How RNA unfolds and refolds

Intrinsically disordered regions regulate RhlE RNA helicase functions in bacteria

RNA helicases-central enzymes in RNA metabolism-often feature intrinsically disordered regions (IDRs) that enable phase separation and complex molecular interactions. In the bacterial pathogen Pseudomonas aeruginosa, the non-redundant RhlE1 and RhlE2 RNA helicases share a conserved REC catalytic core but differ in C-terminal IDRs. Here, we show how the IDR diversity defines RhlE RNA helicase specificity of function. Both IDRs facilitate RNA binding and phase separation, localizing proteins in cytoplasmic clusters. However, RhlE2 IDR is more efficient in enhancing REC core RNA unwinding, exhibits a greater tendency for phase separation, and interacts with the RNase E endonuclease, a crucial player in mRNA degradation. Swapping IDRs results in chimeric proteins that are biochemically active but functionally distinct as compared to their native counterparts. The RECRhlE1-IDRRhlE2 chimera improves cold growth of a rhlE1 mutant, gains interaction with RNase E and affects a subset of both RhlE1 and RhlE2 RNA targets. The RECRhlE2-IDRRhlE1 chimera instead hampers bacterial growth at low temperatures in the absence of RhlE1, with its detrimental effect linked to aberrant RNA droplets. By showing that IDRs modulate both protein core activities and subcellular localization, our study defines the impact of IDR diversity on the functional differentiation of RNA helicases.

Atomistic simulations of RNA duplex thermal denaturation: Sequence- and forcefield-dependence

Double-stranded RNA is the end-product of template-based replication, and is also the functional state of some biological RNAs. Similarly to proteins and DNA, they can be denatured by temperature, with important physiological and technological implications. Here, we use an in silico strategy to probe the thermal denaturation of RNA duplexes. Following previous results that were obtained on a few different duplexes, and which nuanced the canonical 2-state picture of nucleic acid denaturation, we here specifically address three different aspects that greatly improve our description of the temperature-induced dsRNA separation. First, we investigate the effect of the spatial distribution of weak and strong base-pairs among the duplex sequence. We show that the deviations from the two-state dehybridization mechanism are more pronounced when a strong core is flanked with weak extremities, while duplexes with a weak core but strong extremities exhibit a two-state behavior, which can be explained by the key role played by base fraying. This was later verified by generating artificial hairpin or circular states containing one or two locked duplex extremities, which results in an important reinforcement of the entire HB structure of the duplex and higher melting temperatures. Finally, we demonstrate that our results are little sensitive to the employed combination of RNA and water forcefields. The trends in thermal stability among the different sequences as well as the observed unfolding mechanisms (and the deviations from a two-state scenario) remain the same regardless of the employed atomistic models. However, our study points to possible limitations of recent reparametrizations of the Amber RNA forcefield, which sometimes results in duplexes that readily denature under ambient conditions, in contradiction with available experimental results.

RNA folding pathways from all-atom simulations with a variationally improved history-dependent bias

Atomically detailed simulations of RNA folding have proven very challenging in view of the difficulties of developing realistic force fields and the intrinsic computational complexity of sampling rare conformational transitions. As a step forward in tackling these issues, we extend to RNA an enhanced path-sampling method previously successfully applied to proteins. In this scheme, the information about the RNA's native structure is harnessed by a soft history-dependent biasing force promoting the generation of productive folding trajectories in an all-atom force field with explicit solvent. A rigorous variational principle is then applied to minimize the effect of the bias. Here, we report on an application of this method to RNA molecules from 20 to 47 nucleotides long and increasing topological complexity. By comparison with analog simulations performed on small proteins with similar size and architecture, we show that the RNA folding landscape is significantly more frustrated, even for relatively small chains with a simple topology. The predicted RNA folding mechanisms are found to be consistent with the available experiments and some of the existing coarse-grained models. Due to its computational performance, this scheme provides a promising platform to efficiently gather atomistic RNA folding trajectories, thus retain the information about the chemical composition of the sequence.

Toward a Molecular Mechanism of Complementary RNA Duplexes Denaturation

RNA duplexes are relatively rare but play very important biological roles. As an end-product of template-based RNA replication, they also have key implications for hypothetical primitive forms of life. Unless they are specifically separated by enzymes, these duplexes denature upon a temperature increase. However, mechanistic and kinetic aspects of RNA (and DNA) duplex thermal denaturation remain unclear at the microscopic level. We propose an in silico strategy that probes the thermal denaturation of RNA duplexes and allows for an extensive conformational space exploration along a wide temperature range with atomistic precision. We show that this approach first accounts for the strong sequence and length dependence of the duplexes melting temperature, reproducing the trends seen in the experiments and predicted by nearest-neighbor models. The simulations are then instrumental at providing a molecular picture of the temperature-induced strand separation. The textbook canonical "all-or-nothing" two-state model, very much inspired by the protein folding mechanism, can be nuanced. We demonstrate that a temperature increase leads to significantly distorted but stable structures with extensive base-fraying at the extremities, and that the fully formed duplexes typically do not form around melting. The duplex separation therefore appears as much more gradual than commonly thought.

Stability of DNA and RNA hairpins: a comparative study based on ox-DNA

Advances in single-molecule experiments on macromolecular crowding urgently need an efficient simulation method to resolve their discrepancies quantitatively. Ox-DNA model has been since reworked to treat the thermodynamics and mechanical properties of DNA/RNA hairpin at a stretching force. In hopping experiments, the critical forces of RNA hairpins at different temperatures are greater than those of DNA hairpins, in addition, the Gibbs free energy at a fixed temperature required to convert an RNA hairpin into a single-stranded molecule at zero force is obviously greater than that of DNA hairpin and gradually decreases by increasing the temperature. As far as force-ramping experiments are concerned, the first-rupture forces of RNA/DNA hairpins corresponding to the maximum probability density linearly pertain to the force-loading rate, with those of RNA hairpins being greater. The extended ox-DNA model could potentially identify the interaction between biologically inert polymer and RNA/DNA hairpins in crowded environments.

