Simulations of RNA interactions with monovalent ions

Biomolecular condensates are characterized by interphase electric potentials

Biomolecular condensates form via processes that combine phase separation and reversible associations of multivalent macromolecules. Condensates can be two- or multi-phase systems defined by coexisting dense and dilute phases. Here, we show that solution ions can partition asymmetrically across coexisting phases defined by condensates formed by intrinsically disordered proteins or homopolymeric RNA molecules. Our findings were enabled by direct measurements of the activities of cations and anions within coexisting phases of protein and RNA condensates. Asymmetries in ion partitioning between coexisting phases vary with protein sequence, condensate type, salt concentration, and ion type. The Donnan equilibrium set up by asymmetrical partitioning of solution ions generates interphase electric potentials known as Donnan and Nernst potentials. Our measurements show that the interphase potentials of condensates are of the same order of magnitude as membrane potentials of membrane-bound organelles. Interphase potentials quantify the degree to which microenvironments of coexisting phases are different from one another. Importantly, and based on condensate-specific interphase electric potentials, which are membrane-like potentials of membraneless bodies, we reason that condensates are mesoscale capacitors that store charge. Interphase potentials lead to electric double layers at condensate interfaces. This helps explain recent observations of condensate interfaces being electrochemically active.

Solutes unmask differences in clustering versus phase separation of FET proteins

Phase separation and percolation contribute to phase transitions of multivalent macromolecules. Contributions of percolation are evident through the viscoelasticity of condensates and through the formation of heterogeneous distributions of nano- and mesoscale pre-percolation clusters in sub-saturated solutions. Here, we show that clusters formed in sub-saturated solutions of FET (FUS-EWSR1-TAF15) proteins are affected differently by glutamate versus chloride. These differences on the nanoscale, gleaned using a suite of methods deployed across a wide range of protein concentrations, are prevalent and can be unmasked even though the driving forces for phase separation remain unchanged in glutamate versus chloride. Strikingly, differences in anion-mediated interactions that drive clustering saturate on the micron-scale. Beyond this length scale the system separates into coexisting phases. Overall, we find that sequence-encoded interactions, mediated by solution components, make synergistic and distinct contributions to the formation of pre-percolation clusters in sub-saturated solutions, and to the driving forces for phase separation.

Sensitivity of the RNA Structure to Ion Conditions as Probed by Molecular Dynamics Simulations of Common Canonical RNA Duplexes

RNA molecules play a key role in countless biochemical processes. RNA interactions, which are of highly diverse nature, are determined by the fact that RNA is a highly negatively charged polyelectrolyte, which leads to intimate interactions with an ion atmosphere. Although RNA molecules are formally single-stranded, canonical (Watson-Crick) duplexes are key components of folded RNAs. A double-stranded (ds) RNA is also important for the design of RNA-based nanostructures and assemblies. Despite the fact that the description of canonical dsRNA is considered the least problematic part of RNA modeling, the imperfect shape and flexibility of dsRNA can lead to imbalances in the simulations of larger RNAs and RNA-containing assemblies. We present a comprehensive set of molecular dynamics (MD) simulations of four canonical A-RNA duplexes. Our focus was directed toward the characterization of the influence of varying ion concentrations and of the size of the solvation box. We compared several water models and four RNA force fields. The simulations showed that the A-RNA shape was most sensitive to the RNA force field, with some force fields leading to a reduced inclination of the A-RNA duplexes. The ions and water models played a minor role. The effect of the box size was negligible, and even boxes with a small fraction of the bulk solvent outside the RNA hydration sphere were sufficient for the simulation of the dsRNA.

Thermodynamics and kinetics of an A-U RNA base pair under force studied by molecular dynamics simulations

Mechanical force has been widely used to study RNA folding and unfolding. Understanding how the force affects the opening and closing of a single base pair, which is a basic step for RNA folding and unfolding and a fundamental behavior in some important biological activities, is crucial to understanding the mechanism of RNA folding and unfolding under mechanical force. In this work, we investigated the opening and closing process of an RNA base pair under mechanical force with constant-force stretching molecular dynamics simulations. It was found that high mechanical force results in overstretching, and the open state is a high-energy state. The enthalpy and entropy change of the base-pair opening-closing transition were obtained and the results at low forces were in good agreement with the nearest-neighbor model. The temperature and force dependence of the opening and closing rates were also obtained. The position of the transition state for the base-pair opening-closing transition under mechanical force was determined. The free energy barrier of opening a base pair without force is the enthalpy increase, and the work done by the force from the closed state to the transition state decreases the barrier and increases the opening rate. The free energy barrier of closing the base pair without force results from the entropy loss, and the work done by the force from the open state to the transition state increases the barrier and decreases the closing rate. The transition rates are strongly dependent on the temperature and force, while the transition path times are weakly dependent on force and temperature.

