurrent neural networks, which has previously shown great success in solving other sequence-to-sequence prediction tasks such as machine translation. The model is trained on 50,000 experimental reaction examples from the United States patent literature, which span 10 broad reaction types that are commonly used by medicinal chemists. We find that our model performs comparably with a rule-based expert system baseline model, and also overcomes certain limitations associated with rule-based expert systems and with any machine learning approach that contains a rule-based expert system component. Our model provides an important first step toward solving the challenging problem of computational retrosynthetic analysis.

N-Methyl-d-aspartate (NMDA) receptors, key neuronal receptors playing the central role in learning and memory, are heavily glycosylated in vivo. Astonishingly little is known about the structure, dynamics, and physiological relevance of glycans attached to them. We recently demonstrated that certain glycans on the ligand binding domain (LBD) of NMDA receptors (NMDARs) can serve as intramolecular potentiators, changing EC50 of NMDAR coagonists. In this work, we use molecular dynamics trajectories, in aggregate 86.5 μs long, of the glycosylated LBD of the GluN1 subunit of the NMDAR to investigate the behavior of glycans on NMDARs. Though all glycans in our simulations were structurally the same (Man5), the dynamics of glycans at different locations on NMDARs was surprisingly different. The slowest-time scale motions that we detected in various glycans in some cases corresponded to a flipping of parts of glycans relative to each other, while in other cases they reduced to a head-to-tail bending of a glycan. We predict that time scales of conformational changes in glycans on the GluN1 LBD of NMDARs range from nanoseconds to at least hundreds of microseconds. Some of the conformational changes in the glycans correlate with the physiologically important clamshell-like opening and closing of the GluN1 LBD domain. Thus, glycans are an integral part of NMDARs, and computational models of NMDARs should include glycans to faithfully represent the structure and the dynamics of these receptors.

Markov state models (MSMs) are a powerful framework for analyzing protein dynamics. MSMs require the decomposition of conformation space into states via clustering, which can be cross-validated when a prediction method is available for the clustering method. We present an algorithm for predicting cluster assignments of new data points with Ward’s minimum variance method. We then show that clustering with Ward’s method produces better or equivalent cross-validated MSMs for protein folding than other clustering algorithms.

Metadynamics is a powerful enhanced molecular dynamics sampling method that accelerates simulations by adding history-dependent multidimensional Gaussians along selective collective variables (CVs). In practice, choosing a small number of slow CVs remains challenging due to the inherent high dimensionality of biophysical systems. Here we show that time-structure based independent component analysis (tICA), a recent advance in Markov state model literature, can be used to identify a set of variationally optimal slow coordinates for use as CVs for Metadynamics. We show that linear and nonlinear tICA-Metadynamics can complement existing MD studies by explicitly sampling the system’s slowest modes and can even drive transitions along the slowest modes even when no such transitions are observed in unbiased simulations.

Multitask deep learning has emerged as a powerful tool for computational drug discovery. However, despite a number of preliminary studies, multitask deep networks have yet to be widely deployed in the pharmaceutical and biotech industries. This lack of acceptance stems from both software difficulties and lack of understanding of the robustness of multitask deep networks. Our work aims to resolve both of these barriers to adoption. We introduce a high-quality open-source implementation of multitask deep networks as part of the DeepChem open-source platform. Our implementation enables simple python scripts to construct, fit, and evaluate sophisticated deep models. We use our implementation to analyze the performance of multitask deep networks and related deep models on four collections of pharmaceutical data (three of which have not previously been analyzed in the literature). We split these data sets into train/valid/test using time and neighbor splits to test multitask deep learning performance under challenging conditions. Our results demonstrate that multitask deep networks are surprisingly robust and can offer strong improvement over random forests. Our analysis and open-source implementation in DeepChem provide an argument that multitask deep networks are ready for widespread use in commercial drug discovery.

Recent advances in machine learning have made significant contributions to drug discovery. Deep neural networks in particular have been demonstrated to provide significant boosts in predictive power when inferring the properties and activities of small-molecule compounds (Ma, J. et al. J. Chem. Inf. Model. 2015, 55, 263–274). However, the applicability of these techniques has been limited by the requirement for large amounts of training data. In this work, we demonstrate how one-shot learning can be used to significantly lower the amounts of data required to make meaningful predictions in drug discovery applications. We introduce a new architecture, the iterative refinement long short-term memory, that, when combined with graph convolutional neural networks, significantly improves learning of meaningful distance metrics over small-molecules. We open source all models introduced in this work as part of DeepChem, an open-source framework for deep-learning in drug discovery (Ramsundar, B. deepchem.io. https://github.com/deepchem/deepchem, 2016).

MSMBuilder is a software package for building statistical models of high-dimensional time-series data. It is designed with a particular focus on the analysis of atomistic simulations of biomolecular dynamics such as protein folding and conformational change. MSMBuilder is named for its ability to construct Markov state models (MSMs), a class of models that has gained favor among computational biophysicists. In addition to both well-established and newer MSM methods, the package includes complementary algorithms for understanding time-series data such as hidden Markov models and time-structure based independent component analysis. MSMBuilder boasts an easy to use command-line interface, as well as clear and consistent abstractions through its Python application programming interface. MSMBuilder was developed with careful consideration for compatibility with the broader machine learning community by following the design of scikit-learn. The package is used primarily by practitioners of molecular dynamics, but is just as applicable to other computational or experimental time-series measurements.

We present a united-atom model (gb-fb15) for the molecular dynamics simulation of hydrated liquid-crystalline dipalmitoylphosphatidylcholine (DPPC) phospholipid bilayers. This model was constructed through the parameter-space minimization of a regularized least-squares objective function via the ForceBalance method. The objective function was computed using a training set of experimental bilayer area per lipid and deuterium order parameter. This model was validated by comparison to experimental volume per lipid, X-ray scattering form factor, thermal area expansivity, area compressibility modulus, and lipid lateral diffusion coefficient. These comparisons demonstrate that gb-fb15 is robust to temperature variation and an improvement over the original model for both the training and validation properties.

