Measuring similarity between dynamic ensembles of biomolecules

DNA mismatches reveal conformational penalties in protein-DNA recognition

Transcription factors recognize specific genomic sequences to regulate complex gene-expression programs. Although it is well-established that transcription factors bind to specific DNA sequences using a combination of base readout and shape recognition, some fundamental aspects of protein-DNA binding remain poorly understood1,2. Many DNA-binding proteins induce changes in the structure of the DNA outside the intrinsic B-DNA envelope. However, how the energetic cost that is associated with distorting the DNA contributes to recognition has proven difficult to study, because the distorted DNA exists in low abundance in the unbound ensemble3-9. Here we use a high-throughput assay that we term SaMBA (saturation mismatch-binding assay) to investigate the role of DNA conformational penalties in transcription factor-DNA recognition. In SaMBA, mismatched base pairs are introduced to pre-induce structural distortions in the DNA that are much larger than those induced by changes in the Watson-Crick sequence. Notably, approximately 10% of mismatches increased transcription factor binding, and for each of the 22 transcription factors that were examined, at least one mismatch was found that increased the binding affinity. Mismatches also converted non-specific sites into high-affinity sites, and high-affinity sites into 'super sites' that exhibit stronger affinity than any known canonical binding site. Determination of high-resolution X-ray structures, combined with nuclear magnetic resonance measurements and structural analyses, showed that many of the DNA mismatches that increase binding induce distortions that are similar to those induced by protein binding-thus prepaying some of the energetic cost incurred from deforming the DNA. Our work indicates that conformational penalties are a major determinant of protein-DNA recognition, and reveals mechanisms by which mismatches can recruit transcription factors and thus modulate replication and repair activities in the cell10,11.

Distance-Based Metrics for Comparing Conformational Ensembles of Intrinsically Disordered Proteins

Intrinsically disordered proteins are proteins whose native functional states represent ensembles of highly diverse conformations. Such ensembles are a challenge for quantitative structure comparisons because their conformational diversity precludes optimal superimposition of the atomic coordinates necessary for deriving common similarity measures such as the root mean-square deviation of these coordinates. Here, we introduce superimposition-free metrics that are based on computing matrices of the Cα-Cα distance distributions within ensembles and comparing these matrices between ensembles. Differences between two matrices yield information on the similarity between specific regions of the polypeptide, whereas the global structural similarity is captured by the root mean-square difference between the medians of the Cα-Cα distance distributions of two ensembles. Together, our metrics enable rigorous investigations of structure-function relationships in conformational ensembles of intrinsically disordered proteins derived using experimental restraints or by molecular simulations and for proteins containing both structured and disordered regions.

Salt Dependence of A-Form RNA Duplexes: Structures and Implications

The biological functions of RNA range from gene regulation through catalysis and depend critically on its structure and flexibility. Conformational variations of flexible, non-base-paired components, including RNA hinges, bulges, or single-stranded tails, are well documented. Recent work has also identified variations in the structure of ubiquitous, base-paired duplexes found in almost all functional RNAs. Duplexes anchor the structures of folded RNAs, and their surface features are recognized by partner molecules. To date, no consistent picture has been obtained that describes the range of conformations assumed by RNA duplexes. Here, we apply wide angle, solution X-ray scattering (WAXS) to quantify these variations, by sampling length scales characteristic of helical geometries under different solution conditions. To identify the radius, helical rise, twist, and length of dsRNA helices, we exploit molecular dynamics generated structures, explicit solvent models, and ensemble optimization methods. Our results quantify the substantial and salt-dependent deviations of double-stranded (ds) RNA duplexes from the assumed canonical A-form conformation. Recent experiments underscore the need to properly describe the structures of RNA duplexes when interpreting the salt dependence of RNA conformations.

NMR characterization of RNA small molecule interactions

Exciting discoveries of naturally occurring ligand-sensing and disease-linked noncoding RNAs have promoted significant interests in understanding RNA-small molecule interactions. NMR spectroscopy is a powerful tool for characterizing intermolecular interactions. In this review, we describe protocols and approaches for applying NMR spectroscopy to investigate interactions between RNA and small molecules. We review protocols for RNA sample preparation, methods for identifying RNA-binding small molecules, approaches for mapping RNA-small molecule interactions, determining complex structures, and characterizing binding kinetics. We hope this review will provide a guideline to streamline NMR applications in studying RNA-small molecule interactions, facilitating both basic mechanistic understandings of RNA functions and translational efforts in developing RNA-targeted therapeutics.