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.

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

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

The mutual interactions of RNA, counterions and water - quantifying the electrostatics at the phosphate-water interface

The structure and dynamics of polyanionic biomolecules, like RNA, are decisively determined by their electric interactions with the water molecules and the counterions in the environment. The solvation dynamics of the biomolecules involves a subtle balance of non-covalent and many-body interactions with structural fluctuations due to thermal motion occurring in a femto- to subnanosecond time range. This complex fluctuating many particle scenario is crucial in defining the properties of biological interfaces with far reaching significance for the folding of RNA structures and for facilitating RNA-protein interactions. Given the inherent complexity, suited model systems, carefully calibrated and benchmarked by experiments, are required to quantify the relevant interactions of RNA with the aqueous environment. In this feature article we summarize our recent progress in the understanding of the electrostatics at the biological interface of double stranded RNA (dsRNA) and transfer RNA (tRNA). Dimethyl phosphate (DMP) is introduced as a viable and rigorously accessible model system allowing the interaction strength with water molecules and counterions, their relevant fluctuation timescales and the spatial reach of interactions to be established. We find strong (up to ≈90 MV cm-1) interfacial electric fields with fluctuations extending up to ≈20 THz and demonstrate how the asymmetric stretching vibration νAS(PO2)- of the polarizable phosphate group can serve as the most sensitive probe for interfacial interactions, establishing a rigorous link between simulations and experiment. The approach allows for the direct interfacial observation of interactions of biologically relevant Mg2+ counterions with phosphate groups in contact pair geometries via the rise of a new absorption band imposed by exchange repulsion interactions at short interatomic distances. The systematic extension to RNA provides microscopic insights into the changes of the hydration structure that accompany the temperature induced melting of the dsRNA double helix and quantify the ionic interactions in the folded tRNA. The results show that pairs of negatively charged phosphate groups and Mg2+ ions represent a key structural feature of RNA embedded in water. They highlight the importance of binding motifs made of contact pairs in the electrostatic stabilization of RNA structures that have a strong impact on the surface potential and enable the fine tuning of the local electrostatic properties which are expected to be relevant for mediating the interactions between biomolecules.

The Time Scale of Electronic Resonance in Oxidized DNA as Modulated by Solvent Response: An MD/QM-MM Study

The time needed to establish electronic resonant conditions for charge transfer in oxidized DNA has been evaluated by molecular dynamics simulations followed by QM/MM computations which include counterions and a realistic solvation shell. The solvent response is predicted to take ca. 800-1000 ps to bring two guanine sites into resonance, a range of values in reasonable agreement with the estimate previously obtained by a kinetic model able to correctly reproduce the observed yield ratios of oxidative damage for several sequences of oxidized 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.

Ion counting demonstrates a high electrostatic field generated by the nucleosome

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

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.

The nearest neighbor and next nearest neighbor effects on the thermodynamic and kinetic properties of RNA base pair

The thermodynamic and kinetic parameters of an RNA base pair with different nearest and next nearest neighbors were obtained through long-time molecular dynamics simulation of the opening-closing switch process of the base pair near its melting temperature. The results indicate that thermodynamic parameters of GC base pair are dependent on the nearest neighbor base pair, and the next nearest neighbor base pair has little effect, which validated the nearest-neighbor model. The closing and opening rates of the GC base pair also showed nearest neighbor dependences. At certain temperature, the closing and opening rates of the GC pair with nearest neighbor AU is larger than that with the nearest neighbor GC, and the next nearest neighbor plays little role. The free energy landscape of the GC base pair with the nearest neighbor GC is rougher than that with nearest neighbor AU.

