SAXS studies of ion-nucleic acid interactions

Small-Angle X-ray Scattering (SAXS) Combined with SAXS-Driven Molecular Dynamics for Structural Analysis of Multistranded RNA Assemblies

Nucleic acids (RNA and DNA) play crucial roles in all living organisms and find wide utility in clinical settings. The convergence of rationally designed nucleic acid multistranded assemblies with embedded therapeutic properties has led to the development of a platform based on nucleic acid nanoparticles (NANPs). NANPs incorporate various functional moieties to deliver their combinations to diseased cells in a highly controlled manner. Given that the structure and composition of NANPs can also influence their immunorecognition and biological activities, thorough verification of all designs is essential. We introduce an experimental pipeline for small-angle X-ray scattering (SAXS) to gather structural details about the solution-state NANPs assembled from up to 12 RNA strands. To the best of our knowledge, this study represents the largest multistranded RNA nanoassemblies characterized in this manner to date. We show that synchronized implementation of SAXS-driven molecular dynamics simulations reveals the diverse conformational landscape inhabited by these assemblies and provides insights into their immunorecognition. The developed strategy expands the capabilities of therapeutic nucleic acids and emerging nucleic acid nanotechnologies.

Implicit Solvent with Explicit Ions Generalized Born Model in Molecular Dynamics: Application to DNA

The ion atmosphere surrounding highly charged biomolecules, such as nucleic acids, is crucial for their dynamics, structure, and interactions. Here, we develop an approach for the explicit treatment of ions within an implicit solvent framework suitable for atomistic simulations of biomolecules. The proposed implicit solvent/explicit ions model, GBION, is based on a modified generalized Born (GB) model; it includes separate, modified GB terms for solute-ion and ion-ion interactions. The model is implemented in the AMBER package (version 24), and its performance is thoroughly investigated in atomistic molecular dynamics (MD) simulations of double-stranded DNA on a microsecond time scale. The aggregate characteristics of monovalent (Na+ and K+) and trivalent (Cobalt Hexammine, CoHex3+) counterion distributions around double-stranded DNA predicted by the model are in reasonable agreement with the experiment (where available), all-atom explicit water MD simulations, and the expectation from the Manning condensation theory. The radial distributions of monovalent cations around DNA are reasonably close to the ones obtained using the explicit water model: expressed in units of energy, the maximum deviations of local ion concentrations from the explicit solvent reference are within 1 kBT, comparable to the corresponding deviations expected between different established explicit water models. The proposed GBION model is able to simulate DNA fragments in a large volume of solvent with explicit ions with little additional computational overhead compared with the fully implicit GB treatment of ions. Ions simulated using the developed model explore conformational space at least 2 orders of magnitude faster than in the explicit solvent. These advantages allowed us to observe and explore an unexpected "stacking" mode of DNA condensation in the presence of trivalent counterions (CoHex3+) that was revealed by recent experiments.

Hindered intermolecular stacking of anti-parallel telomeric G-quadruplexes

Telomeric G-quadruplexes (G4s) are non-canonical DNA structures composed of TTAGGG repeats. They are extensively studied both as biomolecules key for genome stability and as promising building blocks and functional elements in synthetic biology and nanotechnology. This is why it is extremely important to understand how the interaction between G4s is affected by their topology. We used small-angle x-ray scattering to investigate the end-to-end stacking of antiparallel telomeric G-quadruplexes formed by the sequence AG3(T2AG3)3. To represent the experimental data, we developed a highly efficient coarse-grained fitting tool, which successfully described the samples as an equilibrium mixture of monomeric and dimeric G4 species. Our findings indicate that the antiparallel topology prevents the formation of long multimeric structures under self-crowding conditions, unlike the hybrid/parallel structures formed by the same DNA sequence. This result supports the idea that the stacking of monomeric G-quadruplexes is strongly affected by the presence of diagonal loops.

Supramolecular DNA-based catalysis in organic solvents

The distinct folding accompanied by its polymorphic character renders DNA G-quadruplexes promising biomolecular building blocks to construct novel DNA-based and supramolecular assemblies. However, the highly polar nature of DNA limits the use of G-quadruplexes to water as a solvent. In addition, the archetypical G-quadruplex fold needs to be stabilized by metal-cations, which is usually a potassium ion. Here, we show that a noncovalent PEGylation process enabled by electrostatic interactions allows the first metal-free G-quadruplexes in organic solvents. Strikingly, incorporation of an iron-containing porphyrin renders the self-assembled metal-free G-quadruplex catalytically active in organic solvents. Hence, these "supraG4zymes" enable DNA-based catalysis in organic media. The results will allow the broad utilization of DNA G-quadruplexes in nonaqueous environments.