Conformations of an RNA Helix-Junction-Helix Construct Revealed by SAXS Refinement of MD Simulations

RNA is involved in a broad range of biological processes that extend far beyond translation. Many of RNA's recently discovered functions rely on folding to a specific conformation or transitioning between conformations. The RNA structure contains rigid, short basepaired regions connected by more flexible linkers. Studies of model constructs such as small helix-junction-helix (HJH) motifs are useful in understanding how these elements work together to determine RNA conformation. Here, we reveal the full ensemble of solution structures assumed by a model RNA HJH. We apply small-angle x-ray scattering and an ensemble optimization method to selectively refine models generated by all-atom molecular dynamics simulations. The expectation of a broad distribution of helix orientations, at and above physiological ionic strength, is not met. Instead, this analysis shows that the HJH structures are dominated by two distinct conformations at moderate to high ionic strength. Atomic structures, selected from the molecular dynamics simulations, reveal strong base-base interactions in the junction that critically constrain the conformational space available to the HJH molecule and lead to a surprising re-extension at high salt. These results are corroborated by comparison with previous single-molecule fluorescence resonance energy transfer experiments on the same constructs.

Increasing the length of poly-pyrimidine bulges broadens RNA conformational ensembles with minimal impact on stacking energetics

Helical elements separated by bulges frequently undergo transitions between unstacked and coaxially stacked conformations during the folding and function of noncoding RNAs. Here, we examine the dynamic properties of poly-pyrimidine bulges of varying length (n = 1-4, 7) across a range of Mg²⁺ concentrations using HIV-1 TAR RNA as a model system and solution NMR spectroscopy. In the absence of Mg²⁺, helices linked by bulges with n ≥ 3 residues adopt predominantly unstacked conformations (stacked population <15%), whereas one-bulge and two-bulge motifs adopt predominantly stacked conformations (stacked population >74%). In the presence of 3 mM Mg²⁺, the helices predominantly coaxially stack (stacked population >84%), regardless of bulge length, and the midpoint for the Mg²⁺-dependent stacking transition is within threefold regardless of bulge length. In the absence of Mg²⁺, the difference between free energy of interhelical coaxial stacking across the bulge variants is estimated to be ∼2.9 kcal/mol, based on an NMR chemical shift mapping with stacking being more energetically disfavored for the longer bulges. This difference decreases to ∼0.4 kcal/mol in the presence of Mg²⁺ NMR RDCs and resonance intensity data show increased dynamics in the stacked state with increasing bulge length in the presence of Mg²⁺ We propose that Mg²⁺ helps to neutralize the growing electrostatic repulsion in the stacked state with increasing bulge length thereby increasing the number of coaxial conformations that are sampled. Energetically compensated interhelical stacking dynamics may help to maximize the conformational adaptability of RNA and allow a wide range of conformations to be optimally stabilized by proteins and ligands.

Acceleration of biomolecular kinetics in Gaussian accelerated molecular dynamics

Recent studies demonstrated that Gaussian accelerated molecular dynamics (GaMD) is a robust computational technique, which provides simultaneous unconstrained enhanced sampling and free energy calculations of biomolecules. However, the exact acceleration of biomolecular dynamics or speedup of kinetic rates in GaMD simulations and, more broadly, in enhanced sampling methods, remains a challenging task to be determined. Here, the GaMD acceleration is examined using alanine dipeptide in explicit solvent as a biomolecular model system. Relative to long conventional molecular dynamics simulation, GaMD simulations exhibited ∼36-67 times speedup for sampling of the backbone dihedral transitions. The acceleration depended on level of the GaMD boost potential. Furthermore, Kramers' rate theory was applied to estimate GaMD acceleration using simulation-derived diffusion coefficients, curvatures and barriers of free energy profiles. In most cases, the calculations also showed significant speedup of dihedral transitions in GaMD, although the GaMD acceleration factors tended to be underestimated by ∼3-96 fold. Because greater boost potential can be applied in GaMD simulations of systems with increased sizes, which potentially leads to higher acceleration, it is subject to future studies on accelerating the dynamics and recovering kinetic rates of larger biomolecules such as proteins and protein-protein/nucleic acid complexes.

