Competitive interaction of monovalent cations with DNA from 3D-RISM

Dynamics Playing a Key Role in the Covalent Binding of Inhibitors to Focal Adhesion Kinase

Covalent kinase inhibitors (CKIs) have recently garnered considerable attention, yet the rational design of CKIs continues to pose a great challenge. In the discovery of CKIs targeting focal adhesion kinase (FAK), it has been observed that the chemical structure of the linkers plays a key role in achieving covalent targeting of FAK. However, the mechanism behind the observation remains elusive. In this work, we employ a comprehensive suite of advanced computational methods to investigate the mechanism of CKIs covalently targeting FAK. We reveal that the linker of an inhibitor influences the contacts between the warhead and residue(s) and the residence time in active conformation, thereby dictating the inhibitor's capability to bind covalently to FAK. This study reflects the complexity of CKI design and underscores the importance of considering the dynamic interactions and residence times for the successful development of covalent drugs.

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.

Modern Alchemical Free Energy Methods for Drug Discovery Explained

This Perspective provides a contextual explanation of the current state-of-the-art alchemical free energy methods and their role in drug discovery as well as highlights select emerging technologies. The narrative attempts to answer basic questions about what goes on "under the hood" in free energy simulations and provide general guidelines for how to run simulations and analyze the results. It is the hope that this work will provide a valuable introduction to students and scientists in the field.

MD simulations of macromolecular crystals: Implications for the analysis of Bragg and diffuse scattering

Some of our most detailed information about structure and dynamics of macromolecules comes from X-ray-diffraction studies in crystalline environments. More than 170,000 atomic models have been deposited in the Protein Data Bank, and the number of observations (typically of intensities of Bragg diffraction peaks) is generally quite large, when compared to other experimental methods. Nevertheless, the general agreement between calculated and observed intensities is far outside the experimental precision, and the majority of scattered photons fall between the sharp Bragg peaks, and are rarely taken into account. This chapter considers how molecular dynamics simulations can be used to explore the connections between microscopic behavior in a crystalline lattice and observed scattering intensities, and point the way to new atomic models that could more faithfully recapitulate Bragg intensities and extract useful information from the diffuse scattering that lies between those peaks.

Two Opposing Effects of Monovalent Cations on the Stability of i-Motif Structure

At acidic pH, cytosine-rich single-stranded DNA can be folded into a tetraplex structure called i-motif (iM). In recent studies, the effect of monovalent cations on the stability of iM structure has been addressed, but a consensus about the issue has not been reached yet. Thus, we investigated the effects of various factors on the stability of iM structure using fluorescence resonance energy transfer (FRET)-based analysis for three types of iM derived from human telomere sequences. We confirmed that the protonated cytosine-cytosine (C:C⁺) base pair is destabilized as the concentration of monovalent cations (Li⁺, Na⁺, K⁺) increases and that Li⁺ has the greatest tendency of destabilization. Intriguingly, monovalent cations would play an ambivalent role in iM formation by making single-stranded DNA flexible and pliant for an iM structure. In particular, we found that Li⁺ has a notably greater flexibilizing effect than Na⁺ and K⁺. All taken together, we conclude that the stability of iM structure is controlled by the subtle balance of the two counteractive effects of monovalent cations: electrostatic screening and disruption of cytosine base pairing.

Sequence-Specific Structural Features and Solvation Properties of Transcription Factor Binding DNA Motifs: Insights from Molecular Dynamics Simulation

Sequence-specific recognition of transcription factor (TF) binding motifs in the target site of DNA over the vast amount of non-target DNA is of primary importance for the transcriptional regulation of gene expression by the TFs. Binding of TFs to the target site of DNA relies not only on the direct contact formation but also on the structural and conformational features of DNA. Recognition of DNA structural features or shape readout by proteins is an important factor in the context of TF-DNA interaction. Based on the atomistic molecular simulation, here we report the sequence-dependent unique structural features, solvation, and ion-binding properties of biologically relevant AT- and GC-rich human TF binding motifs in DNA. Counterion and water distribution around the motif is found to be sensitive to the motif sequence, which is accompanied with the DNA shape features. The motif sequence affects the electrostatic potential along the grooves, and cytosine methylation alters the DNA shape features. Characteristic solvation properties of TF binding motif DNA fragments infer that an ionic environment and hydration influences are essential to describe TF-DNA interactions.