Impact of Divalent Cations on In-Layer Positional Order of DNA-Based Liquid Crystals: Implications for DNA Condensation

The layered liquid crystalline phases formed by DNA molecules, which include rigid and flexible segments ("gapped DNA"), enable the study of both end-to-end stacking and side-to-side (helix-to-helix) lateral interactions, forming a model system to study such interactions at physiologically relevant DNA and ion concentrations. The observed layer structure exhibits long-range interlayer and in-layer positional correlations. In particular, the in-layer order has implications for DNA condensation, as it reflects whether these normally repulsive interactions become attractive under certain ionic conditions. Using synchrotron small-angle X-ray scattering measurements, we investigate the impact of divalent Mg2+ cations (in addition to a constant 150 mM Na+) on the stability of the inter- and in-layer DNA ordering as a function of temperature between 5 and 65 °C. DNA constructs with different terminal base pairings were created to mediate the strength of the attractive end-to-end stacking interactions between the blunt ends of the gapped DNA constructs. We demonstrate that the stabilities at a fixed DNA concentration of both interlayer and in-layer order are significantly enhanced even at a few mM Mg2+ concentration. The stabilities are even higher at 30 mM Mg2+; however, a marked decrease is observed at 100 mM Mg2+, suggesting a change in the nature of side-by-side interactions within this Mg2+ concentration range. We discuss the implications of these results in terms of counterion-mediated DNA-DNA attraction and DNA condensation.

Quantitative Determination of Metal Ion Adsorption on Cellulose Nanocrystals Surfaces

Nanocellulose is a bio-based material that holds significant potential in the field of water purification. Of particular interest is their potential use as a key sorbent material for the removal of metal ions from solution. However, the structure of metal ions adsorbed onto cellulose surfaces is not well understood. The focus of this work is to determine quantitatively the three-dimensional distribution of metal ions of different valencies surrounding negatively charged carboxylate functionalized cellulose nanocrystals (CNCs) using anomalous small-angle X-ray scattering (ASAXS). These distributions can affect the water and ionic permeability in these materials. The data show that increasing the carboxylate density on the surface of the CNCs from 740 to 1100 mmol/kg changed the nature of the structure of the adsorbed ions from a monolayer into a multilayer structure. The monolayer was modeled as a Stern layer around the CNC nanoparticles, whereas the multilayer structure was modeled as a diffuse layer on top of the Stern layer around the nanoparticles. Within the Stern layer, the maximum ion density increases from 1680 to 4350 mmol of Rb+/(kg of CNC) with the increase in the carboxylate density on the surface of the nanoparticles. Additionally, the data show that CNCs can leverage multiple mechanisms, such as electrostatic attraction and the chaotropic effect, to adsorb ions of different valencies. By understanding the spatial organization of the adsorbed metal ions, the design of cellulose-based sorbents can be further optimized to improve the uptake capacity and selectivity in separation applications.

Condensation Goes Viral: A Polymer Physics Perspective

The past decade has seen a revolution in our understanding of how the cellular environment is organized, where an incredible body of work has provided new insights into the role played by membraneless organelles. These rapid advancements have been made possible by an increasing awareness of the peculiar physical properties that give rise to such bodies and the complex biology that enables their function. Viral infections are not extraneous to this. Indeed, in host cells, viruses can harness existing membraneless compartments or, even, induce the formation of new ones. By hijacking the cellular machinery, these intracellular bodies can assist in the replication, assembly, and packaging of the viral genome as well as in the escape of the cellular immune response. Here, we provide a perspective on the fundamental polymer physics concepts that may help connect and interpret the different observed phenomena, ranging from the condensation of viral genomes to the phase separation of multicomponent solutions. We complement the discussion of the physical basis with a description of biophysical methods that can provide quantitative insights for testing and developing theoretical and computational models.

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.

Small-angle X-ray microdiffraction from fibrils embedded in tissue thin sections

Small-angle X-ray scattering (SAXS) from fibrils embedded in a fixed, thin section of tissue includes contributions from the fibrils, the polymeric matrix surrounding the fibrils, other constituents of the tissue, and cross-terms due to the spatial correlation between fibrils and neighboring molecules. This complex mixture severely limits the amount of information that can be extracted from scattering studies. However, availability of micro- and nano-beams has made the measurement of scattering from very small volumes possible, which, in some cases, may be dominated by a single fibrillar constituent. In such cases, information about the predominant species may be accessible. Nevertheless, even in these cases, the correlations between the positions of fibrils and other constituents have a significant impact on the observed scattering. Here, strategies are proposed to extract partial information about fibril structure and tissue organization on the basis of SAXS from samples of this type. It is shown that the spatial correlation function of the fibril in the direction perpendicular to the fibril axis can be computed and contains information about the predominant fibril structure and the organization of the surrounding tissue matrix. This has significant advantages over approaches based on techniques developed for X-ray solution scattering. Examples of correlation calculations in different types of samples are given to demonstrate the information that can be obtained from these measurements.