Conformational ensemble comparison for small molecules in drug discovery

Quantification of three-dimensional similarity between small molecules is a fundamental tool of rational drug design. However, there are no widely-adopted scoring approaches for comparing whole conformational ensembles between molecules. Such scores would be desirable for scenarios in which properties of a molecule have been measured (e.g. activity against a target) but the relevant three dimensional structure is not known. In this study, a set of three complementary ensemble comparison scores is proposed. These are the maximum similarity between any pair of conformations; the proportion of the whole set of the conformations that are matched to within a threshold 3D similarity score; and the average value over these matched conformations of the molecular shape descriptor 'σ-fct', introduced by Ballester et al. The utility of this scoring set is demonstrated in three case studies. The first is an attempt to discriminate between the conformational behaviours of a series of compounds with varying types of cyclisations and other conformationally-significant modifications; the second is an analysis of the more and less active members of a series of GPR119 agonists plus an analysis of a series of orexin-1 antagonists; and the third case study is an attempt to obtain enrichment of active against inactive compounds for a subset of the DUD·E dataset, by ensemble comparison against an active reference compound.

High-performance virtual screening by targeting a high-resolution RNA dynamic ensemble

Dynamic ensembles hold great promise in advancing RNA-targeted drug discovery. Here we subjected the transactivation response element (TAR) RNA from human immunodeficiency virus type-1 to experimental high-throughput screening against ~100,000 drug-like small molecules. Results were augmented with 170 known TAR-binding molecules and used to generate sublibraries optimized for evaluating enrichment when virtually screening a dynamic ensemble of TAR determined by combining NMR spectroscopy data and molecular dynamics simulations. Ensemble-based virtual screening scores molecules with an area under the receiver operator characteristic curve of ~0.85-0.94 and with ~40-75% of all hits falling within the top 2% of scored molecules. The enrichment decreased significantly for ensembles generated from the same molecular dynamics simulations without input NMR data and for other control ensembles. The results demonstrate that experimentally determined RNA ensembles can significantly enrich libraries with true hits and that the degree of enrichment is dependent on the accuracy of the ensemble.

RNA Structural Dynamics As Captured by Molecular Simulations: A Comprehensive Overview

With both catalytic and genetic functions, ribonucleic acid (RNA) is perhaps the most pluripotent chemical species in molecular biology, and its functions are intimately linked to its structure and dynamics. Computer simulations, and in particular atomistic molecular dynamics (MD), allow structural dynamics of biomolecular systems to be investigated with unprecedented temporal and spatial resolution. We here provide a comprehensive overview of the fast-developing field of MD simulations of RNA molecules. We begin with an in-depth, evaluatory coverage of the most fundamental methodological challenges that set the basis for the future development of the field, in particular, the current developments and inherent physical limitations of the atomistic force fields and the recent advances in a broad spectrum of enhanced sampling methods. We also survey the closely related field of coarse-grained modeling of RNA systems. After dealing with the methodological aspects, we provide an exhaustive overview of the available RNA simulation literature, ranging from studies of the smallest RNA oligonucleotides to investigations of the entire ribosome. Our review encompasses tetranucleotides, tetraloops, a number of small RNA motifs, A-helix RNA, kissing-loop complexes, the TAR RNA element, the decoding center and other important regions of the ribosome, as well as assorted others systems. Extended sections are devoted to RNA-ion interactions, ribozymes, riboswitches, and protein/RNA complexes. Our overview is written for as broad of an audience as possible, aiming to provide a much-needed interdisciplinary bridge between computation and experiment, together with a perspective on the future of the field.

Statistical Measures to Quantify Similarity between Molecular Dynamics Simulation Trajectories

Molecular dynamics simulation is commonly employed to explore protein dynamics. Despite the disparate timescales between functional mechanisms and molecular dynamics (MD) trajectories, functional differences are often inferred from differences in conformational ensembles between two proteins in structure-function studies that investigate the effect of mutations. A common measure to quantify differences in dynamics is the root mean square fluctuation (RMSF) about the average position of residues defined by Cα-atoms. Using six MD trajectories describing three native/mutant pairs of beta-lactamase, we make comparisons with additional measures that include Jensen-Shannon, modifications of Kullback-Leibler divergence, and local p-values from 1-sample Kolmogorov-Smirnov tests. These additional measures require knowing a probability density function, which we estimate by using a nonparametric maximum entropy method that quantifies rare events well. The same measures are applied to distance fluctuations between Cα-atom pairs. Results from several implementations for quantitative comparison of a pair of MD trajectories are made based on fluctuations for on-residue and residue-residue local dynamics. We conclude that there is almost always a statistically significant difference between pairs of 100 ns all-atom simulations on moderate-sized proteins as evident from extraordinarily low p-values.

