We present a new estimator for computing free energy differences and thermodynamic expectations as well as their uncertainties from samples obtained from multiple equilibrium states via either simulation or experiment. The estimator, which we call the multistate Bennett acceptance ratio estimator ͑MBAR͒ because it reduces to the Bennett acceptance ratio estimator ͑BAR͒ when only two states are considered, has significant advantages over multiple histogram reweighting methods for combining data from multiple states. It does not require the sampled energy range to be discretized to produce histograms, eliminating bias due to energy binning and significantly reducing the time complexity of computing a solution to the estimating equations in many cases. Additionally, an estimate of the statistical uncertainty is provided for all estimated quantities. In the large sample limit, MBAR is unbiased and has the lowest variance of any known estimator for making use of equilibrium data collected from multiple states. We illustrate this method by producing a highly precise estimate of the potential of mean force for a DNA hairpin system, combining data from multiple optical tweezer measurements under constant force bias.

OpenMM is a molecular dynamics simulation toolkit with a unique focus on extensibility. It allows users to easily add new features, including forces with novel functional forms, new integration algorithms, and new simulation protocols. Those features automatically work on all supported hardware types (including both CPUs and GPUs) and perform well on all of them. In many cases they require minimal coding, just a mathematical description of the desired function. They also require no modification to OpenMM itself and can be distributed independently of OpenMM. This makes it an ideal tool for researchers developing new simulation methods, and also allows those new methods to be immediately available to the larger community.

It has recently become practical to construct Markov state models (MSMs) that reproduce the long-time statistical conformational dynamics of biomolecules using data from molecular dynamics simulations. MSMs can predict both stationary and kinetic quantities on long timescales (e.g. milliseconds) using a set of atomistic molecular dynamics simulations that are individually much shorter, thus addressing the well-known sampling problem in molecular dynamics simulation. In addition to providing predictive quantitative models, MSMs greatly facilitate both the extraction of insight into biomolecular mechanism (such as folding and functional dynamics) and quantitative comparison with single-molecule and ensemble kinetics experiments. A variety of methodological advances and software packages now bring the construction of these models closer to routine practice. Here, we review recent progress in this field, considering theoretical and methodological advances, new software tools, and recent applications of these approaches in several domains of biochemistry and biophysics, commenting on remaining challenges.

OpenMM is a software toolkit for performing molecular simulations on a range of high performance computing architectures. It is based on a layered architecture: the lower layers function as a reusable library that can be invoked by any application, while the upper layers form a complete environment for running molecular simulations. The library API hides all hardware-specific dependencies and optimizations from the users and developers of simulation programs: they can be run without modification on any hardware on which the API has been implemented. The current implementations of OpenMM include support for graphics processing units using the OpenCL and CUDA frameworks. In addition, OpenMM was designed to be extensible, so new hardware architectures can be accommodated and new functionality (e.g., energy terms and integrators) can be easily added.

Alchemical free energy calculations are becoming a useful tool for calculating absolute binding free energies of small molecule ligands to proteins. Here, we find that the presence of multiple metastable ligand orientations can cause convergence problems when distance restraints alone are used. We demonstrate that the use of orientational restraints can greatly accelerate the convergence of these calculations. However, even with this acceleration, we find that sufficient sampling requires substantially longer simulations than are used in many published protocols. To further accelerate convergence, we introduce a new method of configuration space decomposition by orientation which reduces required simulation lengths by at least a factor of 5 in the cases examined. Our method is easily parallelizable, well suited for cases where a ligand cocrystal structure is not available, and can utilize initial orientations generated by docking packages.

Recent calorimetric studies of small molecule interactions with biomolecular targets have generated renewed interest in the phenomenon of entropy-enthalpy compensation. In these studies, entropic and enthalpic contributions to binding are observed to vary substantially and in an opposing manner as the ligand or protein is modified while the binding free energy varies little. In severe examples, engineered enthalpic gains can lead to completely compensating entropic penalties, frustrating ligand design. Here, we examine the evidence for compensation, as well as its potential origins, prevalence, severity, and ramifications for ligand engineering. We find the evidence for severe compensation to be weak in light of the large magnitude of and correlation between errors in experimental measurements of entropic and enthalpic contributions to binding, though a limited form of compensation may be common. Given the difficulty of predicting or measuring entropic and enthalpic changes to useful precision, or using this information in design, we recommend ligand engineering efforts instead focus on computational and experimental methodologies to directly assess changes in binding free energy.

SUMMARY Somatic mutations in isocitrate dehydrogenase 1 or 2 (IDH1/2) contribute to the pathogenesis of cancer via production of the ‘oncometabolite’ D-2-hydroxyglutarate (D-2HG). Elevated D-2HG can block differentiation of malignant cells by functioning as a competitive inhibitor of alpha-ketoglutarate (α-KG)-dependent enzymes, including Jumonji family histone lysine demethylases. 2HG is a chiral molecule that can exist in either the D- or L- enantiomer. Although cancer-associated IDH1/2 mutations produce D-2HG, biochemical studies have demonstrated that L-2HG also functions as a potent inhibitor of α-KG-dependent enzymes. Here we report that under conditions of oxygen limitation, mammalian cells selectively produce L-2HG via enzymatic reduction of α-KG. Hypoxia-induced L-2HG is not mediated by IDH1 or IDH2, but instead results from promiscuous substrate usage primarily by lactate dehydrogenase A (LDHA). During hypoxia, the resulting increase in L-2HG is necessary and sufficient for the induction of increased methylation of histone repressive marks, including histone 3 lysine 9 (H3K9me3).

Proteins are synthesized by the ribosome and generally must fold to become functionally active. Although it is commonly assumed that the ribosome affects the folding process, this idea has been extremely difficult to demonstrate. We have developed an experimental system to investigate the folding of single ribosome-bound stalled nascent polypeptides with optical tweezers. In T4 lysozyme, synthesized in a reconstituted in vitro translation system, the ribosome slows the formation of stable tertiary interactions and the attainment of the native state relative to the free protein. Incomplete T4 lysozyme polypeptides misfold and aggregate when free in solution, but they remain folding-competent near the ribosomal surface. Altogether, our results suggest that the ribosome not only decodes the genetic information and synthesizes polypeptides, but also promotes efficient de novo attainment of the native state.