Contrast variation SAXS: Sample preparation protocols, experimental procedures, and data analysis

Proteins and nucleic acids, alone and in complex are among the essential building blocks of living organisms. Obtaining a molecular level understanding of their structures, and the changes that occur as they interact, is critical for expanding our knowledge of life processes or disease progression. Here, we motivate and describe an application of solution small angle X-ray scattering (SAXS) which provides valuable information about the structures, ensembles, compositions and dynamics of protein-nucleic acid complexes in solution, in equilibrium and time-resolved studies. Contrast variation (CV-) SAXS permits the visualization of the distinct molecular constituents (protein and/or nucleic acid) within a complex. CV-SAXS can be implemented in two modes. In the simplest, the protein within the complex is effectively rendered invisible by the addition of an inert contrast agent at an appropriate concentration. Under these conditions, the structure, or structural changes of only the nucleic acid component of the complex can be studied in detail. The second mode permits observation of both components of the complex: the protein and the nucleic acid. This approach requires the acquisition of SAXS profiles on the complex at different concentrations of a contrast agent. Here, we review CV-SAXS as applied to protein-nucleic acid complexes in both modes. We provide some theoretical framework for CV-SAXS but focus primarily on providing the necessary information required to implement a successful experiment including experimental design, sample quality assessment, and data analysis.

Getting to the bottom of lncRNA mechanism: structure-function relationships

While long non-coding RNAs are known to play key roles in disease and development, relatively few structural studies have been performed for this important class of RNAs. Here, we review functional studies of long non-coding RNAs and expose the need for high-resolution 3-D structural studies, discussing the roles of long non-coding RNAs in the cell and how structure–function relationships might be used to elucidate further understanding. We then describe structural studies of other classes of RNAs using chemical probing, nuclear magnetic resonance, small-angle X-ray scattering, X-ray crystallography, and cryogenic electron microscopy (cryo-EM). Next, we review early structural studies of long non-coding RNAs to date and describe the way forward for the structural biology of long non-coding RNAs in terms of cryo-EM.

Experimental approaches for investigating ion atmospheres around nucleic acids and proteins

Ionic interactions are crucial to biological functions of DNA, RNA, and proteins. Experimental research on how ions behave around biological macromolecules has lagged behind corresponding theoretical and computational research. In the 21st century, quantitative experimental approaches for investigating ionic interactions of biomolecules have become available and greatly facilitated examinations of theoretical electrostatic models. These approaches utilize anomalous small-angle X-ray scattering, atomic emission spectroscopy, mass spectrometry, or nuclear magnetic resonance (NMR) spectroscopy. We provide an overview on the experimental methodologies that can quantify and characterize ions within the ion atmospheres around nucleic acids, proteins, and their complexes.

Multivalent Ion-Mediated Attraction between Like-Charged Colloidal Particles: Nonmonotonic Dependence on the Particle Charge

Ion-mediated effective interactions are important for the structure and stability of charged particles such as colloids and nucleic acids. It has been known that the intrinsic electrostatic repulsion between like-charged particles can be modulated into effective attraction by multivalent ions. In this work, we examined the dependence of multivalent ion-mediated attraction between like-charged colloidal particles on the particle charge in a wide range by extensive Monte Carlo simulations. Our calculations show that for both divalent and trivalent salts, the effective attraction between like-charged colloidal particles becomes stronger with the increase of the particle charge, whereas it gradually becomes weakened when the particle charge exceeds a "critical" value. Correspondingly, as the particle charge is increased, the driving force for such effective attraction transits from an attractive electrostatic force to an attractive depletion force, and the attraction weakening by high particle charges is attributed to the transition of electrostatic force from attraction to repulsion. Our analyses suggest that the attractive depletion force and the repulsive electrostatic force at high particle charges result from the Coulomb depletion which suppresses the counterion condensation in the limited region between two like-charged colloidal particles. Moreover, our extensive calculations indicate that the "critical" particle charge decreases apparently for larger ions and smaller colloidal particles due to stronger Coulomb depletion and decreases slightly at higher salt concentrations due to the slightly enhanced Coulomb depletion in the intervening space between colloidal particles. Encouragingly, we derived an analytical formula for the "critical" particle charge based on the Lindemann melting law.

Simple and Analytical Model of RNA Collapse

An analytical model for the free energy change during collapse of an RNA molecule from an extended to a compact conformation is proposed. It considers explicit binding of water and ion molecules to the RNA and the exchange of these molecules with the aqueous solution. Microscopic states of the system are captured on a two-dimensional square lattice and evaluated using contact energies. We compute the free energy as a function of a collapse variable and the number of ions bound to the RNA. The major driving force to the collapse of the RNA chain is the gain in water entropy once expelled from the surface of the RNA molecule illustrated by decomposing the free energy into species contributions and their energy and entropy components. The sensitivity of the conclusions of the model to variations in parameters is computed and appears to be weak.

Additive Modulation of DNA-DNA Interactions by Interstitial Ions

Quantitative understanding of biomolecular electrostatics, particularly involving multivalent ions and highly charged surfaces, remains lacking. Ion-modulated interactions between nucleic acids provide a model system in which electrostatics plays a dominant role. Using ordered DNA arrays neutralized by spherical cobalt³⁺ hexammine and Mg²⁺ ions, we investigate how the interstitial ions modulate DNA-DNA interactions. Using methods of ion counting, osmotic stress, and x-ray diffraction, we systematically determine thermodynamic quantities, including ion chemical potentials, ion partition, DNA osmotic pressure and force, and DNA-DNA spacing. Analyses of the multidimensional data provide quantitative insights into their interdependencies. The key finding of this study is that DNA-DNA forces are observed to linearly depend on the partition of interstitial ions, suggesting the dominant role of ion-DNA coupling. Further implications are discussed in light of physical theories of electrostatic interactions and like-charge attraction.

