Determining the Locations of Ions and Water around DNA from X-Ray Scattering Measurements

Advances, Applications, and Perspectives in Small-Angle X-ray Scattering of RNA

RNAs exhibit a plethora of functions far beyond transmitting genetic information. Often, RNA functions are entailed in their structure, be it as a regulatory switch, protein binding site, or providing catalytic activity. Structural information is a prerequisite for a full understanding of RNA-regulatory mechanisms. Owing to the inherent dynamics, size, and instability of RNA, its structure determination remains challenging. Methods such as NMR spectroscopy, X-ray crystallography, and cryo-electron microscopy can provide high-resolution structures; however, their limitations make structure determination, even for small RNAs, cumbersome, if at all possible. Although at a low resolution, small-angle X-ray scattering (SAXS) has proven valuable in advancing structure determination of RNAs as a complementary method, which is also applicable to large-sized RNAs. Here, we review the technological and methodological advancements of RNA SAXS. We provide examples of the powerful inclusion of SAXS in structural biology and discuss possible future applications to large RNAs.

Sensitivity of the RNA Structure to Ion Conditions as Probed by Molecular Dynamics Simulations of Common Canonical RNA Duplexes

RNA molecules play a key role in countless biochemical processes. RNA interactions, which are of highly diverse nature, are determined by the fact that RNA is a highly negatively charged polyelectrolyte, which leads to intimate interactions with an ion atmosphere. Although RNA molecules are formally single-stranded, canonical (Watson-Crick) duplexes are key components of folded RNAs. A double-stranded (ds) RNA is also important for the design of RNA-based nanostructures and assemblies. Despite the fact that the description of canonical dsRNA is considered the least problematic part of RNA modeling, the imperfect shape and flexibility of dsRNA can lead to imbalances in the simulations of larger RNAs and RNA-containing assemblies. We present a comprehensive set of molecular dynamics (MD) simulations of four canonical A-RNA duplexes. Our focus was directed toward the characterization of the influence of varying ion concentrations and of the size of the solvation box. We compared several water models and four RNA force fields. The simulations showed that the A-RNA shape was most sensitive to the RNA force field, with some force fields leading to a reduced inclination of the A-RNA duplexes. The ions and water models played a minor role. The effect of the box size was negligible, and even boxes with a small fraction of the bulk solvent outside the RNA hydration sphere were sufficient for the simulation of the dsRNA.

Insights into DNA solvation found in protein-DNA structures

The proteins that bind double-helical DNA present various microenvironments that sense and/or induce signals in the genetic material. The high-resolution structures of protein-DNA complexes reveal the nature of both the microenvironments and the conformational responses in DNA and protein. Complex networks of interactions within the structures somehow tie the protein and DNA together and induce the observed spatial forms. Here we show how the cumulative buildup of amino acid atoms around the sugars, phosphates, and bases in different protein-DNA complexes produces a binding cloud around the double helix and how different types of atoms fill that cloud. Rather than focusing on the principles of molecular binding and recognition suggested by the arrangements of amino acids and nucleotides in the macromolecular complexes, we consider the proteins in contact with DNA as organized solvents. We describe differences in the mix of atoms that come in closest contact with DNA, subtle sequence-dependent features in the microenvironment of the sugar-phosphate backbone, a direct link between the localized buildup of ionic species and the electrostatic potential surfaces of the DNA bases, and sites of atomic buildup above and below the basepair planes that transmit the unique features of the base environments along the chain backbone. The inferences about solvation that can be drawn from the survey provide new stimuli for improvement of nucleic acid force fields and fresh ideas for exploration of the properties of DNA in solution.

Diffusion NMR-based comparison of electrostatic influences of DNA on various monovalent cations

Counterions are important constituents for the structure and function of nucleic acids. Using 7Li and 133Cs nuclear magnetic resonance (NMR) spectroscopy, we investigated how ionic radii affect the behavior of counterions around DNA through diffusion measurements of Li+ and Cs+ ions around a 15-bp DNA duplex. Together with our previous data on 23Na+ and 15NH4+ ions around the same DNA under the same conditions, we were able to compare the dynamics of four different monovalent ions around DNA. From the apparent diffusion coefficients at varied concentrations of DNA, we determined the diffusion coefficients of these cations inside and outside the ion atmosphere around DNA (Db and Df, respectively). We also analyzed ionic competition with K+ ions for the ion atmosphere and assessed the relative affinities of these cations for DNA. Interestingly, all cations (i.e., Li+, Na+, NH4+, and Cs+) analyzed by diffusion NMR spectroscopy exhibited nearly identical Db/Df ratios despite the differences in their ionic radii, relative affinities, and diffusion coefficients. These results, along with the theoretical relationship between diffusion and entropy, suggest that the entropy change due to the release of counterions from the ion atmosphere around DNA is also similar regardless of the monovalent ion types. These findings and the experimental diffusion data on the monovalent ions are useful for examination of computational models for electrostatic interactions or ion solvation.

K-edge anomalous SAXS for protein solution structure modeling

K-edge anomalous SAXS intensity was measured from a small, dimeric, partly unstructured protein segment of myosin X by using cupric ions bound to its C-terminal polyhistidine tags. Energy-dependent anomalous SAXS can provide key location-specific information about metal-labeled protein structures in solution that cannot be obtained from routine SAXS analysis. However, anomalous SAXS is seldom used for protein research due to practical difficulties, such as a lack of generic multivalent metal-binding tags and the challenges of measuring weak anomalous signal at the metal absorption edge. This pilot feasibility study suggests that weak K-edge anomalous SAXS signal can be obtained from transition metals bound to terminally located histidine tags of small proteins. The measured anomalous signal can provide information about the distribution of all metal–protein distances in the complex. Such an anomalous SAXS signal can assist in the modeling and validation of structured or unstructured proteins in solution and may potentially become a new addition to the repertoire of techniques in integrative structural biology.