Predicting Ion Effects in an RNA Conformational Equilibrium

We develop a partial charge-based tightly bound ion (PCTBI) model for the ion effects in RNA folding. On the basis of the Monte Carlo tightly bound ion (MCTBI) approach, the model can account for ion fluctuation and correlation effects, and can predict the ion distribution around the RNA. Furthermore, unlike the previous coarse-grained RNA charge models, where negative charges are placed on the phosphates only, the current new model considers the detailed all-atom partial charge distribution on the RNA. Thus, the model not only keeps the advantage of the MCTBI model, but also has the potential to provide important detailed information unattainable by the previous MCTBI models. For example, the model predicts the reduction in ion binding upon protein binding and ion-induced conformational switches. For hepatitis C virus genomic RNA, the model predicts a Mg²⁺-induced stabilization of a kissing motif for a cis-acting regulatory element in the genomic RNA. Extensive theory-experiment comparisons support the reliability of the theoretical predictions. Therefore, the model may serve as a robust starting point for further development of an accurate method for ion effects in an RNA conformational equilibrium and RNA-cofactor interactions.

Understanding the mechanical response of double-stranded DNA and RNA under constant stretching forces using all-atom molecular dynamics

Multiple biological processes involve the stretching of nucleic acids (NAs). Stretching forces induce local changes in the molecule structure, inhibiting or promoting the binding of proteins, which ultimately affects their functionality. Understanding how a force induces changes in the structure of NAs at the atomic level is a challenge. Here, we use all-atom, microsecond-long molecular dynamics to simulate the structure of dsDNA and dsRNA subjected to stretching forces up to 20 pN. We determine all of the elastic constants of dsDNA and dsRNA and provide an explanation for three striking differences in the mechanical response of these two molecules: the threefold softer stretching constant obtained for dsRNA, the opposite twist-stretch coupling, and its nontrivial force dependence. The lower dsRNA stretching resistance is linked to its more open structure, whereas the opposite twist-stretch coupling of both molecules is due to the very different evolution of molecules' interstrand distance with the stretching force. A reduction of this distance leads to overwinding in dsDNA. In contrast, dsRNA is not able to reduce its interstrand distance and can only elongate by unwinding. Interstrand distance is directly correlated with the slide base-pair parameter and its different behavior in dsDNA and dsRNA traced down to changes in the sugar pucker angle of these NAs.

The thermodynamics and kinetics of a nucleotide base pair

The thermodynamic and kinetic parameters of an RNA base pair were obtained through a long-time molecular dynamics simulation of the opening-closing switch process of the base pair near its melting temperature. The thermodynamic parameters were in good agreement with the nearest-neighbor model. The opening rates showed strong temperature dependence, however, the closing rates showed only weak temperature dependence. The transition path time was weakly temperature dependent and was insensitive to the energy barrier. The diffusion constant exhibited super-Arrhenius behavior. The free energy barrier of breaking a single base stack results from the enthalpy increase, ΔH, caused by the disruption of hydrogen bonding and base-stacking interactions. The free energy barrier of base pair closing comes from the unfavorable entropy loss, ΔS, caused by the restriction of torsional angles. These results suggest that a one-dimensional free energy surface is sufficient to accurately describe the dynamics of base pair opening and closing, and the dynamics are Brownian.

Monte Carlo Tightly Bound Ion Model: Predicting Ion-Binding Properties of RNA with Ion Correlations and Fluctuations

Experiments have suggested that ion correlation and fluctuation effects can be potentially important for multivalent ions in RNA folding. However, most existing computational methods for the ion electrostatics in RNA folding tend to ignore these effects. The previously reported tightly bound ion (TBI) model can treat ion correlation and fluctuation but its applicability to biologically important RNAs is severely limited by the low computational efficiency. Here, on the basis of Monte Carlo sampling for the many-body ion distribution, we develop a new computational model, the Monte Carlo tightly bound ion (MCTBI) model, for ion-binding properties around an RNA. Because of an enhanced sampling algorithm for ion distribution, the model leads to a significant improvement in computational efficiency. For example, for a 160-nt RNA, the model causes a more than 10-fold increase in the computational efficiency, and the improvement in computational efficiency is more pronounced for larger systems. Furthermore, unlike the earlier model that describes ion distribution using the number of bound ions around each nucleotide, the current MCTBI model is based on the three-dimensional coordinates of the ions. The higher efficiency of the model allows us to treat the ion effects for medium to large RNA molecules, RNA-ligand complexes, and RNA-protein complexes. This new model together with proper RNA conformational sampling and the energetics model may serve as a starting point for further development for the ion effects in RNA folding and conformational changes and for large nucleic acid systems.