Cancer cell discrimination and dynamic viability monitoring through wash-free bioimaging using AIEgens

Cancer cell discrimination and cellular viability monitoring are closely related to human health. A universal and convenient fluorescence system with a dual function of wide-spectrum cancer cell discrimination and dynamic cellular viability monitoring is desperately needed, and is still extremely challenging. Herein we present a series of aggregation-induced emission luminogens (AIEgens) (denoted as IVP) which can allow accurate discrimination between cancer and normal cells and dynamic monitoring of cellular viability through mitochondria-nucleolus migration. By regulating the lengths and positions of alkyl chains in IVP molecules, we systematically studied the discrimination behavior of these AIEgens between cancer cells and normal cells and further investigated how they can migrate between the mitochondria and nucleolus based on the change of mitochondrial membrane potential (ΔΨ m). Using IVP-02 as a model molecule, wash-free bioimaging, excellent two-photon properties, and low cytotoxicity were demonstrated. This present work proves that these designed IVP AIEgens show great potential for cancer identification and metastasis monitoring, as well as activity evaluation and screening of drugs.

Thermodynamic stability condition can judge whether a nanoparticle dispersion can be considered a solution in a single phase

Establishing that a nanoparticle dispersion can, in fact, be treated as a solution has an important practical ramification, namely the application of solubility theories for solvent selection. However, what distinguishes a solution and dispersion has remained ambiguously understood. Based on the recent progress in statistical thermodynamics on multiple-component solutions, here we establish the condition upon which a nanoparticle dispersion can be considered a single-phased solution. We shall provide experimental evidence already found in the literature showing the solution nature of nanoparticle dispersions.

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.

Ribosomal Protein L11 Selectively Stabilizes a Tertiary Structure of the GTPase Center rRNA Domain

The GTPase Center (GAC) RNA domain in bacterial 23S rRNA is directly bound by ribosomal protein L11, and this complex is essential to ribosome function. Previous cocrystal structures of the 58-nucleotide GAC RNA bound to L11 revealed the intricate tertiary fold of the RNA domain, with one monovalent and several divalent ions located in specific sites within the structure. Here, we report a new crystal structure of the free GAC that is essentially identical to the L11-bound structure, which retains many common sites of divalent ion occupation. This new structure demonstrates that RNA alone folds into its tertiary structure with bound divalent ions. In solution, we find that this tertiary structure is not static, but rather is best described as an ensemble of states. While L11 protein cannot bind to the GAC until the RNA has adopted its tertiary structure, new experimental data show that L11 binds to Mg²⁺-dependent folded states, which we suggest lie along the folding pathway of the RNA. We propose that L11 stabilizes a specific GAC RNA tertiary state, corresponding to the crystal structure, and that this structure reflects the functionally critical conformation of the rRNA domain in the fully assembled ribosome.

Visualizing Disordered Single-Stranded RNA: Connecting Sequence, Structure, and Electrostatics

Disordered homopolymeric regions of single-stranded RNA, such as U or A tracts, are found within functional RNAs where they play distinct roles in defining molecular structure and facilitating recognition by partners. Despite this prominence, details of conformational and biophysical properties of these regions have not yet been resolved. We apply a number of experimental techniques to investigate the conformations of these biologically important motifs and provide quantitative measurements of their ion atmospheres. Single strands of RNA display pronounced sequence-dependent conformations that relate to the unique ion atmospheres each attracts. Chains of rU bases are relatively unstructured under all conditions, while chains of rA bases display distinct ordering through stacking or clustering motifs, depending on the composition of the surrounding solution. These dramatic structural differences are consistent with the measured disparity in ion composition and atmospheres around each homopolymer, revealing a complex interplay of base, ion, and single-strand ordering. The unique structural and ionic signatures of homopolymer ssRNAs explains their role(s) in folding structured RNAs and may explain their distinct recognition by protein partners.

Electrostatically PEGylated DNA enables salt-free hybridization in water

Chemically modified nucleic acids have long served as a very important class of bio-hybrid structures. In particular, the modification with PEG has advanced the scope and performance of oligonucleotides in materials science, catalysis and therapeutics. Most of the applications involving pristine or modified DNA rely on the potential of DNA to form a double-stranded structure. However, a substantial requirement for metal-cations to achieve hybridization has restricted the range of applications. To extend the applicability of DNA in salt-free or low ionic strength aqueous medium, we introduce noncovalent DNA-PEG constructs that allow canonical base-pairing between individually PEGylated complementary strands resulting in a double-stranded structure in salt-free aqueous medium. This method relies on grafting of amino-terminated PEG polymers electrostatically onto the backbone of DNA, which results in the formation of a PEG-envelope. The specific charge interaction of PEG molecules with DNA, absolute absence of metal ions within the PEGylated DNA molecules and formation of a double helix that is significantly more stable than the duplex in an ionic buffer have been unequivocally demonstrated using multiple independent characterization techniques.