Determination of the conformational ensemble of the TAR RNA by X-ray scattering interferometry

The conformational ensembles of structured RNA's are crucial for biological function, but they remain difficult to elucidate experimentally. We demonstrate with HIV-1 TAR RNA that X-ray scattering interferometry (XSI) can be used to determine RNA conformational ensembles. X-ray scattering interferometry (XSI) is based on site-specifically labeling RNA with pairs of heavy atom probes, and precisely measuring the distribution of inter-probe distances that arise from a heterogeneous mixture of RNA solution structures. We show that the XSI-based model of the TAR RNA ensemble closely resembles an independent model derived from NMR-RDC data. Further, we show how the TAR RNA ensemble changes shape at different salt concentrations. Finally, we demonstrate that a single hybrid model of the TAR RNA ensemble simultaneously fits both the XSI and NMR-RDC data set and show that XSI can be combined with NMR-RDC to further improve the quality of the determined ensemble. The results suggest that XSI-RNA will be a powerful approach for characterizing the solution conformational ensembles of RNAs and RNA-protein complexes under diverse solution conditions.

Insights into Watson-Crick/Hoogsteen breathing dynamics and damage repair from the solution structure and dynamic ensemble of DNA duplexes containing m1A

In the canonical DNA double helix, Watson-Crick (WC) base pairs (bps) exist in dynamic equilibrium with sparsely populated (∼0.02-0.4%) and short-lived (lifetimes ∼0.2-2.5 ms) Hoogsteen (HG) bps. To gain insights into transient HG bps, we used solution-state nuclear magnetic resonance spectroscopy, including measurements of residual dipolar couplings and molecular dynamics simulations, to examine how a single HG bp trapped using the N1-methylated adenine (m1A) lesion affects the structural and dynamic properties of two duplexes. The solution structure and dynamic ensembles of the duplexes reveals that in both cases, m1A forms a m1A•T HG bp, which is accompanied by local and global structural and dynamic perturbations in the double helix. These include a bias toward the BI backbone conformation; sugar repuckering, major-groove directed kinking (∼9°); and local melting of neighboring WC bps. These results provide atomic insights into WC/HG breathing dynamics in unmodified DNA duplexes as well as identify structural and dynamic signatures that could play roles in m1A recognition and repair.

Defining Low-Dimensional Projections to Guide Protein Conformational Sampling

Exploring the conformational space of proteins is critical to characterize their functions. Numerous methods have been proposed to sample a protein's conformational space, including techniques developed in the field of robotics and known as sampling-based motion-planning algorithms (or sampling-based planners). However, these algorithms suffer from the curse of dimensionality when applied to large proteins. Many sampling-based planners attempt to mitigate this issue by keeping track of sampling density to guide conformational sampling toward unexplored regions of the conformational space. This is often done using low-dimensional projections as an indirect way to reduce the dimensionality of the exploration problem. However, how to choose an appropriate projection and how much it influences the planner's performance are still poorly understood issues. In this article, we introduce two methodologies defining low-dimensional projections that can be used by sampling-based planners for protein conformational sampling. The first method leverages information about a protein's flexibility to construct projections that can efficiently guide conformational sampling, when expert knowledge is available. The second method builds similar projections automatically, without expert intervention. We evaluate the projections produced by both methodologies on two conformational search problems involving three middle-size proteins. Our experiments demonstrate that (i) defining projections based on expert knowledge can benefit conformational sampling and (ii) automatically constructing such projections is a reasonable alternative.

