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

Solid-State Nanopore Real-Time Assay for Monitoring Cas9 Endonuclease Reactivity

The field of nanopore sensing is now moving beyond nucleic acid sequencing. An exciting avenue is the use of nanopore platforms for the monitoring of biochemical reactions. Biological nanopores have been used for this application, but solid-state nanopore approaches have lagged. This is due to the necessity of using higher salt conditions (e.g., 4 M LiCl) to improve the signal-to-noise ratio which completely abolish the activities of many biochemical reactions. We pioneered a polymer electrolyte solid-state nanopore approach that maintains a high signal-to-noise ratio even at a physiologically relevant salt concentration. Here, we report the monitoring of the restriction enzyme SwaI and CRISPR-Cas9 endonuclease activities under physiological salt conditions and in real time. We investigated the dsDNA cleavage activity of these enzymes in a range of digestion buffers and elucidated the off-target activity of CRISPR-Cas9 ribonucleoprotein endonuclease in the presence of single base pair mismatches. This approach enables the application of solid-state nanopores for the dynamic monitoring of biochemical reactions under physiological salt conditions.

Effects of Alkali-Metal Counterions on the Vibrational Dynamics of the DNA Hydration Shell

The effects of alkali-metal ions (Li+, Na+, K+, Rb+, and Cs+) on the vibrational dynamics of the DNA ion-hydration shell were studied through classical molecular dynamics simulations. As a result, the vibrational spectra of the DNA-water-salt systems were calculated within the framework of two approaches, using dipole-dipole and velocity-velocity autocorrelation functions. We dissect the effect of the individual compartments of the DNA double helix (minor groove, major groove, and phosphate groups) on the behavior of the systems. The obtained spectra have a different shape in the case of structure-making and structure-breaking ions. This difference becomes more prominent for the ions interacting with DNA, especially in the case of structure-breaking ions in the minor groove of the double helix. The obtained spectra of DNA do not show a significant effect of counterion type, except for Li+, which influences the vibrational modes of the DNA phosphates. The analysis of the spectra of water vibrations around ions revealed an isosbestic point at ∼70 cm-1, which appears as a response to the confinement induced by interaction with the DNA double helix and counterions. The obtained results are important for understanding the structural and dynamical organization of the DNA ion-hydration shell.

Hydrated Magnesium Ion-Uracil and Magnesium Chloride-Uracil Clusters Revealed by Ab Initio Study

The study focuses on the interaction between canonical uracil and its rare tautomers with Mg2+ and MgCl2 in the microcosmic water environment and aims to elucidate how ions interact with nucleobase and the cation-anion correlation effect involved using density functional theory calculations. The structures of the Ura-Mg2+(H2O)0-6 and Ura-MgCl2(H2O)0-6 clusters are characterized and show that the water molecules preferentially interact with Mg2+/MgCl2, and Mg2+ adopts a hexacoordination pattern in both Ura-Mg2+(H2O)0-6 and Ura-MgCl2(H2O)0-6 clusters. When uracil interacts with Mg2+ in (H2O)0-6 environments, it tends to favor the formation of keto-enol structures. However, in the presence of Cl- cooperating with Mg2+, the Ura-MgCl2(H2O)0-6 complexes prefer to form diketo structures. The proton transfer mechanism shows that the initial solvation can promote the change from the keto-enol structure to the diketo structure, which is strengthened by the analysis of the Ura-Mg2+(H2O)6 and Ura-MgCl2(H2O)6 structures in the aqueous phase using the PCM model. Additionally, reduced density gradient, atom in molecules, and energy decomposition analysis combined with charge transfer analysis were carried out to obtain the variation law of the interactions between Mg2+ and Ura with the water number increasing, thereby revealing the interaction mechanism of uracil with magnesium ion and the effect of Cl- on the interaction between Mg2+ and uracil.

Balancing Group 1 Monoatomic Ion-Polar Compound Interactions in the Polarizable Drude Force Field: Application in Protein and Nucleic Acid Systems

An accurate force field (FF) is the foundation of reliable results from molecular dynamics (MD) simulations. In our recently published work, we developed a protocol to generate atom pair-specific Lennard-Jones (known as NBFIX in CHARMM) and through-space Thole dipole screening (NBTHOLE) parameters in the context of the Drude polarizable FF based on readily accessible quantum mechanical (QM) data to fit condensed phase experimental thermodynamic benchmarks, including the osmotic pressure, diffusion coefficient, ionic conductivity, and solvation free energy, when available. In the present work, the developed protocol is applied to generate NBFIX and NBTHOLE parameters for interactions between monatomic ions (specifically Li+, Na+, K+, Rb+, Cs+, and Cl-) and common functional groups found in proteins and nucleic acids. The parameters generated for each ion-functional group pair were then applied to the corresponding functional groups within proteins or nucleic acids followed by MD simulations to analyze the distribution of ions around these biomolecules. The modified FF successfully addresses the issue of overbinding observed in a previous iteration of the Drude FF. Quantitatively, the model accurately reproduces the effective charge of proteins and demonstrates a level of charge neutralization for a double-helix B-DNA in good agreement with the counterion condensation theory. Additionally, simulations involving ion competition correlate well with experimental results, following the trend Li+ > Na+ ≈ K+ > Rb+. These results validate the refined model for group 1 ion-biomolecule interactions that will facilitate the application of the polarizable Drude FF in systems in which group 1 ions play an important role.

