Counting ions around DNA with anomalous small-angle X-ray scattering

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.

Impact of Ion-Mixing Entropy on Orientational Preferences of DNA Helices: FRET Measurements and Computer Simulations

Biological processes require DNA and RNA helices to pack together in specific interhelical orientations. While electrostatic repulsion between backbone charges is expected to be maximized when helices are in parallel alignment, such orientations are commonplace in nature. To better understand how the repulsion is overcome, we used experimental and computational approaches to investigate how the orientational preferences of DNA helices depend on the concentration and valence of mobile cations. We used Förster resonance energy transfer (FRET) to probe the relative orientations of two 24-bp helices held together via a freely rotating PEG linker. At low cation concentrations, the helices preferred more "cross"-like orientations over those closer to parallel, and this preference was reduced with increasing salt concentrations. The results were in good quantitative agreement with Poisson-Boltzmann (PB) calculations for monovalent salt (Na+). However, PB underestimated the ability of mixtures of monovalent and divalent ions (Mg2+) to reduce the conformational preference. As a complementary approach, we performed all-atom molecular dynamics (MD) simulations and found better agreement with the experimental results. While MD and PB predict similar electrostatic forces, MD predicts a greater accumulation of Mg2+ in the ion atmosphere surrounding the DNA. Mg2+ occupancy is predicted to be greater in conformations close to the parallel orientation than in conformations close to the crossed orientation, enabling a greater release of Na+ ions and providing an entropic gain (one bound ion for two released). MD predicts an entropy gain larger than that of PB because of the increased Mg2+ occupancy. The entropy changes have a negligible effect at low Mg2+ concentrations because the free energies are dominated by electrostatic repulsion. However, as the Mg2+ concentration increases, charge screening is more effective and the mixing entropy produces readily detectable changes in packing preferences. Our results underline the importance of mixing entropy of counterions in nucleic acid interactions and provide a new understanding on the impact of a mixed ion atmosphere on the packing of DNA helices.

Small-angle scattering techniques for peptide and peptide hybrid nanostructures and peptide-based biomaterials

The use of small-angle scattering (SAS) in the study of the self-assembly of peptides and peptide conjugates (lipopeptides, polymer-peptide conjugates and others) is reviewed, highlighting selected research that illustrates different methods and analysis techniques. Both small-angle x-ray scattering (SAXS) and small-angle neutron scattering (SANS) are considered along with examples that exploit their unique capabilities. For SAXS, this includes the ability to perform rapid measurements enabling high throughput or fast kinetic studies and measurements under dilute conditions. For SANS, contrast variation using H2O/D2O mixtures enables the study of peptides interacting with lipids and TR-SANS (time-resolved SANS) studies of exchange kinetics and/or peptide-induced structural changes. Examples are provided of studies measuring form factors of different self-assembled structures (micelles, fibrils, nanotapes, nanotubes etc) as well as structure factors from ordered phases (lyotropic mesophases), peptide gels and hybrid materials such as membranes formed by mixing peptides with polysaccharides or peptide/liposome mixtures. SAXS/WAXS (WAXS: wide-angle x-ray scattering) on peptides and peptide hybrids is also discussed, and the review concludes with a perspective on potential future directions for research in the field.

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.

RNA Captures More Cations than DNA: Insights from Molecular Dynamics Simulations

The distribution of cations around nucleic acids is essential for a broad variety of processes ranging from DNA condensation and RNA folding to the detection of biomolecules in biosensors. Predicting the exact distribution of ions remains challenging since the distribution and, hence, a broad variety of nucleic acid properties depend on the salt concentration, the valency of the ions, and the ion type. Despite the importance, a general theory to quantify ion-specific effects for highly charged biomolecules is still lacking. Moreover, recent experiments reveal that despite their similar building blocks, DNA and RNA duplexes can react differently to the same ionic conditions. The aim of our current work is to provide a comprehensive set of molecular dynamics simulations using more than 180 μs of simulation time. For the mono- and divalent cations Li⁺, Na⁺, K⁺, Cs⁺, Ca²⁺, Sr²⁺, and Ba²⁺, the simulations allow us to reveal the ion-specific distributions and binding patterns for DNA and RNA duplexes. The microscopic insights from the simulations display the origin of ion-specificity and shed light on the question of why DNA and RNA show opposing behavior in the same ionic conditions. Finally, the detailed binding patterns from the simulations reveal why RNA can capture more cations than DNA.