Thermodynamics and kinetics of an A-U RNA base pair under force studied by molecular dynamics simulations

Mechanical force has been widely used to study RNA folding and unfolding. Understanding how the force affects the opening and closing of a single base pair, which is a basic step for RNA folding and unfolding and a fundamental behavior in some important biological activities, is crucial to understanding the mechanism of RNA folding and unfolding under mechanical force. In this work, we investigated the opening and closing process of an RNA base pair under mechanical force with constant-force stretching molecular dynamics simulations. It was found that high mechanical force results in overstretching, and the open state is a high-energy state. The enthalpy and entropy change of the base-pair opening-closing transition were obtained and the results at low forces were in good agreement with the nearest-neighbor model. The temperature and force dependence of the opening and closing rates were also obtained. The position of the transition state for the base-pair opening-closing transition under mechanical force was determined. The free energy barrier of opening a base pair without force is the enthalpy increase, and the work done by the force from the closed state to the transition state decreases the barrier and increases the opening rate. The free energy barrier of closing the base pair without force results from the entropy loss, and the work done by the force from the open state to the transition state increases the barrier and decreases the closing rate. The transition rates are strongly dependent on the temperature and force, while the transition path times are weakly dependent on force and temperature.

Exploring the Energy Landscape of Riboswitches Using Collective Variables Based on Tertiary Contacts

Messenger RNA regulatory elements, such as riboswitches, can display a high degree of flexibility. By characterizing their energy landscapes, and corresponding distributions of 3D configurations, structure-function relationships can be elucidated. Molecular dynamics simulation with enhanced sampling is an important strategy used to computationally access free energy landscapes characterizing the accessible 3D conformations of RNAs. While tertiary contacts are thought to play important roles in RNA dynamics, it is difficult, in explicit solvent, to sample the formation and breakage of tertiary contacts, such as helix-helix interactions, pseudoknot interactions, and junction interactions, while maintaining intact secondary structure elements. To this end, we extend previously developed collective variables and metadynamics efforts, to establish a simple metadynamics protocol, which utilizes only one collective variable, based on multiple tertiary contacts, to characterize the underlying free energy landscape of any RNA molecule. We develop a modified collective variable, the tertiary contacts distance (Q_TC), which can probe the formation and breakage of all or selectively chosen tertiary contacts of the RNA. The SAM-I riboswitch in the presence of three ionic and substrate conditions was investigated and validated against the structure ensemble previously generated using SAXS experiments. This efficient and easy to implement all-atom MD simulation based approach incorporating metadynamics to study RNA conformational dynamics can also be transferred to any other type of biomolecule.

Folding Free Energy Determination of an RNA Three-Way Junction Using Fluctuation Theorems

Nonequilibrium work relations and fluctuation theorems permit us to extract equilibrium information from nonequilibrium measurements. They find application in single-molecule pulling experiments where molecular free energies can be determined from irreversible work measurements by using unidirectional (e.g., Jarzynski’s equality) and bidirectional (e.g., Crooks fluctuation theorem and Bennet’s acceptance ratio (BAR)) methods. However, irreversibility and the finite number of pulls limit their applicability: the higher the dissipation, the larger the number of pulls necessary to estimate ΔG within a few kBT. Here, we revisit pulling experiments on an RNA three-way junction (3WJ) that exhibits significant dissipation and work-distribution long tails upon mechanical unfolding. While bidirectional methods are more predictive, unidirectional methods are strongly biased. We also consider a cyclic protocol that combines the forward and reverse work values to increase the statistics of the measurements. For a fixed total experimental time, faster pulling rates permit us to efficiently sample rare events and reduce the bias, compensating for the increased dissipation. This analysis provides a more stringent test of the fluctuation theorem in the large irreversibility regime.

TPP Riboswitch Populates Holo-Form-like Structure Even in the Absence of Cognate Ligand at High Mg2+ Concentration

Riboswitches are noncoding RNA that regulate gene expression by folding into specific three-dimensional structures (holo-form) upon binding by their cognate ligand in the presence of Mg²⁺. Riboswitch functioning is also hypothesized to be under kinetic control requiring large cognate ligand concentrations. We ask the question under thermodynamic conditions, can the riboswitches populate structures similar to the holo-form only in the presence of Mg²⁺ and absence of cognate ligand binding. We addressed this question using thiamine pyrophosphate (TPP) riboswitch as a model system and computer simulations using a coarse-grained model for RNA. The folding free energy surface (FES) shows that with the initial increase in Mg²⁺ concentration ([Mg²⁺]), the aptamer domain (AD) of TPP riboswitch undergoes a barrierless collapse in its dimensions. On further increase in [Mg²⁺], intermediates separated by barriers appear on the FES, and one of the intermediates has a TPP ligand-binding competent structure. We show that site-specific binding of the Mg²⁺ aids in the formation of tertiary contacts. For [Mg²⁺] greater than physiological concentration, AD folds into a structure similar to the crystal structure of the TPP holo-form even in the absence of the TPP ligand. The folding kinetics shows that TPP AD populates an intermediate due to the misalignment of two arms present in the structure, which acts as a kinetic trap, leading to larger folding timescales. The predictions of the intermediate structures from the simulations are amenable for experimental verification.

The Energy Landscape Perspective: Encoding Structure and Function for Biomolecules

The energy landscape perspective is outlined with particular reference to biomolecules that perform multiple functions. We associate these multifunctional molecules with multifunnel energy landscapes, illustrated by some selected examples, where understanding the organisation of the landscape has provided new insight into function. Conformational selection and induced fit may provide alternative routes to realisation of multifunctionality, exploiting the possibility of environmental control and distinct binding modes.

Stem-loop formation drives RNA folding in mechanical unzipping experiments

Accurate knowledge of RNA hybridization is essential for understanding RNA structure and function. Here we mechanically unzip and rezip a 2-kbp RNA hairpin and derive the 10 nearest-neighbor base pair (NNBP) RNA free energies in sodium and magnesium with 0.1 kcal/mol precision using optical tweezers. Notably, force-distance curves (FDCs) exhibit strong irreversible effects with hysteresis and several intermediates, precluding the extraction of the NNBP energies with currently available methods. The combination of a suitable RNA synthesis with a tailored pulling protocol allowed us to obtain the fully reversible FDCs necessary to derive the NNBP energies. We demonstrate the equivalence of sodium and magnesium free-energy salt corrections at the level of individual NNBP. To characterize the irreversibility of the unzipping-rezipping process, we introduce a barrier energy landscape of the stem-loop structures forming along the complementary strands, which compete against the formation of the native hairpin. This landscape correlates with the hysteresis observed along the FDCs. RNA sequence analysis shows that base stacking and base pairing stabilize the stem-loops that kinetically trap the long-lived intermediates observed in the FDC. Stem-loops formation appears as a general mechanism to explain a wide range of behaviors observed in RNA folding.