Measuring Local Electrostatic Potentials Around Nucleic Acids by Paramagnetic NMR Spectroscopy

Electrostatic potentials around macromolecules in the presence of mobile charges are difficult to assess especially for highly charged systems. Here, we report measurements of local electrostatic potentials around DNA by paramagnetic NMR. Through quantitative analysis of NMR paramagnetic relaxation enhancement arising from positively charged or neutral paramagnetic cosolutes, we were able to determine local electrostatic potentials around 1H nuclei at >100 sites in major and minor grooves of 13C,15N-labeled 15-bp DNA at 100 mM NaCl. Our experimental electrostatic potential data directly confirmed the Coulombic end effects of DNA. The effective near-surface electrostatic potentials from the NMR data were in good agreement with the theoretical predictions with the Poisson-Boltzmann equation. This NMR method allows for unprecedented experimental investigations into the electrostatic properties of nucleic acids.

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.

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.

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.

Peripheral Methionine Residues Impact Flavin Photoreduction and Protonation in an Engineered LOV Domain Light Sensor

Proton-coupled electron transfer reactions play critical roles in many aspects of sensory phototransduction. In the case of flavoprotein light sensors, reductive quenching of flavin excited states initiates chemical and conformational changes that ultimately transmit light signals to downstream targets. These reactions generally require neighboring aromatic residues and proton-donating side chains for rapid and coordinated electron and proton transfer to flavin. Although photoreduction of flavoproteins can produce either the anionic (ASQ) or neutral semiquinone (NSQ), the factors that favor one over the other are not well understood. Here we employ a biologically active variant of the light-oxygen-voltage (LOV) domain protein VVD devoid of the adduct-forming Cys residue (VVD-III) to probe the mechanism of flavin photoreduction and protonation. A series of isosteric and conservative residue replacements studied by rate measurements, fluorescence quantum yields, FTIR difference spectroscopy, and molecular dynamics simulations indicate that tyrosine residues facilitate charge recombination reactions that limit sustained flavin reduction, whereas methionine residues facilitate radical propagation and quenching and also gate solvent access for flavin protonation. Replacement of a single surface Met residue with Leu favors formation of the ASQ over the NSQ and desensitizes photoreduction to oxidants. In contrast, increasing site hydrophilicity by Gln substitution promotes rapid NSQ formation and weakens the influence of the redox environment. Overall, the photoreactivity of VVD-III can be understood in terms of redundant electron donors, internal hole quenching, and coupled proton transfer reactions that all depend upon protein conformation, dynamics, and solvent penetration.

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.

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.

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.

Calculation of salt-dependent free energy of binding of β-lactoglobulin homodimer formation and mechanism of dimer formation using molecular dynamics simulation and three-dimensional reference interaction site model (3D-RISM): diffuse salt ions and non-polar interactions between the monomers favor the dimer formation

There are several important phenomena in chemistry, biology, and physics where molecules (or parts of a molecule) having charges of the same sign come closer together and become stable. DNA condensation, RNA folding, colloid-colloid interactions are some of the examples of this kind. In the current work, we have investigated how β-lactoglobulin, a protein found in milk, in spite of carrying +13 charge, favors the homodimer formation in the presence of salt. We have focussed on calculating the protein-protein binding free energy in the presence of salt and identifying the thermodynamic and microscopic mechanism of the process. Estimation of binding free energy of this salt-dependent process is done by combining molecular dynamics simulation with statistical mechanical theory of three-dimensional reference interaction site model (3D-RISM). Binding free energy is evaluated from the chemical potential of the solutes as opposed to potential of mean force calculation, which gives only a constrained free energy. Our calculated values semi-quantitatively match with the experimental results. By examining the different components of binding free energy, we have found that the role of salt ions (especially of Cl^-) is to shift the equilibrium towards the dimer. Non-polar (Lennard-Jones) interactions between the monomers is also favorable to the binding free energy. However, water slightly disfavors the dimer formation. For the microscopic mechanism, heterogeneous of both Na⁺ and Cl^- near the charged residues at the binding interface and change of this charge distribution on dimer formation contribute to the stability. A fine-tuning of enthalpic and entropic effects of salt ions is found to operate at different salt concentrations. Both thermodynamic and microscopic mechanism of dimer formation gives detailed insight into the complex electrostatics of charged protein-protein binding.