Structure, stability and specificity of the binding of ssDNA and ssRNA with proteins

Recognition of single-stranded DNA (ssDNA) or single-stranded RNA (ssRNA) is important for many fundamental cellular functions. A variety of single-stranded DNA-binding proteins (ssDBPs) and single-stranded RNA-binding proteins (ssRBPs) have evolved that bind ssDNA and ssRNA, respectively, with varying degree of affinities and specificities to form complexes. Structural studies of these complexes provide key insights into their recognition mechanism. However, computational modeling of the specific recognition process and to predict the structure of the complex is challenging, primarily due to the heterogeneity of their binding energy landscape and the greater flexibility of ssDNA or ssRNA compared with double-stranded nucleic acids. Consequently, considerably fewer computational studies have explored interactions between proteins and single-stranded nucleic acids compared with protein interactions with double-stranded nucleic acids. Here, we report a newly developed energy-based coarse-grained model to predict the structure of ssDNA–ssDBP and ssRNA–ssRBP complexes and to assess their sequence-specific interactions and stabilities. We tuned two factors that can modulate specific recognition: base–aromatic stacking strength and the flexibility of the single-stranded nucleic acid. The model was successfully applied to predict the binding conformations of 12 distinct ssDBP and ssRBP structures with their cognate ssDNA and ssRNA partners having various sequences. Estimated binding energies agreed well with the corresponding experimental binding affinities. Bound conformations from the simulation showed a funnel-shaped binding energy distribution where the native-like conformations corresponded to the energy minima. The various ssDNA–protein and ssRNA–protein complexes differed in the balance of electrostatic and aromatic energies. The lower affinity of the ssRNA–ssRBP complexes compared with the ssDNA–ssDBP complexes stems from lower flexibility of ssRNA compared to ssDNA, which results in higher rate constants for the dissociation of the complex (k_off) for complexes involving the former.

Quantifying bimolecular self-assembly is pivotal to understanding cellular function. In recent years, a large progress has been made in understanding the structure and biophysics of protein-protein interactions. Particularly, various computational tools are available for predicting these structures and to estimate their stability and the driving forces of their formation. The understating of the interactions between proteins and nucleic acids, however, is still limited, presumably due to the involvement of non-specific interactions as well as the high conformational plasticity that may demand an induced-fit mechanism. In particular, the interactions between proteins and single-stranded nucleic acids (i.e., single-stranded DNA and RNA) is very challenging due to their high flexibility. Furthermore, the interface between proteins and single-stranded nucleic acids is often chemically more heterogeneous than the interface between proteins and double-stranded DNA. In this study, we developed a coarse-grained computational model to predict the structure of complexes between proteins and single-stranded nucleic acids. The model was applied to estimate binding affinities and the estimated binding energies agreed well with the corresponding experimental binding affinities. The kinetics of association as well as the specificity of the complexes between proteins and ssDNA are different than those with ssRNA, mostly due to differences in their conformational flexibility.

Predicting Site-Binding Modes of Ions and Water to Nucleic Acids Using Molecular Solvation Theory

Site binding of ions and water shapes nucleic acids folding, dynamics, and biological function, complementing the more diffuse, nonspecific "territorial" ion binding. Unlike territorial binding, prediction of site-specific binding to nucleic acids remains an unsolved challenge in computational biophysics. This work presents a new toolset based on the 3D-RISM molecular solvation theory and topological analysis that predicts cation and water site binding to nucleic acids. 3D-RISM is shown to accurately capture alkali cations and water binding to the central channel, transversal loops, and grooves of the Oxytricha nova's telomeres' G-quadruplex ( Oxy-GQ), in agreement with high-resolution crystallographic data. To improve the computed cation occupancy along the Oxy-GQ central channel, it was necessary to refine and validate new cation-oxygen parameters using structural and thermodynamic data available for crown ethers and ion channels. This single set of parameters that describes both localized and delocalized binding to various biological systems is used to gain insight into cation occupancy along the Oxy-GQ channel under various salt conditions. The paper concludes with prospects for extending the method to predict divalent cation binding to nucleic acids. This work advances the forefront of theoretical methods able to provide predictive insight into ion atmosphere effects on nucleic acids function.

"End-to-end" stacking of small dsRNA

PELDOR (pulsed electron-electron double resonance) is an established method to study intramolecular distances and can give evidence for conformational changes and flexibilities. However, it can also be used to study intermolecular interactions as for example oligerimization. Here, we used PELDOR to study the "end-to-end" stacking of small double-stranded (ds) RNAs. For this study, the dsRNA molecules were only singly labeled with the spin label TPA to avoid multispin effects and to measure only the intermolecular stacking interactions. It can be shown that small dsRNAs tend to assemble to rod-like structures due to π-π interactions between the base pairs at the end of the strands. On the one hand, these interactions can influence or complicate measurements aimed at the determining of the structure and dynamics of the dsRNA molecule itself. On the other hand, it can be interesting to study such intermolecular stacking interactions in more detail, as for example their dependence on ion concentration. We quantitatively determined the stacking probability as a function of the monovalent NaCl salt and the dsRNA concentration. From these data, the dissociation constant K_d was deduced and found to depend on the ratio between the NaCl salt and dsRNA concentrations. Additionally, the distances and distance distributions obtained predict a model for the stacking geometry of dsRNAs. Introducing a nucleotide overhangs at one end of the dsRNA molecule restricts the stacking to the other end, leading only to dimer formations. Introducing such an overhang at both ends of the dsRNA molecule fully suppresses stacking, as we demonstrate by PELDOR experiments quantitatively.

