Quantitative tests of a reconstitution model for RNA folding thermodynamics and kinetics.

Decades of study of the architecture and function of structured RNAs have led to the perspective that RNA tertiary structure is modular, made of locally stable domains that retain their structure across RNAs. We formalize a hypothesis inspired by this modularity-that RNA folding thermodynamics and kinetics can be quantitatively predicted from separable energetic contributions of the individual components of a complex RNA. This reconstitution hypothesis considers RNA tertiary folding in terms of ΔGalign, the probability of aligning tertiary contact partners, and ΔGtert, the favorable energetic contribution from the formation of tertiary contacts in an aligned state. This hypothesis predicts that changes in the alignment of tertiary contacts from different connecting helices and junctions (ΔGHJH) or from changes in the electrostatic environment (ΔG+/-) will not affect the energetic perturbation from a mutation in a tertiary contact (ΔΔGtert). Consistent with these predictions, single-molecule FRET measurements of folding of model RNAs revealed constant ΔΔGtert values for mutations in a tertiary contact embedded in different structural contexts and under different electrostatic conditions. The kinetic effects of these mutations provide further support for modular behavior of RNA elements and suggest that tertiary mutations may be used to identify rate-limiting steps and dissect folding and assembly pathways for complex RNAs. Overall, our model and results are foundational for a predictive understanding of RNA folding that will allow manipulation of RNA folding thermodynamics and kinetics. Conversely, the approaches herein can identify cases where an independent, additive model cannot be applied and so require additional investigation.

Kinetic and thermodynamic framework for P4-P6 RNA reveals tertiary motif modularity and modulation of the folding preferred pathway.

The past decade has seen a wealth of 3D structural information about complex structured RNAs and identification of functional intermediates. Nevertheless, developing a complete and predictive understanding of the folding and function of these RNAs in biology will require connection of individual rate and equilibrium constants to structural changes that occur in individual folding steps and further relating these steps to the properties and behavior of isolated, simplified systems. To accomplish these goals we used the considerable structural knowledge of the folded, unfolded, and intermediate states of P4-P6 RNA. We enumerated structural states and possible folding transitions and determined rate and equilibrium constants for the transitions between these states using single-molecule FRET with a series of mutant P4-P6 variants. Comparisons with simplified constructs containing an isolated tertiary contact suggest that a given tertiary interaction has a stereotyped rate for breaking that may help identify structural transitions within complex RNAs and simplify the prediction of folding kinetics and thermodynamics for structured RNAs from their parts. The preferred folding pathway involves initial formation of the proximal tertiary contact. However, this preference was only ∼10 fold and could be reversed by a single point mutation, indicating that a model akin to a protein-folding contact order model will not suffice to describe RNA folding. Instead, our results suggest a strong analogy with a modified RNA diffusion-collision model in which tertiary elements within preformed secondary structures collide, with the success of these collisions dependent on whether the tertiary elements are in their rare binding-competent conformations.

Multiple native states reveal persistent ruggedness of an RNA folding landscape.

According to the 'thermodynamic hypothesis', the sequence of a biological macromolecule defines its folded, active (or 'native') structure as a global energy minimum in the folding landscape. However, the enormous complexity of folding landscapes of large macromolecules raises the question of whether there is in fact a unique global minimum corresponding to a unique native conformation or whether there are deep local minima corresponding to alternative active conformations. The folding of many proteins is well described by two-state models, leading to highly simplified representations of protein folding landscapes with a single native conformation. Nevertheless, accumulating experimental evidence suggests a more complex topology of folding landscapes with multiple active conformations that can take seconds or longer to interconvert. Here we demonstrate, using single-molecule experiments, that an RNA enzyme folds into multiple distinct native states that interconvert on a timescale much longer than that of catalysis. These data demonstrate that severe ruggedness of RNA folding landscapes extends into conformational space occupied by native conformations.

Single-molecule dataset (SMD): a generalized storage format for raw and processed single-molecule data.