Integral equation models for solvent in macromolecular crystals

The solvent can occupy up to ∼70% of macromolecular crystals, and hence, having models that predict solvent distributions in periodic systems could improve the interpretation of crystallographic data. Yet, there are few implicit solvent models applicable to periodic solutes, and crystallographic structures are commonly solved assuming a flat solvent model. Here, we present a newly developed periodic version of the 3D-reference interaction site model (RISM) integral equation method that is able to solve efficiently and describe accurately water and ion distributions in periodic systems; the code can compute accurate gradients that can be used in minimizations or molecular dynamics simulations. The new method includes an extension of the Ornstein–Zernike equation needed to yield charge neutrality for charged solutes, which requires an additional contribution to the excess chemical potential that has not been previously identified; this is an important consideration for nucleic acids or any other charged system where most or all the counter- and co-ions are part of the “disordered” solvent. We present several calculations of proteins, RNAs, and small molecule crystals to show that x-ray scattering intensities and the solvent structure predicted by the periodic 3D-RISM solvent model are in closer agreement with the experiment than are intensities computed using the default flat solvent model in the refmac5 or phenix refinement programs, with the greatest improvement in the 2 to 4 Å range. Prospects for incorporating integral equation models into crystallographic refinement are discussed.

Porphyrin Binding and Irradiation Promote G-Quadruplex DNA Dimeric Structure

Nucleic acid sequences rich in guanines can organize into noncanonical DNA G-quadruplexes (G4s) of variable size. The design of small molecules stabilizing the structure of G4s is a rapidly growing area for the development of novel anticancer therapeutic strategies and bottom-up nanotechnologies. Among a multitude of binders, porphyrins are very attractive due to their light activation that can make them valuable conformational regulators of G4s. Here, a structure-based strategy, integrating complementary probes, is employed to study the interaction between TMPyP4 porphyrin and a 22-base human telomeric sequence (Tel22) before and after irradiation with blue light. Porphyrin binding is discovered to promote Tel22 dimerization, while light irradiation of the Tel22-TMPyP4 complex controls dimer fraction. Such a change in quaternary structure is found to be strictly correlated with modifications at the secondary structure level, thus providing an unprecedented link between the degree of dimerization and the underlying conformational changes in G4s.

Analytical Cryo-Scanning Electron Microscopy of Hydrated Polymers and Microgels

Despite the fact that scanning electron microscopes (SEM) coupled with energy-dispersive X-ray microanalysis (EDS) has been commercially available for more than a half-century, SEM/EDS continues to develop and open new opportunities to study the morphology of advanced materials. This is particularly true in applications to hydrated soft matter. Developments in field-emission electron sources that enable low-voltage imaging of uncoated polymers, silicon-drift detectors that enable high-efficiency collection of X-rays characteristic of light elements, and cryogenic methods to effectively cryo-fix hydrated samples have opened new opportunities to apply techniques relatively well established in hard-materials applications to challenging new problems involving synthetic polymers. We have applied cryo-SEM imaging and spatially resolved EDS to collect new information characterizing polyelectrolyte microgels. These are charged gel particles with dimensions in the range of 0.1-100 μm. Perhaps most notable is the fact that the high hydration levels-the samples are mostly water-allow robust calibration curves to be generated using frozen-hydrated buffers with known salt and/or hydrocarbon compositions. Such calibration curves enable quantitative composition measurements in the low-concentration extremes associated with high-swelling hydrogels. We use an experimentally derived carbon calibration curve to determine the microgel swell ratio, Q. The swell ratio, arguably, is the single most important gel characteristic because it is directly related to the mesh size of the networked polymer, which in turn determines many of the gel's mechanical and transport properties. While Q can be experimentally measured in macroscopic gels based on weight measurements in the dry and hydrated states, it is very difficult to measure in a microgel, and the fact that EDS in a cryo-SEM can determine Q from a single X-ray spectrum is significant. Furthermore, because of the electrostatic charge distributed along the polymer chains, the presence and concentration of counter-ions play a critical role in polyelectrolyte systems. While conceptually understood for decades, experimental measurements of counter-ion concentrations have been largely limited to a relatively small set of materials that involve macroscopic samples. By developing calibration curves from frozen-hydrated buffer of known ionic strength, we measure the concentration of Na counter-ions in microgels of poly(acrylic acid) (PAA) with a limit of detection of ∼0.014 M. Such measurements may help resolve some long-standing questions in polyelectrolyte science concerning counter-ion condensation. Even in the absence of a calibration curve, we show that spatially resolved X-ray spectroscopy can map the spatial distribution of a cationic oligopeptide complexed within a hydrated PAA microgel because of the nitrogen fingerprint that, albeit at very low concentration, is unique to the peptide. We look specifically at the case of a microgel with a so-called core-shell structure, where, again, the underlying polyelectrolyte science responsible for core-shell formation remains incompletely understood. These examples highlight how a modern cryo-SEM can be exploited to quantitatively characterize hydrated soft matter. The approach is almost certain to continue its development and impact as the base of experienced practitioners, the accessibility to well-configured microscopes, and the abundance of challenging problems involving hydrated soft matter all continue to grow.

Anomalous SAXS at P12 beamline EMBL Hamburg: instrumentation and applications

Small-angle X-ray scattering (SAXS) is an established method for studying nanostructured systems and in particular biological macromolecules in solution. To obtain element-specific information about the sample, anomalous SAXS (ASAXS) exploits changes of the scattering properties of selected atoms when the energy of the incident X-rays is close to the binding energy of their electrons. While ASAXS is widely applied to condensed matter and inorganic systems, its use for biological macromolecules is challenging because of the weak anomalous effect. Biological objects are often only available in small quantities and are prone to radiation damage, which makes biological ASAXS measurements very challenging. The BioSAXS beamline P12 operated by the European Molecular Biology Laboratory (EMBL) at the PETRA III storage ring (DESY, Hamburg) is dedicated to studies of weakly scattering objects. Here, recent developments at P12 allowing for ASAXS measurements are presented. The beamline control, data acquisition and data reduction pipeline of the beamline were adapted to conduct ASAXS experiments. Modelling tools were developed to compute ASAXS patterns from atomic models, which can be used to analyze the data and to help designing appropriate data collection strategies. These developments are illustrated with ASAXS experiments on different model systems performed at the P12 beamline.