Sensing the structural and conformational properties of single-stranded nucleic acids using electrometry and molecular simulations

Inferring the 3D structure and conformation of disordered biomolecules, e.g., single stranded nucleic acids (ssNAs), remains challenging due to their conformational heterogeneity in solution. Here, we use escape-time electrometry (ETe) to measure with sub elementary-charge precision the effective electrical charge in solution of short to medium chain length ssNAs in the range of 5-60 bases. We compare measurements of molecular effective charge with theoretically calculated values for simulated molecular conformations obtained from Molecular Dynamics simulations using a variety of forcefield descriptions. We demonstrate that the measured effective charge captures subtle differences in molecular structure in various nucleic acid homopolymers of identical length, and also that the experimental measurements can find agreement with computed values derived from coarse-grained molecular structure descriptions such as oxDNA, as well next generation ssNA force fields. We further show that comparing the measured effective charge with calculations for a rigid, charged rod-the simplest model of a nucleic acid-yields estimates of molecular structural dimensions such as linear charge spacings that capture molecular structural trends observed using high resolution structural analysis methods such as X-ray scattering. By sensitively probing the effective charge of a molecule, electrometry provides a powerful dimension supporting inferences of molecular structural and conformational properties, as well as the validation of biomolecular structural models. The overall approach holds promise for a high throughput, microscopy-based biomolecular analytical approach offering rapid screening and inference of molecular 3D conformation, and operating at the single molecule level in solution.

Influence of ion and hydration atmospheres on RNA structure and dynamics: insights from advanced theoretical and computational methods

RNA, a highly charged biopolymer composed of negatively charged phosphate groups, defies electrostatic repulsion to adopt well-defined, compact structures. Hence, the presence of positively charged metal ions is crucial not only for RNA's charge neutralization, but they also coherently decorate the ion atmosphere of RNA to stabilize its compact fold. This feature article elucidates various modes of close RNA-ion interactions, with a special emphasis on Mg2+ as an outer-sphere and inner-sphere ion. Through examples, we highlight how inner-sphere chelated Mg2+ stabilizes RNA pseudoknots, while outer-sphere ions can also exert long-range electrostatic interactions, inducing groove narrowing, coaxial helical stacking, and RNA ring formation. In addition to investigating the RNA's ion environment, we note that the RNA's hydration environment is relatively underexplored. Our study delves into its profound interplay with the structural dynamics of RNA, employing state-of-the-art atomistic simulation techniques. Through examples, we illustrate how specific ions and water molecules are associated with RNA functions, leveraging atomistic simulations to identify preferential ion binding and hydration sites. However, understanding their impact(s) on the RNA structure remains challenging due to the involvement of large length and long time scales associated with RNA's dynamic nature. Nevertheless, our contributions and recent advances in coarse-grained simulation techniques offer insights into large-scale structural changes dynamically linked to the RNA ion atmosphere. In this connection, we also review how different cutting-edge computational simulation methods provide a microscopic lens into the influence of ions and hydration on RNA structure and dynamics, elucidating distinct ion atmospheric components and specific hydration layers and their individual and collective impacts.

Competitive Influence of Alkali Metals in the Ion Atmosphere on Nucleic Acid Duplex Stability

The nonspecific atmosphere around nucleic acids, often termed the ion atmosphere, encompasses a collection of weak ion-nucleic acid interactions. Although nonspecific, the ion atmosphere has been shown to influence nucleic acid folding and structural stability. Studies investigating the composition of the ion atmosphere have shown competitive occupancy of the atmosphere between metal ions in the same solution. Many studies have investigated single ion effects on nucleic acid secondary structure stability; however, no comprehensive studies have investigated how the competitive occupancy of mixed ions in the ion atmosphere influences nucleic acid secondary structure stability. Here, six oligonucleotides were optically melted in buffers containing molar quantities, or mixtures, of either XCl (X = Li, K, Rb, or Cs) or NaCl. A correction factor was developed to better predict RNA duplex stability in solutions containing mixed XCl/NaCl. For solutions containing a 1:1 mixture of XCl/NaCl, one alkali metal chloride contributed more to duplex stability than the other. Overall, there was a 54% improvement in predictive capabilities with the correction factor compared with the standard 1.0 M NaCl nearest-neighbor models. This correction factor can be used in models to better predict RNA secondary structure in solutions containing mixed XCl/NaCl.

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.

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.