Protein function is inextricably linked to protein dynamics. As we move from a static structural picture to a dynamic ensemble view of protein structure and function, novel computational paradigms are required for observing and understanding conformational dynamics of proteins and its functional implications. In principle, molecular dynamics simulations can provide the time evolution of atomistic models of proteins, but the long time scales associated with functional dynamics make it difficult to observe rare dynamical transitions. The issue of extracting essential functional components of protein dynamics from noisy simulation data presents another set of challenges in obtaining an unbiased understanding of protein motions. Therefore, a methodology that provides a statistical framework for efficient sampling and a human-readable view of the key aspects of functional dynamics from data analysis is required. The Markov state model (MSM), which has recently become popular worldwide for studying protein dynamics, is an example of such a framework.In this Account, we review the use of Markov state models for efficient sampling of the hierarchy of time scales associated with protein dynamics, automatic identification of key conformational states, and the degrees of freedom associated with slow dynamical processes. Applications of MSMs for studying long time scale phenomena such as activation mechanisms of cellular signaling proteins has yielded novel insights into protein function. In particular, from MSMs built using large-scale simulations of GPCRs and kinases, we have shown that complex conformational changes in proteins can be described in terms of structural changes in key structural motifs or “molecular switches” within the protein, the transitions between functionally active and inactive states of proteins proceed via multiple pathways, and ligand or substrate binding modulates the flux through these pathways. Finally, MSMs also provide a theoretical toolbox for studying the effect of nonequilibrium perturbations on conformational dynamics. Considering that protein dynamics in vivo occur under nonequilibrium conditions, MSMs coupled with nonequilibrium statistical mechanics provide a way to connect cellular components to their functional environments. Nonequilibrium perturbations of protein folding MSMs reveal the presence of dynamically frozen glass-like states in their conformational landscape. These frozen states are also observed to be rich in β-sheets, which indicates their possible role in the nucleation of β-sheet rich aggregates such as those observed in amyloid-fibril formation. Finally, we describe how MSMs have been used to understand the dynamical behavior of intrinsically disordered proteins such as amyloid-β, human islet amyloid polypeptide, and p53. While certainly not a panacea for studying functional dynamics, MSMs provide a rigorous theoretical foundation for understanding complex entropically dominated processes and a convenient lens for viewing protein motions.

As simulators attempt to replicate the dynamics of large cellular components in silico, problems related to sampling slow, glassy degrees of freedom in molecular systems will be amplified manyfold. It is tempting to augment simulation techniques with external biases to overcome such barriers with ease; biased simulations, however, offer little utility unless equilibrium properties of interest (both kinetic and thermodynamic) can be recovered from the data generated. In this Article, we present a general scheme that harnesses the power of Markov state models (MSMs) to extract equilibrium kinetic properties from molecular dynamics trajectories collected on biased potential energy surfaces. We first validate our reweighting protocol on a simple two-well potential, and we proceed to test our method on potential-biased simulations of the Trp-cage miniprotein. In both cases, we find that equilibrium populations, time scales, and dynamical processes are reliably reproduced as compared to gold standard, unbiased data sets. We go on to discuss the limitations of our dynamical reweighting approach, and we suggest auspicious target systems for further application.

The allure of a molecular dynamics simulation is that, given a sufficiently accurate force field, it can provide an atomic-level view of many interesting phenomena in biology. However, the result of a simulation is a large, high-dimensional time series that is difficult to interpret. Recent work has introduced the time-structure based Independent Components Analysis (tICA) method for analyzing MD, which attempts to find the slowest decorrelating linear functions of the molecular coordinates. This method has been used in conjunction with Markov State Models (MSMs) to provide estimates of the characteristic eigenprocesses contained in a simulation (e.g., protein folding, ligand binding). Here, we extend the tICA method using the kernel trick to arrive at nonlinear solutions. This is a substantial improvement as it allows for kernel-tICA (ktICA) to provide estimates of the characteristic eigenprocesses directly without building an MSM.

Molecular dynamics with explicit solvent is favored for its ability to more correctly simulate aqueous biological processes and has become routine thanks to increasingly powerful computational resources. However, analysis techniques including Markov state models (MSMs) ignore solvent atoms and focus solely on solute coordinates despite solvent being implicated in myriad biological phenomena. We present a unified framework called “solvent-shells featurization” for including solvent degrees of freedom in analysis and show that this method produces better models. We apply this method to simulations of dewetting in the two-domain protein BphC to generate a predictive MSM and identify functional water molecules. Furthermore, the proposed methodology could be easily extended for building MSMs of any systems with indistinguishable components.

Life is fundamentally a nonequilibrium phenomenon. At the expense of dissipated energy, living things perform irreversible processes that allow them to propagate and reproduce. Within cells, evolution has designed nanoscale machines to do meaningful work with energy harnessed from a continuous flux of heat and particles. As dictated by the Second Law of Thermodynamics and its fluctuation theorem corollaries, irreversibility in nonequilibrium processes can be quantified in terms of how much entropy such dynamics produce. In this work, we seek to address a fundamental question linking biology and nonequilibrium physics: can the evolved dissipative pathways that facilitate biomolecular function be identified by their extent of entropy production in general relaxation processes? We here synthesize massive molecular dynamics simulations, Markov state models (MSMs), and nonequilibrium statistical mechanical theory to probe dissipation in two key classes of signaling proteins: kinases and G-protein–coupled receptors (GPCRs). Applying machinery from large deviation theory, we use MSMs constructed from protein simulations to generate dynamics conforming to positive levels of entropy production. We note the emergence of an array of peaks in the dynamical response (transient analogs of phase transitions) that draw the proteins between distinct levels of dissipation, and we see that the binding of ATP and agonist molecules modifies the observed dissipative landscapes. Overall, we find that dissipation is tightly coupled to activation in these signaling systems: dominant entropy-producing trajectories become localized near important barriers along known biological activation pathways. We go on to classify an array of equilibrium and nonequilibrium molecular switches that harmonize to promote functional dynamics.

Given the large number of crystal structures and NMR ensembles that have been solved to date, classical molecular dynamics (MD) simulations have become powerful tools in the atomistic study of the kinetics and thermodynamics of biomolecular systems on ever increasing time scales. By virtue of the high-dimensional conformational state space that is explored, the interpretation of large-scale simulations faces difficulties not unlike those in the big data community. We address this challenge by introducing a method called clustering based feature selection (CB-FS) that employs a posterior analysis approach. It combines supervised machine learning (SML) and feature selection with Markov state models to automatically identify the relevant degrees of freedom that separate conformational states. We highlight the utility of the method in the evaluation of large-scale simulations and show that it can be used for the rapid and automated identification of relevant order parameters involved in the functional transitions of two exemplary cell-signaling proteins central to human disease states.

Molecular similarity has been effectively applied to many problems in cheminformatics and computational drug discovery, but modern methods can be prohibitively expensive for large-scale applications. The SCISSORS method rapidly approximates measures of pairwise molecular similarity such as ROCS and LINGO Tanimotos, acting as a filter to quickly reduce the size of a problem. We report an in-depth analysis of SCISSORS performance, including a mapping of the SCISSORS error distribution, benchmarking, and investigation of several algorithmic modifications. We show that SCISSORS can accurately predict multiconformer similarity and suggest a method for estimating optimal SCISSORS parameters in a data set-specific manner. These results are a useful resource for researchers seeking to incorporate SCISSORS into molecular similarity applications.

