Spatial distribution of competing ions around DNA in solution

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.

Opto-Electrostatic Determination of Nucleic Acid Double-Helix Dimensions and the Structure of the Molecule–Solvent Interface

A DNA molecule is highly electrically charged in solution. The electrical potential at the molecular surface is known to vary strongly with the local geometry of the double helix and plays a pivotal role in DNA–protein interactions. Further out from the molecular surface, the electrical field propagating into the surrounding electrolyte bears fingerprints of the three-dimensional arrangement of the charged atoms in the molecule. However, precise extraction of the structural information encoded in the electrostatic “far field” has remained experimentally challenging. Here, we report an optical microscopy-based approach that detects the field distribution surrounding a charged molecule in solution, revealing geometric features such as the radius and the average rise per basepair of the double helix with up to sub-Angstrom precision, comparable with traditional molecular structure determination techniques like X-ray crystallography and nuclear magnetic resonance. Moreover, measurement of the helical radius furnishes an unprecedented view of both hydration and the arrangement of cations at the molecule–solvent interface. We demonstrate that a probe in the electrostatic far field delivers structural and chemical information on macromolecules, opening up a new dimension in the study of charged molecules and interfaces in solution.

Twist-diameter coupling drives DNA twist changes with salt and temperature

DNA deformations upon environmental changes, e.g., salt and temperature, play crucial roles in many biological processes and material applications. Here, our magnetic tweezers experiments observed that the increase in NaCl, KCl, or RbCl concentration leads to substantial DNA overwinding. Our simulations and theoretical calculation quantitatively explain the salt-induced twist change through the mechanism: More salt enhances the screening of interstrand electrostatic repulsion and hence reduces DNA diameter, which is transduced to twist increase through twist-diameter coupling. We determined that the coupling constant is 4.5 ± 0.8 k_BT/(degrees∙nm) for one base pair. The coupling comes from the restraint of the contour length of DNA backbone. On the basis of this coupling constant and diameter-dependent DNA conformational entropy, we predict the temperature dependence of DNA twist Δω_bp/ΔT ≈ -0.01 degree/°C, which agrees with our and previous experimental results. Our analysis suggests that twist-diameter coupling is a common driving force for salt- and temperature-induced DNA twist changes.

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.

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.

Porphyrin Binding and Irradiation Promote G-Quadruplex DNA Dimeric Structure

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

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.

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.

Dynamics of K+ counterions around DNA double helix in the external electric field: A molecular dynamics study

The structure of DNA double helix is stabilized by metal counterions condensed to a diffuse layer around the macromolecule. The dynamics of counterions in real conditions is governed by the electric fields from DNA and other biological macromolecules. In the present work the molecular dynamics study was performed for the system of DNA double helix with neutralizing K⁺ counterions and for the system of KCl salt solution in an external electric field of different strength (up to 32mV/Å). The analysis of ionic conductivities of these systems has shown that the counterions around the DNA double helix are slowed down compared with the KCl salt solution. The calculated values of ion mobility are within (0.05-0.4)mS/cm depending on the orientation of the external electric field relatively to the double helix. Under the electric field parallel to the macromolecule K⁺ counterions move along the grooves of the double helix staying longer in the places with narrower minor groove. Under the electric field perpendicular to the macromolecule the dynamics of counterions is less affected by DNA atoms, and starting with the electric field values about 30mV/Å the double helix undergoes a phase transition from a double-stranded to a single-strand state.

Base-Pairs' Correlated Oscillation Effects on the Charge Transfer in Double-Helix B-DNA Molecules

By introducing a suitable renormalization process, the charge carrier and phonon dynamics of a double-stranded helical DNA molecule are expressed in terms of an effective Hamiltonian describing a linear chain, where the renormalized transfer integrals explicitly depend on the relative orientations of the Watson-Crick base pairs, and the renormalized on-site energies are related to the electronic parameters of consecutive base pairs along the helix axis, as well as to the low-frequency phonons' dispersion relation. The existence of synchronized collective oscillations enhancing the π-π orbital overlapping among different base pairs is disclosed from the study of the obtained analytical dynamical equations. The role of these phonon-correlated, long-range oscillation effects on the charge transfer properties of double-stranded DNA homopolymers is discussed in terms of the resulting band structure.

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.