Effects of Preferential Counterion Interactions on the Specificity of RNA Folding

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

Revealing the distinct folding phases of an RNA three-helix junction

Remarkable new insight has emerged into the biological role of RNA in cells. RNA folding and dynamics enable many of these newly discovered functions, calling for an understanding of RNA self-assembly and conformational dynamics. Because RNAs pass through multiple structures as they fold, an ensemble perspective is required to visualize the flow through fleetingly populated sets of states. Here, we combine microfluidic mixing technology and small angle X-ray scattering (SAXS) to measure the Mg-induced folding of a small RNA domain, the tP5abc three helix junction. Our measurements are interpreted using ensemble optimization to select atomically detailed structures that recapitulate each experimental curve. Structural ensembles, derived at key stages in both time-resolved studies and equilibrium titrations, reproduce the features of known intermediates, and more importantly, offer a powerful new structural perspective on the time-progression of folding. Distinct collapse phases along the pathway appear to be orchestrated by specific interactions with Mg ions. These key interactions subsequently direct motions of the backbone that position the partners of tertiary contacts for later bonding, and demonstrate a remarkable synergy between Mg and RNA across numerous time-scales.

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.

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.

Crystallinity of Double-Stranded RNA-Antimicrobial Peptide Complexes Modulates Toll-Like Receptor 3-Mediated Inflammation

Double-stranded RNA (dsRNA) induces production of pro-inflammatory cytokines in normal human epidermal keratinocytes (NHEK) by specific binding to endosomal Toll-like receptor-3 (TLR3). Recently, it has been shown that hyperactivation of TLR3 in psoriatic keratinocytes by dsRNA can occur in the presence of human antimicrobial peptide (AMP) LL37. Here, we combine synchrotron X-ray scattering, microscopy, computer simulations, and measurements of NHEK cytokine production to elucidate a previously unanticipated form of specific molecular pattern recognition. LL37 and similar α-helical AMPs can form pro-inflammatory nanocrystalline complexes with dsRNA that are recognized by TLR3 differently than dsRNA alone. dsRNA complexes that activate IL-6 production in NHEK and those that do not are both able to enter cells and co-localize with TLR3. However, the crystallinity of these AMP-dsRNA complexes, specifically the geometric spacing between parallel dsRNA and the repeat number of ordered dsRNA, strongly influences the level of TLR3 activation. Crystalline complexes that present dsRNA at a spacing that matches with the steric size of TLR3 can recruit and engage multiple TLR3 receptors, driving receptor clustering and immune amplification, whereas crystalline complexes that exhibit poor steric matching do not. Reverse-transcription quantitative PCR of IL-6 during siRNA knockdown of TLR3 confirms that cytokine production is due to TLR3: High levels of IL-6 transcription are observed for sterically matched complexes without TLR3 knockdown, whereas such activity is abrogated with TLR3 knockdown.

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.

X-ray Scattering Studies of Protein Structural Dynamics

X-ray scattering is uniquely suited to the study of disordered systems and thus has the potential to provide insight into dynamic processes where diffraction methods fail. In particular, while X-ray crystallography has been a staple of structural biology for more than half a century and will continue to remain so, a major limitation of this technique has been the lack of dynamic information. Solution X-ray scattering has become an invaluable tool in structural and mechanistic studies of biological macromolecules where large conformational changes are involved. Such systems include allosteric enzymes that play key roles in directing metabolic fluxes of biochemical pathways, as well as large, assembly-line type enzymes that synthesize secondary metabolites with pharmaceutical applications. Furthermore, crystallography has the potential to provide information on protein dynamics via the diffuse scattering patterns that are overlaid with Bragg diffraction. Historically, these patterns have been very difficult to interpret, but recent advances in X-ray detection have led to a renewed interest in diffuse scattering analysis as a way to probe correlated motions. Here, we will review X-ray scattering theory and highlight recent advances in scattering-based investigations of protein solutions and crystals, with a particular focus on complex enzymes.

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.

Visualizing single-stranded nucleic acids in solution

Single-stranded nucleic acids (ssNAs) are ubiquitous in many key cellular functions. Their flexibility limits both the number of high-resolution structures available, leaving only a small number of protein-ssNA crystal structures, while forcing solution investigations to report ensemble averages. A description of the conformational distributions of ssNAs is essential to more fully characterize biologically relevant interactions. We combine small angle X-ray scattering (SAXS) with ensemble-optimization methods (EOM) to dynamically build and refine sets of ssNA structures. By constructing candidate chains in representative dinucleotide steps and refining the models against SAXS data, a broad array of structures can be obtained to match varying solution conditions and strand sequences. In addition to the distribution of large scale structural parameters, this approach reveals, for the first time, intricate details of the phosphate backbone and underlying strand conformations. Such information on unperturbed strands will critically inform a detailed understanding of an array of problems including protein-ssNA binding, RNA folding and the polymer nature of NAs. In addition, this scheme, which couples EOM selection with an iteratively refining pool to give confidence in the underlying structures, is likely extendable to the study of other flexible systems.