The development of accurate molecular mechanics force fields is a significant challenge that must be addressed for the continued success of molecular simulation. We developed the ForceBalance method to automatically derive accurate force field parameters using flexible combinations of experimental and theoretical reference data. The method is demonstrated in the parametrization of two rigid water models, yielding new parameter sets (TIP3P-FB and TIP4P-FB) that accurately describe many physical properties of water.Keywords: force field; ForceBalance; optimization; TIP3P; TIP4P; water; water model;

Markov state models provide a powerful framework for the analysis of biomolecular conformation dynamics in terms of their metastable states and transition rates. These models provide both a quantitative and comprehensible description of the long-time scale dynamics of large molecular dynamics with a Master equation and have been successfully used to study protein folding, protein conformational change, and protein–ligand binding. However, to achieve satisfactory performance, existing methodologies often require expert intervention when defining the model’s discrete state space. While standard model selection methodologies focus on the minimization of systematic bias and disregard statistical error, we show that by consideration of the states’ conditional distribution over conformations, both sources of error can be balanced evenhandedly. Application of techniques that consider both systematic bias and statistical error on two 100 μs molecular dynamics trajectories of the Fip35 WW domain shows agreement with existing techniques based on self-consistency of the model’s relaxation time scales with more suitable results in regimes in which those time scale-based techniques encourage overfitting. By removing the need for expert tuning, these methods should reduce modeling bias and lower the barriers to entry in Markov state model construction.

The extent to which glass-like kinetics govern dynamics in protein folding has been heavily debated. Here, we address the subject with an application of space-time perturbation theory to the dynamics of protein folding Markov state models. Borrowing techniques from the s-ensemble method, we argue that distinct active and inactive phases exist for protein folding dynamics, and that kinetics for specific systems can fall into either dynamical regime. We do not, however, observe a true glass transition in any system studied. We go on to discuss how these inactive and active phases might relate to general protein folding properties.

Markov State Models (MSMs) provide an automated framework to investigate the dynamical properties of high-dimensional molecular simulations. These models can provide a human-comprehensible picture of the underlying process and have been successfully used to study protein folding, protein aggregation, protein ligand binding, and other biophysical systems. The MSM requires the construction of a discrete state-space such that two points are in the same state if they can interconvert rapidly. In the following, we suggest an improved method, which utilizes second order Independent Component Analysis (also known as time-structure based Independent Component Analysis, or tICA), to construct the state-space. We apply this method to simulations of NTL9 (provided by Lindorff-Larsen et al. Science2011, 334, 517–520) and show that the MSM is an improvement over previously built models using conventional distance metrics. Additionally, the resulting model provides insight into the role of non-native contacts by revealing many slow time scales associated with compact, non-native states.

Statistical modeling of long timescale dynamics with Markov state models (MSMs) has been shown to be an effective strategy for building quantitative and qualitative insight into protein folding processes. Existing methodologies, however, rely on geometric clustering using distance metrics such as root mean square deviation (RMSD), assuming that geometric similarity provides an adequate basis for the kinetic partitioning of phase space. Here, inspired by advances in the machine learning community, we introduce a new approach for learning a distance metric explicitly constructed to model kinetic similarity. This approach enables the construction of models, especially in the regime of high anisotropy in the diffusion constant, with fewer states than was previously possible. Application of this technique to the analysis of two ultralong molecular dynamics simulations of the FiP35 WW domain identifies discrete near-native relaxation dynamics in the millisecond regime that were not resolved in previous analyses.

We report the iAMOEBA (“inexpensive AMOEBA”) classical polarizable water model. The iAMOEBA model uses a direct approximation to describe electronic polarizability, in which the induced dipoles are determined directly from the permanent multipole electric fields and do not interact with one another. The direct approximation reduces the computational cost relative to a fully self-consistent polarizable model such as AMOEBA. The model is parameterized using ForceBalance, a systematic optimization method that simultaneously utilizes training data from experimental measurements and high-level ab initio calculations. We show that iAMOEBA is a highly accurate model for water in the solid, liquid, and gas phases, with the ability to fully capture the effects of electronic polarization and predict a comprehensive set of water properties beyond the training data set including the phase diagram. The increased accuracy of iAMOEBA over the fully polarizable AMOEBA model demonstrates ForceBalance as a method that allows the researcher to systematically improve empirical models by efficiently utilizing the available data.

The electric field created by a condensed-phase environment is a powerful and convenient descriptor for intermolecular interactions. Not only does it provide a unifying language to compare many different types of interactions, but it also possesses clear connections to experimental observables, such as vibrational Stark effects. We calculate here the electric fields experienced by a vibrational chromophore (the carbonyl group of acetophenone) in an array of solvents of diverse polarities using molecular dynamics simulations with the AMOEBA polarizable force field. The mean and variance of the calculated electric fields correlate well with solvent-induced frequency shifts and band broadening, suggesting Stark effects as the underlying mechanism of these key solution-phase spectral effects. Compared to fixed-charge and continuum models, AMOEBA was the only model examined that could describe nonpolar, polar, and hydrogen bonding environments in a consistent fashion. Nevertheless, we found that fixed-charge force fields and continuum models were able to replicate some results of the polarizable simulations accurately, allowing us to clearly identify which properties and situations require explicit polarization and/or atomistic representations to be modeled properly, and to identify for which properties and situations simpler models are sufficient. We also discuss the ramifications of these results for modeling electrostatics in complex environments, such as proteins.

Protein folding is a fundamental process in biology, key to understanding many human diseases. Experimentally, proteins often appear to fold via simple two- or three-state mechanisms involving mainly native-state interactions, yet recent network models built from atomistic simulations of small proteins suggest the existence of many possible metastable states and folding pathways. We reconcile these two pictures in a combined experimental and simulation study of acyl-coenzyme A binding protein (ACBP), a two-state folder (folding time ∼10 ms) exhibiting residual unfolded-state structure, and a putative early folding intermediate. Using single-molecule FRET in conjunction with side-chain mutagenesis, we first demonstrate that the denatured state of ACBP at near-zero denaturant is unusually compact and enriched in long-range structure that can be perturbed by discrete hydrophobic core mutations. We then employ ultrafast laminar-flow mixing experiments to study the folding kinetics of ACBP on the microsecond time scale. These studies, along with Trp-Cys quenching measurements of unfolded-state dynamics, suggest that unfolded-state structure forms on a surprisingly slow (∼100 μs) time scale, and that sequence mutations strikingly perturb both time-resolved and equilibrium smFRET measurements in a similar way. A Markov state model (MSM) of the ACBP folding reaction, constructed from over 30 ms of molecular dynamics trajectory data, predicts a complex network of metastable stables, residual unfolded-state structure, and kinetics consistent with experiment but no well-defined intermediate preceding the main folding barrier. Taken together, these experimental and simulation results suggest that the previously characterized fast kinetic phase is not due to formation of a barrier-limited intermediate but rather to a more heterogeneous and slow acquisition of unfolded-state structure.