Charge Density of Cation Determines Inner versus Outer Shell Coordination to Phosphate in RNA

Divalent cations are often required to fold RNA, which is a highly charged polyanion. Condensation of ions, such as Mg²⁺ or Ca²⁺, in the vicinity of RNA renormalizes the effective charges on the phosphate groups, thus minimizing the intra RNA electrostatic repulsion. The prevailing view is that divalent ions bind diffusively in a nonspecific manner. In sharp contrast, we arrive at the exact opposite conclusion using a theory for the interaction of ions with the phosphate groups using RISM theory in conjunction with simulations based on an accurate three-interaction-site RNA model. The divalent ions bind in a nucleotide-specific manner using either the inner (partially dehydrated) or outer (fully hydrated) shell coordination. The high charge density Mg²⁺ ion has a preference to bind to the outer shell, whereas the opposite is the case for Ca²⁺. Surprisingly, we find that bridging interactions, involving ions that are coordinated to two or more phosphate groups, play a crucial role in maintaining the integrity of the folded state. Their importance could become increasingly prominent as the size of the RNA increases. Because the modes of interaction of divalent ions with DNA are likely to be similar, we propose that specific inner and outer shell coordination could play a role in DNA condensation, and perhaps genome organization as well.

Pattern preferences of DNA nucleotide motifs by polyamines putrescine2+, spermidine3+ and spermine4

The interactions of natural polyamines (putrescine2+, spermidine3+ and spermine4+) with DNA double helix are studied to characterize their nucleotide sequence pattern preference. Atomistic Molecular Dynamics simulations have been carried out for three systems consisting of the same DNA fragment d(CGCGAATTCGCGAATTCGCG) with different polyamines. The results show that polyamine molecules are localized with well-recognized patterns along the double helix with different residence times. We observed a clear hierarchy in the residence times of the polyamines, with the longest residence time (ca 100ns) in the minor groove. The analysis of the sequence dependence shows that polyamine molecules prefer the A-tract regions of the minor groove - in its narrowest part. The preferable localization of putrescine2+, spermidine3+ and spermine4+ in the minor groove with A-tract motifs is correlated with modulation of the groove width by a specific nucleotide sequences. We did develop a theoretical model pointing to the electrostatic interactions as the main driving force in this phenomenon, making it even more prominent for polyamines with higher charges. The results of the study explain the specificity of polyamine interactions with A-tract region of the DNA double helix which is also observed in experiments.

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.

Enzymatic Degradation of DNA Probed by In Situ X-ray Scattering

Label-free in situ X-ray scattering from protein spherical nucleic acids (Pro-SNAs, consisting of protein cores densely functionalized with covalently bound DNA) was used to elucidate the enzymatic reaction pathway for the DNase I-induced degradation of DNA. Time-course small-angle X-ray scattering (SAXS) and gel electrophoresis reveal a two-state system with time-dependent populations of intact and fully degraded DNA in the Pro-SNAs. SAXS shows that in the fully degraded state, the DNA strands forming the outer shell of the Pro-SNA were completely digested. SAXS analysis of reactions with different Pro-SNA concentrations reveals a reaction pathway characterized by a slow, rate determining DNase I-Pro-SNA association, followed by rapid DNA hydrolysis. Molecular dynamics (MD) simulations provide the distributions of monovalent and divalent ions around the Pro-SNA, relevant to the activity of DNase I. Taken together, in situ SAXS in conjunction with MD simulations yield key mechanistic and structural insights into the interaction of DNA with DNase I. The approach presented here should prove invaluable in probing other enzyme-catalyzed reactions on the nanoscale.

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

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

Predicting Monovalent Ion Correlation Effects in Nucleic Acids

Ion correlation and fluctuation can play a potentially significant role in metal ion-nucleic acid interactions. Previous studies have focused on the effects for multivalent cations. However, the correlation and fluctuation effects can be important also for monovalent cations around the nucleic acid surface. Here, we report a model, gMCTBI, that can explicitly treat discrete distributions of both monovalent and multivalent cations and can account for the correlation and fluctuation effects for the cations in the solution. The gMCTBI model enables investigation of the global ion binding properties as well as the detailed discrete distributions of the bound ions. Accounting for the ion correlation effect for monovalent ions can lead to more accurate predictions, especially in a mixed monovalent and multivalent salt solution, for the number and location of the bound ions. Furthermore, although the monovalent ion-mediated correlation does not show a significant effect on the number of bound ions, the correlation may enhance the accumulation of monovalent ions near the nucleic acid surface and hence affect the ion distribution. The study further reveals novel ion correlation-induced effects in the competition between the different cations around nucleic acids.