Computer-aided comprehensive explorations of RNA structural polymorphism through complementary simulation methods

While RNA folding was originally seen as a simple problem to solve, it has been shown that the promiscuous interactions of the nucleobases result in structural polymorphism, with several competing structures generally observed for non-coding RNA. This inherent complexity limits our understanding of these molecules from experiments alone, and computational methods are commonly used to study RNA. Here, we discuss three advanced sampling schemes, namely Hamiltonian-replica exchange molecular dynamics (MD), ratchet-and-pawl MD and discrete path sampling, as well as the HiRE-RNA coarse-graining scheme, and highlight how these approaches are complementary with reference to recent case studies. While all computational methods have their shortcomings, the plurality of simulation methods leads to a better understanding of experimental findings and can inform and guide experimental work on RNA polymorphism.

RNA Modeling with the Computational Energy Landscape Framework

The recent advances in computational abilities, such as the enormous speed-ups provided by GPU computing, allow for large scale computational studies of RNA molecules at an atomic level of detail. As RNA molecules are known to adopt multiple conformations with comparable energies, but different two-dimensional structures, all-atom models are necessary to better describe the structural ensembles for RNA molecules. This point is important because different conformations can exhibit different functions, and their regulation or mis-regulation is linked to a number of diseases. Problematically, the energy barriers between different conformational ensembles are high, resulting in long time scales for interensemble transitions. The computational potential energy landscape framework was designed to overcome this problem of broken ergodicity by use of geometry optimization. Here, we describe the algorithms used in the energy landscape explorations with the OPTIM and PATHSAMPLE programs, and how they are used in biomolecular simulations. We present a recent case study of the 5'-hairpin of RNA 7SK to illustrate how the method can be applied to interpret experimental results, and to obtain a detailed description of molecular properties.

Complex Conformational Dynamics of the Heart Failure-Associated Pre-miRNA-377 Hairpin Revealed by Single-Molecule Optical Tweezers

Pre-miRNA-377 is a hairpin-shaped regulatory RNA associated with heart failure. Here, we use single-molecule optical tweezers to unzip pre-miRNA-377 and study its stability and dynamics. We show that magnesium ions have a strong stabilizing effect, and that sodium ions stabilize the hairpin more than potassium ions. The hairpin unfolds in a single step, regardless of buffer composition. Interestingly, hairpin folding occurs either in a single step (type 1) or through the formation of intermediates, in multiple steps (type 2) or gradually (type 3). Type 3 occurs only in the presence of both sodium and magnesium, while type 1 and 2 take place in all buffers, with type 1 being the most prevalent. By reducing the size of the native hairpin loop from fourteen to four nucleotides, we demonstrate that the folding heterogeneity originates from the large size of the hairpin loop. Further, while efficient pre-miRNA-377 binders are lacking, we demonstrate that the recently developed C2 ligand displays bimodal activity: it enhances the mechanical stability of the pre-miRNA-377 hairpin and perturbs its folding. The knowledge regarding pre-miRNA stability and dynamics that we provide is important in understanding its regulatory function and how it can be modulated to achieve a therapeutic effect, e.g., in heart failure treatment.

Effect of ligand binding on riboswitch folding: Theory and simulations

The effect of ligand binding on the conformational transitions of the add A-riboswitch in cellular environments is investigated theoretically within the framework of the generalized Langevin equation combined with steered molecular dynamics simulations. Results for the transition path time distribution provide an estimate of the transit times, which are difficult to determine experimentally. The time for the conformational transitions of the riboswitch aptamer is longer for the ligand bound state as compared to that of the unbound one. The transition path time of the riboswitch follows a counterintuitive trend as it decreases with an increase in the barrier height. The mean transition path time of either transitions of the riboswitch in the ligand bound/unbound state increases with an increase in the complexity of the surrounding environment due to the caging effect. The results of the probability density function, transition path time distribution, and mean transition path time obtained from the theory qualitatively agree with those obtained from the simulations and with earlier experimental and theoretical studies.

Formation of frameshift-stimulating RNA pseudoknots is facilitated by remodeling of their folding intermediates

Programmed –1 ribosomal frameshifting is an essential regulation mechanism of translation in viruses and bacteria. It is stimulated by mRNA structures inside the coding region. As the structure is unfolded repeatedly by consecutive translating ribosomes, whether it can refold properly each time is important in performing its function. By using single-molecule approaches and molecular dynamics simulations, we found that a frameshift-stimulating RNA pseudoknot folds sequentially through its upstream stem S1 and downstream stem S2. In this pathway, S2 folds from the downstream side and tends to be trapped in intermediates. By masking the last few nucleotides to mimic their gradual emergence from translating ribosomes, S2 can be directed to fold from the upstream region. The results show that the intermediates are greatly suppressed, suggesting that mRNA refolding may be modulated by ribosomes. Moreover, masking the first few nucleotides of S1 favors the folding from S2 and yields native pseudoknots, which are stable enough to retrieve the masked nucleotides. We hypothesize that translating ribosomes can remodel an intermediate mRNA structure into a stable conformation, which may in turn stimulate backward slippage of the ribosome. This supports an interactive model of ribosomal frameshifting and gives an insightful account addressing previous experimental observations.

Regulation of polyphosphate glucokinase gene expression through co-transcriptional processing in Mycobacterium tuberculosis H37Rv

Transcription is a molecular process that involves the synthesis of RNA chain into the 5'-3' direction, and simultaneously nascent RNA chain tends to form geometric structures, known as co-transcriptional folding. This folding determines the functional properties of RNA molecules and possibly has a critical role during the synthesis. This functioning includes the characterized properties of riboswitches and ribozymes, which are significant when the transcription rate is comparable to the cellular environment. This study reports a novel non-coding region important in the genetic expression of polyphosphate glucokinase (ppgk) in Mycobacterium tuberculosis. This non-coding element of ppgk gene undergoes cleavage activity during the transcriptional process in Mycobacterium tuberculosis. We revealed that cleavage occurs within the nascent RNA, and the resultant cleaved 3'RNA fragment carries the Shine- Dalgarno (SD) sequence and expression platform. We concluded co-transcriptional processing at the non-coding region as the required mechanism for ppgk expression that remains constitutive within the bacterial environment. This study defines the molecular mechanism dependent on the transient but highly active structural features of the nascent RNA.