Recent hardware and software advances have enabled simulation studies of protein systems on biophysically relevant time scales, often revealing the need for improved force fields. Although early force field development was limited by the lack of direct comparisons between simulation and experiment, recent work from several laboratories has demonstrated direct calculation of NMR observables from protein simulations. Here, we quantitatively evaluate 11 recent molecular dynamics force fields in combination with 5 solvent models against a suite of 524 chemical shift and J coupling (3JHNHα, 3JHNCβ, 3JHαC′, 3JHNC′, and 3JHαN) measurements on dipeptides, tripeptides, tetra-alanine, and ubiquitin. Of the force fields examined (ff96, ff99, ff03, ff03*, ff03w, ff99sb*, ff99sb-ildn, ff99sb-ildn-phi, ff99sb-ildn-NMR, CHARMM27, and OPLS-AA), two force fields (ff99sb-ildn-phi, ff99sb-ildn-NMR) combining recent side chain and backbone torsion modifications achieved high accuracy in our benchmark. For the two optimal force fields, the calculation error is comparable to the uncertainty in the experimental comparison. This observation suggests that extracting additional force field improvements from NMR data may require increased accuracy in J coupling and chemical shift prediction. To further investigate the limitations of current force fields, we also consider conformational populations of dipeptides, which were recently estimated using vibrational spectroscopy.

A simple model is presented that describes general features of protein folding, in good agreement with experimental results and detailed all-atom simulations. Starting from microscopic physics, and with no free parameters, this model predicts that protein folding occurs remarkably quickly because native-like states are kinetic hubs. A hub-like network arises naturally out of microscopic physical concerns, specifically the kinetic longevity of native contacts during a search of globular conformations. The model predicts folding times scaling as τf ∼ eξN in the number of residues, but because the model shows ξ is small, the folding times are much faster than Levinthal’s approximation. Importantly, the folding time scale is found to be small due to the topology and structure of the network. We show explicitly how our model agrees with generic experimental features of the folding process, including the scaling of τf with N, two-state thermodynamics, a sharp peak in CV, and native-state fluctuations.

Markov state models constructed from molecular dynamics simulations have recently shown success at modeling protein folding kinetics. Here we introduce two methods, flux PCCA+ (FPCCA+) and sliding constraint rate estimation (SCRE), that allow accurate rate models from protein folding simulations. We apply these techniques to fourteen massive simulation datasets generated by Anton and Folding@home. Our protocol quantitatively identifies the suitability of describing each system using two-state kinetics and predicts experimentally detectable deviations from two-state behavior. An analysis of the villin headpiece and FiP35 WW domain detects multiple native substates that are consistent with experimental data. Applying the same protocol to GTT, NTL9, and protein G suggests that some beta containing proteins can form long-lived native-like states with small register shifts. Even the simplest protein systems show folding and functional dynamics involving three or more states.

Membrane interfaces are critical to many cellular functions, yet the vast array of molecular components involved make the fundamental physics of interaction difficult to define. Water has been shown to play an important role in the dynamics of small biological systems, for example when trapped in hydrophobic regions, but the molecular details of water have generally been thought dispensable when considering large membrane interfaces. Nevertheless, spectroscopic data indicate that water has distinct, ordered behavior near membrane surfaces. While coarse-grained simulations have achieved success recently in aiding understanding the dynamics of membrane assemblies, it is natural to ask, does the missing chemical nature of water play an important role? We have therefore performed atomic-resolution simulations of vesicle fusion to understand the role of chemical detail, particularly the molecular structure of water, in membrane fusion and at membrane interfaces more generally. These membrane interfaces present a form of hydrophilic confinement, yielding surprising, non-bulk-like water behavior.

Two strategies have been recently employed to push molecular simulation to long, biologically relevant time scales: projection-based analysis of results from specialized hardware producing a small number of ultralong trajectories and the statistical interpretation of massive parallel sampling performed with Markov state models (MSMs). Here, we assess the MSM as an analysis method by constructing a Markov model from ultralong trajectories, specifically two previously reported 100 μs trajectories of the FiP35 WW domain (Shaw, D. E. Science 2010, 330, 341−346). We find that the MSM approach yields novel insights. It discovers new statistically significant folding pathways, in which either beta-hairpin of the WW domain can form first. The rates of this process approach experimental values in a direct quantitative comparison (time scales of 5.0 μs and 100 ns), within a factor of ∼2. Finally, the hub-like topology of the MSM and identification of a holo conformation predicts how WW domains may function through a conformational selection mechanism.

Markov state models (MSMs) have proven themselves to be effective statistical and quantitative models for understanding protein folding dynamics. As stochastic networks, MSMs allow for descriptions of parallel folding pathways and facilitate quantitative comparison to experiments conducted at the ensemble level. While this complex network structure is advantageous in many respects, a simple topological description of these graphs is elusive. In this Article, we compare a series of protein folding MSMs to the topology of the Cayley tree, a graph structure on which dynamics are intuitive. We go on to introduce and test new sampling schemes that have potential to improve automated model construction, a critical step toward making Markov state modeling more accessible to general users.

Markov state models provide a framework for understanding the fundamental states and rates in the conformational dynamics of biomolecules. We describe an improved protocol for constructing Markov state models from molecular dynamics simulations. The new protocol includes advances in clustering, data preparation, and model estimation; these improvements lead to significant increases in model accuracy, as assessed by the ability to recapitulate equilibrium and kinetic properties of reference systems. A high-performance implementation of this protocol, provided in MSMBuilder2, is validated on dynamics ranging from picoseconds to milliseconds.

The SCISSORS method for approximating chemical similarities has shown excellent empirical performance on a number of real-world chemical data sets but lacks theoretically proven bounds on its worst-case error performance. This paper first proves reductions showing SCISSORS to be equivalent to two previous kernel methods: kernel principal components analysis and the rank-k Nyström approximation of a Gram matrix. These reductions allow the use of generalization bounds on these techniques to show that the expected error in SCISSORS approximations of molecular similarity kernels is bounded in expected pairwise inner product error, in matrix 2-norm and Frobenius norm for full kernel matrix approximations and in root-mean-square deviation for approximated matrices. Finally, we show that the actual performance of SCISSORS is significantly better than these worst-case bounds, indicating that chemical space is well-structured for chemical sampling algorithms.