Identification of metal ion-binding sites in RNA structures using deep learning method

Metal ion is an indispensable factor for the proper folding, structural stability and functioning of RNA molecules. However, it is very difficult for experimental methods to detect them in RNAs. With the increase of experimentally resolved RNA structures, it becomes possible to identify the metal ion-binding sites in RNA structures through in-silico methods. Here, we propose an approach called Metal3DRNA to identify the binding sites of the most common metal ions (Mg2+, Na+ and K+) in RNA structures by using a three-dimensional convolutional neural network model. The negative samples, screened out based on the analysis for binding surroundings of metal ions, are more like positive ones than the randomly selected ones, which are beneficial to a powerful predictor construction. The microenvironments of the spatial distributions of C, O, N and P atoms around a sample are extracted as features. Metal3DRNA shows a promising prediction power, generally surpassing the state-of-the-art methods FEATURE and MetalionRNA. Finally, utilizing the visualization method, we inspect the contributions of nucleotide atoms to the classification in several cases, which provides a visualization that helps to comprehend the model. The method will be helpful for RNA structure prediction and dynamics simulation study. Availability and implementation: The source code is available at https://github.com/ChunhuaLiLab/Metal3DRNA.

Computational Study of the pH-Dependent Ionic Environment around β-Lactoglobulin

Ions are involved in multiple biological processes and may exist bound to biomolecules or may be associated with their surface. Although the presence of ions in nucleic acids has traditionally gained more interest, ion-protein interactions, often with a marked dependency on pH, are beginning to gather attention. Here we present a detailed analysis on the binding and distribution of ions around β-lactoglobulin using a constant-pH MD (CpHMD) method, at a pH range 3-8, and compare it with the more traditional Poisson-Boltzmann (PB) model and the existing experimental data. Most analyses used ion concentration maps built around the protein, obtained from either the CpHMD simulations or PB calculations. The requirements of approximate charge neutrality and ionic strength equal to bulk, imposed on the MD box, imply that the absolute value of the ion excess should be half the protein charge, which is in agreement with experimental observation on other proteins ( Proc. Natl. Acad. Sci. U.S.A. 2021, 118, e2015879118) and lends support to this protocol. In addition, the protein total charge (including territorially bound ions) estimated with MD is in excellent agreement with electrophoretic measurements. Overall, the CpHMD simulations show good agreement with the nonlinear form of the PB (NLPB) model but not with its linear form, which involves a theoretical inconsistency in the calculation of the concentration maps. In several analyses, the observed pH-dependent trends for the counterions and co-ions are those generally expected, and the ion concentration maps correctly converge to the bulk ionic strength as one moves away from the protein. Despite the overall similarity, the CpHMD and NLPB approaches show some discrepancies when analyzed in more detail, which may be related to an apparent overestimation of counterion excess and underestimation of co-ion exclusion by the NLPB model, particularly at short distances from the protein.

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.

Alternative RNA Conformations: Companion or Combatant

RNA molecules, in one form or another, are involved in almost all aspects of cell physiology, as well as in disease development. The diversity of the functional roles of RNA comes from its intrinsic ability to adopt complex secondary and tertiary structures, rivaling the diversity of proteins. The RNA molecules form dynamic ensembles of many interconverting conformations at a timescale of seconds, which is a key for understanding how they execute their cellular functions. Given the crucial role of RNAs in various cellular processes, we need to understand the RNA molecules from a structural perspective. Central to this review are studies aimed at revealing the regulatory role of conformational equilibria in RNA in humans to understand genetic diseases such as cancer and neurodegenerative diseases, as well as in pathogens such as bacteria and viruses so as to understand the progression of infectious diseases. Furthermore, we also summarize the prior studies on the use of RNA structures as platforms for the rational design of small molecules for therapeutic applications.

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.

Mutual effects between single-stranded DNA conformation and Na+-Mg2+ ion competition in mixed salt solutions

The ion-dependence of single-stranded DNA (ssDNA) conformational changes has attracted growing attention because of its biological and technological importance. Although single-species ion effects have been extensively explored, it is challenging to study the ssDNA conformational properties under mixed monovalent/divalent ion conditions due to the complications of ssDNA flexibility and ion-ion competition. In this study, we apply Langevin dynamics simulations to investigate mixed Na⁺/Mg²⁺ ion-dependent ssDNA conformations. The ssDNA structure is described using a coarse-grained model, in which the phosphate, base, and sugar of each nucleotide are represented by three different beads. A novel improvement in our simulation model is that mixed-salt-related electrostatic interactions are computed via combining Manning counterion condensation (MCC) theory with the Monte Carlo tightly bound ion (MCTBI) model. Based on this MCC-MCTBI combination, we report new empirical functions to describe the ion-concentration-dependent and ssDNA conformation/structure-dependent electrostatic effects. The calculation results relating to the ion binding properties and the simulation results relating to the ssDNA conformational properties are validated against experimental results. In addition, our simulation results suggest a quantitative relationship between the ssDNA conformation and Na⁺-Mg²⁺ competition; this in turn reveals their mutual impact in the ion atmosphere.