Dynamical ensemble of the active state and transition state mimic for the RNA-cleaving 8-17 DNAzyme in solution

We perform molecular dynamics simulations, based on recent crystallographic data, on the 8-17 DNAzyme at four states along the reaction pathway to determine the dynamical ensemble for the active state and transition state mimic in solution. A striking finding is the diverse roles played by Na+ and Pb2+ ions in the electrostatically strained active site that impact all four fundamental catalytic strategies, and share commonality with some features recently inferred for naturally occurring hammerhead and pistol ribozymes. The active site Pb2+ ion helps to stabilize in-line nucleophilic attack, provides direct electrostatic transition state stabilization, and facilitates leaving group departure. A conserved guanine residue is positioned to act as the general base, and is assisted by a bridging Na+ ion that tunes the pKa and facilitates in-line fitness. The present work provides insight into how DNA molecules are able to solve the RNA-cleavage problem, and establishes functional relationships between the mechanism of these engineered DNA enzymes with their naturally evolved RNA counterparts. This adds valuable information to our growing body of knowledge on general mechanisms of phosphoryl transfer reactions catalyzed by RNA, proteins and DNA.

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.

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.

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.

Representation of DNA environment: Spiral staircase distribution function

In the present study, we investigated the local structure of DNA and its environment using a new visualization technique. The spiral staircase distribution function (SSDF) is determined as two-dimensional density distribution of atoms of water and ligands in local reference frames linked with each base pair of poly-DNA molecule, either GC or AT. This property of SSDF provides opportunity to study sequence-specific binding of ions, peptides, and other agents derived from a molecular dynamics computer simulation. The spatial structure of double-stranded DNA environment in water solution containing either Mg²⁺ or Na⁺ ions was investigated using of SSDF. The distributions of ions around GC and AT base pairs are shown separately. It is observed that Mg²⁺ ions interact with DNA atoms by means of the layer of water molecules and penetrate into the major groove only. Na⁺ ions have a direct contact with DNA atoms and penetrate both into the major and minor grooves of DNA. © 2018 Wiley Periodicals, Inc.

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

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

Theory Meets Experiment: Metal Ion Effects in HCV Genomic RNA Kissing Complex Formation

The long-range base pairing between the 5BSL3. 2 and 3′X domains in hepatitis C virus (HCV) genomic RNA is essential for viral replication. Experimental evidence points to the critical role of metal ions, especially Mg²⁺ ions, in the formation of the 5BSL3.2:3′X kissing complex. Furthermore, NMR studies suggested an important ion-dependent conformational switch in the kissing process. However, for a long time, mechanistic understanding of the ion effects for the process has been unclear. Recently, computational modeling based on the Vfold RNA folding model and the partial charge-based tightly bound ion (PCTBI) model, in combination with the NMR data, revealed novel physical insights into the role of metal ions in the 5BSL3.2-3′X system. The use of the PCTBI model, which accounts for the ion correlation and fluctuation, gives reliable predictions for the ion-dependent electrostatic free energy landscape and ion-induced population shift of the 5BSL3.2:3′X kissing complex. Furthermore, the predicted ion binding sites offer insights about how ion-RNA interactions shift the conformational equilibrium. The integrated theory-experiment study shows that Mg²⁺ ions may be essential for HCV viral replication. Moreover, the observed Mg²⁺-dependent conformational equilibrium may be an adaptive property of the HCV genomic RNA such that the equilibrium is optimized to the intracellular Mg²⁺ concentration in liver cells for efficient viral replication.