Molecular Mechanisms of DNA Replication and Repair Machinery: Insights from Microscopic Simulations

Reproduction, the hallmark of biological activity, requires making an accurate copy of the genetic material to allow the progeny to inherit parental traits. In all living cells, the process of DNA replication is carried out by a concerted action of multiple protein species forming a loose protein-nucleic acid complex, the replisome. Proofreading and error correction generally accompany replication but also occur independently, safeguarding genetic information through all phases of the cell cycle. Advances in biochemical characterization of intracellular processes, proteomics and the advent of single-molecule biophysics have brought about a treasure trove of information awaiting to be assembled into an accurate mechanistic model of the DNA replication process. In this review, we describe recent efforts to model elements of DNA replication and repair processes using computer simulations, an approach that has gained immense popularity in many areas of molecular biophysics but has yet to become mainstream in the DNA metabolism community. We highlight the use of diverse computational methods to address specific problems of the fields and discuss unexplored possibilities that lie ahead for the computational approaches in these areas.

Facilitated Diffusion Mechanisms in DNA Base Excision Repair and Transcriptional Activation

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

Asymmetric electrolytes near structured dielectric interfaces

The ion distribution of electrolytes near interfaces with dielectric contrast has important consequences for electrochemical processes and many other applications. To date, most studies of such systems have focused on geometrically simple interfaces, for which dielectric effects are analytically solvable or computationally tractable. However, all real surfaces display nontrivial structure at the nanoscale and have, in particular, a nonuniform local curvature. Using a recently developed, highly efficient computational method, we investigate the effect of surface geometry on ion distribution and interface polarization. We consider an asymmetric 2:1 electrolyte bounded by a sinusoidally deformed solid surface. We demonstrate that even when the surface is neutral, the electrolyte acquires a nonuniform ion density profile near the surface. This profile is asymmetric and leads to an effective charging of the surface. We furthermore show that the induced charge is modulated by the local curvature. The effective charge is opposite in sign to the multivalent ions and is larger in concave regions of the surface.

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.

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.

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.

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.

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.

Effects of Hfq on the conformation and compaction of DNA

Hfq is a bacterial pleiotropic regulator that mediates several aspects of nucleic acids metabolism. The protein notably influences translation and turnover of cellular RNAs. Although most previous contributions concentrated on Hfq's interaction with RNA, its association to DNA has also been observed in vitro and in vivo. Here, we focus on DNA-compacting properties of Hfq. Various experimental technologies, including fluorescence microscopy imaging of single DNA molecules confined inside nanofluidic channels, atomic force microscopy and small angle neutron scattering have been used to follow the assembly of Hfq on DNA. Our results show that Hfq forms a nucleoprotein complex, changes the mechanical properties of the double helix and compacts DNA into a condensed form. We propose a compaction mechanism based on protein-mediated bridging of DNA segments. The propensity for bridging is presumably related to multi-arm functionality of the Hfq hexamer, resulting from binding of the C-terminal domains to the duplex. Results are discussed in regard to previous results obtained for H-NS, with important implications for protein binding related gene regulation.

Multiscale methods for computational RNA enzymology

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

Ion distributions around left- and right-handed DNA and RNA duplexes: a comparative study

The ion atmosphere around nucleic acids is an integral part of their solvated structure. However, detailed aspects of the ionic distribution are difficult to probe experimentally, and comparative studies for different structures of the same sequence are almost non-existent. Here, we have used large-scale molecular dynamics simulations to perform a comparative study of the ion distribution around (5'-CGCGCGCGCGCG-3')2 dodecamers in solution in B-DNA, A-RNA, Z-DNA and Z-RNA forms. The CG sequence is very sensitive to ionic strength and it allows the comparison with the rare but important left-handed forms. The ions investigated include Na(+), K(+) and Mg(2 +), with various concentrations of their chloride salts. Our results quantitatively describe the characteristics of the ionic distributions for different structures at varying ionic strengths, tracing these differences to nucleic acid structure and ion type. Several binding pockets with rather long ion residence times are described, both for the monovalent ions and for the hexahydrated Mg[(H2O)6](2+) ion. The conformations of these binding pockets include direct binding through desolvated ion bridges in the GpC steps in B-DNA and A-RNA; direct binding to backbone oxygens; binding of Mg[(H2O)6](2+) to distant phosphates, resulting in acute bending of A-RNA; tight 'ion traps' in Z-RNA between C-O2 and the C-O2' atoms in GpC steps; and others.

Close encounters with DNA

Over the past ten years, the all-atom molecular dynamics method has grown in the scale of both systems and processes amenable to it and in its ability to make quantitative predictions about the behavior of experimental systems. The field of computational DNA research is no exception, witnessing a dramatic increase in the size of systems simulated with atomic resolution, the duration of individual simulations and the realism of the simulation outcomes. In this topical review, we describe the hallmark physical properties of DNA from the perspective of all-atom simulations. We demonstrate the amazing ability of such simulations to reveal the microscopic physical origins of experimentally observed phenomena. We also discuss the frustrating limitations associated with imperfections of present atomic force fields and inadequate sampling. The review is focused on the following four physical properties of DNA: effective electric charge, response to an external mechanical force, interaction with other DNA molecules and behavior in an external electric field.