RNA Electrostatics: How Ribozymes Engineer Active Sites to Enable Catalysis

Electrostatic interactions are fundamental to RNA structure and function, and intimately influenced by solvation and the ion atmosphere. RNA enzymes, or ribozymes, are catalytic RNAs that are able to enhance reaction rates over a million-fold, despite having only a limited repertoire of building blocks and available set of chemical functional groups. Ribozyme active sites usually occur at junctions where negatively charged helices come together, and in many cases leverage this strained electrostatic environment to recruit metal ions in solution that can assist in catalysis. Similar strategies have been implicated in related artificially engineered DNA enzymes. Herein, we apply Poisson-Boltzmann, 3D-RISM, and molecular simulations to study a set of metal-dependent small self-cleaving ribozymes (hammerhead, pistol, and Varkud satellite) as well as an artificially engineered DNAzyme (8-17) to examine electrostatic features and their relation to the recruitment of monovalent and divalent metal ions important for activity. We examine several fundamental roles for these ions that include: (1) structural integrity of the catalytically active state, (2) pKa tuning of residues involved in acid-base catalysis, and (3) direct electrostatic stabilization of the transition state via Lewis acid catalysis. Taken together, these examples demonstrate how RNA electrostatics orchestrates the site-specific and territorial binding of metal ions to play important roles in catalysis.

Twisting DNA by salt

The structure and properties of DNA depend on the environment, in particular the ion atmosphere. Here, we investigate how DNA twist -one of the central properties of DNA- changes with concentration and identity of the surrounding ions. To resolve how cations influence the twist, we combine single-molecule magnetic tweezer experiments and extensive all-atom molecular dynamics simulations. Two interconnected trends are observed for monovalent alkali and divalent alkaline earth cations. First, DNA twist increases monotonously with increasing concentration for all ions investigated. Second, for a given salt concentration, DNA twist strongly depends on cation identity. At 100 mM concentration, DNA twist increases as Na+ < K+ < Rb+ < Ba2+ < Li+ ≈ Cs+ < Sr2+ < Mg2+ < Ca2+. Our molecular dynamics simulations reveal that preferential binding of the cations to the DNA backbone or the nucleobases has opposing effects on DNA twist and provides the microscopic explanation of the observed ion specificity. However, the simulations also reveal shortcomings of existing force field parameters for Cs+ and Sr2+. The comprehensive view gained from our combined approach provides a foundation for understanding and predicting cation-induced structural changes both in nature and in DNA nanotechnology.

Anion-specific structure and stability of guanidinium-bound DNA origami

While the folding of DNA into rationally designed DNA origami nanostructures has been studied extensively with the aim of increasing structural diversity and introducing functionality, the fundamental physical and chemical properties of these nanostructures remain largely elusive. Here, we investigate the correlation between atomistic, molecular, nanoscopic, and thermodynamic properties of DNA origami triangles. Using guanidinium (Gdm) as a DNA-stabilizing but potentially also denaturing cation, we explore the dependence of DNA origami stability on the identity of the accompanying anions. The statistical analyses of atomic force microscopy (AFM) images and circular dichroism (CD) spectra reveals that sulfate and chloride exert stabilizing and destabilizing effects, respectively, already below the global melting temperature of the DNA origami triangles. We identify structural transitions during thermal denaturation and show that heat capacity changes ΔC_p determine the temperature sensitivity of structural damage. The different hydration shells of the anions and their potential to form Gdm⁺ ion pairs in concentrated salt solutions modulate ΔC_p by altered wetting properties of hydrophobic DNA surface regions as shown by molecular dynamics simulations. The underlying structural changes on the molecular scale become amplified by the large number of structurally coupled DNA segments and thereby find nanoscopic correlations in AFM images.

Acid-Base Equilibrium and Dielectric Environment Regulate Charge in Supramolecular Nanofibers

Peptide amphiphiles are a class of molecules that can self-assemble into a variety of supramolecular structures, including high-aspect-ratio nanofibers. It is challenging to model and predict the charges in these supramolecular nanofibers because the ionization state of the peptides are not fixed but liable to change due to the acid-base equilibrium that is coupled to the structural organization of the peptide amphiphile molecules. Here, we have developed a theoretical model to describe and predict the amount of charge found on self-assembled peptide amphiphiles as a function of pH and ion concentration. In particular, we computed the amount of charge of peptide amphiphiles nanofibers with the sequence C₁₆ − V₂A₂E₂. In our theoretical formulation, we consider charge regulation of the carboxylic acid groups, which involves the acid-base chemical equilibrium of the glutamic acid residues and the possibility of ion condensation. The charge regulation is coupled with the local dielectric environment by allowing for a varying dielectric constant that also includes a position-dependent electrostatic solvation energy for the charged species. We find that the charges on the glutamic acid residues of the peptide amphiphile nanofiber are much lower than the same functional group in aqueous solution. There is a strong coupling between the charging via the acid-base equilibrium and the local dielectric environment. Our model predicts a much lower degree of deprotonation for a position-dependent relative dielectric constant compared to a constant dielectric background. Furthermore, the shape and size of the electrostatic potential as well as the counterion distribution are quantitatively and qualitatively different. These results indicate that an accurate model of peptide amphiphile self-assembly must take into account charge regulation of acidic groups through acid–base equilibria and ion condensation, as well as coupling to the local dielectric environment.