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.

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.

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.

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

Nucleic acids carry a negative charge, attracting salt ions and water. Interactions with these components of the solvent drive DNA to condense, RNA to fold, and proteins to bind. To understand these biological processes, knowledge of solvent structure around the nucleic acids is critical. Yet, because they are often disordered, ions and water evade detection by x-ray crystallography and other high-resolution methods. Small-angle x-ray scattering (SAXS) is uniquely sensitive to the spatial correlations between solutes and the surrounding solvent. Thus, SAXS provides an experimental constraint to guide or test emerging solvation theories. However, the interpretation of SAXS profiles is nontrivial because of the difficulty in separating the scattering signals of each component: the macromolecule, ions, and hydration water. Here, we demonstrate methods for robustly deconvoluting these signals, facilitating a more straightforward comparison with theory. Using SAXS data collected on an absolute intensity scale for short DNA duplexes in solution with Na(+), K(+), Rb(+), or Cs(+) counterions, we mathematically decompose the scattering profiles into components (DNA, water, and ions) and validate the decomposition using anomalous scattering measurements. In addition, we generate a library of physically motivated ion atmosphere models and rank them by agreement with the scattering data. The best-fit models have relatively compact ion atmospheres when compared to predictions from the mean-field Poisson-Boltzmann theory of electrostatics. Thus, the x-ray scattering methods presented here provide a valuable measurement of the global structure of the ion atmosphere that can be used to test electrostatics theories that go beyond the mean-field approximation.

Flexibility of short DNA helices with finite-length effect: From base pairs to tens of base pairs

Flexibility of short DNA helices is important for the biological functions such as nucleosome formation and DNA-protein recognition. Recent experiments suggest that short DNAs of tens of base pairs (bps) may have apparently higher flexibility than those of kilo bps, while there is still the debate on such high flexibility. In the present work, we have studied the flexibility of short DNAs with finite-length of 5-50 bps by the all-atomistic molecular dynamics simulations and Monte Carlo simulations with the worm-like chain model. Our microscopic analyses reveal that short DNAs have apparently high flexibility which is attributed to the significantly strong bending and stretching flexibilities of ∼6 bps at each helix end. Correspondingly, the apparent persistence length lp of short DNAs increases gradually from ∼29 nm to ∼45 nm as DNA length increases from 10 to 50 bps, in accordance with the available experimental data. Our further analyses show that the short DNAs with excluding ∼6 bps at each helix end have the similar flexibility with those of kilo bps and can be described by the worm-like chain model with lp ∼ 50 nm.

Accurate small and wide angle x-ray scattering profiles from atomic models of proteins and nucleic acids

A new method is introduced to compute X-ray solution scattering profiles from atomic models of macromolecules. The three-dimensional version of the Reference Interaction Site Model (RISM) from liquid-state statistical mechanics is employed to compute the solvent distribution around the solute, including both water and ions. X-ray scattering profiles are computed from this distribution together with the solute geometry. We describe an efficient procedure for performing this calculation employing a Lebedev grid for the angular averaging. The intensity profiles (which involve no adjustable parameters) match experiment and molecular dynamics simulations up to wide angle for two proteins (lysozyme and myoglobin) in water, as well as the small-angle profiles for a dozen biomolecules taken from the BioIsis.net database. The RISM model is especially well-suited for studies of nucleic acids in salt solution. Use of fiber-diffraction models for the structure of duplex DNA in solution yields close agreement with the observed scattering profiles in both the small and wide angle scattering (SAXS and WAXS) regimes. In addition, computed profiles of anomalous SAXS signals (for Rb(+) and Sr(2+)) emphasize the ionic contribution to scattering and are in reasonable agreement with experiment. In cases where an absolute calibration of the experimental data at q = 0 is available, one can extract a count of the excess number of waters and ions; computed values depend on the closure that is assumed in the solution of the Ornstein-Zernike equations, with results from the Kovalenko-Hirata closure being closest to experiment for the cases studied here.

Small-angle X-ray scattering: a bridge between RNA secondary structures and three-dimensional topological structures

Whereas the structures of small to medium-sized well folded RNA molecules often can be determined by either X-ray crystallography or NMR spectroscopy, obtaining structural information for large RNAs using experimental, computational, or combined approaches remains a major interest and challenge. RNA is very sensitive to small-angle X-ray scattering (SAXS) due to high electron density along phosphate-sugar backbones, whose scattering contribution dominates SAXS intensity. For this reason, SAXS is particularly useful in obtaining global RNA structural information that outlines backbone topologies and, therefore, molecular envelopes. Such information is extremely valuable in bridging the gap between the secondary structures and three-dimensional topological structures of RNA molecules, particularly those that have proven difficult to study using other structure-determination methods. Here we review published results of RNA topological structures derived from SAXS data or in combination with other experimental data, as well as details on RNA sample preparation for SAXS experiments.