Predicting dynamic cellular protein-RNA interactions by deep learning using in vivo RNA structures

Interactions with RNA-binding proteins (RBPs) are integral to RNA function and cellular regulation, and dynamically reflect specific cellular conditions. However, presently available tools for predicting RBP-RNA interactions employ RNA sequence and/or predicted RNA structures, and therefore do not capture their condition-dependent nature. Here, after profiling transcriptome-wide in vivo RNA secondary structures in seven cell types, we developed PrismNet, a deep learning tool that integrates experimental in vivo RNA structure data and RBP binding data for matched cells to accurately predict dynamic RBP binding in various cellular conditions. PrismNet results for 168 RBPs support its utility for both understanding CLIP-seq results and largely extending such interaction data to accurately analyze additional cell types. Further, PrismNet employs an "attention" strategy to computationally identify exact RBP-binding nucleotides, and we discovered enrichment among dynamic RBP-binding sites for structure-changing variants (riboSNitches), which can link genetic diseases with dysregulated RBP bindings. Our rich profiling data and deep learning-based prediction tool provide access to a previously inaccessible layer of cell-type-specific RBP-RNA interactions, with clear utility for understanding and treating human diseases.

In vivo structural characterization of the SARS-CoV-2 RNA genome identifies host proteins vulnerable to repurposed drugs

Severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) is the cause of the ongoing coronavirus disease 2019 (COVID-19) pandemic. Understanding of the RNA virus and its interactions with host proteins could improve therapeutic interventions for COVID-19. By using icSHAPE, we determined the structural landscape of SARS-CoV-2 RNA in infected human cells and from refolded RNAs, as well as the regulatory untranslated regions of SARS-CoV-2 and six other coronaviruses. We validated several structural elements predicted in silico and discovered structural features that affect the translation and abundance of subgenomic viral RNAs in cells. The structural data informed a deep-learning tool to predict 42 host proteins that bind to SARS-CoV-2 RNA. Strikingly, antisense oligonucleotides targeting the structural elements and FDA-approved drugs inhibiting the SARS-CoV-2 RNA binding proteins dramatically reduced SARS-CoV-2 infection in cells derived from human liver and lung tumors. Our findings thus shed light on coronavirus and reveal multiple candidate therapeutics for COVID-19 treatment.

Molecular mechanisms underlying the extreme mechanical anisotropy of the flaviviral exoribonuclease-resistant RNAs (xrRNAs)

Mechanical anisotropy is an essential property for many biomolecules to assume their structures, functions and applications, however, the mechanisms for their direction-dependent mechanical responses remain elusive. Herein, by using a single-molecule nanopore sensing technique, we explore the mechanisms of directional mechanical stability of the xrRNA1 RNA from ZIKA virus (ZIKV), which forms a complex ring-like architecture. We reveal extreme mechanical anisotropy in ZIKV xrRNA1 which highly depends on Mg²⁺ and the key tertiary interactions. The absence of Mg²⁺ and disruption of the key tertiary interactions strongly affect the structural integrity and attenuate mechanical anisotropy. The significance of ring structures in RNA mechanical anisotropy is further supported by steered molecular dynamics simulations in combination with force distribution analysis. We anticipate the ring structures can be used as key elements to build RNA-based nanostructures with controllable mechanical anisotropy for biomaterial and biomedical applications.

Mg2+ Sensing by an RNA Fragment: Role of Mg2+-Coordinated Water Molecules

RNA molecules selectively bind to specific metal ions to populate their functional active states, making it important to understand their source of ion selectivity. In large RNA systems, metal ions interact with the RNA at multiple locations, making it difficult to decipher the precise role of ions in folding. To overcome this complexity, we studied the role of different metal ions (Mg²⁺, Ca²⁺, and K⁺) in the folding of a small RNA hairpin motif (5'-ucCAAAga-3') using unbiased all-atom molecular dynamics simulations. The advantage of studying this system is that it requires specific binding of a single metal ion to fold to its native state. We find that even for this small RNA, the folding free energy surface (FES) is multidimensional as different metal ions present in the solution can simultaneously facilitate folding. The FES shows that specific binding of a metal ion is indispensable for its folding. We further show that in addition to the negatively charged phosphate groups, the spatial organization of electronegative nucleobase atoms drives the site-specific binding of the metal ions. Even though the binding site cannot discriminate between different metal ions, RNA folds efficiently only in a Mg²⁺ solution. We show that the rigid network of Mg²⁺-coordinated water molecules facilitates the formation of important interactions in the transition state. The other metal ions such as K⁺ and Ca²⁺ cannot facilitate the formation of such interactions. These results allow us to hypothesize possible metal-sensing mechanisms in large metalloriboswitches and also provide useful insights into the design of appropriate collective variables for studying large RNA molecules using enhanced sampling methods.

Modeling Loop Composition and Ion Concentration Effects in RNA Hairpin Folding Stability

The ability to accurately predict RNA hairpin structure and stability for different loop sequences and salt conditions is important for understanding, modeling, and designing larger RNA folds. However, traditional RNA secondary structure models cannot treat loop-sequence and ionic effects on RNA hairpin folding. Here, we describe a general, three-dimensional (3D) conformation-based computational method for modeling salt concentration-dependent conformational distributions and the detailed 3D structures for a set of three RNA hairpins that contain a variable, 15-nucleotide loop sequence. For a given RNA sequence, the new, to our knowledge, method integrates a Vfold2D two-dimensional structure folding model with IsRNA coarse-grained molecular dynamics 3D folding simulations and Monte Carlo tightly bound ion estimations of ion-mediated electrostatic interactions. The model predicts free-energy landscapes for the different RNA hairpin-forming sequences with variable salt conditions. The theoretically predicted results agree with the experimental fluorescence measurements, validating the strategy. Furthermore, the theoretical model goes beyond the experimental results by enabling in-depth 3D structural analysis, revealing energetic mechanisms for the sequence- and salt-dependent folding stability. Although the computational framework presented here is developed for RNA hairpin systems, the general method may be applied to investigate other RNA systems, such as multiway junctions or pseudoknots in mixed metal ion solutions.

Challenges and perspectives for structural biology of lncRNAs-the example of the Xist lncRNA A-repeats

Following the discovery of numerous long non-coding RNA (lncRNA) transcripts in the human genome, their important roles in biology and human disease are emerging. Recent progress in experimental methods has enabled the identification of structural features of lncRNAs. However, determining high-resolution structures is challenging as lncRNAs are expected to be dynamic and adopt multiple conformations, which may be modulated by interaction with protein binding partners. The X-inactive specific transcript (Xist) is necessary for X inactivation during dosage compensation in female placental mammals and one of the best-studied lncRNAs. Recent progress has provided new insights into the domain organization, molecular features, and RNA binding proteins that interact with distinct regions of Xist. The A-repeats located at the 5′ end of the transcript are of particular interest as they are essential for mediating silencing of the inactive X chromosome. Here, we discuss recent progress with elucidating structural features of the Xist lncRNA, focusing on the A-repeats. We discuss the experimental and computational approaches employed that have led to distinct structural models, likely reflecting the intrinsic dynamics of this RNA. The presence of multiple dynamic conformations may also play an important role in the formation of the associated RNPs, thus influencing the molecular mechanism underlying the biological function of the Xist A-repeats. We propose that integrative approaches that combine biochemical experiments and high-resolution structural biology in vitro with chemical probing and functional studies in vivo are required to unravel the molecular mechanisms of lncRNAs.