Phosphate Vibrations Probe Electric Fields in Hydrated Biomolecules: Spectroscopy, Dynamics, and Interactions

Electric interactions have a strong impact on the structure and dynamics of biomolecules in their native water environment. Given the variety of water arrangements in hydration shells and the femto- to subnanosecond time range of structural fluctuations, there is a strong quest for sensitive noninvasive probes of local electric fields. The stretching vibrations of phosphate groups, in particular the asymmetric (PO₂)⁻ stretching vibration ν_AS(PO₂)⁻, allow for a quantitative mapping of dynamic electric fields in aqueous environments via a field-induced redshift of their transition frequencies and concomitant changes of vibrational line shapes. We present a systematic study of ν_AS(PO₂)⁻ excitations in molecular systems of increasing complexity, including dimethyl phosphate (DMP), short DNA and RNA duplex structures, and transfer RNA (tRNA) in water. A combination of linear infrared absorption, two-dimensional infrared (2D-IR) spectroscopy, and molecular dynamics (MD) simulations gives quantitative insight in electric-field tuning rates of vibrational frequencies, electric field and fluctuation amplitudes, and molecular interaction geometries. Beyond neat water environments, the formation of contact ion pairs of phosphate groups with Mg²⁺ ions is demonstrated via frequency upshifts of the ν_AS(PO₂)⁻ vibration, resulting in a distinct vibrational band. The frequency positions of contact geometries are determined by an interplay of attractive electric and repulsive exchange interactions.

Magnesium Contact Ions Stabilize the Tertiary Structure of Transfer RNA: Electrostatics Mapped by Two-Dimensional Infrared Spectra and Theoretical Simulations

Ions interacting with hydrated RNA play a central role in defining its secondary and tertiary structure. While spatial arrangements of ions, water molecules, and phosphate groups have been inferred from X-ray studies, the role of electrostatic and other noncovalent interactions in stabilizing compact folded RNA structures is not fully understood at the molecular level. Here, we demonstrate that contact ion pairs of magnesium (Mg²⁺) and phosphate groups embedded in local water shells stabilize the tertiary equilibrium structure of transfer RNA (tRNA). Employing dialyzed tRNA^Phe from yeast and tRNA from Escherichia coli, we follow the population of Mg²⁺ sites close to phosphate groups of the ribose-phosphodiester backbone step by step, combining linear and nonlinear infrared spectroscopy of phosphate vibrations with molecular dynamics simulations and ab initio vibrational frequency calculations. The formation of up to six Mg²⁺/phosphate contact pairs per tRNA and local field-induced reorientations of water molecules balance the phosphate–phosphate repulsion in nonhelical parts of tRNA, thus stabilizing the folded structure electrostatically. Such geometries display limited sub-picosecond fluctuations in the arrangement of water molecules and ion residence times longer than 1 μs. At higher Mg²⁺ excess, the number of contact ion pairs per tRNA saturates around 6 and weakly interacting ions prevail. Our results suggest a predominance of contact ion pairs over long-range coupling of the ion atmosphere and the biomolecule in defining and stabilizing the tertiary structure of tRNA.

Assessment of AMBER Force Fields for Simulations of ssDNA

Single-stranded DNA (ssDNA) plays an important role in biological processes and is used in DNA nanotechnology and other novel applications. Many important research questions can be addressed with molecular simulations of ssDNA molecules; however, no dedicated force field for ssDNA has been developed, and there is limited experimental information about ssDNA structures. This study assesses the accuracy and applicability of existing Amber force fields for all-atom simulations of ssDNA, such as ff99, bsc0, bsc1, and OL15, in implicit and explicit solvents via comparison to available experimental data, such as Forster resonance energy transfer and small angle X-ray scattering. We observed that some force fields agree better with experiments than others mainly due to the difference in parameterization of the propensity for hydrogen bonding and base stacking. Overall, the Amber ff99 force field in the IGB5 or IGB8 implicit solvent and the bsc1 force field in the explicit TIP3P solvent had the best agreement with experiment.

Elucidating the Role of Microprocessor Protein DGCR8 in Bending RNA Structures

Although conformational dynamics of RNA molecules are potentially important in microRNA (miRNA) processing, the role of the protein binding partners in facilitating the requisite structural changes is not well understood. In previous work, we and others have demonstrated that nonduplex structural elements and the conformational flexibility they support are necessary for efficient RNA binding and cleavage by the proteins associated with the two major stages of miRNA processing. However, recent studies showed that the protein DGCR8 binds primary miRNA and duplex RNA with similar affinities. Here, we study RNA binding by a small recombinant construct of the DGCR8 protein and the RNA conformation changes that result. This construct, the DGCR8 core, contains two double-stranded RNA-binding domains (dsRBDs) and a C-terminal tail. To assess conformational changes resulting from binding, we applied small-angle x-ray scattering with contrast variation to detect conformational changes of primary-miR-16-1 in complex with the DGCR8 core. This method reports only on the RNA conformation within the complex and suggests that the protein bends the RNA upon binding. Supporting work using smFRET to study the conformation of RNA duplexes bound to the core also shows bending. Together, these studies elucidate the role of DGCR8 in interacting with RNA during the early stages of miRNA processing.

Dynamics of Ionic Interactions at Protein-Nucleic Acid Interfaces

Molecular association of proteins with nucleic acids is required for many biological processes essential to life. Electrostatic interactions via ion pairs (salt bridges) of nucleic acid phosphates and protein side chains are crucial for proteins to bind to DNA or RNA. Counterions around the macromolecules are also key constituents for the thermodynamics of protein–nucleic acid association. Until recently, there had been only a limited amount of experiment-based information about how ions and ionic moieties behave in biological macromolecular processes. In the past decade, there has been significant progress in quantitative experimental research on ionic interactions with nucleic acids and their complexes with proteins. The highly negatively charged surfaces of DNA and RNA electrostatically attract and condense cations, creating a zone called the ion atmosphere. Recent experimental studies were able to examine and validate theoretical models on ions and their mobility and interactions with macromolecules. The ionic interactions are highly dynamic. The counterions rapidly diffuse within the ion atmosphere. Some of the ions are released from the ion atmosphere when proteins bind to nucleic acids, balancing the charge via intermolecular ion pairs of positively charged side chains and negatively charged backbone phosphates. Previously, the release of counterions had been implicated indirectly by the salt-concentration dependence of the association constant.

Recently, direct detection of counterion release by NMR spectroscopy has become possible and enabled more accurate and quantitative analysis of the counterion release and its entropic impact on the thermodynamics of protein–nucleic acid association. Recent studies also revealed the dynamic nature of ion pairs of protein side chains and nucleic acid phosphates. These ion pairs undergo transitions between two major states. In one of the major states, the cation and the anion are in direct contact and form hydrogen bonds. In the other major state, the cation and the anion are separated by water. Transitions between these states rapidly occur on a picosecond to nanosecond time scale. When proteins interact with nucleic acids, interfacial arginine (Arg) and lysine (Lys) side chains exhibit considerably different behaviors. Arg side chains show a higher propensity to form rigid contacts with nucleotide bases, whereas Lys side chains tend to be more mobile at the molecular interfaces. The dynamic ionic interactions may facilitate adaptive molecular recognition and play both thermodynamic and kinetic roles in protein–nucleic acid interactions.

