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RNA folding is enabled by interactions between the nucleic acid and its ion atmosphere, the mobile sheath of aqueous ions that surrounds and stabilizes it. Understanding the ion atmosphere requires the interplay of experiment and theory. However, even an apparently simple experiment to probe the ion atmosphere, measuring the dependence of DNA duplex stability upon ion concentration and identity, suffers from substantial complexity, because the unfolded ensemble contains many conformational states that are difficult to treat accurately with theory. To minimize this limitation, we measured the unfolding equilibrium of a DNA hairpin using a single-molecule optical trapping assay, in which the unfolded state is constrained to a limited set of elongated conformations. The unfolding free energy increased linearly with the logarithm of monovalent cation concentration for several cations, such that smaller cations tended to favor the folded state. Mg(2+) stabilized the hairpin much more effectively at low concentrations than did any of the monovalent cations. Poisson-Boltzmann theory captured trends in hairpin stability measured for the monovalent cation titrations with reasonable accuracy, but failed to do so for the Mg(2+) titrations. This finding is consistent with previous work, suggesting that Poisson-Boltzmann and other mean-field theories fail for higher valency cations where ion-ion correlation effects may become significant. The high-resolution data herein, because of the straightforward nature of both the folded and the unfolded states, should serve as benchmarks for the development of more accurate electrostatic theories that will be needed for a more quantitative and predictive understanding of nucleic acid folding.

Structured RNAs must fold into their native structures and discriminate against a large number of alternative ones, an especially difficult task given the limited information content of RNA's nucleotide alphabet. The simplest motifs within structured RNAs are two helices joined by nonhelical junctions. To uncover the fundamental behavior of these motifs and to elucidate the underlying physical forces and challenges faced by structured RNAs, we computationally and experimentally studied a tethered duplex model system composed of two helices joined by flexible single- or double-stranded polyethylene glycol tethers, whose lengths correspond to those typically observed in junctions from structured RNAs. To dissect the thermodynamic properties of these simple motifs, we computationally probed how junction topology, electrostatics, and tertiary contact location influenced folding stability. Small-angle X-ray scattering was used to assess our predictions. Single- or double-stranded junctions, independent of sequence, greatly reduce the space of allowed helical conformations and influencing the preferred location and orientation of their adjoining helices. A double-stranded junction guides the helices along a hinge-like pathway. In contrast, a single-stranded junction samples a broader set of conformations and has different preferences than the double-stranded junction. In turn, these preferences determine the stability and distinct specificities of tertiary structure formation. These sequence-independent effects suggest that properties as simple as a junction's topology can generally define the accessible conformational space, thereby stabilizing desired structures and assisting in discriminating against misfolded structures. Thus, junction topology provides a fundamental strategy for transcending the limitations imposed by the low information content of RNA primary sequence.

The large electrostatic repulsion arising from the negatively-charged backbone of RNA molecules presents a large barrier to folding. Solution counterions assist in the folding process by screening this electrostatic repulsion. While early research interpreted the effect of these counterions in terms of an empirical ligand-binding model, theories based on physical models have supplanted them and revised our view of the roles that ions play in folding. Instead of specific ion-binding sites, most ions in solution interact inside an “ion atmosphere” – a fluctuating cloud of non-specifically associated ions surrounding any charged molecule. Recent advances in experiments have begun the task of characterizing the ion atmosphere, yielding valuable data that has revealed deficiencies in Poisson-Boltzmann theory, the most widely-used theory of the ion atmosphere. The continued development of experiments will help guide the development of improved theories, with the ultimate goal of understanding RNA folding and function and nucleic acid/protein interactions from a quantitative perspective.