In vitro selection of l-DNA aptamers that bind a structured d-RNA molecule

The development of structure-specific RNA binding reagents remains a central challenge in RNA biochemistry and drug discovery. Previously, we showed in vitro selection techniques could be used to evolve l-RNA aptamers that bind tightly to structured d-RNAs. However, whether similar RNA-binding properties can be achieved using aptamers composed of l-DNA, which has several practical advantages compared to l-RNA, remains unknown. Here, we report the discovery and characterization of the first l-DNA aptamers against a structured RNA molecule, precursor microRNA-155, thereby establishing the capacity of DNA and RNA molecules of the opposite handedness to form tight and specific ‘cross-chiral’ interactions with each other. l-DNA aptamers bind pre-miR-155 with low nanomolar affinity and high selectivity despite the inability of l-DNA to interact with native d-RNA via Watson–Crick base pairing. Furthermore, l-DNA aptamers inhibit Dicer-mediated processing of pre-miRNA-155. The sequence and structure of l-DNA aptamers are distinct from previously reported l-RNA aptamers against pre-miR-155, indicating that l-DNA and l-RNA interact with the same RNA sequence through unique modes of recognition. Overall, this work demonstrates that l-DNA may be pursued as an alternative to l-RNA for the generation of RNA-binding aptamers, providing a robust and practical approach for targeting structured RNAs.

The influence of device handles in single-molecule experiments

We deduce a fully analytical model to predict the artifacts of the device handles in single molecule force spectroscopy experiments. As we show, neglecting the handle stiffness can lead to crucial overestimation or underestimation of the stability properties and unfolding thresholds of multistable molecules.

Nanomechanics and co-transcriptional folding of Spinach and Mango

Recent advances in fluorogen-binding “light-up” RNA aptamers have enabled protein-free detection of RNA in cells. Detailed biophysical characterization of folding of G-Quadruplex (GQ)-based light-up aptamers such as Spinach, Mango and Corn is still lacking despite the potential implications on their folding and function. In this work we employ single-molecule fluorescence-force spectroscopy to examine mechanical responses of Spinach2, iMangoIII and MangoIV. Spinach2 unfolds in four discrete steps as force is increased to 7 pN and refolds in reciprocal steps upon force relaxation. In contrast, GQ-core unfolding in iMangoIII and MangoIV occurs in one discrete step at forces >10 pN and refolding occurred at lower forces showing hysteresis. Co-transcriptional folding using superhelicases shows reduced misfolding propensity and allowed a folding pathway different from refolding. Under physiologically relevant pico-Newton levels of force, these aptamers may unfold in vivo and subsequently misfold. Understanding of the dynamics of RNA aptamers will aid engineering of improved fluorogenic modules for cellular applications.

Light-up aptamers are widely used for fluorescence visualization of non-coding RNA in vivo. Here the authors employ single-molecule fluorescence-force spectroscopy to characterize the mechanical responses of the G-Quadruplex based light-up aptamers Spinach2, iMangoIII and MangoIV, which is of interest for the development of improved fluorogenic modules for imaging applications.

Predicting Monovalent Ion Correlation Effects in Nucleic Acids

Ion correlation and fluctuation can play a potentially significant role in metal ion-nucleic acid interactions. Previous studies have focused on the effects for multivalent cations. However, the correlation and fluctuation effects can be important also for monovalent cations around the nucleic acid surface. Here, we report a model, gMCTBI, that can explicitly treat discrete distributions of both monovalent and multivalent cations and can account for the correlation and fluctuation effects for the cations in the solution. The gMCTBI model enables investigation of the global ion binding properties as well as the detailed discrete distributions of the bound ions. Accounting for the ion correlation effect for monovalent ions can lead to more accurate predictions, especially in a mixed monovalent and multivalent salt solution, for the number and location of the bound ions. Furthermore, although the monovalent ion-mediated correlation does not show a significant effect on the number of bound ions, the correlation may enhance the accumulation of monovalent ions near the nucleic acid surface and hence affect the ion distribution. The study further reveals novel ion correlation-induced effects in the competition between the different cations around nucleic acids.

The interplay between molecular flexibility and RNA chemical probing reactivities analyzed at the nucleotide level via an extensive molecular dynamics study

Determination of the tridimensional structure of ribonucleic acid molecules is fundamental for understanding their function in the cell. A common method to investigate RNA structures of large molecules is the use of chemical probes such as SHAPE (2^'-hydroxyl acylation analyzed by primer extension) reagents, DMS (dimethyl sulfate) and CMCT (1-cyclohexyl-3-(2-morpholinoethyl) carbodiimide metho-p-toluene sulfate), the reaction of which is dependent on the local structural properties of each nucleotide. In order to understand the interplay between local flexibility, sugar pucker, canonical pairing and chemical reactivity of the probes, we performed all-atom molecular dynamics simulations on a set of RNA molecules for which both tridimensional structure and chemical probing data are available and we analyzed the correlations between geometrical parameters and the chemical reactivity. Our study confirms that SHAPE reactivity is guided by the local flexibility of the different chemical moieties but suggests that a combination of multiple parameters is needed to better understand the implications of the reactivity at the molecular level. This is also the case for DMS and CMCT for which the reactivity appears to be more complex than commonly accepted.

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.

Molecular Simulations of Ion Effects on the Thermodynamics of RNA Folding

How ions affect RNA folding thermodynamics and kinetics is an important but a vexing problem that remains unsolved. Experiments have shown that the free-energy change, Δ G( c), of RNA upon folding varies with the salt concentration ( c) as, Δ G( c) = k _c ln  c + const, where the coefficient k _c is proportional to the difference in the ion preferential coefficient, ΔΓ. We performed simulations of a coarse-grained model, by modeling electrostatic interactions implicitly and with explicit representation of ions, to elucidate the molecular underpinnings of the relationship between Δ G and ΔΓ. The simulations quantitatively reproduce the heat capacity for a pseudoknot, thus validating the model. We show that Δ G( c), calculated directly from ΔΓ, varies linearly with ln  c ( c < 0.2 M), for a hairpin and the pseudoknot, demonstrating a molecular link between the two quantities. Explicit ion simulations also show the linear dependence of Δ G( c) on ln  c at all c with k _c = 2 k_B T, except that Δ G( c) values are shifted by ∼2 kcal/mol higher than experiments. The discrepancy is due to an underestimation of Γ for both the folded and unfolded states while giving accurate values for ΔΓ. The predictions for the salt dependence of ΔΓ are amenable to test using single-molecule pulling experiments. The framework provided here can be used to obtain accurate thermodynamics for other RNA molecules as well.