As the fastest folding protein, the villin headpiece (HP35) serves as an important bridge between simulation and experimental studies of protein folding. Despite the simplicity of this system, experiments continue to reveal a number of surprises, including structure in the unfolded state and complex equilibrium dynamics near the native state. Using 2.5 ms of molecular dynamics and Markov state models, we connect to current experimental results in three ways. First, we present and validate a novel method for the quantitative prediction of triplet–triplet energy transfer experiments. Second, we construct a many-state model for HP35 that is consistent with previous experiments. Finally, we predict contact-formation time traces for all 1,225 possible triplet–triplet energy transfer experiments on HP35.

Water plays a unique role in all living organisms. Not only is it nature’s ubiquitous solvent, but it also actively takes part in many cellular processes. In particular, the structure and properties of interfacial water near biomolecules such as proteins are often related to the function of the respective molecule. It can therefore be highly instructive to study the local water density around solutes in cellular systems, particularly when solvent-mediated forces such as the hydrophobic effect are relevant. Computational methods such as molecular dynamics (MD) simulations seem well suited to study these systems at the atomic level. However, due to sampling requirements, it is not clear that MD simulations are, indeed, the method of choice to obtain converged densities at a given level of precision. We here compare the calculation of local water densities with two different methods: MD simulations and the three-dimensional reference interaction site model with the Kovalenko−Hirata closure (3D-RISM-KH). In particular, we investigate the convergence of the local water density to assess the required simulation times for different levels of resolution. Moreover, we provide a quantitative comparison of the densities calculated with MD and with 3D-RISM-KH and investigate the effect of the choice of the water model for both methods. Our results show that 3D-RISM-KH yields density distributions that are very similar to those from MD up to a 0.5 Å resolution, but for significantly reduced computational cost. The combined use of MD and 3D-RISM-KH emerges as an auspicious perspective for efficient solvent sampling in dynamical systems.

Molecular kinetics underlies all biological phenomena and, like many other biological processes, may best be understood in terms of networks. These networks, called Markov state models (MSMs), are typically built from physical simulations. Thus, they are capable of quantitative prediction of experiments and can also provide an intuition for complex conformational changes. Their primary application has been to protein folding; however, these technologies and the insights they yield are transferable. For example, MSMs have already proved useful in understanding human diseases, such as protein misfolding and aggregation in Alzheimer's disease.

Protein folding is a classic grand challenge that is relevant to numerous human diseases, such as protein misfolding diseases like Alzheimer’s disease. Solving the folding problem will ultimately require a combination of theory, simulation, and experiment, with theory and simulation providing an atomically detailed picture of both the thermodynamics and kinetics of folding and experimental tests grounding these models in reality. However, theory and simulation generally fall orders of magnitude short of biologically relevant time scales. Here we report significant progress toward closing this gap: an atomistic model of the folding of an 80-residue fragment of the λ repressor protein with explicit solvent that captures dynamics on a 10 milliseconds time scale. In addition, we provide a number of predictions that warrant further experimental investigation. For example, our model’s native state is a kinetic hub, and biexponential kinetics arises from the presence of many free-energy basins separated by barriers of different heights rather than a single low barrier along one reaction coordinate (the previously proposed incipient downhill folding scenario).

While several experimental techniques now exist for characterizing protein unfolded states, all-atom simulation of unfolded states has been challenging due to the long time scales and conformational sampling required. We address this problem by using a combination of accelerated calculations on graphics processor units and distributed computing to simulate tens of thousands of molecular dynamics trajectories each up to ∼10 μs (for a total aggregate simulation time of 127 ms). We used this approach in conjunction with Trp-Cys contact quenching experiments to characterize the unfolded structure and dynamics of protein L. We employed a polymer theory method to make quantitative comparisons between high-temperature simulated and chemically denatured experimental ensembles and find that reaction-limited quenching rates calculated from simulation agree remarkably well with experiment. In both experiment and simulation, we find that unfolded-state intramolecular diffusion rates are very slow compared to highly denatured chains and that a single-residue mutation can significantly alter unfolded-state dynamics and structure. This work suggests a view of the unfolded state in which surprisingly low diffusion rates could limit folding and opens the door for all-atom molecular simulation to be a useful predictive tool for characterizing protein unfolded states along with experiments that directly measure intramolecular diffusion.

To date, the slowest-folding proteins folded ab initio by all-atom molecular dynamics simulations have had folding times in the range of nanoseconds to microseconds. We report simulations of several folding trajectories of NTL9(1−39), a protein which has a folding time of ∼1.5 ms. Distributed molecular dynamics simulations in implicit solvent on GPU processors were used to generate ensembles of trajectories out to ∼40 μs for several temperatures and starting states. At a temperature less than the melting point of the force field, we observe a small number of productive folding events, consistent with predictions from a model of parallel uncoupled two-state simulations. The posterior distribution of the folding rate predicted from the data agrees well with the experimental folding rate (∼640/s). Markov State Models (MSMs) built from the data show a gap in the implied time scales indicative of two-state folding and heterogeneous pathways connecting diffuse mesoscopic substates. Structural analysis of the 14 out of 2000 macrostates transited by the top 10 folding pathways reveals that native-like pairing between strands 1 and 2 only occurs for macrostates with pfold > 0.5, suggesting β12 hairpin formation may be rate-limiting. We believe that using simulation data such as these to seed adaptive resampling simulations will be a promising new method for achieving statistically converged descriptions of folding landscapes at longer time scales than ever before.

Computer simulations can complement experiments by providing insight into molecular kinetics with atomic resolution. Unfortunately, even the most powerful supercomputers can only simulate small systems for short time scales, leaving modeling of most biologically relevant systems and time scales intractable. In this work, however, we show that molecular simulations driven by adaptive sampling of networks called Markov State Models (MSMs) can yield tremendous time and resource savings, allowing previously intractable calculations to be performed on a routine basis on existing hardware. We also introduce a distance metric (based on the relative entropy) for comparing MSMs. We primarily employ this metric to judge the convergence of various sampling schemes but it could also be employed to assess the effects of perturbations to a system (e.g., determining how changing the temperature or making a mutation changes a system’s dynamics).

Algorithms for several emerging large-scale problems in cheminformatics have as their rate-limiting step the evaluation of relatively slow chemical similarity measures, such as structural similarity or three-dimensional (3-D) shape comparison. In this article we present SCISSORS, a linear-algebraical technique (related to multidimensional scaling and kernel principal components analysis) to rapidly estimate chemical similarities for several popular measures. We demonstrate that SCISSORS faithfully reflects its source similarity measures for both Tanimoto calculation and rank ordering. After an efficient precalculation step on a database, SCISSORS affords several orders of magnitude of speedup in database screening. SCISSORS furthermore provides an asymptotic speedup for large similarity matrix construction problems, reducing the number of conventional slow similarity evaluations required from quadratic to linear scaling.