Direct Measurement of Interhelical DNA Repulsion and Attraction by Quantitative Cross-Linking

To better understand the forces that mediate nucleic acid compaction in biology, we developed the disulfide cross-linking approach xHEED (X-linking of Helices to measure Electrostatic Effects at Distance) to measure the distance-dependent encounter frequency of two DNA helices in solution. Using xHEED, we determined the distance that the electrostatic potential extends from DNA helices, the dependence of this distance on ionic conditions, and the magnitude of repulsion when two helices approach one another. Across all conditions tested, the potential falls to that of the bulk solution within 15 Å of the major groove surface. For separations of ∼30 Å, we measured a repulsion of 1.8 kcal/mol in low monovalent ion concentration (30 mM Na+), with higher Na+ concentrations ameliorating this repulsion, and 2 M Na+ or 100 mM Mg2+ eliminating it. Strikingly, we found full screening at very low Co3+ concentrations and net attraction at higher concentrations, without the higher-order DNA condensation that typically complicates studies of helical attraction. Our measurements define the relevant distances for electrostatic interactions of nucleic-acid helices in biology and introduce a new method to propel further understanding of how these forces impact biological processes.

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.

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.

Contact pairs of RNA with magnesium ions-electrostatics beyond the Poisson-Boltzmann equation

The electrostatic interaction of RNA with its aqueous environment is most relevant for defining macromolecular structure and biological function. The attractive interaction of phosphate groups in the RNA backbone with ions in the water environment leads to the accumulation of positively charged ions in the first few hydration layers around RNA. Electrostatics of this ion atmosphere and the resulting ion concentration profiles have been described by solutions of the nonlinear Poisson-Boltzmann equation and atomistic molecular dynamics (MD) simulations. Much less is known on contact pairs of RNA phosphate groups with ions at the RNA surface, regarding their abundance, molecular geometry, and role in defining RNA structure. Here, we present a combined theoretical and experimental study of interactions of a short RNA duplex with magnesium (Mg2+) ions. MD simulations covering a microsecond time range give detailed hydration geometries as well as electrostatics and spatial arrangements of phosphate-Mg2+ pairs, including both pairs in direct contact and separated by a single water layer. The theoretical predictions are benchmarked by linear infrared absorption and nonlinear two-dimensional infrared spectra of the asymmetric phosphate stretch vibration which probes both local interaction geometries and electric fields. Contact pairs of phosphate groups and Mg2+ ions are identified via their impact on the vibrational frequency position and line shape. A quantitative analysis of infrared spectra for a range of Mg2+-excess concentrations and comparison with fluorescence titration measurements shows that on average 20-30% of the Mg2+ ions interacting with the RNA duplex form contact pairs. The experimental and MD results are in good agreement. In contrast, calculations based on the nonlinear Poisson-Boltzmann equation fail in describing the ion arrangement, molecular electrostatic potential, and local electric field strengths correctly. Our results underline the importance of local electric field mapping and molecular-level simulations to correctly account for the electrostatics at the RNA-water interface.

Cation enrichment in the ion atmosphere is promoted by local hydration of DNA

Electrostatic interactions are central to the structure and function of nucleic acids, including their folding, condensation, and interaction with proteins and other charged molecules. These interactions are profoundly affected by ions surrounding nucleic acids, the constituents of the so-called ion atmosphere. Here, we report precise Fourier Transform-Terahertz/Far-Infrared (FT-THz/FIR) measurements in the frequency range 30-500 cm^-1 for a 24-bp DNA solvated in a series of alkali halide (NaCl, NaF, KCl, CsCl, and CsF) electrolyte solutions which are sensitive to changes in the ion atmosphere. Cation excess in the ion atmosphere is detected experimentally by observation of cation modes of Na⁺, K⁺, and Cs⁺ in the frequency range between 70-90 cm^-1. Based on MD simulations, we propose that the magnitude of cation excess (which is salt specific) depends on the ability of the electrolyte to perturb the water network at the DNA interface: In the NaF atmosphere, the ions reduce the strength of interactions between water and the DNA more than in case of a NaCl electrolyte. Here, we explicitly take into account the solvent contribution to the chemical potential in the ion atmosphere: A decrease in the number of bound water molecules in the hydration layer of DNA is correlated with enhanced density fluctuations, which decrease the free energy cost of ion-hydration, thus promoting further ion accumulation within the DNA atmosphere. We propose that taking into account the local solvation is crucial for understanding the ion atmosphere.