Many-body effect in ion binding to RNA

Ion-mediated electrostatic interactions play an important role in RNA folding stability. For a RNA in a solution with higher Mg(2+) ion concentration, more counterions in the solution can bind to the RNA, causing a strong many-body coupling between the bound ions. The many-body effect can change the effective potential of mean force between the tightly bound ions. This effect tends to dampen ion binding and lower RNA folding stability. Neglecting the many-body effect leads to a systematic error (over-estimation) of RNA folding stability at high Mg(2+) ion concentrations. Using the tightly bound ion model combined with a conformational ensemble model, we investigate the influence of the many-body effect on the ion-dependent RNA folding stability. Comparisons with the experimental data indicate that including the many-body effect led to much improved predictions for RNA folding stability at high Mg(2+) ion concentrations. The results suggest that the many-body effect can be important for RNA folding in high concentrations of multivalent ions. Further investigation showed that the many-body effect can influence the spatial distribution of the tightly bound ions and the effect is more pronounced for compact RNA structures and structures prone to the formation of local clustering of ions.

Modified Poisson–Boltzmann equations for characterizing biomolecular solvation

Methods for computing electrostatic interactions often account implicitly for the solvent, due to the much smaller number of degrees of freedom involved. In the Poisson–Boltzmann (PB) approach the electrostatic potential is obtained by solving the Poisson–Boltzmann equation (PBE), where the solvent region is modeled as a homogeneous medium with a high dielectric constant. PB however is not exempt of problems. It does not take into account for example the sizes of the ions in the atmosphere surrounding the solute, nor does it take into account the inhomogeneous dielectric response of water due to the presence of a highly charged surface. In this paper we review two major modifications of PB that circumvent these problems, namely the size-modified PB (SMPB) equation and the Dipolar Poisson–Boltzmann Langevin (DPBL) model. In SMPB, steric effects between ions are accounted for with a lattice gas model. In DPBL, the solvent region is no longer modeled as a homogeneous dielectric media but rather as an assembly of self-orienting interacting dipoles of variable density. This model results in a dielectric profile that transits smoothly from the solute to the solvent region as well as in a variable solvent density that depends on the charges of the solute. We show successful applications of the DPBL formalism to computing the solvation free energies of isolated ions in water. Further developments of more accurately modified PB models are discussed.

Ion competition in condensed DNA arrays in the attractive regime

Physical origin of DNA condensation by multivalent cations remains unsettled. Here, we report quantitative studies of how one DNA-condensing ion (Cobalt(3+) Hexammine, or Co(3+)Hex) and one nonDNA-condensing ion (Mg(2+)) compete within the interstitial space in spontaneously condensed DNA arrays. As the ion concentrations in the bath solution are systematically varied, the ion contents and DNA-DNA spacings of the DNA arrays are determined by atomic emission spectroscopy and x-ray diffraction, respectively. To gain quantitative insights, we first compare the experimentally determined ion contents with predictions from exact numerical calculations based on nonlinear Poisson-Boltzmann equations. Such calculations are shown to significantly underestimate the number of Co(3+)Hex ions, consistent with the deficiencies of nonlinear Poisson-Boltzmann approaches in describing multivalent cations. Upon increasing the concentration of Mg(2+), the Co(3+)Hex-condensed DNA array expands and eventually redissolves as a result of ion competition weakening DNA-DNA attraction. Although the DNA-DNA spacing depends on both Mg(2+) and Co(3+)Hex concentrations in the bath solution, it is observed that the spacing is largely determined by a single parameter of the DNA array, the fraction of DNA charges neutralized by Co(3+)Hex. It is also observed that only ∼20% DNA charge neutralization by Co(3+)Hex is necessary for spontaneous DNA condensation. We then show that the bath ion conditions can be reduced to one variable with a simplistic ion binding model, which is able to describe the variations of both ion contents and DNA-DNA spacings reasonably well. Finally, we discuss the implications on the nature of interstitial ions and cation-mediated DNA-DNA interactions.