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.

Dynamics of Cations around DNA and Protein as Revealed by 23Na Diffusion NMR Spectroscopy

Counterions are vital for the structure and function of biomolecules. However, the behavior of counterions remains elusive due to the difficulty in characterizing mobile ions. Here, we demonstrate that the dynamics of cations around biological macromolecules can be revealed by ²³Na diffusion nuclear magnetic resonance (NMR) spectroscopy. NMR probe hardware capable of generating strong magnetic field gradients enables ²³Na NMR-based diffusion measurements for Na⁺ ions in solutions of biological macromolecules and their complexes. The dynamic properties of Na⁺ ions interacting with the macromolecules can be investigated using apparent ²³Na diffusion coefficients measured under various conditions. Our diffusion data clearly show that Na⁺ ions retain high mobility within the ion atmosphere around DNA. The ²³Na diffusion NMR method also permits direct observation of the release of Na⁺ ions from nucleic acids upon protein-nucleic acid association. The entropy change due to the ion release can be estimated from the diffusion data.

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.

ASAXS measurements on ferritin and apoferritin at the bioSAXS beamline P12 (PETRA III, DESY)

Small-angle X-ray scattering is widely utilized to study biological macromol-ecules in solution. For samples containing specific (e.g. metal) atoms, additional information can be obtained using anomalous scattering. Here, measuring samples at different energies close to the absorption edges of relevant elements provides specific structural details. However, anomalous small-angle X-ray scattering (ASAXS) applications to dilute macromolecular solutions are challenging owing to the overall low anomalous scattering effect. Here, pilot ASAXS experiments from dilute solutions of ferritin and cobalt-loaded apoferritin are reported. These samples were investigated near the resonance X-ray K edges of Fe and Co, respectively, at the EMBL P12 bioSAXS beamline at PETRA III, DESY. Thanks to the high brilliance of the P12 beamline, ASAXS experiments are feasible on dilute protein solutions, allowing one to extract the Fe- or Co-specific anomalous dispersion terms from the ASAXS data. The data were subsequently used to determine the spatial distribution of either iron or cobalt atoms incorporated into the ferritin/apoferritin protein cages.

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.

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.

Accurate Determination of the Quantity and Spatial Distribution of Counterions around a Spherical Macroion

The accurate distribution of countercations (Rb⁺ and Sr²⁺ ) around a rigid, spherical, 2.9-nm size polyoxometalate cluster, {Mo₁₃₂ }^42- , is determined by anomalous small-angle X-ray scattering. Both Rb⁺ and Sr²⁺ ions lead to shorter diffuse lengths for {Mo₁₃₂ } than prediction. Most Rb⁺ ions are closely associated with {Mo₁₃₂ } by staying near the skeleton of {Mo₁₃₂ } or in the Stern layer, whereas more Sr²⁺ ions loosely associate with {Mo₁₃₂ } in the diffuse layer. The stronger affinity of Rb⁺ ions towards {Mo₁₃₂ } than that of Sr²⁺ ions explains the anomalous lower critical coagulation concentration of {Mo₁₃₂ } with Rb⁺ compared to Sr²⁺ . The anomalous behavior of {Mo₁₃₂ } can be attributed to majority of negative charges being located at the inner surface of its cavity. The longer anion-cation distance weakens the Coulomb interaction, making the enthalpy change owing to the breakage of hydration layers of cations more important in regulating the counterion-{Mo₁₃₂ } interaction.