Electrostatic forces, acting between helices and modulated by the presence of the ion atmosphere, are key determinants in the energetic balance that governs RNA folding. Previous studies have employed Poisson-Boltzmann (PB) theory to compute the energetic contribution of these forces in RNA folding. However, the complex interaction of these electrostatic forces with RNA features such as tertiary contact formation, specific ion-binding, and complex interhelical junctions present in prior studies precluded a rigorous evaluation of PB theory, especially in physiologically important Mg(2+) solutions. To critically assess PB theory, we developed a model system that isolates these electrostatic forces. The model system, composed of two DNA duplexes tethered by a polyethylene glycol junction, is an analog for the unfolded state of canonical helix-junction-helix motifs found in virtually all structured RNAs. This model system lacks the complicating features that have precluded a critical assessment of PB in prior studies, ensuring that interhelical electrostatic forces dominate the behavior of the system. The system's simplicity allows PB predictions to be directly compared with small-angle X-ray scattering experiments over a range of monovalent and divalent ion concentrations. These comparisons indicate that PB is a reasonable description of the underlying electrostatic energies for monovalent ions, but large deviations are observed for divalent ions. The validation of PB for monovalent solutions allows analysis of the change in the conformational ensemble of this simple motif as salt concentration is changed. Addition of ions allows the motif to sample more compact microstates, increasing its conformational entropy. The increase of conformational entropy presents an additional barrier to folding by stabilizing the unfolded state. Neglecting this effect will adversely impact the accuracy of folding analyses and models.

We present a systematic analysis of the aggregation number and shape of micelles formed by nine detergents commonly used in the study of membrane proteins. Small-angle X-ray scattering measurements are reported for glucosides with 8 and 9 alkyl carbons (OG/NG), maltosides and phosphocholines with 10 and 12 alkyl carbons (DM/DDM and FC-10/FC-12), 1,2-dihexanoyl-sn-glycero-phosphocholine (DHPC), 1-palmitoyl-2-hydroxy-sn-glycero-3-[phospho-rac-(1-glycerol)] (LPPG), and 3-[(3-cholamidopropyl)dimethylammonio]-1-propane sulfonate (CHAPS). The SAXS intensities are well described by two-component ellipsoid models, with a dense outer shell corresponding to the detergent head groups and a less electron dense hydrophobic core. These models provide an intermediate resolution view of micelle size and shape. In addition, we show that Guinier analysis of the forward scattering intensity can be used to obtain an independent and model-free measurement of the micelle aggregation number and radius of gyration. This approach has the advantage of being easily generalizable to protein-detergent complexes, where simple geometric models are inapplicable. Furthermore, we have discovered that the position of the second maximum in the scattering intensity provides a direct measurement of the characteristic head group-head group spacing across the micelle core. Our results for the micellar aggregation numbers and dimensions agree favorably with literature values as far as they are available. We de novo determine the shape of FC-10, FC-12, DM, LPPG, and CHAPS micelles and the aggregation numbers of FC-10 and OG to be ca. 50 and 250, respectively. Combined, these data provide a comprehensive view of the determinants of micelle formation and serve as a starting point to correlate detergent properties with detergent-protein interactions.

Small-angle X-ray scattering can be a valuable tool in the structural characterization of membrane protein–detergent complexes (PDCs). However, a major challenge is to separate the PDC scattering signal from that of the `empty' detergent micelle in a protein–detergent mixture. We briefly review an approach that allows approximate determination of the PDC scattering signal at low momentum transfer and present a novel approach that employs a singular value decomposition (SVD) and fitting of scattering data collected at different protein–detergent stoichiometries. The SVD approach allows the scattering profile for the PDC over the entire measured momentum transfer range to be obtained, it is applicable to strongly scattering detergents and can take into account interparticle interference. The two approaches are contrasted and an application to the membrane protein TM0026 from Thermotoga maritima is presented.

Several algorithms are available to reconstruct low-resolution electron density maps of biological macromolecules from small-angle solution scattering data. These algorithms have been extensively applied to proteins and protein complexes. Here, we demonstrate their applicability to nucleic acids by reconstructing a set of RNA and DNA molecules of known three-dimensional structure from their small-angle X-ray scattering profiles. The overall size and shape of the molecules get reproduced well in all tested cases. Furthermore, we show that the generated bead models can be used as inputs for electrostatic calculations. The number of ions bound under different solution conditions computed from numerical solutions of the Poisson–Boltzmann equation for bead models agrees very well with results of calculations on all atom models derived from crystallography. The predictions from Poisson–Boltzmann theory also agree generally well with experimentally determined ion binding numbers.