Aqueous Contact Ion Pairs of Phosphate Groups with Na+, Ca2+ and Mg2+ – Structural Discrimination by Femtosecond Infrared Spectroscopy and Molecular Dynamics Simulations

The extent of contact and solvent shared ion pairs of phosphate groups with Na+, Ca2+ and Mg2+ ions in aqueous environment and their relevance for the stability of polyanionic DNA and RNA structures is highly debated. Employing the asymmetric phosphate stretching vibration of dimethyl phosphate (DMP), a model system of the sugar-phosphate backbone of DNA and RNA, we present linear infrared, femtosecond infrared pump-probe and absorptive 2D-IR spectra that report on contact ion pair formation via the presence of blue shifted spectral signatures. Compared to the linear infrared spectra, the nonlinear spectra reveal contact ion pairs with increased sensitivity because the spectra accentuate differences in peak frequency, transition dipole moment strength, and excited state lifetime. The experimental results are corroborated by long time scale MD simulations, benchmarked by density functional simulations on phosphate-ion-water clusters. The microscopic interpretation reveals subtle structural differences of ion pairs formed by the phosphate group and the ions Na+, Ca2+ and Mg2+. Intricate properties of the solvation shell around the phosphate group and the ion are essential to explain the experimental observations. The present work addresses a challenging to probe topic with the help of a model system and establishes new experimental data of contact ion pair formation, thereby underlining the potential of nonlinear 2D-IR spectroscopy as an analytical probe of phosphate-ion interactions in complex biological systems.

Mechanism of sequence-based separation of single-stranded DNA in capillary zone electrophoresis

Separation of DNA by length using CGE is a mature field. Separation of DNA by sequence, in contrast, is a more difficult problem. Existing techniques generally rely upon changes in intrinsic or induced differences in conformation. Previous work in our group showed that sets of ssDNA of the same length differing in sequence by as little as a single base could be separated by CZE using simple buffers at high ionic strength. Here, we explore the basis of the separation using circular dichroism spectroscopy, fluorescence anisotropy, and small angle X-ray scattering. The results reveal sequence-dependent differences among the same length strands, but the trends in the differences are not correlated to the migration order of the strands in the CZE separation. They also indicate that the separation is based on intrinsic differences among the strands that do not change with increasing ionic strength; rather, increasing ionic strength has a greater effect on electroosmotic mobility in the normal direction than on electrophoretic mobility of the strands in the reverse direction. This increases the migration time of the strands in the normal direction, allowing more time for the same-length strands to be teased apart based on very small differences in the intrinsic properties of the strands of different sequence. Regression analysis was used to model the intrinsic differences among DNA strands in order to gain insight into the relationship between mobility and sequence that underlies the separation.

Contact Ion Pairs of Phosphate Groups in Water: Two-Dimensional Infrared Spectroscopy of Dimethyl Phosphate and ab Initio Simulations

The interaction of phosphate groups with ions in an aqueous environment has a strong impact on the structure and folding processes of DNA and RNA. The dynamic variety of ionic arrangements, including both contact pairs and water separated ions, and the molecular coupling mechanisms are far from being understood. In a combined experimental and theoretical approach, we address the properties of contact ion pairs of the prototypical system dimethyl phosphate with Na⁺, Ca²⁺, and Mg²⁺ ions in water. Linear and femtosecond two-dimensional infrared (2D-IR) spectroscopy of the asymmetric (PO₂)^- stretching vibration separates and characterizes the different species via their blue-shifted vibrational signatures and 2D-IR line shapes. Phosphate-magnesium contact pairs stand out as the most compact geometry while the contact pairs with Ca²⁺ and Na⁺ display a wider structural variation. Microscopic density functional theory simulations rationalize the observed frequency shifts and reveal distinct differences between the contact geometries.

Counterion-Dependent Mechanisms of DNA Origami Nanostructure Stabilization Revealed by Atomistic Molecular Simulation

The DNA origami technique has proven to have tremendous potential for therapeutic and diagnostic applications like drug delivery, but the relatively low concentrations of cations in physiological fluids cause destabilization and degradation of DNA origami constructs preventing in vivo applications. To reveal the mechanisms behind DNA origami stabilization by cations, we performed atomistic molecular dynamics simulations of a DNA origami rectangle in aqueous solvent with varying concentrations of magnesium and sodium as well as polyamines like oligolysine and spermine. We explored the binding of these ions to DNA origami in detail and found that the mechanism of stabilization differs between ion types considerably. While sodium binds weakly and quickly exchanges with the solvent, magnesium and spermine bind close to the origami with spermine also located in between helices, stabilizing the crossovers characteristic for DNA origami and reducing repulsion of parallel helices. In contrast, oligolysine of length ten prevents helix repulsion by binding to adjacent helices with its flexible side chains, spanning the gap between the helices. Shorter oligolysine molecules with four subunits are weak stabilizers as they lack both the ability to connect helices and to prevent helix repulsion. This work thus shows how the binding modes of ions influence the stabilization of DNA origami nanostructures on a molecular level.

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.

Competitive Binding of Mg2+ and Na+ Ions to Nucleic Acids: From Helices to Tertiary Structures

Nucleic acids generally reside in cellular aqueous solutions with mixed divalent/monovalent ions, and the competitive binding of divalent and monovalent ions is critical to the structures of nucleic acids because of their polyanionic nature. In this work, we first proposed a general and effective method for simulating a nucleic acid in mixed divalent/monovalent ion solutions with desired bulk ion concentrations via molecular dynamics (MD) simulations and investigated the competitive binding of Mg²⁺/Na⁺ ions to various nucleic acids by all-atom MD simulations. The extensive MD-based examinations show that single MD simulations conducted using the proposed method can yield desired bulk divalent/monovalent ion concentrations for various nucleic acids, including RNA tertiary structures. Our comprehensive analyses show that the global binding of Mg²⁺/Na⁺ to a nucleic acid is mainly dependent on its structure compactness, as well as Mg²⁺/Na⁺ concentrations, rather than the specific structure of the nucleic acid. Specifically, the relative global binding of Mg²⁺ over Na⁺ is stronger for a nucleic acid with higher effective surface charge density and higher relative Mg²⁺/Na⁺ concentrations. Furthermore, the local binding of Mg²⁺/Na⁺ to a phosphate of a nucleic acid mainly depends on the local phosphate density in addition to Mg²⁺/Na⁺ concentrations.