Quantifying the thickness of the electrical double layer neutralizing a planar electrode: the capacitive compactness

The spatial extension of the ionic cloud neutralizing a charged colloid or an electrode is usually characterized by the Debye length associated with the supporting charged fluid in the bulk. This spatial length arises naturally in the linear Poisson-Boltzmann theory of point charges, which is the cornerstone of the widely used Derjaguin-Landau-Verwey-Overbeek formalism describing the colloidal stability of electrified macroparticles. By definition, the Debye length is independent of important physical features of charged solutions such as the colloidal charge, electrostatic ion correlations, ionic excluded volume effects, or specific short-range interactions, just to mention a few. In order to include consistently these features to describe more accurately the thickness of the electrical double layer of an inhomogeneous charged fluid in planar geometry, we propose here the use of the capacitive compactness concept as a generalization of the compactness of the spherical electrical double layer around a small macroion (González-Tovar et al., J. Chem. Phys. 2004, 120, 9782). To exemplify the usefulness of the capacitive compactness to characterize strongly coupled charged fluids in external electric fields, we use integral equations theory and Monte Carlo simulations to analyze the electrical properties of a model molten salt near a planar electrode. In particular, we study the electrode's charge neutralization, and the maximum inversion of the net charge per unit area of the electrode-molten salt system as a function of the ionic concentration, and the electrode's charge. The behaviour of the associated capacitive compactness is interpreted in terms of the charge neutralization capacity of the highly correlated charged fluid, which evidences a shrinking/expansion of the electrical double layer at a microscopic level. The capacitive compactness and its first two derivatives are expressed in terms of experimentally measurable macroscopic properties such as the differential and integral capacity, the electrode's surface charge density, and the mean electrostatic potential at the electrode's surface.

How Water's Properties Are Encoded in Its Molecular Structure and Energies

How are water's material properties encoded within the structure of the water molecule? This is pertinent to understanding Earth's living systems, its materials, its geochemistry and geophysics, and a broad spectrum of its industrial chemistry. Water has distinctive liquid and solid properties: It is highly cohesive. It has volumetric anomalies-water's solid (ice) floats on its liquid; pressure can melt the solid rather than freezing the liquid; heating can shrink the liquid. It has more solid phases than other materials. Its supercooled liquid has divergent thermodynamic response functions. Its glassy state is neither fragile nor strong. Its component ions-hydroxide and protons-diffuse much faster than other ions. Aqueous solvation of ions or oils entails large entropies and heat capacities. We review how these properties are encoded within water's molecular structure and energies, as understood from theories, simulations, and experiments. Like simpler liquids, water molecules are nearly spherical and interact with each other through van der Waals forces. Unlike simpler liquids, water's orientation-dependent hydrogen bonding leads to open tetrahedral cage-like structuring that contributes to its remarkable volumetric and thermal properties.

Counting the ions surrounding nucleic acids

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

MCTBI: a web server for predicting metal ion effects in RNA structures

Metal ions play critical roles in RNA structure and function. However, web servers and software packages for predicting ion effects in RNA structures are notably scarce. Furthermore, the existing web servers and software packages mainly neglect ion correlation and fluctuation effects, which are potentially important for RNAs. We here report a new web server, the MCTBI server (http://rna.physics.missouri.edu/MCTBI), for the prediction of ion effects for RNA structures. This server is based on the recently developed MCTBI, a model that can account for ion correlation and fluctuation effects for nucleic acid structures and can provide improved predictions for the effects of metal ions, especially for multivalent ions such as Mg²⁺ effects, as shown by extensive theory-experiment test results. The MCTBI web server predicts metal ion binding fractions, the most probable bound ion distribution, the electrostatic free energy of the system, and the free energy components. The results provide mechanistic insights into the role of metal ions in RNA structure formation and folding stability, which is important for understanding RNA functions and the rational design of RNA structures.