LINGOs are a holographic measure of chemical similarity based on text comparison of SMILES strings. We present a new algorithm for calculating LINGO similarities amenable to parallelization on SIMD architectures (such as GPUs and vector units of modern CPUs). We show that it is nearly 3× as fast as existing algorithms on a CPU, and over 80× faster than existing methods when run on a GPU.

Understanding molecular kinetics, and particularly protein folding, is a classic grand challenge in molecular biophysics. Network models, such as Markov state models (MSMs), are one potential solution to this problem. MSMs have recently yielded quantitative agreement with experimentally derived structures and folding rates for specific systems, leaving them positioned to potentially provide a deeper understanding of molecular kinetics that can lead to experimentally testable hypotheses. Here we use existing MSMs for the villin headpiece and NTL9, which were constructed from atomistic simulations, to accomplish this goal. In addition, we provide simpler, humanly comprehensible networks that capture the essence of molecular kinetics and reproduce qualitative phenomena like the apparent two-state folding often seen in experiments. Together, these models show that protein dynamics are dominated by stochastic jumps between numerous metastable states and that proteins have heterogeneous unfolded states (many unfolded basins that interconvert more rapidly with the native state than with one another) yet often still appear two-state. Most importantly, we find that protein native states are hubs that can be reached quickly from any other state. However, metastability and a web of nonnative states slow the average folding rate. Experimental tests for these findings and their implications for other fields, like protein design, are also discussed.

Influenza virus attaches to and infects target cells via binding of cell-surface glycans by the viral hemagglutinin. This binding specificity is considered a major reason why avian influenza is typically poorly transmitted between humans, while swine influenza is better transmitted due to glycan similarity between the human and swine upper respiratory tract. Predicting mutations that control glycan binding is thus important to continued surveillance against new pandemic influenza strains. We have designed a molecular-dynamics approach for scoring potential mutants with predictive power for both receptor-binding-domain and allosteric mutations similar to those identified from clinical isolates of avian influenza. We have performed thousands of simulations of 17 different hemagglutinin mutants totaling >1 ms in length and employ a Bayesian model to rank mutations that disrupt the stability of the hemagglutinin−ligand complex. Based on our simulations, we predict a significantly increased koff for seven of these mutants. This means of using molecular dynamics analysis to make experimentally verifiable predictions offers a potentially general method to identify ligand-binding mutants, particularly allosteric ones. Our analysis of ligand dissociation provides a means to evaluate mutants prior to experimental mutagenesis and testing and constitutes an important step toward understanding the determinants of ligand binding by H5N1 influenza

Simulating the conformational dynamics of biomolecules is extremely difficult due to the rugged nature of their free energy landscapes and multiple long-lived, or metastable, states. Generalized ensemble (GE) algorithms, which have become popular in recent years, attempt to facilitate crossing between states at low temperatures by inducing a random walk in temperature space. Enthalpic barriers may be crossed more easily at high temperatures; however, entropic barriers will become more significant. This poses a problem because the dominant barriers to conformational change are entropic for many biological systems, such as the short RNA hairpin studied here. We present a new efficient algorithm for conformational sampling, called the adaptive seeding method (ASM), which uses nonequilibrium GE simulations to identify the metastable states, and seeds short simulations at constant temperature from each of them to quantitatively determine their equilibrium populations. Thus, the ASM takes advantage of the broad sampling possible with GE algorithms but generally crosses entropic barriers more efficiently during the seeding simulations at low temperature. We show that only local equilibrium is necessary for ASM, so very short seeding simulations may be used. Moreover, the ASM may be used to recover equilibrium properties from existing datasets that failed to converge, and is well suited to running on modern computer clusters.

In this work, we develop a fully Bayesian method for the calculation of probability distributions of single-exponential rates for any single-molecule process. These distributions can even be derived when no transitions from one state to another have been observed, since in that case the data can be used to estimate a lower bound on the rate. Using a Bayesian hypothesis test, one can easily test whether a transition occurs at the same rate or at different rates in two data sets. We illustrate these methods with molecular dynamics simulations of the folding of a β-sheet protein. However, the theory presented here can be used on any data from simulation or experiment for which a two-state description is appropriate.

The ribosome is a large complex catalyst responsible for the synthesis of new proteins, an essential function for life. New proteins emerge from the ribosome through an exit tunnel as nascent polypeptide chains. Recent findings indicate that tunnel interactions with the nascent polypeptide chain might be relevant for the regulation of translation. However, the specific ribosomal structural features that mediate this process are unknown. Performing molecular dynamics simulations, we are studying the interactions between components of the ribosome exit tunnel and different chemical probes (specifically different amino acid side chains or monovalent inorganic ions). Our free-energy maps describe the physicochemical environment of the tunnel, revealing binding crevices and free-energy barriers for single amino acids and ions. Our simulations indicate that transport out of the tunnel could be different for diverse amino acid species. In addition, our results predict a notable protein–RNA interaction between a flexible 23S rRNA tetraloop (gate) and ribosomal protein L39 (latch) that could potentially obstruct the tunnel's exit. By relating our simulation data to earlier biochemical studies, we propose that ribosomal features at the exit of the tunnel can play a role in the regulation of nascent chain exit and ion flux. Moreover, our free-energy maps may provide a context for interpreting sequence-dependent nascent chain phenomenology.

Although most experimental and theoretical studies of protein folding involve proteins in vitro, the effects of spatial confinement may complicate protein folding in vivo. In this study, we examine the folding dynamics of villin (a small fast folding protein) with explicit solvent confined to an inert nanopore. We have calculated the probability of folding before unfolding (P fold) under various confinement regimes. Using P fold correlation techniques, we observed two competing effects. Confining protein alone promotes folding by destabilizing the unfolded state. In contrast, confining both protein and solvent gives rise to a solvent-mediated effect that destabilizes the native state. When both protein and solvent are confined we see unfolding to a compact unfolded state different from the unfolded state seen in bulk. Thus, we demonstrate that the confinement of solvent has a significant impact on protein kinetics and thermodynamics. We conclude with a discussion of the implications of these results for folding in confined environments such as the chaperonin cavity in vivo.