Effects of Preferential Counterion Interactions on the Specificity of RNA Folding

The real-time search for native RNA structure is essential for the operation of regulatory RNAs. We previously reported that a fraction of the Azoarcus ribozyme achieves a compact structure in less than a millisecond. To scrutinize the forces that drive initial folding steps, we used time-resolved SAXS to compare the folding dynamics of this ribozyme in thermodynamically isostable concentrations of different counterions. The results show that the size of the fast-folding population increases with the number of available counterions and correlates with the flexibility of initial RNA structures. Within 1 ms of folding, Mg²⁺ exhibits a smaller preferential interaction coefficient per charge, ΔΓ₊/ Z, than Na⁺ or [Co(NH₃)₆]³⁺. The lower ΔΓ₊/ Z corresponds to a smaller yield of folded RNA, although Mg²⁺ stabilizes native RNA more efficiently than other ions at equilibrium. These results suggest that strong Mg²⁺-RNA interactions impede the search for globally native structure during early folding stages.

Modeling Structure, Stability, and Flexibility of Double-Stranded RNAs in Salt Solutions

Double-stranded (ds) RNAs play essential roles in many processes of cell metabolism. The knowledge of three-dimensional (3D) structure, stability, and flexibility of dsRNAs in salt solutions is important for understanding their biological functions. In this work, we further developed our previously proposed coarse-grained model to predict 3D structure, stability, and flexibility for dsRNAs in monovalent and divalent ion solutions through involving an implicit structure-based electrostatic potential. The model can make reliable predictions for 3D structures of extensive dsRNAs with/without bulge/internal loops from their sequences, and the involvement of the structure-based electrostatic potential and corresponding ion condition can improve the predictions for 3D structures of dsRNAs in ion solutions. Furthermore, the model can make good predictions for thermal stability for extensive dsRNAs over the wide range of monovalent/divalent ion concentrations, and our analyses show that the thermally unfolding pathway of dsRNA is generally dependent on its length as well as its sequence. In addition, the model was employed to examine the salt-dependent flexibility of a dsRNA helix, and the calculated salt-dependent persistence lengths are in good accordance with experiments.

Mechanical Cooperativity in DNA Cruciform Structures

Unlike short-range chemical bonds that maintain chemical properties of a biological molecule, long-range mechanical interactions determine mechanochemical properties of molecules. Limited by experimental approaches, however, direct quantification of such mechanical interactions is challenging. Using magneto-optical tweezers, herein we found torque can change the topology and mechanochemical property of DNA cruciform, a naturally occurring structure consisting of two opposing hairpin arms. Both mechanical and thermodynamic stabilities of DNA cruciforms increase with positive torque, which have been attributed to the topological coupling between DNA template and the cruciform. The coupling exists simultaneously in both arms of a cruciform, which coordinates the folding and unfolding of the cruciform, leading to a mechanical cooperativity not observed previously. As DNA torque readily varies during transcriptions, our finding suggests that DNA cruciforms can modulate transcriptions by adjusting their properties according to the torque.

The nearest neighbor and next nearest neighbor effects on the thermodynamic and kinetic properties of RNA base pair

The thermodynamic and kinetic parameters of an RNA base pair with different nearest and next nearest neighbors were obtained through long-time molecular dynamics simulation of the opening-closing switch process of the base pair near its melting temperature. The results indicate that thermodynamic parameters of GC base pair are dependent on the nearest neighbor base pair, and the next nearest neighbor base pair has little effect, which validated the nearest-neighbor model. The closing and opening rates of the GC base pair also showed nearest neighbor dependences. At certain temperature, the closing and opening rates of the GC pair with nearest neighbor AU is larger than that with the nearest neighbor GC, and the next nearest neighbor plays little role. The free energy landscape of the GC base pair with the nearest neighbor GC is rougher than that with nearest neighbor AU.

Theory of FRET "Spectroscopic Ruler" for Short Distances: Application to Polyproline

Förster resonance energy transfer (FRET) is an important mechanism for the estimation of intermolecular distances, e.g., in fluorescent labeled proteins. The interpretations of FRET experiments with standard Förster theory relies on the following approximations: (i) a point-dipole approximation (PDA) for the coupling between transition densities of the chromophores, (ii) a screening of this coupling by the inverse optical dielectric constant of the medium, and (iii) the assumption of fast isotropic sampling over the mutual orientations of the chromophores. These approximations become critical, in particular, at short intermolecular distances, where the PDA and the screening model become invalid and the variation of interchromophore distances, and not just orientations, has a critical influence on the excitation energy transfer. Here, we present a quantum chemical/electrostatic/molecular dynamics (MD) method that goes beyond all of the above approximations. The Poisson-TrEsp method for the ab initio/electrostatic calculation of excitonic couplings in a dielectric medium is combined with all-atom molecular dynamics (MD) simulations to calculate FRET efficiencies. The method is applied to analyze single-molecule experiments on a polyproline helix of variable length labeled with Alexa dyes. Our method provides a quantitative explanation of the overestimation of FRET efficiencies by the standard Förster theory for short interchromophore distances for this system. A detailed analysis of the different levels of approximation that connect the present Poisson-TrEsp/MD method with Förster theory reveals error compensation effects, between the PDA and the neglect of correlations in interchromophore distances and orientations on one hand and the neglect of static disorder in orientations and interchromophore distances on the other. Whereas the first two approximations are found to decrease the FRET efficiency, the latter two overcompensate this decrease and are responsible for the overestimation of the FRET efficiency by Förster theory.