Contributions and competition of Mg2+ and K+ in folding and stabilization of the Twister ribozyme

Native folded and compact intermediate states of RNA typically involve tertiary structures in the presence of divalent ions such as Mg²⁺ in a background of monovalent ions. In a recent study, we have shown how the presence of Mg²⁺ impacts the transition from partially unfolded to folded states through a "push-pull" mechanism where the ion both favors and disfavors the sampling of specific phosphate-phosphate interactions. To further understand the ion atmosphere of RNA in folded and partially folded states results from atomistic umbrella sampling and oscillating chemical potential grand canonical Monte Carlo/molecular dynamics (GCMC/MD) simulations are used to obtain atomic-level details of the distributions of Mg²⁺ and K⁺ ions around Twister RNA. Results show the presence of 100 mM Mg²⁺ to lead to increased charge neutralization over that predicted by counterion condensation theory. Upon going from partially unfolded to folded states, overall charge neutralization increases at all studied ion concentrations that, while associated with an increase in the number of direct ion-phosphate interactions, is fully accounted for by the monovalent K⁺ ions. Furthermore, K⁺ preferentially interacts with purine N7 atoms of helical regions in partially unfolded states, thereby potentially stabilizing the helical regions. Thus, both secondary helical structures and formation of tertiary structures leads to increased counterion condensation, thereby stabilizing those structural features of Twister. Notably, it is shown that K⁺ can act as a surrogate for Mg²⁺ by participating in specific interactions with nonsequential phosphate pairs that occur in the folded state, explaining the ability of Twister to self-cleave at submillimolar Mg²⁺ concentrations.

Multivalent ions and biomolecules: Attempting a comprehensive perspective

Ions are ubiquitous in nature. They play a key role for many biological processes on the molecular scale, from molecular interactions, to mechanical properties, to folding, to self-organisation and assembly, to reaction equilibria, to signalling, to energy and material transport, to recognition etc. Going beyond monovalent ions to multivalent ions, the effects of the ions are frequently not only stronger (due to the obviously higher charge), but qualitatively different. A typical example is the process of binding of multivalent ions, such as Ca2+ , to a macromolecule and the consequences of this ion binding such as compaction, collapse, potential charge inversion and precipitation of the macromolecule. Here we review these effects and phenomena induced by multivalent ions for biological (macro)molecules, from the "atomistic/molecular" local picture of (potentially specific) interactions to the more global picture of phase behaviour including, e. g., crystallisation, phase separation, oligomerisation etc. Rather than attempting an encyclopedic list of systems, we rather aim for an embracing discussion using typical case studies. We try to cover predominantly three main classes: proteins, nucleic acids, and amphiphilic molecules including interface effects. We do not cover in detail, but make some comparisons to, ion channels, colloidal systems, and synthetic polymers. While there are obvious differences in the behaviour of, and the relevance of multivalent ions for, the three main classes of systems, we also point out analogies. Our attempt of a comprehensive discussion is guided by the idea that there are not only important differences and specific phenomena with regard to the effects of multivalent ions on the main systems, but also important similarities. We hope to bridge physico-chemical mechanisms, concepts of soft matter, and biological observations and connect the different communities further.

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.

Molecular dynamics simulations of alkaline earth metal ions binding to DNA reveal ion size and hydration effects

Classical molecular dynamics simulations reveal size-dependent trends of alkaline earth metal ions binding to DNA are due to ion size and hydration behavior.

Theory and simulations for RNA folding in mixtures of monovalent and divalent cations

RNA molecules cannot fold in the absence of counterions. Experiments are typically performed in the presence of monovalent and divalent cations. How to treat the impact of a solution containing a mixture of both ion types on RNA folding has remained a challenging problem for decades. By exploiting the large concentration difference between divalent and monovalent ions used in experiments, we develop a theory based on the reference interaction site model (RISM), which allows us to treat divalent cations explicitly while keeping the implicit screening effect due to monovalent ions. Our theory captures both the inner shell and outer shell coordination of divalent cations to phosphate groups, which we demonstrate is crucial for an accurate calculation of RNA folding thermodynamics. The RISM theory for ion-phosphate interactions when combined with simulations based on a transferable coarse-grained model allows us to predict accurately the folding of several RNA molecules in a mixture containing monovalent and divalent ions. The calculated folding free energies and ion-preferential coefficients for RNA molecules (pseudoknots, a fragment of the rRNA, and the aptamer domain of the adenine riboswitch) are in excellent agreement with experiments over a wide range of monovalent and divalent ion concentrations. Because the theory is general, it can be readily used to investigate ion and sequence effects on DNA properties.

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.