Theory and Modeling of RNA Structure and Interactions with Metal Ions and Small Molecules

In addition to continuous rapid progress in RNA structure determination, probing, and biophysical studies, the past decade has seen remarkable advances in the development of a new generation of RNA folding theories and models. In this article, we review RNA structure prediction models and models for ion-RNA and ligand-RNA interactions. These new models are becoming increasingly important for a mechanistic understanding of RNA function and quantitative design of RNA nanotechnology. We focus on new methods for physics-based, knowledge-based, and experimental data-directed modeling for RNA structures and explore the new theories for the predictions of metal ion and ligand binding sites and metal ion-dependent RNA stabilities. The integration of these new methods with theories about the cellular environment effects in RNA folding, such as molecular crowding and cotranscriptional kinetic effects, may ultimately lead to an all-encompassing RNA folding model.

Direct Comparison of Amino Acid and Salt Interactions with Double-Stranded and Single-Stranded DNA from Explicit-Solvent Molecular Dynamics Simulations

Given the ubiquitous nature of protein-DNA interactions, it is important to understand the interaction thermodynamics of individual amino acid side chains for DNA. One way to assess these preferences is to perform molecular dynamics (MD) simulations. Here we report MD simulations of 20 amino acid side chain analogs interacting simultaneously with both a 70-base-pair double-stranded DNA and with a 70-nucleotide single-stranded DNA. The relative preferences of the amino acid side chains for dsDNA and ssDNA match well with values deduced from crystallographic analyses of protein-DNA complexes. The estimated apparent free energies of interaction for ssDNA, on the other hand, correlate well with previous simulation values reported for interactions with isolated nucleobases, and with experimental values reported for interactions with guanosine. Comparisons of the interactions with dsDNA and ssDNA indicate that, with the exception of the positively charged side chains, all types of amino acid side chain interact more favorably with ssDNA, with intercalation of aromatic and aliphatic side chains being especially notable. Analysis of the data on a base-by-base basis indicates that positively charged side chains, as well as sodium ions, preferentially bind to cytosine in ssDNA, and that negatively charged side chains, and chloride ions, preferentially bind to guanine in ssDNA. These latter observations provide a novel explanation for the lower salt dependence of DNA duplex stability in GC-rich sequences relative to AT-rich sequences.

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

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

Submolecular Structure and Orientation of Oligonucleotide Duplexes Tethered to Gold Electrodes Probed by Infrared Reflection Absorption Spectroscopy: Effect of the Electrode Potentials

Unique electronic and ligand recognition properties of the DNA double helix provide basis for DNA applications in biomolecular electronic and biosensor devices. However, the relation between the structure of DNA at electrified interfaces and its electronic properties is still not well understood. Here, potential-driven changes in the submolecular structure of DNA double helices composed of either adenine-thymine (dAdT)₂₅ or cytosine-guanine (dGdC)₂₀ base pairs tethered to the gold electrodes are for the first time analyzed by in situ polarization modulation infrared reflection absorption spectroscopy (PM IRRAS) performed under the electrochemical control. It is shown that the conformation of the DNA duplexes tethered to gold electrodes via the C₆ alkanethiol linker strongly depends on the nucleic acid sequence composition. The tilt of purine and pyrimidine rings of the complementary base pairs (dAdT and dGdC) depends on the potential applied to the electrode. By contrast, neither the conformation nor orientation of the ionic in character phosphate-sugar backbone is affected by the electrode potentials. At potentials more positive than the potential of zero charge (pzc), a gradual tilting of the double helix is observed. In this tilted orientation, the planes of the complementary purine and pyrimidine rings lie ideally parallel to each other. These potentials do not affect the integral stability of the DNA double helix at the charged interface. At potentials more negative than the pzc, DNA helices adopt a vertical to the gold surface orientation. Tilt of the purine and pyrimidine rings depends on the composition of the double helix. In monolayers composed of (dAdT)₂₅ molecules the rings of the complementary base pairs lie parallel to each other. By contrast, the tilt of purine and pyrimidine rings in (dGdC)₂₀ helices depends on the potential applied to the electrode. Such potential-induced mobility of the complementary base pairs can destabilize the helix structure at a submolecular level. These pioneer results on the potential-driven changes in the submolecular structure of double stranded DNA adsorbed on conductive supports contribute to further understanding of the potential-driven sequence-specific electronic properties of surface-tethered oligonucleotides.

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

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

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

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