The 5΄ UTR of the type I toxin ZorO can both inhibit and enhance translation

Many bacterial type I toxin mRNAs possess a long 5΄ untranslated region (UTR) that serves as the target site of the corresponding antitoxin sRNA. This is the case for the zorO-orzO type I system where the OrzO antitoxin base pairs to the 174-nucleotide zorO 5΄ UTR. Here, we demonstrate that the full-length 5΄ UTR of the zorO type I toxin hinders its own translation independent of the sRNA whereas a processed 5΄ UTR (zorO Δ28) promotes translation. The full-length zorO 5΄ UTR folds into an extensive secondary structure sequestering the ribosome binding site (RBS). Processing of the 5΄ UTR does not alter the RBS structure, but opens a large region (EAP region) located upstream of the RBS. Truncation of this EAP region impairs zorO translation, but this defect can be rescued upon exposing the RBS. Additionally, the region spanning +35 to +50 of the zorO mRNA is needed for optimal translation of zorO. Importantly, the positive and negative effects on translation imparted by the 5΄ UTR can be transferred onto a reporter gene, indicative that the 5΄ UTR can solely drive regulation. Moreover, we show that the OrzO sRNA can inhibit zorO translation via base pairing to the of the EAP region.

MCTBI: a web server for predicting metal ion effects in RNA structures

Metal ions play critical roles in RNA structure and function. However, web servers and software packages for predicting ion effects in RNA structures are notably scarce. Furthermore, the existing web servers and software packages mainly neglect ion correlation and fluctuation effects, which are potentially important for RNAs. We here report a new web server, the MCTBI server (http://rna.physics.missouri.edu/MCTBI), for the prediction of ion effects for RNA structures. This server is based on the recently developed MCTBI, a model that can account for ion correlation and fluctuation effects for nucleic acid structures and can provide improved predictions for the effects of metal ions, especially for multivalent ions such as Mg²⁺ effects, as shown by extensive theory-experiment test results. The MCTBI web server predicts metal ion binding fractions, the most probable bound ion distribution, the electrostatic free energy of the system, and the free energy components. The results provide mechanistic insights into the role of metal ions in RNA structure formation and folding stability, which is important for understanding RNA functions and the rational design of RNA structures.

Oligomerization of the tetramerization domain of p53 probed by two- and three-color single-molecule FRET

We describe a method that combines two- and three-color single-molecule FRET spectroscopy with 2D FRET efficiency-lifetime analysis to probe the oligomerization process of intrinsically disordered proteins. This method is applied to the oligomerization of the tetramerization domain (TD) of the tumor suppressor protein p53. TD exists as a monomer at subnanomolar concentrations and forms a dimer and a tetramer at higher concentrations. Because the dissociation constants of the dimer and tetramer are very close, as we determine in this paper, it is not possible to characterize different oligomeric species by ensemble methods, especially the dimer that cannot be readily separated. However, by using single-molecule FRET spectroscopy that includes measurements of fluorescence lifetime and two- and three-color FRET efficiencies with corrections for submillisecond acceptor blinking, we show that it is possible to obtain structural information for individual oligomers at equilibrium and to determine the dimerization kinetics. From these analyses, we show that the monomer is intrinsically disordered and that the dimer conformation is very similar to that of the tetramer but the C terminus of the dimer is more flexible.

Understanding the kinetic mechanism of RNA single base pair formation

RNA functions are intrinsically tied to folding kinetics. The most elementary step in RNA folding is the closing and opening of a base pair. Understanding this elementary rate process is the basis for RNA folding kinetics studies. Previous studies mostly focused on the unfolding of base pairs. Here, based on a hybrid approach, we investigate the folding process at level of single base pairing/stacking. The study, which integrates molecular dynamics simulation, kinetic Monte Carlo simulation, and master equation methods, uncovers two alternative dominant pathways: Starting from the unfolded state, the nucleotide backbone first folds to the native conformation, followed by subsequent adjustment of the base conformation. During the base conformational rearrangement, the backbone either retains the native conformation or switches to nonnative conformations in order to lower the kinetic barrier for base rearrangement. The method enables quantification of kinetic partitioning among the different pathways. Moreover, the simulation reveals several intriguing ion binding/dissociation signatures for the conformational changes. Our approach may be useful for developing a base pair opening/closing rate model.

Exploded view of higher order G-quadruplex structures through click-chemistry assisted single-molecule mechanical unfolding

Due to the long-range nature of high-order interactions between distal components in a biomolecule, transition dynamics of tertiary structures is often too complex to profile using conventional methods. Inspired by the exploded view in mechanical drawing, here, we used laser tweezers to mechanically dissect high-order DNA structures into two constituting G-quadruplexes in the promoter of the human telomerase reverse transcriptase (hTERT) gene. Assisted with click-chemistry coupling, we sandwiched one G-quadruplex with two dsDNA handles while leaving the other unit free. Mechanical unfolding through these handles revealed transition dynamics of the targeted quadruplex in a native environment, which is named as native mechanical segmentation (NMS). Comparison between unfolding of an NMS construct and that of truncated G-quadruplex constructs revealed a quadruplex-quadruplex interaction with 2 kcal/mol stabilization energy. After mechanically targeting the two G-quadruplexes together, the same interaction was observed during the first unfolding step. The unfolding then proceeded through disrupting the weaker G-quadruplex at the 5'-end, followed by the stronger G-quadruplex at the 3'-end via various intermediates. Such a pecking order in unfolding well reflects the hierarchical nature of nucleic acid structures. With surgery-like precisions, we anticipate this NMS approach offers unprecedented perspective to decipher dynamic transitions in complex biomacromolecules.

Using sm-FRET and denaturants to reveal folding landscapes

RNA folding studies aim to clarify the relationship among sequence, tridimensional structure, and biological function. In the last decade, the application of single-molecule fluorescence resonance energy transfer (sm-FRET) techniques to investigate RNA structure and folding has revealed the details of conformational changes and timescale of the process leading to the formation of biologically active RNA structures with subnanometer resolution on millisecond timescales. In this review, we initially summarize the first wave of single-molecule FRET-based RNA techniques that focused on analyzing the influence of mono- and divalent metal ions on RNA function, and how these studies have provided very valuable information about folding pathways and the presence of intermediate and low-populated states. Next, we describe a second generation of single-molecule techniques that combine sm-FRET with the use of chemical denaturants as an emerging powerful approach to reveal information about the dynamics and energetics of RNA folding that remains hidden using conventional sm-FRET approaches. The main advantages of using the competing interplay between folding agents such as metal ions and denaturants to observe and manipulate the dynamics of RNA folding and RNA-ligand interactions is discussed in the context of the adenine riboswitch aptamer.