Hexahydrated Mg2+ Binding and Outer-Shell Dehydration on RNA Surface

The interaction between metal ions, especially Mg²⁺ ions, and RNA plays a critical role in RNA folding. Upon binding to RNA, a metal ion that is fully hydrated in bulk solvent can become dehydrated. Here we use molecular dynamics simulation to investigate the dehydration of bound hexahydrated Mg²⁺ ions. We find that a hydrated Mg²⁺ ion in the RNA groove region can involve significant dehydration in the outer hydration shell. The first or innermost hydration shell of the Mg²⁺ ion, however, is retained during the simulation because of the strong ion-water electrostatic attraction. As a result, water-mediated hydrogen bonding remains an important form for Mg²⁺-RNA interaction. Analysis for ions at different binding sites shows that the most pronounced water deficiency relative to the fully hydrated state occurs at a radial distance of around 11 Å from the center of the ion. Based on the independent 200 ns molecular dynamics simulations for three different RNA structures (Protein Data Bank: 1TRA, 2TPK, and 437D), we find that Mg²⁺ ions overwhelmingly dominate over monovalent ions such as Na⁺ and K⁺ in ion-RNA binding. Furthermore, application of the free energy perturbation method leads to a quantitative relationship between the Mg²⁺ dehydration free energy and the local structural environment. We find that ΔΔG_hyd, the change of the Mg²⁺ hydration free energy upon binding to RNA, varies linearly with the inverse distance between the Mg²⁺ ion and the nearby nonbridging oxygen atoms of the phosphate groups, and ΔΔG_hyd can reach -2.0 kcal/mol and -3.0 kcal/mol for an Mg²⁺ ion bound to the surface and to the groove interior, respectively. In addition, the computation results in an analytical formula for the hydration ratio as a function of the average inverse Mg²⁺-O distance. The results here might be useful for further quantitative investigations of ion-RNA interactions in RNA folding.

Predicting RNA-Metal Ion Binding with Ion Dehydration Effects

Metal ions play essential roles in nucleic acids folding and stability. The interaction between metal ions and nucleic acids can be highly complicated because of the interplay between various effects such as ion correlation, fluctuation, and dehydration. These effects may be particularly important for multivalent ions such as Mg²⁺ ions. Previous efforts to model ion correlation and fluctuation effects led to the development of the Monte Carlo tightly bound ion model. Here, by incorporating ion hydration/dehydration effects into the Monte Carlo tightly bound ion model, we develop a, to our knowledge, new approach to predict ion binding. The new model enables predictions for not only the number of bound ions but also the three-dimensional spatial distribution of the bound ions. Furthermore, the new model reveals several intriguing features for the bound ions such as the mutual enhancement/inhibition in ion binding between the fully hydrated (diffuse) ions, the outer-shell dehydrated ions, and the inner-shell dehydrated ions and novel features for the monovalent-divalent ion interplay due to the hydration effect.

Crystal Structure of a Tetrameric DNA Fold-Back Quadruplex

DNA can adopt many structures beyond the Watson-Crick duplex. However, the bounds of DNA structural diversity and how these structures might regulate biological processes is only beginning to be understood. Here, we describe the 1.05 Å resolution crystal structure of a DNA oligonucleotide that self-associates to form a non-G-quadruplex fold-back structure. Distinct from previously described fold-back quadruplexes, two-fold-back dimers interact through noncanonical and Watson-Crick interactions to form a tetrameric assembly. These interactions include a hexad base pairing arrangement from two C-G-G base triples. The assembly is dependent on divalent cations, and the interface between the dimeric units creates a cavity in which a cation resides. This structure provides new sequence and structural contexts for the formation of fold-back quadruplexes, further highlighting the potential biological importance of this type of noncanonical DNA structure. This structure may also serve as the basis for designing new types of DNA nanoarchitectures or cation sensors based on the strong divalent cation dependence.

Facilitated Diffusion Mechanisms in DNA Base Excision Repair and Transcriptional Activation

Preservation of the coding potential of the genome and highly regulated gene expression over the life span of a human are two fundamental requirements of life. These processes require the action of repair enzymes or transcription factors that efficiently recognize specific sites of DNA damage or transcriptional regulation within a restricted time frame of the cell cycle or metabolism. A failure of these systems to act results in accumulated mutations, metabolic dysfunction, and disease. Despite the multifactorial complexity of cellular DNA repair and transcriptional regulation, both processes share a fundamental physical requirement that the proteins must rapidly diffuse to their specific DNA-binding sites that are embedded within the context of a vastly greater number of nonspecific DNA-binding sites. Superimposed on the needle-in-the-haystack problem is the complex nature of the cellular environment, which contains such high concentrations of macromolecules that the time frame for diffusion is expected to be severely extended as compared to dilute solution. Here we critically review the mechanisms for how these proteins solve the needle-in-the-haystack problem and how the effects of cellular macromolecular crowding can enhance facilitated diffusion processes. We restrict the review to human proteins that use stochastic, thermally driven site-recognition mechanisms, and we specifically exclude systems involving energy cofactors or circular DNA clamps. Our scope includes ensemble and single-molecule studies of the past decade or so, with an emphasis on connecting experimental observations to biological function.