Quantitative Studies of an RNA Duplex Electrostatics by Ion Counting

RNAs are one of the most charged polyelectrolytes in nature, and understanding their electrostatics is fundamental to their structure and biological functions. An effective way to characterize the electrostatic field generated by nucleic acids is to quantify interactions between nucleic acids and ions that surround the molecules. These ions form a loosely associated cloud referred to as an ion atmosphere. Although theoretical and computational studies can describe the ion atmosphere around RNAs, benchmarks are needed to guide the development of these approaches, and experiments to date that read out RNA-ion interactions are limited. Here, we present ion counting studies to quantify the number of ions surrounding well-defined model systems of RNA and DNA duplexes. We observe that the RNA duplex attracts more cations and expels fewer anions compared to the DNA duplex, and the RNA duplex interacts significantly stronger with the divalent cation Mg²⁺, despite their identical total charge. These experimental results suggest that the RNA duplex generates a stronger electrostatic field than DNA, as is predicted based on the structural differences between their helices. Theoretical calculations using a nonlinear Poisson-Boltzmann equation give excellent agreement with experiments for monovalent ions but underestimate Mg²⁺-DNA and Mg²⁺-RNA interactions by 20%. These studies provide needed stringent benchmarks to use against other all-atom theoretical models of RNA-ion interactions, interactions that likely must be accurately accounted for in structural, dynamic, and energetic terms to confidently model RNA structure, interactions, and function.

Counterion Exchange in Peptide-Complexed Core-Shell Microgels

The complexation of polyvalent macroions with oppositely charged polyelectrolyte microgels can lead to core-shell structures. The shell is believed to be highly deswollen with a high concentration of counter-macroions. The core is believed to be relatively free of macroions but under a uniform compressive stress due to the deswollen shell. We use cryo-scanning electron microscopy (SEM) with X-ray microanalysis to confirm this understanding. We study poly(acrylic acid) (PAA) microgels which form a core-shell structure when complexed with a small cationic antimicrobial peptide (L5). We follow the spatial distribution of polymer, water, Na counterions, and peptide based on the characteristic X-ray intensities of C, O, Na, and N, respectively. Frozen-hydrated microgel suspensions include buffers of known composition from which calibration curves can be generated and used to quantify both the microgel water and sodium concentrations, the latter with a minimum quantifiable concentration less than 0.048 M. We find that as-synthesized PAA microgels are enriched in Na relative to the surrounding buffer as anticipated from established ideas of counterion shielding of electrostatic charge. The shell in L5-complexed microgels is depleted in Na and enriched in peptide and contains relatively little water. Our measurements furthermore show that shell/core interface is diffuse over a length scale of a few micrometers. Within the limits of detection, the core Na concentration is the same as that in as-synthesized microgels, and the core is free of peptide. The core has a slightly lower water concentration than as-synthesized controls, consistent with the hypothesis that the core is under compression from the shell.

Ion counting demonstrates a high electrostatic field generated by the nucleosome

In eukaryotes, a first step towards the nuclear DNA compaction process is the formation of a nucleosome, which is comprised of negatively charged DNA wrapped around a positively charged histone protein octamer. Often, it is assumed that the complexation of the DNA into the nucleosome completely attenuates the DNA charge and hence the electrostatic field generated by the molecule. In contrast, theoretical and computational studies suggest that the nucleosome retains a strong, negative electrostatic field. Despite their fundamental implications for chromatin organization and function, these opposing views of nucleosome electrostatics have not been experimentally tested. Herein, we directly measure nucleosome electrostatics and find that while nucleosome formation reduces the complex charge by half, the nucleosome nevertheless maintains a strong negative electrostatic field. Our studies highlight the importance of considering the polyelectrolyte nature of the nucleosome and its impact on processes ranging from factor binding to DNA compaction.