RNA Structures as Mediators of Neurological Diseases and as Drug Targets

RNAs adopt diverse folded structures that are essential for function and thus play critical roles in cellular biology. A striking example of this is the ribosome, a complex, three-dimensionally folded macromolecular machine that orchestrates protein synthesis. Advances in RNA biochemistry, structural and molecular biology, and bioinformatics have revealed other non-coding RNAs whose functions are dictated by their structure. It is not surprising that aberrantly folded RNA structures contribute to disease. In this Review, we provide a brief introduction into RNA structural biology and then describe how RNA structures function in cells and cause or contribute to neurological disease. Finally, we highlight successful applications of rational design principles to provide chemical probes and lead compounds targeting structured RNAs. Based on several examples of well-characterized RNA-driven neurological disorders, we demonstrate how designed small molecules can facilitate the study of RNA dysfunction, elucidating previously unknown roles for RNA in disease, and provide lead therapeutics.

Ab initio RNA folding

RNA molecules are essential cellular machines performing a wide variety of functions for which a specific three-dimensional structure is required. Over the last several years, the experimental determination of RNA structures through x-ray crystallography and NMR seems to have reached a plateau in the number of structures resolved each year, but as more and more RNA sequences are being discovered, the need for structure prediction tools to complement experimental data is strong. Theoretical approaches to RNA folding have been developed since the late nineties, when the first algorithms for secondary structure prediction appeared. Over the last 10 years a number of prediction methods for 3D structures have been developed, first based on bioinformatics and data-mining, and more recently based on a coarse-grained physical representation of the systems. In this review we are going to present the challenges of RNA structure prediction and the main ideas behind bioinformatic approaches and physics-based approaches. We will focus on the description of the more recent physics-based phenomenological models and on how they are built to include the specificity of the interactions of RNA bases, whose role is critical in folding. Through examples from different models, we will point out the strengths of physics-based approaches, which are able not only to predict equilibrium structures, but also to investigate dynamical and thermodynamical behavior, and the open challenges to include more key interactions ruling RNA folding.

Coarse-Grained HiRE-RNA Model for ab Initio RNA Folding beyond Simple Molecules, Including Noncanonical and Multiple Base Pairings

HiRE-RNA is a coarse-grained model for RNA structure prediction and the dynamical study of RNA folding. Using a reduced set of particles and detailed interactions accounting for base-pairing and stacking, we show that noncanonical and multiple base interactions are necessary to capture the full physical behavior of complex RNAs. In this paper, we give a full account of the model and present results on the folding, stability, and free energy surfaces of 16 systems with 12 to 76 nucleotides of increasingly complex architectures, ranging from monomers to dimers, using a total of 850 μs of simulation time.

Characterizing excited conformational states of RNA by NMR spectroscopy

Conformational dynamics is a hallmark of diverse non-coding RNA functions. During these functional processes, RNA molecules almost ubiquitously undergo conformational transitions that are tuned to meet distinct structural and kinetic requirements for proper function. A complete mechanistic understanding of RNA function requires comprehensive structural and dynamic knowledge of these complex transitions, which often involve alternative higher-energy conformational states that pose a major challenge for high-resolution structural study by conventional methods. In this review, we describe recent progress in RNA NMR that has started to unveil detailed structural, thermodynamic and kinetic insights into some of these excited conformational states of RNA and their functional roles in biology.

HPLC purification of RNA aptamers up to 59 nucleotides with single-nucleotide resolution

An RNA sample is usually heterogeneous. RNA heterogeneity refers to difference in length or size (i.e., number of nucleotides [nt]), sequence, or alternative but coexisting conformations. Separation and purification of RNA is generally required for investigating the structure and function of RNA, such as RNA catalysis and RNA structure determination by nuclear magnetic resonance or crystallography. Separation and purification of RNA is also required for using RNAs as functional probes and therapeutics as well as building blocks for RNA nanoparticles. Previously established protocols are limited in separating RNAs longer than 25 nt by single-nucleotide resolution. When the length of RNAs becomes longer, single-nucleotide separation of RNAs becomes more challenging. Here we describe protocols, by the use of ion-pair, reverse-phase high-performance liquid chromatography (HPLC), to extend our ability to separate regular RNAs up to 59 nt with single-nucleotide resolution. For chemically modified RNAs at 2' positions on the ribose, we can resolve RNAs of similar sizes even with a 26 Da difference. This is much less than 320 Da, an average single-nucleotide molecular weight difference.

Ion distributions around left- and right-handed DNA and RNA duplexes: a comparative study

The ion atmosphere around nucleic acids is an integral part of their solvated structure. However, detailed aspects of the ionic distribution are difficult to probe experimentally, and comparative studies for different structures of the same sequence are almost non-existent. Here, we have used large-scale molecular dynamics simulations to perform a comparative study of the ion distribution around (5'-CGCGCGCGCGCG-3')2 dodecamers in solution in B-DNA, A-RNA, Z-DNA and Z-RNA forms. The CG sequence is very sensitive to ionic strength and it allows the comparison with the rare but important left-handed forms. The ions investigated include Na(+), K(+) and Mg(2 +), with various concentrations of their chloride salts. Our results quantitatively describe the characteristics of the ionic distributions for different structures at varying ionic strengths, tracing these differences to nucleic acid structure and ion type. Several binding pockets with rather long ion residence times are described, both for the monovalent ions and for the hexahydrated Mg[(H2O)6](2+) ion. The conformations of these binding pockets include direct binding through desolvated ion bridges in the GpC steps in B-DNA and A-RNA; direct binding to backbone oxygens; binding of Mg[(H2O)6](2+) to distant phosphates, resulting in acute bending of A-RNA; tight 'ion traps' in Z-RNA between C-O2 and the C-O2' atoms in GpC steps; and others.

Fast single-molecule FRET spectroscopy: theory and experiment

Single-molecule spectroscopy is widely used to study macromolecular dynamics. Although this technique provides unique information that cannot be obtained at the ensemble level, the possibility of studying fast molecular dynamics is limited by the number of photons detected per unit time (photon count rate), which is proportional to the illumination intensity. However, simply increasing the illumination intensity often does not help because of various photophysical and photochemical problems. In this Perspective, we show how to improve the dynamic range of single-molecule fluorescence spectroscopy at a given photon count rate by considering each and every photon and using a maximum likelihood method. For a photon trajectory with recorded photon colors and inter-photon times, the parameters of a model describing molecular dynamics are obtained by maximizing the appropriate likelihood function. We discuss various likelihood functions, their applicability, and the accuracy of the extracted parameters. The maximum likelihood method has been applied to analyze the experiments on fast two-state protein folding and to measure transition path times. Utilizing other information such as fluorescence lifetimes is discussed in the framework of two-dimensional FRET efficiency-lifetime histograms.