Unconstrained Enhanced Sampling for Free Energy Calculations of Biomolecules: A Review

Free energy calculations are central to understanding the structure, dynamics and function of biomolecules. Yet insufficient sampling of biomolecular configurations is often regarded as one of the main sources of error. Many enhanced sampling techniques have been developed to address this issue. Notably, enhanced sampling methods based on biasing collective variables (CVs), including the widely used umbrella sampling, adaptive biasing force and metadynamics, have been discussed in a recent excellent review (Abrams and Bussi, Entropy, 2014). Here, we aim to review enhanced sampling methods that do not require predefined system-dependent CVs for biomolecular simulations and as such do not suffer from the hidden energy barrier problem as encountered in the CV-biasing methods. These methods include, but are not limited to, replica exchange/parallel tempering, self-guided molecular/Langevin dynamics, essential energy space random walk and accelerated molecular dynamics. While it is overwhelming to describe all details of each method, we provide a summary of the methods along with the applications and offer our perspectives. We conclude with challenges and prospects of the unconstrained enhanced sampling methods for accurate biomolecular free energy calculations.

ENCORE: Software for Quantitative Ensemble Comparison

There is increasing evidence that protein dynamics and conformational changes can play an important role in modulating biological function. As a result, experimental and computational methods are being developed, often synergistically, to study the dynamical heterogeneity of a protein or other macromolecules in solution. Thus, methods such as molecular dynamics simulations or ensemble refinement approaches have provided conformational ensembles that can be used to understand protein function and biophysics. These developments have in turn created a need for algorithms and software that can be used to compare structural ensembles in the same way as the root-mean-square-deviation is often used to compare static structures. Although a few such approaches have been proposed, these can be difficult to implement efficiently, hindering a broader applications and further developments. Here, we present an easily accessible software toolkit, called ENCORE, which can be used to compare conformational ensembles generated either from simulations alone or synergistically with experiments. ENCORE implements three previously described methods for ensemble comparison, that each can be used to quantify the similarity between conformational ensembles by estimating the overlap between the probability distributions that underlie them. We demonstrate the kinds of insights that can be obtained by providing examples of three typical use-cases: comparing ensembles generated with different molecular force fields, assessing convergence in molecular simulations, and calculating differences and similarities in structural ensembles refined with various sources of experimental data. We also demonstrate efficient computational scaling for typical analyses, and robustness against both the size and sampling of the ensembles. ENCORE is freely available and extendable, integrates with the established MDAnalysis software package, reads ensemble data in many common formats, and can work with large trajectory files.

Modulating RNA Alignment Using Directional Dynamic Kinks: Application in Determining an Atomic-Resolution Ensemble for a Hairpin using NMR Residual Dipolar Couplings

Approaches that combine experimental data and computational molecular dynamics (MD) to determine atomic resolution ensembles of biomolecules require the measurement of abundant experimental data. NMR residual dipolar couplings (RDCs) carry rich dynamics information, however, difficulties in modulating overall alignment of nucleic acids have limited the ability to fully extract this information. We present a strategy for modulating RNA alignment that is based on introducing variable dynamic kinks in terminal helices. With this strategy, we measured seven sets of RDCs in a cUUCGg apical loop and used this rich data set to test the accuracy of an 0.8 μs MD simulation computed using the Amber ff10 force field as well as to determine an atomic resolution ensemble. The MD-generated ensemble quantitatively reproduces the measured RDCs, but selection of a sub-ensemble was required to satisfy the RDCs within error. The largest discrepancies between the RDC-selected and MD-generated ensembles are observed for the most flexible loop residues and backbone angles connecting the loop to the helix, with the RDC-selected ensemble resulting in more uniform dynamics. Comparison of the RDC-selected ensemble with NMR spin relaxation data suggests that the dynamics occurs on the ps-ns time scales as verified by measurements of R(1ρ) relaxation-dispersion data. The RDC-satisfying ensemble samples many conformations adopted by the hairpin in crystal structures indicating that intrinsic plasticity may play important roles in conformational adaptation. The approach presented here can be applied to test nucleic acid force fields and to characterize dynamics in diverse RNA motifs at atomic resolution.