Using capillary electrophoresis to characterize the hydrodynamic and electrostatic properties of DNA in solutions containing various monovalent cations

This review describes the results obtained by using free-solution capillary electrophoresis to probe the electrostatic and hydrodynamic properties of DNA in solutions containing various monovalent cations. In brief, we found that the mobilities of double-stranded DNAs (dsDNAs) increase with increasing molecular weight before leveling off and becoming constant at molecular weights ≥400 bp. The mobilities of single-stranded DNAs (ssDNAs) go through a maximum at ∼10-20 nucleotides before decreasing and becoming constant for oligomers larger than ∼30-50 bases. The mobilities of both ss- and dsDNAs increase linearly with the logarithm of increasing charge per unit length and decrease linearly with the logarithm of increasing ionic strength. Surprisingly, ss- and dsDNA mobilities level off and become nearly constant at ionic strengths ≥0.6 M. The thermal stabilities of dsDNAs decrease linearly with increasing solution viscosity. The diffusion coefficients of dsDNA are modulated by the diffusion coefficients of their counterions because of electrostatic DNA-cation coupling interactions. Finally, the anomalously slow mobilities observed for A-tract-containing DNAs can be attributed both to differences in shape and to the preferential localization of small cations in the A-tract minor groove. Since many of these results are mirrored in other polyion-counterion systems, free-solution electrophoresis can be viewed as a reporter of the electrostatics and hydrodynamics of highly charged polyions. New results describing the mobilities of dsDNA analogues of a microRNA-messenger RNA complex are also presented.

Quantifying and visualizing weak interactions between anions and proteins

The molecular properties of proteins are influenced by various ions present in the same solution. While site-specific strong interactions between multivalent metal ions and proteins are well characterized, the behavior of other ions that are only weakly interacting with proteins remains elusive. In the current study, using NMR spectroscopy, we have investigated anion-protein interactions for three proteins that are similar in size but differ in overall charge. Using a unique NMR-based approach, we quantified anions accumulated around the proteins. The determined numbers of anions that are electrostatically attracted to the charged proteins were notably smaller than the overall charge valences and were consistent with predictions from the Poisson-Boltzmann theory. This NMR-based approach also allowed us to measure ionic diffusion and characterize the anions interacting with the positively charged proteins. Our data show that these anions rapidly diffuse while bound to the proteins. Using the same experimental approach, we observed the release of the anions from the protein surface upon the formation of the Antp homeodomain-DNA complex. Using paramagnetic relaxation enhancement (PRE), we visualized the spatial distribution of anions around the free proteins and the Antp homeodomain-DNA complex. The obtained PRE data revealed the localization of anions in the vicinity of the highly positively charged regions of the free Antp homeodomain and provided further evidence of the release of anions from the protein surface upon the protein-DNA association. This study sheds light on the dynamic behavior of anions that electrostatically interact with proteins.

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.

Effects of Phosphoryl Guanidine Modification of Phosphate Residues on the Structure and Hybridization of Oligodeoxyribonucleotides

Phosphoryl guanidine oligonucleotides (PGOs) are promising tools for biological research and development of biosensors and therapeutics. We performed structural and hybridization analyses of octa-, deca-, and dodecamers with all phosphate residues modified by 1,3-dimethylimidazolidine-2-imine moieties. Similarity of the B-form double helix between native and modified duplexes was noted. In PGO duplexes, we detected a decrease in the proportion of C2'-endo and an increased proportion of C1'-exo sugar conformations of the modified chain. Applicability of the two-state model to denaturation transition of all studied duplexes was proved for the first time. Sequence-dependent effects of this modification on hybridization properties were observed. The thermal stability of PGO complexes is almost native at 100 mM NaCl and slightly increases with decreasing ionic strength. An increase in water activity and dramatic changes in interaction with cations and in solvation of PGOs and their duplexes were noted, resulting in slight elevation of the melting temperature after an ionic-strength decrease from 1 M NaCl down to deionized water. Decreased binding of sodium ions and decreased water solvation were documented for PGOs and their duplexes. In contrast to DNA, the PGO duplex formation leads to a release of several cations. The water shell is significantly more disordered near PGOs and their complexes. Nevertheless, changes in solvation during the formation of native and PGO complexes are similar and indicate that it is possible to develop models for predictive calculations of the thermodynamic properties of phosphoryl guanidine oligomers. Our results may help devise an approach for the rational design of PGOs as novel improved molecular probes and tools for many modern methods involving oligonucleotides.

Dynamics of Ionic Interactions at Protein-Nucleic Acid Interfaces

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

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

Hofmeister Series for Metal-Cation-RNA Interactions: The Interplay of Binding Affinity and Exchange Kinetics

A large variety of physicochemical properties involving RNA depends on the type of metal cation present in solution. In order to gain microscopic insight into the origin of these ion specific effects, we apply molecular dynamics simulations to describe the interactions of metal cations and RNA. For the three most common ion binding sites on RNA, we calculate the binding affinities and exchange rates of eight different mono- and divalent metal cations. Our results reveal that binding sites involving phosphate groups preferentially bind metal cations with high charge density (such as Mg²⁺) in inner-sphere conformations while binding sites involving N7 or O6 atoms preferentially bind cations with low charge density (such as K⁺). The binding affinity therefore follows a direct Hofmeister series at the backbone but is reversed at the nucleobases leading to a high selectivity of ion binding sites on RNA. In addition, the exchange rates for cation binding cover almost 5 orders of magnitude, leading to a vastly different time scale for the lifetimes of contact pairs. Taken together, the site-specific binding affinities and the specific lifetime of contact pairs provide the microscopic explanation of ion specific effects observed in a wide variety of macroscopic RNA properties. Finally, combining the results from atomistic simulations with extended Poisson-Boltzmann theory allows us to predict the distribution of metal cations around double-stranded RNA at finite concentrations and to reproduce the results of ion counting experiments with good accuracy.