Explicit ions/implicit water generalized Born model for nucleic acids

The ion atmosphere around highly charged nucleic acid molecules plays a significant role in their dynamics, structure, and interactions. Here we utilized the implicit solvent framework to develop a model for the explicit treatment of ions interacting with nucleic acid molecules. The proposed explicit ions/implicit water model is based on a significantly modified generalized Born (GB) model and utilizes a non-standard approach to define the solute/solvent dielectric boundary. Specifically, the model includes modifications to the GB interaction terms for the case of multiple interacting solutes-disconnected dielectric boundary around the solute-ion or ion-ion pairs. A fully analytical description of all energy components for charge-charge interactions is provided. The effectiveness of the approach is demonstrated by calculating the potential of mean force for Na⁺-Cl^- ion pair and by carrying out a set of Monte Carlo (MC) simulations of mono- and trivalent ions interacting with DNA and RNA duplexes. The monovalent (Na⁺) and trivalent (CoHex³⁺) counterion distributions predicted by the model are in close quantitative agreement with all-atom explicit water molecular dynamics simulations used as reference. Expressed in the units of energy, the maximum deviations of local ion concentrations from the reference are within k _B T. The proposed explicit ions/implicit water GB model is able to resolve subtle features and differences of CoHex distributions around DNA and RNA duplexes. These features include preferential CoHex binding inside the major groove of the RNA duplex, in contrast to CoHex biding at the "external" surface of the sugar-phosphate backbone of the DNA duplex; these differences in the counterion binding patters were earlier shown to be responsible for the observed drastic differences in condensation propensities between short DNA and RNA duplexes. MC simulations of CoHex ions interacting with the homopolymeric poly(dA·dT) DNA duplex with modified (de-methylated) and native thymine bases are used to explore the physics behind CoHex-thymine interactions. The simulations suggest that the ion desolvation penalty due to proximity to the low dielectric volume of the methyl group can contribute significantly to CoHex-thymine interactions. Compared to the steric repulsion between the ion and the methyl group, the desolvation penalty interaction has a longer range and may be important to consider in the context of methylation effects on DNA condensation.

Concentration-dependent and configuration-dependent interactions of monovalent ions with an RNA tetraloop

Monovalent salt solutions have strongly coupled interactions with biopolymers, from large polyelectrolytes to small RNA oligomers. High salt concentrations have been known to induce transitions in the structure of RNA, producing non-canonical configurations and even driving RNA to precipitate out of solution. Using all-atom molecular dynamics simulations, we model a monovalent salt species (KCL) at high concentrations (0.1-3m) and calculate the equilibrium distributions of water and ions around a small tetraloop-forming RNA oligomer in a variety of structural arrangements: folded A-RNA (canonical) and Z-RNA (non-canonical) tetraloops and unfolded configurations. From these data, we calculate the ion preferential binding coefficients and Donnan coefficients for the RNA oligomer as a function of concentration and structure. We find that cation accumulation is highest around non-canonical Z-RNA configurations at concentrations below 0.5m, while unfolded configurations accumulate the most co-ions in all concentrations. By contrast, canonical A-RNA structures consistently show the lowest accumulations for all ion species. Water distributions vary markedly with RNA configuration but show little dependency on KCL concentration. Based on Donnan coefficient calculations, the net charge of the solution at the surface of the RNA decreases linearly as a function of salt concentration and becomes net-neutral near 2.5-3m KCL for folded configurations, while unfolded configurations still show a positive solution charge. Our findings show that all-atom molecular dynamics can describe the equilibrium distributions of monovalent salt in the presence of small RNA oligomers at KCL concentrations where ion correlation effects become important. Furthermore, these results provide valuable insights into the distributions of water and ions near the RNA oligomer surface as a function of structural configuration.

Optical and Structural Characterization of a Chronic Myeloid Leukemia DNA Biosensor

Selective base pairing is the foundation of DNA recognition. Here, we elucidate the molecular and structural details of a FRET-based two-component molecular beacon relying on steady-state fluorescence spectroscopy, small-angle X-ray scattering (SAXS), microscale thermophoresis (MST), and differential electrophoretic mobility. This molecular beacon was designed to detect the most common fusion sequences causing chronic myeloid leukemia, e14a2 and e13a2. The emission spectra indicate that the self-assembly of the different components of the biosensor occurs sequentially, triggered by the fully complementary target. We further assessed the structural alterations leading to the specific fluorescence FRET signature by SAXS, MST, and the differential electrophoretic mobility, where the size range observed is consistent with hybridization and formation of a 1:1:1 complex for the probe in the presence of the complementary target and revelator. These results highlight the importance of different techniques to explore conformational DNA changes in solution and its potential to design and characterize molecular biosensors for genetic disease diagnosis.

Recent developments in small-angle X-ray scattering and hybrid method approaches for biomacromolecular solutions

Small-angle X-ray scattering (SAXS) has become a streamline method to characterize biological macromolecules, from small peptides to supramolecular complexes, in near-native solutions. Modern SAXS requires limited amounts of purified material, without the need for labelling, crystallization, or freezing. Dedicated beamlines at modern synchrotron sources yield high-quality data within or below several milliseconds of exposure time and are highly automated, allowing for rapid structural screening under different solutions and ambient conditions but also for time-resolved studies of biological processes. The advanced data analysis methods allow one to meaningfully interpret the scattering data from monodisperse systems, from transient complexes as well as flexible and heterogeneous systems in terms of structural models. Especially powerful are hybrid approaches utilizing SAXS with high-resolution structural techniques, but also with biochemical, biophysical, and computational methods. Here, we review the recent developments in the experimental SAXS practice and in analysis methods with a specific focus on the joint use of SAXS with complementary methods.

Quantifying the influence of the ion cloud on SAXS profiles of charged proteins

MD simulations and Poisson–Boltzmann calculations predict ion cloud effects on SAXS experiments.

Counting the ions surrounding nucleic acids

Nucleic acids are strongly negatively charged, and thus electrostatic interactions—screened by ions in solution—play an important role in governing their ability to fold and participate in biomolecular interactions. The negative charge creates a region, known as the ion atmosphere, in which cation and anion concentrations are perturbed from their bulk values. Ion counting experiments quantify the ion atmosphere by measuring the preferential ion interaction coefficient: the net total number of excess ions above, or below, the number expected due to the bulk concentration. The results of such studies provide important constraints on theories, which typically predict the full three-dimensional distribution of the screening cloud. This article reviews the state of nucleic acid ion counting measurements and critically analyzes their ability to test both analytical and simulation-based models.

Water Dynamics in the Hydration Shells of Biomolecules

The structure and function of biomolecules are strongly influenced by their hydration shells. Structural fluctuations and molecular excitations of hydrating water molecules cover a broad range in space and time, from individual water molecules to larger pools and from femtosecond to microsecond time scales. Recent progress in theory and molecular dynamics simulations as well as in ultrafast vibrational spectroscopy has led to new and detailed insight into fluctuations of water structure, elementary water motions, electric fields at hydrated biointerfaces, and processes of vibrational relaxation and energy dissipation. Here, we review recent advances in both theory and experiment, focusing on hydrated DNA, proteins, and phospholipids, and compare dynamics in the hydration shells to bulk water.