(Dis)similarity Index To Compare Correlated Motions in Molecular Simulations

Molecular dynamics (MD) simulations are widely used to complement or guide experimental studies in the characterization of protein dynamics, thanks to improvements in force-field accuracy, along with in the software and hardware to sample the conformational landscape of proteins. Among the different applications of MD simulations, the study of correlated motions is largely employed for different purposes. Several metrics have been developed to describe correlated motions in the MD ensemble, such as methods based on Pearson Correlation or Mutual Information. Cross-correlation analysis of MD trajectories is indeed appealing not only to identify residues characterized by coupled fluctuations in protein structures but also since it can be used to extrapolate motions along directions in which major conformational changes should occur, for example on longer time scales than the ones that are actually simulated. Nevertheless, most of the MD studies employ average correlation maps and mostly in a qualitative way, even when different systems or different replicates of the same system are compared. The broad application of correlation metrics in the analysis of MD simulations, especially for comparative purposes, requires a step forward toward more quantitative and accurate comparisons. We thus here employed a simple but effective index, which is based on a normalized Frobenius norm of the differences between protein correlation maps, to compare correlated motions. We applied this index for a quantitative comparison of correlated motions from MD simulations of seven proteins of different size and fold. We also employed the index to assess the robustness of correlation description when multi-replicate MD simulations of a same system are used, and we compared our index to metrics for comparison of structural ensembles such as Root Mean Square Inner Product and the Bhattacharyya Coefficient.

Unveiling Inherent Degeneracies in Determining Population-Weighted Ensembles of Interdomain Orientational Distributions Using NMR Residual Dipolar Couplings: Application to RNA Helix Junction Helix Motifs

A growing number of studies employ time-averaged experimental data to determine dynamic ensembles of biomolecules. While it is well-known that different ensembles can satisfy experimental data to within error, the extent and nature of these degeneracies, and their impact on the accuracy of the ensemble determination remains poorly understood. Here, we use simulations and a recently introduced metric for assessing ensemble similarity to explore degeneracies in determining ensembles using NMR residual dipolar couplings (RDCs) with specific application to A-form helices in RNA. Various target ensembles were constructed representing different domain-domain orientational distributions that are confined to a topologically restricted (<10%) conformational space. Five independent sets of ensemble averaged RDCs were then computed for each target ensemble and a "sample and select" scheme used to identify degenerate ensembles that satisfy RDCs to within experimental uncertainty. We find that ensembles with different ensemble sizes and that can differ significantly from the target ensemble (by as much as ∑Ω ∼ 0.4 where ∑Ω varies between 0 and 1 for maximum and minimum ensemble similarity, respectively) can satisfy the ensemble averaged RDCs. These deviations increase with the number of unique conformers and breadth of the target distribution, and result in significant uncertainty in determining conformational entropy (as large as 5 kcal/mol at T = 298 K). Nevertheless, the RDC-degenerate ensembles are biased toward populated regions of the target ensemble, and capture other essential features of the distribution, including the shape. Our results identify ensemble size as a major source of uncertainty in determining ensembles and suggest that NMR interactions such as RDCs and spin relaxation, on their own, do not carry the necessary information needed to determine conformational entropy at a useful level of precision. The framework introduced here provides a general approach for exploring degeneracies in ensemble determination for different types of experimental data.

Integrative, dynamic structural biology at atomic resolution--it's about time

Biomolecules adopt a dynamic ensemble of conformations, each with the potential to interact with binding partners or perform the chemical reactions required for a multitude of cellular functions. Recent advances in X-ray crystallography, nuclear magnetic resonance (NMR) spectroscopy and other techniques are helping us realize the dream of seeing--in atomic detail--how different parts of biomolecules shift between functional substates using concerted motions. Integrative structural biology has advanced our understanding of the formation of large macromolecular complexes and how their components interact in assemblies by leveraging data from many low-resolution methods. Here, we review the growing opportunities for integrative, dynamic structural biology at the atomic scale, contending there is increasing synergistic potential between X-ray crystallography, NMR and computer simulations to reveal a structural basis for protein conformational dynamics at high resolution.

New insights into Hoogsteen base pairs in DNA duplexes from a structure-based survey

Hoogsteen (HG) base pairs (bps) provide an alternative pairing geometry to Watson-Crick (WC) bps and can play unique functional roles in duplex DNA. Here, we use structural features unique to HG bps (syn purine base, HG hydrogen bonds and constricted C1'-C1' distance across the bp) to search for HG bps in X-ray structures of DNA duplexes in the Protein Data Bank. The survey identifies 106 A•T and 34 G•C HG bps in DNA duplexes, many of which are undocumented in the literature. It also uncovers HG-like bps with syn purines lacking HG hydrogen bonds or constricted C1'-C1' distances that are analogous to conformations that have been proposed to populate the WC-to-HG transition pathway. The survey reveals HG preferences similar to those observed for transient HG bps in solution by nuclear magnetic resonance, including stronger preferences for A•T versus G•C bps, TA versus GG steps, and also suggests enrichment at terminal ends with a preference for 5'-purine. HG bps induce small local perturbations in neighboring bps and, surprisingly, a small but significant degree of DNA bending (∼14°) directed toward the major groove. The survey provides insights into the preferences and structural consequences of HG bps in duplex DNA.