Continuum Electrostatics Approaches to Calculating pKas and Ems in Proteins

Proteins change their charge state through protonation and redox reactions as well as through binding charged ligands. The free energy of these reactions is dominated by solvation and electrostatic energies and modulated by protein conformational relaxation in response to the ionization state changes. Although computational methods for calculating these interactions can provide very powerful tools for predicting protein charge states, they include several critical approximations of which users should be aware. This chapter discusses the strengths, weaknesses, and approximations of popular computational methods for predicting charge states and understanding the underlying electrostatic interactions. The goal of this chapter is to inform users about applications and potential caveats of these methods as well as outline directions for future theoretical and computational research.

Sodium and Potassium Interactions with Nucleic Acids

Metal ions are essential cofactors for the structure and functions of nucleic acids. Yet, the early discovery in the 70s of the crucial role of Mg(2+) in stabilizing tRNA structures has occulted for a long time the importance of monovalent cations. Renewed interest in these ions was brought in the late 90s by the discovery of specific potassium metal ions in the core of a group I intron. Their importance in nucleic acid folding and catalytic activity is now well established. However, detection of K(+) and Na(+) ions is notoriously problematic and the question about their specificity is recurrent. Here we review the different methods that can be used to detect K(+) and Na(+) ions in nucleic acid structures such as X-ray crystallography, nuclear magnetic resonance or molecular dynamics simulations. We also discuss specific versus non-specific binding to different structures through various examples.

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

The composition of the ion atmosphere surrounding nucleic acids affects their folding, condensation and binding to other molecules. It is thus of fundamental importance to gain predictive insight into the formation of the ion atmosphere and thermodynamic consequences when varying ionic conditions. An early step toward this goal is to benchmark computational models against quantitative experimental measurements. Herein, we test the ability of the three dimensional reference interaction site model (3D-RISM) to reproduce preferential interaction parameters determined from ion counting (IC) experiments for mixed alkali chlorides and dsDNA. Calculations agree well with experiment with slight deviations for salt concentrations >200 mM and capture the observed trend where the extent of cation accumulation around the DNA varies inversely with its ionic size. Ion distributions indicate that the smaller, more competitive cations accumulate to a greater extent near the phosphoryl groups, penetrating deeper into the grooves. In accord with experiment, calculated IC profiles do not vary with sequence, although the predicted ion distributions in the grooves are sequence and ion size dependent. Calculations on other nucleic acid conformations predict that the variation in linear charge density has a minor effect on the extent of cation competition.

Using Molecular Simulation to Model High-Resolution Cryo-EM Reconstructions

An explosion of new data from high-resolution cryo-electron microscopy (cryo-EM) studies has produced a large number of data sets for many species of ribosomes in various functional states over the past few years. While many methods exist to produce structural models for lower resolution cryo-EM reconstructions, high-resolution reconstructions are often modeled using crystallographic techniques and extensive manual intervention. Here, we present an automated fitting technique for high-resolution cryo-EM data sets that produces all-atom models highly consistent with the EM density. Using a molecular dynamics approach, atomic positions are optimized with a potential that includes the cross-correlation coefficient between the structural model and the cryo-EM electron density, as well as a biasing potential preserving the stereochemistry and secondary structure of the biomolecule. Specifically, we use a hybrid structure-based/ab initio molecular dynamics potential to extend molecular dynamics fitting. In addition, we find that simulated annealing integration, as opposed to straightforward molecular dynamics integration, significantly improves performance. We obtain atomistic models of the human ribosome consistent with high-resolution cryo-EM reconstructions of the human ribosome. Automated methods such as these have the potential to produce atomistic models for a large number of ribosome complexes simultaneously that can be subsequently refined manually.

TBI server: a web server for predicting ion effects in RNA folding

Background

Metal ions play a critical role in the stabilization of RNA structures. Therefore, accurate prediction of the ion effects in RNA folding can have a far-reaching impact on our understanding of RNA structure and function. Multivalent ions, especially Mg²⁺, are essential for RNA tertiary structure formation. These ions can possibly become strongly correlated in the close vicinity of RNA surface. Most of the currently available software packages, which have widespread success in predicting ion effects in biomolecular systems, however, do not explicitly account for the ion correlation effect. Therefore, it is important to develop a software package/web server for the prediction of ion electrostatics in RNA folding by including ion correlation effects.

Results

The TBI web server http://rna.physics.missouri.edu/tbi_index.html provides predictions for the total electrostatic free energy, the different free energy components, and the mean number and the most probable distributions of the bound ions. A novel feature of the TBI server is its ability to account for ion correlation and ion distribution fluctuation effects.