Biostructural Science Inspired by Next-Generation X-Ray Sources

Next-generation synchrotron radiation sources, such as X-ray free-electron lasers, energy recovery linacs, and ultra-low-emittance storage rings, are catalyzing novel methods of biomolecular microcrystallography and solution scattering. These methods are described and future trends are predicted. Importantly, there is a growing realization that serial microcrystallography and certain cutting-edge solution scattering experiments can be performed at existing storage ring sources by utilizing new technology. In this sense, next-generation sources are serving two distinct functions, namely, provision of new capabilities that require the newer sources and inspiration of new methods that can be performed at existing sources.

Analyzing ion distributions around DNA: sequence-dependence of potassium ion distributions from microsecond molecular dynamics

Microsecond molecular dynamics simulations of B-DNA oligomers carried out in an aqueous environment with a physiological salt concentration enable us to perform a detailed analysis of how potassium ions interact with the double helix. The oligomers studied contain all 136 distinct tetranucleotides and we are thus able to make a comprehensive analysis of base sequence effects. Using a recently developed curvilinear helicoidal coordinate method we are able to analyze the details of ion populations and densities within the major and minor grooves and in the space surrounding DNA. The results show higher ion populations than have typically been observed in earlier studies and sequence effects that go beyond the nature of individual base pairs or base pair steps. We also show that, in some special cases, ion distributions converge very slowly and, on a microsecond timescale, do not reflect the symmetry of the corresponding base sequence.

Multiscale methods for computational RNA enzymology

RNA catalysis is of fundamental importance to biology and yet remains ill-understood due to its complex nature. The multidimensional "problem space" of RNA catalysis includes both local and global conformational rearrangements, changes in the ion atmosphere around nucleic acids and metal ion binding, dependence on potentially correlated protonation states of key residues, and bond breaking/forming in the chemical steps of the reaction. The goal of this chapter is to summarize and apply multiscale modeling methods in an effort to target the different parts of the RNA catalysis problem space while also addressing the limitations and pitfalls of these methods. Classical molecular dynamics simulations, reference interaction site model calculations, constant pH molecular dynamics (CpHMD) simulations, Hamiltonian replica exchange molecular dynamics, and quantum mechanical/molecular mechanical simulations will be discussed in the context of the study of RNA backbone cleavage transesterification. This reaction is catalyzed by both RNA and protein enzymes, and here we examine the different mechanistic strategies taken by the hepatitis delta virus ribozyme and RNase A.

Excluded volume and ion-ion correlation effects on the ionic atmosphere around B-DNA: theory, simulations, and experiments

The ionic atmosphere around a nucleic acid regulates its stability in aqueous salt solutions. One major source of complexity in biological activities involving nucleic acids arises from the strong influence of the surrounding ions and water molecules on their structural and thermodynamic properties. Here, we implement a classical density functional theory for cylindrical polyelectrolytes embedded in aqueous electrolytes containing explicit (neutral hard sphere) water molecules at experimental solvent concentrations. Our approach allows us to include ion correlations as well as solvent and ion excluded volume effects for studying the structural and thermodynamic properties of highly charged cylindrical polyelectrolytes. Several models of size and charge asymmetric mixtures of aqueous electrolytes at physiological concentrations are studied. Our results are in good agreement with Monte Carlo simulations. Our numerical calculations display significant differences in the ion density profiles for the different aqueous electrolyte models studied. However, similar results regarding the excess number of ions adsorbed to the B-DNA molecule are predicted by our theoretical approach for different aqueous electrolyte models. These findings suggest that ion counting experimental data should not be used alone to validate the performance of aqueous DNA-electrolyte models.

Structural studies of a double-stranded RNA from trypanosome RNA editing by small-angle X-ray scattering

We used small-angle X-ray scattering (SAXS) to evaluate the solution structure of a double-stranded RNA with 32 base pairs. We wanted to compare the solution structure to the crystal structure to assess the impact of the crystal lattice on the overall conformation of the RNA. The RNA was designed to self-anneal and form a head-to-head fusion of two identical mRNA/oligo(U) tail domains (the U-helix) from a trypanosome RNA editing substrate formed by the annealing of a guide RNA to a pre-edited mRNA. This substrate is from the U insertion/deletion RNA editing system of trypanosomes. Each strand in the fusion RNA had 16 purines from the pre-mRNA followed by 16 uracils (Us) from the U-tail at the 3' end of the guide RNA. The strands were designed to form a double helix with blunt ends, but each strand had the potential to form hairpins and single-stranded RNA helices. Hairpins could form by the 3' oligouridylate tract folding back to hybridize with the 5' oligopurine tract and forming an intervening loop. Single-stranded helices could form by the stacking of bases in the polypurine tract. Some of the 16 Us 3' to the polypurine tract may have been unstacked and in random coils. Our SAXS studies showed that the RNA formed a mix of single-stranded structures in the absence of MgCl2. In the presence of MgCl2 at concentrations similar to those in the crystal, the solution structure was consistent with the double-stranded, blunt-ended structure, in agreement with the crystal structure. Here we describe the preparation of RNA samples, data collection with an in-house SAXS instrument designed for biological samples, and the processing and modeling of the scattering data.