Defining the Structure of a Protein-Spherical Nucleic Acid Conjugate and Its Counterionic Cloud

Protein-spherical nucleic acid conjugates (Pro-SNAs) are an emerging class of bioconjugates that have properties defined by their protein cores and dense shell of oligonucleotides. They have been used as building blocks in DNA-driven crystal engineering strategies and show promise as agents that can cross cell membranes and affect both protein and DNA-mediated processes inside cells. However, ionic environments surrounding proteins can influence their activity and conformational stability, and functionalizing proteins with DNA substantively changes the surrounding ionic environment in a nonuniform manner. Techniques typically used to determine protein structure fail to capture such irregular ionic distributions. Here, we determine the counterion radial distribution profile surrounding Pro-SNAs dispersed in RbCl with 1 nm resolution through in situ anomalous small-angle X-ray scattering (ASAXS) and classical density functional theory (DFT). SAXS analysis also reveals the radial extension of the DNA and the linker used to covalently attach the DNA to the protein surface. At the experimental salt concentration of 50 mM RbCl, Rb⁺ cations compensate ∼90% of the negative charge due to the DNA and linker. Above 75 mM, DFT calculations predict overcompensation of the DNA charge by Rb⁺. This study suggests a method for exploring Pro-SNA structure and function in different environments through predictions of ionic cloud densities as a function of salt concentration, DNA grafting density, and length. Overall, our study demonstrates that solution X-ray scattering combined with DFT can discern counterionic distribution and submolecular features of highly charged, complex nanoparticle constructs such as Pro-SNAs and related nucleic acid conjugate materials.

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.

The impact of base stacking on the conformations and electrostatics of single-stranded DNA

Single-stranded DNA (ssDNA) is notable for its interactions with ssDNA binding proteins (SSBs) during fundamentally important biological processes including DNA repair and replication. Previous work has begun to characterize the conformational and electrostatic properties of ssDNA in association with SSBs. However, the conformational distributions of free ssDNA have been difficult to determine. To capture the vast array of ssDNA conformations in solution, we pair small angle X-ray scattering with novel ensemble fitting methods, obtaining key parameters such as the size, shape and stacking character of strands with different sequences. Complementary ion counting measurements using inductively coupled plasma atomic emission spectroscopy are employed to determine the composition of the ion atmosphere at physiological ionic strength. Applying this combined approach to poly dA and poly dT, we find that the global properties of these sequences are very similar, despite having vastly different propensities for single-stranded helical stacking. These results suggest that a relatively simple mechanism for the binding of ssDNA to non-specific SSBs may be at play, which explains the disparity in binding affinities observed for these systems.

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.

Studies of the B-Z transition of DNA: The temperature dependence of the free-energy difference, the composition of the counterion sheath in mixed salt, and the preparation of a sample of the 5'-d[T-(m(5) C-G)12 -T] duplex in pure B-DNA or Z-DNA form

It is often envisioned that cations might coordinate at specific sites of nucleic acids and play an important structural role, for instance in the transition between B-DNA and Z-DNA. However, nucleic acid models explicitly devoid of specific sites may also exhibit features previously considered as evidence for specific binding. Such is the case of the "composite cylinder" (or CC) model which spreads out localized features of DNA structure and charge by cylindrical averaging, while sustaining the main difference between the B and Z structures, namely the better immersion of the B-DNA phosphodiester charges in the solution. Here, we analyze the non-electrostatic component of the free-energy difference between B-DNA and Z-DNA. We also compute the composition of the counterion sheath in a wide range of mixed-salt solutions and of temperatures: in contrast with the large difference of composition between the B-DNA and Z-DNA forms, the temperature dependence of sheath composition, previously unknown, is very weak. In order to validate the model, the mixed-salt predictions should be compared to experiment. We design a procedure for future measurements of the sheath composition based on Anomalous Small-Angle X-ray Scattering and complemented by (31) P NMR. With due consideration for the kinetics of the B-Z transition and for the capacity of generating at will the B or Z form in a single sample, the 5'-d[T-(m(5) C-G)12 -T] 26-mer emerges as a most suitable oligonucleotide for this study. Finally, the application of the finite element method to the resolution of the Poisson-Boltzmann equation is described in detail. © 2016 Wiley Periodicals, Inc. Biopolymers 105: 369-384, 2016.