Conclusions

By accounting for the ion correlation and fluctuation effects, the TBI server is a unique online tool for computing ion-mediated electrostatic properties for given RNA structures. The results can provide important data for in-depth analysis for ion effects in RNA folding including the ion-dependence of folding stability, ion uptake in the folding process, and the interplay between the different energetic components.

Multiscale methods for computational RNA enzymology

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

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

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

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.

Dynamics of riboswitches: Molecular simulations

Riboswitch RNAs play key roles in bacterial metabolism and represent a promising new class of antibiotic targets for treatment of infectious disease. While many studies of riboswitches have been performed, the exact mechanism of riboswitch operation is still not fully understood at the atomistic level of detail. Molecular dynamics simulations are useful for interpreting existing experimental data and producing predictions for new experiments. Here, a wide range of computational studies on riboswitches is reviewed. By elucidating the key principles of riboswitch operation, computation may aid in the effort to design more specific antibiotics with affinities greater than those of the native ligand. Such a detailed understanding may be required to improve efficacy and reduce side effects. These studies are laying the groundwork for understanding the action mechanism of new compounds that inhibit riboswitch activity. Future directions such as magnesium effects, large-scale conformational changes, expression platforms and co-transcriptional folding are also discussed. This article is part of a Special Issue entitled: Riboswitches.

Reduced model captures Mg(2+)-RNA interaction free energy of riboswitches

The stability of RNA tertiary structures depends heavily on Mg(2+). The Mg(2+)-RNA interaction free energy that stabilizes an RNA structure can be computed experimentally through fluorescence-based assays that measure Γ2+, the number of excess Mg(2+) associated with an RNA molecule. Previous explicit-solvent simulations predict that the majority of excess Mg(2+) ions interact closely and strongly with the RNA, unlike monovalent ions such as K(+), suggesting that an explicit treatment of Mg(2+) is important for capturing RNA dynamics. Here we present a reduced model that accurately reproduces the thermodynamics of Mg(2+)-RNA interactions. This model is able to characterize long-timescale RNA dynamics coupled to Mg(2+) through the explicit representation of Mg(2+) ions. KCl is described by Debye-Hückel screening and a Manning condensation parameter, which represents condensed K(+) and models its competition with condensed Mg(2+). The model contains one fitted parameter, the number of condensed K(+) ions in the absence of Mg(2+). Values of Γ2+ computed from molecular dynamics simulations using the model show excellent agreement with both experimental data on the adenine riboswitch and previous explicit-solvent simulations of the SAM-I riboswitch. This agreement confirms the thermodynamic accuracy of the model via the direct relation of Γ2+ to the Mg(2+)-RNA interaction free energy, and provides further support for the predictions from explicit-solvent calculations. This reduced model will be useful for future studies of the interplay between Mg(2+) and RNA dynamics.

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.

Ion counting from explicit-solvent simulations and 3D-RISM

The ionic atmosphere around nucleic acids remains only partially understood at atomic-level detail. Ion counting (IC) experiments provide a quantitative measure of the ionic atmosphere around nucleic acids and, as such, are a natural route for testing quantitative theoretical approaches. In this article, we replicate IC experiments involving duplex DNA in NaCl(aq) using molecular dynamics (MD) simulation, the three-dimensional reference interaction site model (3D-RISM), and nonlinear Poisson-Boltzmann (NLPB) calculations and test against recent buffer-equilibration atomic emission spectroscopy measurements. Further, we outline the statistical mechanical basis for interpreting IC experiments and clarify the use of specific concentration scales. Near physiological concentrations, MD simulation and 3D-RISM estimates are close to experimental results, but at higher concentrations (>0.7 M), both methods underestimate the number of condensed cations and overestimate the number of excluded anions. The effect of DNA charge on ion and water atmosphere extends 20-25 Å from its surface, yielding layered density profiles. Overall, ion distributions from 3D-RISMs are relatively close to those from corresponding MD simulations, but with less Na(+) binding in grooves and tighter binding to phosphates. NLPB calculations, on the other hand, systematically underestimate the number of condensed cations at almost all concentrations and yield nearly structureless ion distributions that are qualitatively distinct from those generated by both MD simulation and 3D-RISM. These results suggest that MD simulation and 3D-RISM may be further developed to provide quantitative insight into the characterization of the ion atmosphere around nucleic acids and their effect on structure and stability.