BACKGROUND: Single-molecule techniques have emerged as incisive approaches for addressing a wide range of questions arising in contemporary biological research [Trends Biochem Sci 38:30-37, 2013; Nat Rev Genet 14:9-22, 2013; Curr Opin Struct Biol 2014, 28C:112-121; Annu Rev Biophys 43:19-39, 2014]. The analysis and interpretation of raw single-molecule data benefits greatly from the ongoing development of sophisticated statistical analysis tools that enable accurate inference at the low signal-to-noise ratios frequently associated with these measurements. While a number of groups have released analysis toolkits as open source software [J Phys Chem B 114:5386-5403, 2010; Biophys J 79:1915-1927, 2000; Biophys J 91:1941-1951, 2006; Biophys J 79:1928-1944, 2000; Biophys J 86:4015-4029, 2004; Biophys J 97:3196-3205, 2009; PLoS One 7:e30024, 2012; BMC Bioinformatics 288 11(8):S2, 2010; Biophys J 106:1327-1337, 2014; Proc Int Conf Mach Learn 28:361-369, 2013], it remains difficult to compare analysis for experiments performed in different labs due to a lack of standardization. RESULTS: Here we propose a standardized single-molecule dataset (SMD) file format. SMD is designed to accommodate a wide variety of computer programming languages, single-molecule techniques, and analysis strategies. To facilitate adoption of this format we have made two existing data analysis packages that are used for single-molecule analysis compatible with this format. CONCLUSION: Adoption of a common, standard data file format for sharing raw single-molecule data and analysis outcomes is a critical step for the emerging and powerful single-molecule field, which will benefit both sophisticated users and non-specialists by allowing standardized, transparent, and reproducible analysis practices.

Removal of covalent heterogeneity reveals simple folding behavior for P4-P6 RNA.

RNA folding landscapes have been described alternately as simple and as complex. The limited diversity of RNA residues and the ability of RNA to form stable secondary structures prior to adoption of a tertiary structure would appear to simplify folding relative to proteins. Nevertheless, there is considerable evidence for long-lived misfolded RNA states, and these observations have suggested rugged energy landscapes. Recently, single molecule fluorescence resonance energy transfer (smFRET) studies have exposed heterogeneity in many RNAs, consistent with deeply furrowed rugged landscapes. We turned to an RNA of intermediate complexity, the P4-P6 domain from the Tetrahymena group I intron, to address basic questions in RNA folding. P4-P6 exhibited long-lived heterogeneity in smFRET experiments, but the inability to observe exchange in the behavior of individual molecules led us to probe whether there was a non-conformational origin to this heterogeneity. We determined that routine protocols in RNA preparation and purification, including UV shadowing and heat annealing, cause covalent modifications that alter folding behavior. By taking measures to avoid these treatments and by purifying away damaged P4-P6 molecules, we obtained a population of P4-P6 that gave near-uniform behavior in single molecule studies. Thus, the folding landscape of P4-P6 lacks multiple deep furrows that would trap different P4-P6 molecules in different conformations and contrasts with the molecular heterogeneity that has been seen in many smFRET studies of structured RNAs. The simplicity of P4-P6 allowed us to reliably determine the thermodynamic and kinetic effects of metal ions on folding and to now begin to build more detailed models for RNA folding behavior.

Quantitative and comprehensive decomposition of the ion atmosphere around nucleic acids.

The ion atmosphere around nucleic acids critically affects biological and physical processes such as chromosome packing, RNA folding, and molecular recognition. However, the dynamic nature of the ion atmosphere renders it difficult to characterize. The basic thermodynamic description of this atmosphere, a full accounting of the type and number of associated ions, has remained elusive. Here we provide the first complete accounting of the ion atmosphere, using buffer equilibration and atomic emission spectroscopy (BE-AES) to accurately quantitate the cation association and anion depletion. We have examined the influence of ion size and charge on ion occupancy around simple, well-defined DNA molecules. The relative affinity of monovalent and divalent cations correlates inversely with their size. Divalent cations associate preferentially over monovalent cations; e.g., with Na+ in 4-fold excess of Mg2+ (20 vs 5 mM), the ion atmosphere nevertheless has 3-fold more Mg2+ than Na+. Further, the dicationic polyamine putrescine2+ does not compete effectively for association relative to divalent metal ions, presumably because of its lower charge density. These and other BE-AES results can be used to evaluate and guide the improvement of electrostatic treatments. As a first step, we compare the BE-AES results to predictions from the widely used nonlinear Poisson Boltzmann (NLPB) theory and assess the applicability and precision of this theory. In the future, BE-AES in conjunction with improved theoretical models, can be applied to complex binding and folding equilibria of nucleic acids and their complexes, to parse the electrostatic contribution from the overall thermodynamics of important biological processes.