Polyproline type II (PPII) helix has emerged recently as the dominant paradigm for describing the conformation of unfolded polypeptides. However, most experimental observables used to characterize unfolded proteins typically provide only short-range, sequence-local structural information that is both time- and ensemble-averaged, giving limited detail about the long-range structure of the chain. Here, we report a study of a long-range property: the radius of gyration of an alanine-based peptide, Ace-(diaminobutyric acid)2-(Ala)7-(ornithine)2-NH2. This molecule has previously been studied as a model for the unfolded state of proteins under folding conditions and is believed to adopt a PPII fold based on short-range techniques such as NMR and CD. By using synchrotron radiation and small-angle x-ray scattering, we have determined the radius of gyration of this peptide to be 7.4 ± 0.5 Å, which is significantly less than the value expected from an ideal PPII helix in solution (13.1 Å). To further study this contradiction, we have used molecular dynamics simulations using six variants of the AMBER force field and the GROMOS 53A6 force field. However, in all cases, the simulated ensembles underestimate the PPII content while overestimating the experimental radius of gyration. The conformational model that we propose, based on our small angle x-ray scattering results and what is known about this molecule from before, is that of a very flexible, fluctuating structure that on the level of individual residues explores a wide basin around the ideal PPII geometry but is never, or only rarely, in the ideal extended PPII helical conformation.

There are many unresolved questions regarding the role of water in protein folding. Does water merely induce hydrophobic forces, or does the discrete nature of water play a structural role in folding? Are the nonadditive aspects of water important in determining the folding mechanism? To help to address these questions, we have performed simulations of the folding of a model protein (BBA5) in explicit solvent. Starting 10,000 independent trajectories from a fully unfolded conformation, we have observed numerous folding events, making this work a comprehensive study of the kinetics of protein folding starting from the unfolded state and reaching the folded state and with an explicit solvation model and experimentally validated rates. Indeed, both the raw TIP3P folding rate (4.5 ± 2.5 μs) and the diffusion-constant corrected rate (7.5 ± 4.2 μs) are in strong agreement with the experimentally observed rate of 7.5 ± 3.5 μs. To address the role of water in folding, the mechanism is compared with that predicted from implicit solvation simulations. An examination of solvent density near hydrophobic groups during folding suggests that in the case of BBA5, there are water-induced effects not captured by implicit solvation models, including signs of a “concurrent mechanism” of core collapse and desolvation.

We studied the microsecond folding dynamics of three β hairpins (Trp zippers 1–3, TZ1–TZ3) by using temperature-jump fluorescence and atomistic molecular dynamics in implicit solvent. In addition, we studied TZ2 by using time-resolved IR spectroscopy. By using distributed computing, we obtained an aggregate simulation time of 22 ms. The simulations included 150, 212, and 48 folding events at room temperature for TZ1, TZ2, and TZ3, respectively. The all-atom optimized potentials for liquid simulations (OPLSaa) potential set predicted TZ1 and TZ2 properties well; the estimated folding rates agreed with the experimentally determined folding rates and native conformations were the global potential-energy minimum. The simulations also predicted reasonable unfolding activation enthalpies. This work, directly comparing large simulated folding ensembles with multiple spectroscopic probes, revealed both the surprising predictive ability of current models as well as their shortcomings. Specifically, for TZ1–TZ3, OPLS for united atom models had a nonnative free-energy minimum, and the folding rate for OPLSaa TZ3 was sensitive to the initial conformation. Finally, we characterized the transition state; all TZs fold by means of similar, native-like transition-state conformations.

Recently, we have proposed that, on average, the structure of the unfolded state of small, mostly -helical proteins may be similar to the native structure (the 'mean-structure' hypothesis). After examining thousands of simulations of both the folded and the unfolded states of five polypeptides in atomistic detail at room temperature, we report here a result that seems at odds with the mean-structure hypothesis. Specifically, the average inter-residue distances in the collapsed unfolded structures agree well with the statistics of the ideal random-flight chain with link length of 3.8 Å (the length of one amino acid). A possible resolution of this apparent contradiction is offered by the observation that the inter-residue distances in a typical -helix over short stretches are close to the average distances in an ideal random-flight chain.

Protein folding is difficult to simulate with classical molecular dynamics. Secondary structure motifs such as α-helices and β-hairpins can form in 0.1–10 µs (ref. 1), whereas small proteins have been shown to fold completely in tens of microseconds2. The longest folding simulation to date is a single 1-µs simulation of the villin headpiece3; however, such single runs may miss many features of the folding process as it is a heterogeneous reaction involving an ensemble of transition states4, 5. Here, we have used a distributed computing implementation to produce tens of thousands of 5–20-ns trajectories (700 µs) to simulate mutants of the designed mini-protein BBA5. The fast relaxation dynamics these predict were compared with the results of laser temperature-jump experiments. Our computational predictions are in excellent agreement with the experimentally determined mean folding times and equilibrium constants. The rapid folding of BBA5 is due to the swift formation of secondary structure. The convergence of experimentally and computationally accessible timescales will allow the comparison of absolute quantities characterizing in vitro and in silico (computed) protein folding6.

Simulating protein folding has been a challenging problem for decades due to the long timescales involved (compared with what is possible to simulate) and the challenges of gaining insight from the complex nature of the resulting simulation data. Markov State Models (MSMs) present a means to tackle both of these challenges, yielding simulations on experimentally relevant timescales, statistical significance, and coarse grained representations that are readily humanly understandable. Here, we review this method with the intended audience of non-experts, in order to introduce the method to a broader audience. We review the motivations, methods, and caveats of MSMs, as well as some recent highlights of applications of the method. We conclude by discussing how this approach is part of a paradigm shift in how one uses simulations, away from anecdotal single-trajectory approaches to a more comprehensive statistical approach.

Massively parallel all-atom, explicit solvent molecular dynamics simulations were used to explore the formation and existence of local structure in two small α-helical proteins, the villin headpiece and the helical fragment B of protein A. We report on the existence of transient helices and combinations of helices in the unfolded ensemble, and on the order of formation of helices, which appears to largely agree with previous experimental results. Transient local structure is observed even in the absence of overall native structure. We also calculate sets of residue-residue pairs that are statistically predictive of the formation of given local structures in our simulations.

After reanalyzing simulations of NuG2—a designed mutant of protein G—generated by Lindorff-Larsen et al. with time structure-based independent components analysis and Markov state models as well as performing 1.5 ms of additional sampling on Folding@home, we found an intermediate with a register-shift in one of the β-sheets that was visited along a minor folding pathway. The minor folding pathway was initiated by the register-shifted sheet, which is composed of solely nonnative contacts, suggesting that for some peptides, nonnative contacts can lead to productive folding events. To confirm this experimentally, we suggest a mutational strategy for stabilizing the register shift, as well as an infrared experiment that could observe the nonnative folding nucleus.