The Role of Correlation and Solvation in Ion Interactions with B-DNA

The ionic atmospheres around nucleic acids play important roles in biological function. Large-scale explicit solvent simulations coupled to experimental assays such as anomalous small-angle x-ray scattering can provide important insights into the structure and energetics of such atmospheres but are time- and resource intensive. In this article, we use classical density functional theory to explore the balance among ion-DNA, ion-water, and ion-ion interactions in ionic atmospheres of RbCl, SrCl2, and CoHexCl3 (cobalt hexamine chloride) around a B-form DNA molecule. The accuracy of the classical density functional theory calculations was assessed by comparison between simulated and experimental anomalous small-angle x-ray scattering curves, demonstrating that an accurate model should take into account ion-ion correlation and ion hydration forces, DNA topology, and the discrete distribution of charges on the DNA backbone. As expected, these calculations revealed significant differences among monovalent, divalent, and trivalent cation distributions around DNA. Approximately half of the DNA-bound Rb(+) ions penetrate into the minor groove of the DNA and half adsorb on the DNA backbone. The fraction of cations in the minor groove decreases for the larger Sr(2+) ions and becomes zero for CoHex(3+) ions, which all adsorb on the DNA backbone. The distribution of CoHex(3+) ions is mainly determined by Coulomb and steric interactions, while ion-correlation forces play a central role in the monovalent Rb(+) distribution and a combination of ion-correlation and hydration forces affect the Sr(2+) distribution around DNA. This does not imply that correlations in CoHex solutions are weaker or stronger than for other ions. Steric inaccessibility of the grooves to large CoHex ions leads to their binding at the DNA surface. In this binding mode, first-order electrostatic interactions (Coulomb) dominate the overall binding energy as evidenced by low sensitivity of ionic distribution to the presence or absence of second-order electrostatic correlation interactions.

Does Cation Size Affect Occupancy and Electrostatic Screening of the Nucleic Acid Ion Atmosphere?

Electrostatics are central to all aspects of nucleic acid behavior, including their folding, condensation, and binding to other molecules, and the energetics of these processes are profoundly influenced by the ion atmosphere that surrounds nucleic acids. Given the highly complex and dynamic nature of the ion atmosphere, understanding its properties and effects will require synergy between computational modeling and experiment. Prior computational models and experiments suggest that cation occupancy in the ion atmosphere depends on the size of the cation. However, the computational models have not been independently tested, and the experimentally observed effects were small. Here, we evaluate a computational model of ion size effects by experimentally testing a blind prediction made from that model, and we present additional experimental results that extend our understanding of the ion atmosphere. Giambasu et al. developed and implemented a three-dimensional reference interaction site (3D-RISM) model for monovalent cations surrounding DNA and RNA helices, and this model predicts that Na(+) would outcompete Cs(+) by 1.8-2.1-fold; i.e., with Cs(+) in 2-fold excess of Na(+) the ion atmosphere would contain an equal number of each cation (Nucleic Acids Res. 2015, 43, 8405). However, our ion counting experiments indicate that there is no significant preference for Na(+) over Cs(+). There is an ∼25% preferential occupancy of Li(+) over larger cations in the ion atmosphere but, counter to general expectations from existing models, no size dependence for the other alkali metal ions. Further, we followed the folding of the P4-P6 RNA and showed that differences in folding with different alkali metal ions observed at high concentration arise from cation-anion interactions and not cation size effects. Overall, our results provide a critical test of a computational prediction, fundamental information about ion atmosphere properties, and parameters that will aid in the development of next-generation nucleic acid computational models.

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.

Polyelectrolyte properties of single stranded DNA measured using SAXS and single-molecule FRET: Beyond the wormlike chain model

Nucleic acids are highly charged polyelectrolytes that interact strongly with salt ions. Rigid, base-paired regions are successfully described with wormlike chain models, but nonbase-paired single stranded regions have fundamentally different polymer properties because of their greater flexibility. Recently, attention has turned to single stranded nucleic acids due to the growing recognition of their biological importance, as well as the availability of sophisticated experimental techniques sensitive to the conformation of individual molecules. We investigate polyelectrolyte properties of poly(dT), an important and widely studied model system for flexible single stranded nucleic acids, in physiologically important mixed mono- and divalent salt. We report measurements of the form factor and interparticle interactions using SAXS, end-to-end distances using smFRET, and number of excess ions using ASAXS. We present a coarse-grained model that accounts for flexibility, excluded volume, and electrostatic interactions in these systems. Predictions of the model are validated against experiment. We also discuss the state of all-atom, explicit solvent molecular dynamics simulations of poly(dT), the next step in understanding the complexities of ion interactions with these highly charged and flexible polymers.