Electrophoretic Mobility of DNA in Solutions of High Ionic Strength

The free-solution mobilities of small single-stranded DNA (ssDNA) and double-stranded DNA (dsDNA) have been measured by capillary electrophoresis in solutions containing 0.01-1.0 M sodium acetate. The mobility of dsDNA is greater than that of ssDNA at all ionic strengths because of the greater charge density of dsDNA. The mobilities of both ssDNA and dsDNA decrease with increasing ionic strength until approaching plateau values at ionic strengths greater than ∼0.6 M. Hence, ssDNA and dsDNA appear to interact in a similar manner with the ions in the background electrolyte. For dsDNA, the mobilities predicted by the Manning electrophoresis equation are reasonably close to the observed mobilities, using no adjustable parameters, if the average distance between phosphate residues (the b parameter) is taken to be 1.7 Å. For ssDNA, the predicted mobilities are close to the observed mobilities at ionic strengths ≤0.01 M if the b-value is taken to be 4.1 Å. The predicted and observed mobilities diverge strongly at higher ionic strengths unless the b-value is reduced significantly. The results suggest that ssDNA strands exist as an ensemble of relatively compact conformations at high ionic strengths, with b-values corresponding to the relatively short phosphate-phosphate distances through space.

The roles of structural dynamics in the cellular functions of RNAs

RNAs fold into 3D structures that range from simple helical elements to complex tertiary structures and quaternary ribonucleoprotein assemblies. The functions of many regulatory RNAs depend on how their 3D structure changes in response to a diverse array of cellular conditions. In this Review, we examine how the structural characterization of RNA as dynamic ensembles of conformations, which form with different probabilities and at different timescales, is improving our understanding of RNA function in cells. We discuss the mechanisms of gene regulation by microRNAs, riboswitches, ribozymes, post-transcriptional RNA modifications and RNA-binding proteins, and how the cellular environment and processes such as liquid-liquid phase separation may affect RNA folding and activity. The emerging RNA-ensemble-function paradigm is changing our perspective and understanding of RNA regulation, from in vitro to in vivo and from descriptive to predictive.

Detecting Counterion Dynamics in DNA-Protein Association

Due to a high density of negative charges on its surface, DNA condenses cations as counterions, forming the so-called "ion atmosphere". Although the release of counterions upon DNA-protein association has been postulated to have a major contribution to the binding thermodynamics, this release remains to be confirmed through a direct observation of the ions. Herein, we report the characterization of the ion atmosphere around DNA using NMR spectroscopy and directly detect the release of counterions upon DNA-protein association. NMR-based diffusion data reveal the highly dynamic nature of counterions within the ion atmosphere around DNA. Counterion release is observed as an increase in the apparent ionic diffusion coefficient, which directly provides the number of counterions released upon DNA-protein association.

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.

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.

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.

Complex-type N-glycans on VSV-G pseudotyped HIV exhibit 'tough' sialic and 'brittle' mannose self-adhesions

The complex-type glycan shields of eukaryotic cells have a core layer of mannose residues buried under tiers of sugars that end with sialic acid (SA) residues. We investigate if the self-latching of mannose residues, earlier reported in pure monolayer studies, also manifests in the setting of a complex-type glycan shield. Would distal SA residues impede access to the mannose core? The interactions of mannobiose-, SA-, and lactose-coated probes with the complex-type VSV-G glycan shield on an HIV pseudovirus were studied with force-spectroscopy and gold-nanoparticle solutions. In force spectroscopy, the sugar probes can be forced to sample the depths of the glycan shield, whereas with sugar-coated nanoparticles, only interactions permitted by freely-diffusive contact occur. Deep-indentation mechanics was performed to verify the inferred structure of the engineered virus and to isolate the glycan shield layer for subsequent interaction studies. The adhesion between the sugar-probes and complex-type glycan shield was deconvoluted by comparing against the cross- and self- adhesions between the sugars in pure monolayers. Results from complementing systems were consistent with mannobiose-coated probes latching to the mannose core in the glycan shield, unhindered by the SA and distal sugars, with a short-range 'brittle' release of adhesion resulting in tightly coated viruses. SA-Coated probes, however, adhere to the terminal SA layer of a glycan shield with long-range and mechanically 'tough' adhesions resulting in large-scale virus aggregation. Lactose-coated probes exhibit ill-defined adherence to sialic residues. The selection and positioning of sugars within a glycan shield can influence how carbohydrate surfaces of different composition adhere.

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

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

Predicting 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.