Cation-induced kinetic heterogeneity of the intron-exon recognition in single group II introns

RNA is commonly believed to undergo a number of sequential folding steps before reaching its functional fold, i.e., the global minimum in the free energy landscape. However, there is accumulating evidence that several functional conformations are often in coexistence, corresponding to multiple (local) minima in the folding landscape. Here we use the 5'-exon-intron recognition duplex of a self-splicing ribozyme as a model system to study the influence of Mg(2+) and Ca(2+) on RNA tertiary structure formation. Bulk and single-molecule spectroscopy reveal that near-physiological M(2+) concentrations strongly promote interstrand association. Moreover, the presence of M(2+) leads to pronounced kinetic heterogeneity, suggesting the coexistence of multiple docked and undocked RNA conformations. Heterogeneity is found to decrease at saturating M(2+) concentrations. Using NMR, we locate specific Mg(2+) binding pockets and quantify their affinity toward Mg(2+). Mg(2+) pulse experiments show that M(2+) exchange occurs on the timescale of seconds. This unprecedented combination of NMR and single-molecule Förster resonance energy transfer demonstrates for the first time to our knowledge that a rugged free energy landscape coincides with incomplete occupation of specific M(2+) binding sites at near-physiological M(2+) concentrations. Unconventional kinetics in nucleic acid folding frequently encountered in single-molecule experiments are therefore likely to originate from a spectrum of conformations that differ in the occupation of M(2+) binding sites.

Frequent side chain methyl carbon-oxygen hydrogen bonding in proteins revealed by computational and stereochemical analysis of neutron structures

The propensity of backbone Cα atoms to engage in carbon-oxygen (CH · · · O) hydrogen bonding is well-appreciated in protein structure, but side chain CH · · · O hydrogen bonding remains largely uncharacterized. The extent to which side chain methyl groups in proteins participate in CH · · · O hydrogen bonding is examined through a survey of neutron crystal structures, quantum chemistry calculations, and molecular dynamics simulations. Using these approaches, methyl groups were observed to form stabilizing CH · · · O hydrogen bonds within protein structure that are maintained through protein dynamics and participate in correlated motion. Collectively, these findings illustrate that side chain methyl CH · · · O hydrogen bonding contributes to the energetics of protein structure and folding.

Insights into domain-domain motions in proteins and RNA from solution NMR

Many multidomain proteins and ribonucleic acids consist of domains that autonomously fold and that are linked together by flexible junctions. This architectural design allows domains to sample a wide range of positions with respect to one another, yet do so in a way that retains structural specificity, since the number of sampled conformations remains extremely small compared to the total conformations that would be sampled if the domains were connected by an infinitely long linker. This “tuned” flexibility in interdomain conformation is in turn used in many biochemical processes.

There is great interest in characterizing the dynamic properties of multidomain systems, and moving beyond conventional descriptions in terms of static structures, toward the characterization of population-weighted ensembles describing a distribution of many conformations sampled in solution. There is also great interest in understanding the design principles and underlying physical and chemical interactions that specify the nature of interdomain flexibility. NMR spectroscopy is one of the most powerful techniques for characterizing motions in complex biomolecules and has contributed greatly toward our basic understanding of dynamics in proteins and nucleic acids and its role in folding, recognition, and signaling.

Here, we review methods that have been developed in our laboratories to address these challenges. Our approaches are based on the ability of one domain of the molecule to self-align in a magnetic field, or to dominate the overall orientation of the molecule, so that the conformational freedom of other domains can be assessed by their degree of alignment induced by the aligned part. In turn, this self-alignment ability can be intrinsic or can be caused by tagging appropriate constructs to the molecule of interest. In general, self-alignment is due to magnetic susceptibility anisotropy. Nucleic acids with elongated helices have this feature, as well as several paramagnetic metal centers that can be found in, or attached to, a protein domain.