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.

Quantifying the ion atmosphere of unfolded, single-stranded nucleic acids using equilibrium dialysis and single-molecule methods

To form secondary structure, nucleic acids (NAs) must overcome electrostatic strand–strand repulsion, which is moderated by the surrounding atmosphere of screening ions. The free energy of NA folding therefore depends on the interactions of this ion atmosphere with both the folded and unfolded states. We quantify such interactions using the preferential ion interaction coefficient or ion excess: the number of ions present near the NA in excess of the bulk concentration. The ion excess of the folded, double-helical state has been extensively studied; however, much less is known about the salt-dependent ion excess of the unfolded, single-stranded state. We measure this quantity using three complementary approaches: a direct approach of Donnan equilibrium dialysis read out by atomic emission spectroscopy and two indirect approaches involving either single-molecule force spectroscopy or existing thermal denaturation data. The results of these three approaches, each involving an independent experimental technique, are in good agreement. Even though the single-stranded NAs are flexible polymers that are expected to adopt random-coil configurations, we find that their ion atmosphere is quantitatively described by rod-like models that neglect large-scale conformational freedom, an effect that we explain in terms of the competition between the relevant structural and electrostatic length scales.

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.

Cation-Anion Interactions within the Nucleic Acid Ion Atmosphere Revealed by Ion Counting

The ion atmosphere is a critical structural, dynamic, and energetic component of nucleic acids that profoundly affects their interactions with proteins and ligands. Experimental methods that "count" the number of ions thermodynamically associated with the ion atmosphere allow dissection of energetic properties of the ion atmosphere, and thus provide direct comparison to theoretical results. Previous experiments have focused primarily on the cations that are attracted to nucleic acid polyanions, but have also showed that anions are excluded from the ion atmosphere. Herein, we have systematically explored the properties of anion exclusion, testing the zeroth-order model that anions of different identity are equally excluded due to electrostatic repulsion. Using a series of monovalent salts, we find, surprisingly, that the extent of anion exclusion and cation inclusion significantly depends on salt identity. The differences are prominent at higher concentrations and mirror trends in mean activity coefficients of the electrolyte solutions. Salts with lower activity coefficients exhibit greater accumulation of both cations and anions within the ion atmosphere, strongly suggesting that cation-anion correlation effects are present in the ion atmosphere and need to be accounted for to understand electrostatic interactions of nucleic acids. To test whether the effects of cation-anion correlations extend to nucleic acid kinetics and thermodynamics, we followed the folding of P4-P6, a domain of the Tetrahymena group I ribozyme, via single-molecule fluorescence resonance energy transfer in solutions with different salts. Solutions of identical concentration but lower activity gave slower and less favorable folding. Our results reveal hitherto unknown properties of the ion atmosphere and suggest possible roles of oriented ion pairs or anion-bridged cations in the ion atmosphere for electrolyte solutions of salts with reduced activity. Consideration of these new results leads to a reevaluation of the strengths and limitations of Poisson-Boltzmann theory and highlights the need for next-generation atomic-level models of the ion atmosphere.

Physicochemical Properties of Ion Pairs of Biological Macromolecules

Ion pairs (also known as salt bridges) of electrostatically interacting cationic and anionic moieties are important for proteins and nucleic acids to perform their function. Although numerous three-dimensional structures show ion pairs at functionally important sites of biological macromolecules and their complexes, the physicochemical properties of the ion pairs are not well understood. Crystal structures typically show a single state for each ion pair. However, recent studies have revealed the dynamic nature of the ion pairs of the biological macromolecules. Biomolecular ion pairs undergo dynamic transitions between distinct states in which the charged moieties are either in direct contact or separated by water. This dynamic behavior is reasonable in light of the fundamental concepts that were established for small ions over the last century. In this review, we introduce the physicochemical concepts relevant to the ion pairs and provide an overview of the recent advancement in biophysical research on the ion pairs of biological macromolecules.

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.