Fluorescently labeling synthetic RNAs.

This protocol covers the steps required to incorporate N-hydroxysuccinamide (NHS) functionalized fluorophores into synthetic RNAs containing a residue derivatized with a primary amine. This method has been widely used to label RNA oligonucleotides that are used directly, targeted to a complementary RNA using base pairing rules, or covalently ligated to a RNA of interest (Ha et al., 1999; Hodak et al., 2005; Baum and Silverman, 2007; Sattint et al., 2008; Akiyama and Stone, 2009; Solomatin and Herschlag, 2009). While this technique is quite general, the details of a particular experiment can vary, therefore, it is always important to keep in mind that other labeling strategies are available and should potentially be considered.

Single Molecule Analysis Research Tool (SMART): an integrated approach for analyzing single molecule data.

Single molecule studies have expanded rapidly over the past decade and have the ability to provide an unprecedented level of understanding of biological systems. A common challenge upon introduction of novel, data-rich approaches is the management, processing, and analysis of the complex data sets that are generated. We provide a standardized approach for analyzing these data in the freely available software package SMART: Single Molecule Analysis Research Tool. SMART provides a format for organizing and easily accessing single molecule data, a general hidden Markov modeling algorithm for fitting an array of possible models specified by the user, a standardized data structure and graphical user interfaces to streamline the analysis and visualization of data. This approach guides experimental design, facilitating acquisition of the maximal information from single molecule experiments. SMART also provides a standardized format to allow dissemination of single molecule data and transparency in the analysis of reported data.

Implications of molecular heterogeneity for the cooperativity of biological macromolecules.

Cooperativity, a universal property of biological macromolecules, is typically characterized by a Hill slope, which can provide fundamental information about binding sites and interactions. We demonstrate, through simulations and single-molecule FRET (smFRET) experiments, that molecular heterogeneity lowers bulk cooperativity from the intrinsic value for the individual molecules. As heterogeneity is common in smFRET experiments, appreciation of its influence on fundamental measures of cooperativity is critical for deriving accurate molecular models.

Measuring the energetic coupling of tertiary contacts in RNA folding using single molecule fluorescence resonance energy transfer.

Tertiary contacts are critical to stabilizing the folded conformations of structured RNAs. In some cases, these contacts have been shown to interact with positive cooperativity. Measuring the energetic coupling of tertiary contact formation is among the most basic physical characterizations of a structured RNA. With proper experimental design, single-molecule fluorescence resonance energy transfer (smFRET) allows the rigorous determination of the energetic coupling. This chapter aims to provide a general experimental approach to measuring the energetic coupling of tertiary contacts, using smFRET.

Probing nucleic acid-ion interactions with buffer exchange-atomic emission spectroscopy.

The ion atmosphere of nucleic acids directly affects measured biochemical and biophysical properties. However, study of the ion atmosphere is difficult due to its diffuse and dynamic nature. Standard techniques available have significant limitations in sensitivity, specificity, and directness of the assays. Buffer exchange-atomic emission spectroscopy (BE-AES) was developed to overcome many of the limitations of previously available techniques. This technique can provide a complete accounting of all ions constituting the ionic atmosphere of a nucleic acid at thermodynamic equilibrium. Although initially developed for the study of the ion atmosphere of nucleic acids, BE-AES has also been applied to study site-bound ions in RNA and protein.