We have performed simulated tempering molecular dynamics simulations to study the thermodynamics of the headpiece of the Huntingtin (Htt) protein (N17Htt). With converged sampling, we found this peptide is highly helical, as previously proposed. Interestingly, this peptide is also found to adopt two different and seemingly stable states. The region from residue 4 (L) to residue 9 (K) has a strong helicity from our simulations, which is supported by experimental studies. However, contrary to what was initially proposed, we have found that simulations predict the most populated state as a two-helix bundle rather than a single straight helix, although a significant percentage of structures do still adopt a single linear helix. The fact that Htt aggregation is nucleation dependent infers the importance of a critical transition. It has been shown that N17Htt is involved in this rate-limiting step. In this study, we propose two possible mechanisms for this nucleating event stemming from the transition between two-helix bundle state and single-helix state for N17Htt and the experimentally observed interactions between the N17Htt and polyQ domains. More strikingly, an extensive hydrophobic surface area is found to be exposed to solvent in the dominant monomeric state of N17Htt. We propose the most fundamental role played by N17Htt would be initializing the dimerization and pulling the polyQ chains into adequate spatial proximity for the nucleation event to proceed.

Markov state models (MSMs) have proven to be useful tools in simulating large and slowly-relaxing biological systems like proteins. MSMs model proteins through dynamics on a discrete-state energy landscape, allowing molecules to effectively sample large regions of phase space. In this work, we use aspects of MSMs to ask: is protein folding mechanistically robust? We first provide a definition of mechanism in the context of Markovian models, and we later use perturbation theory and the concept of parametric sloppiness to show that parts of the MSM eigenspectrum are resistant to perturbation. We introduce a new, to our knowledge, Bayesian metric by which eigenspectrum robustness can be evaluated, and we discuss the implications of mechanistic robustness and possible new applications of MSMs to understanding biophysical phenomena.

We describe molecular dynamics simulations resulting in the folding the Fip35 Hpin1 WW domain. The simulations were run on a distributed set of graphics processors, which are capable of providing up to two orders of magnitude faster computation than conventional processors. Using the Folding@home distributed computing system, we generated thousands of independent trajectories in an implicit solvent model, totaling over 2.73 ms of simulations. A small number of these trajectories folded; the folding proceeded along several distinct routes and the system folded into two distinct three-stranded β-sheet conformations, showing that the folding mechanism of this system is distinctly heterogeneous.

Amyloid beta (Aβ) peptide plays an important role in Alzheimer’s disease. A number of mutations in the Aβ sequence lead to familial Alzheimer’s disease, congophilic amyloid angiopathy, or hereditary cerebral hemorrhage with amyloid. Using molecular dynamics simulations of ∼200 μs for each system, we characterize and contrast the consequences of four pathogenic mutations (Italian, Dutch, Arctic, and Iowa) for the structural ensemble of the Aβ monomer. The four familial mutations are found to have distinct consequences for the monomer structure.

Developing an understanding of protein misfolding processes presents a crucial challenge for unlocking the mysteries of human disease. In this article, we present our observations of β-sheet-rich misfolded states on a number of protein dynamical landscapes investigated through molecular dynamics simulation and Markov state models. We employ a nonequilibrium statistical mechanical theory to identify the glassy states in a protein’s dynamics, and we discuss the nonnative, β-sheet-rich states that play a distinct role in the slowest dynamics within seven protein folding systems. We highlight the fundamental similarity between these states and the amyloid structures responsible for many neurodegenerative diseases, and we discuss potential consequences for mechanisms of protein aggregation and intermolecular amyloid formation.

The aggregation of amyloid beta (Aβ) peptides plays an important role in the development of Alzheimer's disease. Despite extensive effort, it has been difficult to characterize the secondary and tertiary structure of the Aβ monomer, the starting point for aggregation, due to its hydrophobicity and high aggregation propensity. Here, we employ extensive molecular dynamics simulations with atomistic protein and water models to determine structural ensembles for Aβ42, Aβ40, and Aβ42-E22K (the Italian mutant) monomers in solution. Sampling of a total of >700 microseconds in all-atom detail with explicit solvent enables us to observe the effects of peptide length and a pathogenic mutation on the disordered Aβ monomer structural ensemble. Aβ42 and Aβ40 have crudely similar characteristics but reducing the peptide length from 42 to 40 residues reduces β-hairpin formation near the C-terminus. The pathogenic Italian E22K mutation induces helix formation in the region of residues 20–24. This structural alteration may increase helix-helix interactions between monomers, resulting in altered mechanism and kinetics of Aβ oligomerization.

We recently developed a polarizable atomic multipole refinement method assisted by the AMOEBA force field for macromolecular crystallography. Compared to standard refinement procedures, the method uses a more rigorous treatment of x-ray scattering and electrostatics that can significantly improve the resultant information contained in an atomic model. We applied this method to high-resolution lysozyme and trypsin data sets, and validated its utility for precisely describing biomolecular electron density, as indicated by a 0.4–0.6% decrease in the R- and Rfree-values, and a corresponding decrease in the relative energy of 0.4–0.8 Kcal/mol/residue. The re-refinements illustrate the ability of force-field electrostatics to orient water networks and catalytically relevant hydrogens, which can be used to make predictions regarding active site function, activity, and protein-ligand interaction energies. Re-refinement of a DNA crystal structure generates the zigzag spine pattern of hydrogen bonding in the minor groove without manual intervention. The polarizable atomic multipole electrostatics model implemented in the AMOEBA force field is applicable and informative for crystal structures solved at any resolution.

Folding and misfolding of the collagen triple helix are studied through molecular dynamics simulations of two collagenlike peptides, [(POG)10]3 and [(POG)4POA(POG)5]3, which are models for wild-type and mutant collagen, respectively. To extract long time dynamics from short trajectories, we employ Markov state models. By analyzing thermodynamic and kinetic quantities calculated from the Markov state models, we examine folding mechanisms of the collagen triple helix and consequences of glycine mutations. We find that the C-to-N zipping of the collagen triple helix must be initiated by a nucleation event consisting of formation of three stable hydrogen bonds, and that zipping through a glycine mutation site requires a renucleation event which also consists of formation of three stable hydrogen bonds. Our results also suggest that slow kinetics, rather than free energy differences, is mainly responsible for the stability of the collagen triple helix.

Binding of cell surface glycans by influenza hemagglutinin controls viral attachment and infection of host cells. This binding is a three-way interaction between viral proteins, host glycans, and viral glycans; many structural details of this interaction have been difficult to resolve. Here, we use a series of 100-ns molecular dynamics simulations to further analyze available crystallographic data on hemagglutinin-ligand interactions. Based on our simulations, we predict that the viral glycans contact the host glycans within 1–2 residues of the ligand-binding site. We also predict that the glycan-glycan interactions contain both stabilizing and destabilizing components. These predictions suggest a structural means to explain why changes to viral glycosylation alter the efficiency and selectivity of ligand binding. We also predict that the proximity of these interactions to the ligand-binding pocket will impact the binding affinity of small glycomimetic ligands analogous to the influenza neuraminidase inhibitors currently in clinical use.