Determination of Ion Atmosphere Effects on the Nucleic Acid Electrostatic Potential and Ligand Association Using AH+·C Wobble Formation in Double-Stranded DNA

The high charge density of nucleic acids and resulting ion atmosphere profoundly influence the conformational landscape of RNA and DNA and their association with small molecules and proteins. Electrostatic theories have been applied to quantitatively model the electrostatic potential surrounding nucleic acids and the effects of the surrounding ion atmosphere, but experimental measures of the potential and tests of these models have often been complicated by conformational changes and multisite binding equilibria, among other factors. We sought a simple system to further test the basic predictions from electrostatics theory and to measure the energetic consequences of the nucleic acid electrostatic field. We turned to a DNA system developed by Bevilacqua and co-workers that involves a proton as a ligand whose binding is accompanied by formation of an internal AH⁺·C wobble pair [Siegfried, N. A., et al. Biochemistry, 2010, 49, 3225]. Consistent with predictions from polyelectrolyte models, we observed logarithmic dependences of proton affinity versus salt concentration of −0.96 ± 0.03 and −0.52 ± 0.01 with monovalent and divalent cations, respectively, and these results help clarify prior results that appeared to conflict with these fundamental models. Strikingly, quantitation of the ion atmosphere content indicates that divalent cations are preferentially lost over monovalent cations upon A·C protonation, providing experimental indication of the preferential localization of more highly charged cations to the inner shell of the ion atmosphere. The internal AH⁺·C wobble system further allowed us to parse energetic contributions and extract estimates for the electrostatic potential at the position of protonation. The results give a potential near the DNA surface at 20 mM Mg²⁺ that is much less substantial than at 20 mM K⁺ (−120 mV vs −210 mV). These values and difference are similar to predictions from theory, and the potential is substantially reduced at higher salt, also as predicted; however, even at 1 M K⁺ the potential remains substantial, counter to common assumptions. The A·C protonation module allows extraction of new properties of the ion atmosphere and provides an electrostatic meter that will allow local electrostatic potential and energetics to be measured within nucleic acids and their complexes with proteins.

Extracting water and ion distributions from solution x-ray scattering experiments

Small-angle X-ray scattering measurements can provide valuable information about the solvent environment around biomolecules, but it can be difficult to extract solvent-specific information from observed intensity profiles. Intensities are proportional to the square of scattering amplitudes, which are complex quantities. Amplitudes in the forward direction are real, and the contribution from a solute of known structure (and from the waters it excludes) can be estimated from theory; hence, the amplitude arising from the solvent environment can be computed by difference. We have found that this "square root subtraction scheme" can be extended to non-zero q values, out to 0.1 Å(-1) for the systems considered here, since the phases arising from the solute and from the water environment are nearly identical in this angle range. This allows us to extract aspects of the water and ion distributions (beyond their total numbers), by combining experimental data for the complete system with calculations for the solutes. We use this approach to test molecular dynamics and integral-equation (3D-RISM (three-dimensional reference interaction site model)) models for solvent structure around myoglobin, lysozyme, and a 25 base-pair duplex DNA. Comparisons can be made both in Fourier space and in terms of the distribution of interatomic distances in real space. Generally, computed solvent distributions arising from the MD simulations fit experimental data better than those from 3D-RISM, even though the total small-angle X-ray scattering patterns are very similar; this illustrates the potential power of this sort of analysis to guide the development of computational models.

Tuning RNA Flexibility with Helix Length and Junction Sequence

The increasing awareness of RNA's central role in biology calls for a new understanding of how RNAs, like proteins, recognize biological partners. Because RNA is inherently flexible, it assumes a variety of conformations. This conformational flexibility can be a critical aspect of how RNA attracts and binds molecular partners. Structurally, RNA consists of rigid basepaired duplexes, separated by flexible non-basepaired regions. Here, using an RNA system consisting of two short helices, connected by a single-stranded (non-basepaired) junction, we explore the role of helix length and junction sequence in determining the range of conformations available to a model RNA. Single-molecule Förster resonance energy transfer reports on the RNA conformation as a function of either mono- or divalent ion concentration. Electrostatic repulsion between helices dominates at low salt concentration, whereas junction sequence effects determine the conformations at high salt concentration. Near physiological salt concentrations, RNA conformation is sensitive to both helix length and junction sequence, suggesting a means for sensitively tuning RNA conformations.

Predicting 3D Structure, Flexibility, and Stability of RNA Hairpins in Monovalent and Divalent Ion Solutions

A full understanding of RNA-mediated biology would require the knowledge of three-dimensional (3D) structures, structural flexibility, and stability of RNAs. To predict RNA 3D structures and stability, we have previously proposed a three-bead coarse-grained predictive model with implicit salt/solvent potentials. In this study, we further develop the model by improving the implicit-salt electrostatic potential and including a sequence-dependent coaxial stacking potential to enable the model to simulate RNA 3D structure folding in divalent/monovalent ion solutions. The model presented here can predict 3D structures of RNA hairpins with bulges/internal loops (<77 nucleotides) from their sequences at the corresponding experimental ion conditions with an overall improved accuracy compared to the experimental data; the model also makes reliable predictions for the flexibility of RNA hairpins with bulge loops of different lengths at several divalent/monovalent ion conditions. In addition, the model successfully predicts the stability of RNA hairpins with various loops/stems in divalent/monovalent ion solutions.

Conformational Changes and Flexibility of DNA Devices Observed by Small-Angle X-ray Scattering

Self-assembled DNA origami nanostructures enable the creation of precisely defined shapes at the molecular scale. Dynamic DNA devices that are capable of switching between defined conformations could afford completely novel functionalities for diagnostic, therapeutic, or engineering applications. Developing such objects benefits strongly from experimental feedback about conformational changes and 3D structures, ideally in solution, free of potential biases from surface attachment or labeling. Here, we demonstrate that small-angle X-ray scattering (SAXS) can quantitatively resolve the conformational changes of a DNA origami two-state switch device as a function of the ionic strength of the solution. In addition, we show how SAXS data allow for refinement of the predicted idealized three-dimensional structure of the DNA object using a normal mode approach based on an elastic network model. The results reveal deviations from the idealized design geometries that are otherwise difficult to resolve. Our results establish SAXS as a powerful tool to investigate conformational changes and solution structures of DNA origami and we anticipate our methodology to be broadly applicable to increasingly complex DNA and RNA devices.