Understanding nucleic acid-ion interactions

Ions surround nucleic acids in what is referred to as an ion atmosphere. As a result, the folding and dynamics of RNA and DNA and their complexes with proteins and with each other cannot be understood without a reasonably sophisticated appreciation of these ions' electrostatic interactions. However, the underlying behavior of the ion atmosphere follows physical rules that are distinct from the rules of site binding that biochemists are most familiar and comfortable with. The main goal of this review is to familiarize nucleic acid experimentalists with the physical concepts that underlie nucleic acid-ion interactions. Throughout, we provide practical strategies for interpreting and analyzing nucleic acid experiments that avoid pitfalls from oversimplified or incorrect models. We briefly review the status of theories that predict or simulate nucleic acid-ion interactions and experiments that test these theories. Finally, we describe opportunities for going beyond phenomenological fits to a next-generation, truly predictive understanding of nucleic acid-ion interactions.

Counterion distribution surrounding spherical nucleic acid-Au nanoparticle conjugates probed by small-angle x-ray scattering

The radial distribution of monovalent cations surrounding spherical nucleic acid-Au nanoparticle conjugates (SNA-AuNPs) is determined by in situ small-angle x-ray scattering (SAXS) and classical density functional theory (DFT) calculations. Small differences in SAXS intensity profiles from SNA-AuNPs dispersed in a series of solutions containing different monovalent ions (Na(+), K(+), Rb(+), or Cs(+)) are measured. Using the "heavy ion replacement" SAXS (HIRSAXS) approach, we extract the cation-distribution-dependent contribution to the SAXS intensity and show that it agrees with DFT predictions. The experiment-theory comparisons reveal the radial distribution of cations as well as the conformation of the DNA in the SNA shell. The analysis shows an enhancement to the average cation concentration in the SNA shell that can be up to 15-fold, depending on the bulk solution ionic concentration. The study demonstrates the feasibility of HIRSAXS in probing the distribution of monovalent cations surrounding nanoparticles with an electron dense core (e.g., metals).

Electrostatics of nucleic acid folding under conformational constraint

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

SAXS studies of ion-nucleic acid interactions

Positively charged ions, atoms, or molecules compensate the high negative charge of the nucleic acid backbone. Their presence is critical to the biological function of DNA and RNA. This review focuses on experimental studies probing (a) interactions between small ions and nucleic acids and (b) ion-mediated interactions between nucleic acid duplexes. Experimental results on these simple model systems can be compared with specific theoretical models to validate their predictions. Small angle X-ray scattering (SAXS) provides unique insight into these interactions. Anomalous SAXS reports the spatial correlations of condensed (e.g., locally concentrated) counterions to individual DNA or RNA duplexes. SAXS very effectively reports interactions between nucleic acid helices, which range from strongly repulsive to strongly attractive depending on the ionic species present. The sign and strength of interparticle interactions are easily deduced from dramatic changes in the scattering profiles of interacting duplexes.

Instrumental developments for anomalous small-angle X-ray scattering from soft matter systems

An optimized instrument for anomalous small-angle X-ray scattering from charged soft matter is described. The experimental setup takes special care for single-photon detection sensitivity, high energy resolution of the monochromator,in situcalibration of intensity and energy, and the avoidance of radiation damage. Measured intensities are normalized to an absolute scale online, which can be further decomposed to resonant and non-resonant contributions. The performance of the instrument is demonstrated by an example involving cationic surfactant micelles with bromide counter-ions. The counter-ion profile around the micelle is deduced from the analysis of anomalous scattering near theK-absorption edge of bromine. Two different approaches yield similar results for the radial profile of the counter-ions, showing strong condensation of the counter-ions on the micellar surface, in agreement with the inference from electrochemical methods.

Computational exploration of mobile ion distributions around RNA duplex

Atomically detailed distributions of ions around an A-form RNA are computed. Different mixtures of monovalent and divalent ions are considered explicitly. Studies of tightly bound and of diffusive (but bound) ions around 25 base pairs RNA are conducted in explicit solvent. Replica exchange simulations provide detailed equilibrium distributions with moderate computing resources (20 ns of simulation using 64 replicas). The simulations show distinct behavior of single and double charged cations. Binding of Mg(2+) ion includes tight binding to specific sites while Na(+) binds only diffusively. The tight binding of Mg(2+) is with a solvation shell while Na(+) can bind directly to RNA. Negative mobile ions can be found near the RNA but must be assisted by proximate and mobile cations. At distances larger than 16 A from the RNA center, a model of RNA as charged rod in a continuum of ionic solution provides quantitative description of the ion density (the same as in atomically detailed simulation). At shorter distances, the structure of RNA (and ions) has a significant impact on the pair correlation functions. Predicted binding sites of Mg(2+) at the RNA surface are in accord with structures from crystallography. Electric field relaxation is investigated. The relaxation due to solution rearrangements is completed in tens of picoseconds, while the contribution of RNA tumbling continues to a few nanoseconds.