Quantifying Mg2+ Binding to ssDNA Oligomers: A Self-Consistent Field Theory Study at Varying Ionic Strengths and Grafting Densities

The performance of aptamer-based biosensors is crucially impacted by their interactions with physiological metal ions, which can alter their structures and chemical properties. Therefore, elucidating the nature of these interactions carries the utmost importance in the robust design of highly efficient biosensors. We investigated Mg2+ binding to varying sequences of polymers to capture the effects of ionic strength and grafting density on ion binding and molecular reorganization of the polymer layer. The polymers are modeled as ssDNA aptamers using a self-consistent field theory, which accounts for non-covalent ion binding by integrating experimentally-derived binding constants. Our model captures the typical polyelectrolyte behavior of chain collapse with increased ionic strength for the ssDNA chains at low grafting density and exhibits the well-known re-entrant phenomena of stretched chains with increased ionic strength at high grafting density. The binding results suggest that electrostatic attraction between the monomers and Mg2+ plays the dominant role in defining the ion cloud around the ssDNA chains and generates a nearly-uniform ion distribution along the chains containing varying monomer sequences. These findings are in qualitative agreement with recent experimental results for Mg2+ binding to surface-bound ssDNA.

Role of protein interactions in stabilizing canonical DNA features in simulations of DNA in crowded environments

Background

Cellular environments are highly crowded with biological macromolecules resulting in frequent non-specific interactions. While the effect of such crowding on protein structure and dynamics has been studied extensively, very little is known how cellular crowding affects the conformational sampling of nucleic acids.

Results

The effect of protein crowding on the conformational preferences of DNA (deoxyribonucleic acid) is described from fully atomistic molecular dynamics simulations of systems containing a DNA dodecamer surrounded by protein crowders. From the simulations, it was found that DNA structures prefer to stay in B-like conformations in the presence of the crowders. The preference for B-like conformations results from non-specific interactions of crowder proteins with the DNA sugar-phosphate backbone. Moreover, the simulations suggest that the crowder interactions narrow the conformational sampling to canonical regions of the conformational space.

Conclusions

The overall conclusion is that crowding effects may stabilize the canonical features of DNA that are most important for biological function. The results are complementary to a previous study of DNA in reduced dielectric environments where reduced dielectric environments alone led to a conformational shift towards A-DNA. Such a shift was not observed here suggested that the reduced dielectric response of cellular environments is counteracted by non-specific interactions with protein crowders under in vivo conditions.

Electronic supplementary material

The online version of this article (10.1186/s13628-018-0048-y) contains supplementary material, which is available to authorized users.

Predicting RNA-Metal Ion Binding with Ion Dehydration Effects

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

Amino Acid Stabilization of Nucleic Acid Secondary Structure: Kinetic Insights from Single-Molecule Studies

Amino acid and nucleic acid interactions are central in biology and may have played a role in the evolutionary development of protein-based life from an early "RNA Universe." To explore the possible role of single amino acids in promoting nucleic acid folding, single-molecule Förster resonance energy transfer experiments have been implemented with a DNA hairpin construct (7 nucleotide double strand with a 40A loop) as a simple model for secondary structure formation. Exposure to positively charged amino acids (arginine and lysine) is found to clearly stabilize the secondary structure. Kinetically, each amino acid promotes folding by generating a large increase in the folding rate with little change in the unfolding rate. From analysis as a function of temperature, arginine and lysine are found to significantly increase the overall exothermicity of folding while imposing only a small entropic penalty on the folding process. Detailed investigations into the kinetics and thermodynamics of this amino acid-induced folding stability reveal arginine and lysine to interact with nucleic acids in a manner reminiscent of monovalent cations. Specifically, these observations are interpreted in the context of an ion atmosphere surrounding the nucleic acid, in which amino acid salts stabilize folding qualitatively like small monovalent cations but also exhibit differences because of the composition of their side chains.

Influence of Na+ and Mg2+ ions on RNA structures studied with molecular dynamics simulations

The structure of ribonucleic acid (RNA) polymers is strongly dependent on the presence of, in particular Mg2+ cations to stabilize structural features. Only in high-resolution X-ray crystallography structures can ions be identified reliably. Here, we perform molecular dynamics simulations of 24 RNA structures with varying ion concentrations. Twelve of the structures were helical and the others complex folded. The aim of the study is to predict ion positions but also to evaluate the impact of different types of ions (Na+ or Mg2+) and the ionic strength on structural stability and variations of RNA. As a general conclusion Mg2+ is found to conserve the experimental structure better than Na+ and, where experimental ion positions are available, they can be reproduced with reasonable accuracy. If a large surplus of ions is present the added electrostatic screening makes prediction of binding-sites less reproducible. Distinct differences in ion-binding between helical and complex folded structures are found. The strength of binding (ΔG‡ for breaking RNA atom-ion interactions) is found to differ between roughly 10 and 26 kJ/mol for the different RNA atoms. Differences in stability between helical and complex folded structures and of the influence of metal ions on either are discussed.