Nucleic acid polymeric properties and electrostatics: Directly comparing theory and simulation with experiment

Nucleic acids are biopolymers that carry genetic information and are also involved in various gene regulation functions such as gene silencing and protein translation. Because of their negatively charged backbones, nucleic acids are polyelectrolytes. To adequately understand nucleic acid folding and function, we need to properly describe its i) polymer/polyelectrolyte properties and ii) associating ion atmosphere. While various theories and simulation models have been developed to describe nucleic acids and the ions around them, many of these theories/simulations have not been well evaluated due to complexities in comparison with experiment. In this review, I discuss some recent experiments that have been strategically designed for straightforward comparison with theories and simulation models. Such data serve as excellent benchmarks to identify limitations in prevailing theories and simulation parameters.

Protein-DNA and ion-DNA interactions revealed through contrast variation SAXS

Understanding how DNA carries out its biological roles requires knowledge of its interactions with biological partners. Since DNA is a polyanionic polymer, electrostatic interactions contribute significantly. These interactions are mediated by positively charged protein residues or charge compensating cations. Direct detection of these partners and/or their effect on DNA conformation poses challenges, especially for monitoring conformational dynamics in real time. Small-angle x-ray scattering (SAXS) is uniquely sensitive to both the conformation and local environment (i.e. protein partner and associated ions) of the DNA. The primary challenge of studying multi-component systems with SAXS lies in resolving how each component contributes to the measured scattering. Here, we review two contrast variation (CV) strategies that enable targeted studies of the structures of DNA or its associated partners. First, solution contrast variation enables measurement of DNA conformation within a protein-DNA complex by masking out the protein contribution to the scattering profile. We review a specific example, in which the real-time unwrapping of DNA from a nucleosome core particle is measured during salt-induced disassembly. The second method, heavy atom isomorphous replacement, reports the spatial distribution of the cation cloud around duplex DNA by exploiting changes in the scattering strength of cations with varying atomic numbers. We demonstrate the application of this approach to provide the spatial distribution of monovalent cations (Na+, K+, Rb+, Cs+) around a standard 25-base pair DNA. The CV strategies presented here are valuable tools for understanding DNA interactions with its biological partners.

SAXS/SANS on Supercharged Proteins Reveals Residue-Specific Modifications of the Hydration Shell

Water molecules in the immediate vicinity of biomacromolecules, including proteins, constitute a hydration layer characterized by physicochemical properties different from those of bulk water and play a vital role in the activity and stability of these structures, as well as in intermolecular interactions. Previous studies using solution scattering, crystallography, and molecular dynamics simulations have provided valuable information about the properties of these hydration shells, including modifications in density and ionic concentration. Small-angle scattering of x-rays (SAXS) and neutrons (SANS) are particularly useful and complementary techniques to study biomacromolecular hydration shells due to their sensitivity to electronic and nuclear scattering-length density fluctuations, respectively. Although several sophisticated SAXS/SANS programs have been developed recently, the impact of physicochemical surface properties on the hydration layer remains controversial, and systematic experimental data from individual biomacromolecular systems are scarce. Here, we address the impact of physicochemical surface properties on the hydration shell by a systematic SAXS/SANS study using three mutants of a single protein, green fluorescent protein (GFP), with highly variable net charge (+36, -6, and -29). The combined analysis of our data shows that the hydration shell is locally denser in the vicinity of acidic surface residues, whereas basic and hydrophilic/hydrophobic residues only mildly modify its density. Moreover, the data demonstrate that the density modifications result from the combined effect of residue-specific recruitment of ions from the bulk in combination with water structural rearrangements in their vicinity. Finally, we find that the specific surface-charge distributions of the different GFP mutants modulate the conformational space of flexible parts of the protein.

Multi-shell model of ion-induced nucleic acid condensation

We present a semi-quantitative model of condensation of short nucleic acid (NA) duplexes induced by trivalent cobalt(iii) hexammine (CoHex) ions. The model is based on partitioning of bound counterion distribution around single NA duplex into "external" and "internal" ion binding shells distinguished by the proximity to duplex helical axis. In the aggregated phase the shells overlap, which leads to significantly increased attraction of CoHex ions in these overlaps with the neighboring duplexes. The duplex aggregationfree energy is decomposed into attractive and repulsive components in such a way that they can be represented by simple analytical expressions with parameters derived from molecular dynamic simulations and numerical solutions of Poisson equation. The attractive term depends on the fractions of bound ions in the overlapping shells and affinity of CoHex to the "external" shell of nearly neutralized duplex. The repulsive components of the free energy are duplex configurational entropy loss upon the aggregation and the electrostatic repulsion of the duplexes that remains after neutralization by bound CoHex ions. The estimates of the aggregationfree energy are consistent with the experimental range of NA duplex condensation propensities, including the unusually poor condensation of RNA structures and subtle sequence effects upon DNAcondensation. The model predicts that, in contrast to DNA, RNA duplexes may condense into tighter packed aggregates with a higher degree of duplex neutralization. An appreciable CoHex mediated RNA-RNA attraction requires closer inter-duplex separation to engage CoHex ions (bound mostly in the "internal" shell of RNA) into short-range attractive interactions. The model also predicts that longer NA fragments will condense more readily than shorter ones. The ability of this model to explain experimentally observed trends in NAcondensation lends support to proposed NAcondensation picture based on the multivalent "ion binding shells."

SAXS studies of RNA: structures, dynamics, and interactions with partners

Small-angle X-ray scattering, SAXS, is a powerful and easily employed experimental technique that provides solution structures of macromolecules. The size and shape parameters derived from SAXS provide global structural information about these molecules in solution and essentially complement data acquired by other biophysical methods. As applied to protein systems, SAXS is a relatively mature technology: sophisticated tools exist to acquire and analyze data, and to create structural models that include dynamically flexible ensembles. Given the expanding appreciation of RNA's biological roles, there is a need to develop comparable tools to characterize solution structures of RNA, including its interactions with important biological partners. We review the progress toward achieving this goal, focusing on experimental and computational innovations. The use of multiphase modeling, absolute calibration and contrast variation methods, among others, provides new and often unique ways of visualizing this important biological molecule and its essential partners: ions, other RNAs, or proteins. WIREs RNA 2016, 7:512-526. doi: 10.1002/wrna.1349 For further resources related to this article, please visit the WIREs website.