The rapid development of our understanding of the diverse biological roles fulfilled by non-coding RNA has motivated interest in the basic macromolecular behavior, structure, and function of RNA. We focus on two areas in the behavior of complex RNAs. First, we present advances in the understanding of how RNA folding is accomplished in vivo by presenting a mechanism for the action of DEAD-box proteins. Members of this family are intimately associated with almost all cellular processes involving RNA, mediating RNA structural rearrangements and chaperoning their folding. Next, we focus on advances in understanding, and characterizing the basic biophysical forces that govern the folding of complex RNAs. Ultimately we expect that a confluence and synergy between these approaches will lead to profound understanding of RNA and its biology.

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 four-fold excess of Mg2+ (20 vs. 5 mM), the ion atmosphere nevertheless has three-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.

Poisson-Boltzmann (PB) theory is among the most widely applied electrostatic theories in biological and chemical science. Despite its reasonable success in explaining a wide variety of phenomena, it fails to incorporate two basic physical effects, ion size and ion-ion correlations, into its theoretical treatment. Recent experimental work has shown significant deviations from PB theory in competitive monovalent and divalent ion binding to a DNA duplex. The experimental data for monovalent binding are consistent with a hypothesis that attributes these deviations to counterion size. To model the observed differences, we have generalized an existing size-modified Poisson-Boltzmann (SMPB) theory and developed a new numerical implementation that solves the generalized theory around complex, atomistic representations of biological molecules. The results of our analysis show that good agreement to data at monovalent ion concentrations up to approximately 150 mM can be attained by adjusting the ion-size parameters in the new size-modified theory. SMPB calculations employing calibrated ion-size parameters predict experimental observations for other nucleic acid structures and salt conditions, demonstrating that the theory is predictive. We are, however, unable to model the observed deviations in the divalent competition data with a theory that only accounts for size but neglects ion-ion correlations, highlighting the need for theoretical descriptions that further incorporate ion-ion correlations. The accompanying numerical solver has been released publicly, providing the general scientific community the ability to compute SMPB solutions around a variety of different biological structures with only modest computational resources.

Riboswitches are complex folded RNA domains found in noncoding regions of mRNA that regulate gene expression upon small molecule binding. Recently, Breaker and coworkers reported a tandem aptamer riboswitch (VCI-II) that binds glycine cooperatively. Here, we use hydroxyl radical footprinting and small-angle X-ray scattering (SAXS) to study the conformations of this tandem aptamer as a function of Mg(2+) and glycine concentration. We fit a simple three-state thermodynamic model that describes the energetic coupling between magnesium-induced folding and glycine binding. Furthermore, we characterize the structural conformations of each of the three states: In low salt with no magnesium present, the VCI-II construct has an extended overall conformation, presumably representing unfolded structures. Addition of millimolar concentrations of Mg(2+) in the absence of glycine leads to a significant compaction and partial folding as judged by hydroxyl radical protections. In the presence of millimolar Mg(2+) concentrations, the tandem aptamer binds glycine cooperatively. The glycine binding transition involves a further compaction, additional tertiary packing interactions and further uptake of magnesium ions relative to the state in high Mg(2+) but no glycine. Employing density reconstruction algorithms, we obtain low resolution 3-D structures for all three states from the SAXS measurements. These data provide a first glimpse into the structural conformations of the VCI-II aptamer, establish rigorous constraints for further modeling, and provide a framework for future mechanistic studies.

RNA Junctions are flexible regions that join helical elements of secondary structure in RNA. In this poster, we discuss how these elements may contribute to folded RNA stability by promoting tertiary contact formation.