Exploring the electrostatic energy landscape for tetraloop-receptor docking

It has long been appreciated that Mg(2+) is essential for the stabilization of RNA tertiary structure. However, the problem of quantitative prediction for the ion effect in tertiary structure folding remains. By using the virtual bond RNA folding model (Vfold) to generate RNA conformations and the newly improved tightly bound ion model (TBI) to treat ion-RNA interactions, we investigate Mg(2+)-facilitated tetraloop-receptor docking. For the specific construct of the tetraloop-receptor system, the theoretical analysis shows that the Mg(2+)-induced stabilizing force for the docked state is predominantly entropic and the major contribution comes from the entropy of the diffusive ions. Furthermore, our results show that Mg(2+) ions promote tetraloop-receptor docking mainly through the entropy of the diffusive ions. The theoretical prediction agrees with experimental analysis. The method developed in this paper, which combines the theory for the (Mg(2+)) ion effects in RNA folding and RNA conformational sampling, may provide a useful framework for studying the ion effect in the folding of more complex RNA structures.

Conformations of intrinsically disordered proteins are influenced by linear sequence distributions of oppositely charged residues

The functions of intrinsically disordered proteins (IDPs) are governed by relationships between information encoded in their amino acid sequences and the ensembles of conformations that they sample as autonomous units. Most IDPs are polyampholytes, with sequences that include both positively and negatively charged residues. Accordingly, we focus here on the sequence-ensemble relationships of polyampholytic IDPs. The fraction of charged residues discriminates between weak and strong polyampholytes. Using atomistic simulations, we show that weak polyampholytes form globules, whereas the conformational preferences of strong polyampholytes are determined by a combination of fraction of charged residues values and the linear sequence distributions of oppositely charged residues. We quantify the latter using a patterning parameter κ that lies between zero and one. The value of κ is low for well-mixed sequences, and in these sequences, intrachain electrostatic repulsions and attractions are counterbalanced, leading to the unmasking of preferences for conformations that resemble either self-avoiding random walks or generic Flory random coils. Segregation of oppositely charged residues within linear sequences leads to high κ-values and preferences for hairpin-like conformations caused by long-range electrostatic attractions induced by conformational fluctuations. We propose a scaling theory to explain the sequence-encoded conformational properties of strong polyampholytes. We show that naturally occurring strong polyampholytes have low κ-values, and this feature implies a selection for random coil ensembles. The design of sequences with different κ-values demonstrably alters the conformational preferences of polyampholytic IDPs, and this ability could become a useful tool for enabling direct inquiries into connections between sequence-ensemble relationships and functions of IDPs.

RNA/Peptide Binding Driven by Electrostatics-Insight from Bidirectional Pulling Simulations

RNA/protein interactions play crucial roles in controlling gene expression. They are becoming important targets for pharmaceutical applications. Due to RNA flexibility and to the strength of electrostatic interactions, standard docking methods are insufficient. We here present a computational method which allows studying the binding of RNA molecules and charged peptides with atomistic, explicit-solvent molecular dynamics. In our method, a suitable estimate of the electrostatic interaction is used as an order parameter (collective variable) which is then accelerated using bidirectional pulling simulations. Since the electrostatic interaction is only used to enhance the sampling, the approximations used to compute it do not affect the final accuracy. The method is employed to characterize the binding of TAR RNA from HIV-1 and a small cyclic peptide. Our simulation protocol allows blindly predicting the binding pocket and pose as well as the binding affinity. The method is general and could be applied to study other electrostatics-driven binding events.

Ion-mediated RNA structural collapse: effect of spatial confinement

RNAs are negatively charged molecules that reside in cellular environments with macromolecular crowding. Macromolecular confinement can influence the ion effects in RNA folding. In this work, using the recently developed tightly bound ion model for ion fluctuation and correlation, we investigate the effect of confinement on ion-mediated RNA structural collapse for a simple model system. We find that for both Na(+) and Mg(2+), the ion efficiencies in mediating structural collapse/folding are significantly enhanced by the structural confinement. This enhancement of ion efficiency is attributed to the decreased electrostatic free-energy difference between the compact conformation ensemble and the (restricted) extended conformation ensemble due to the spatial restriction.

Predicting ion-nucleic acid interactions by energy landscape-guided sampling

The recently developed Tightly Bound Ion (TBI) model offers improved predictions for ion effect in nucleic acid systems by accounting for ion correlation and fluctuation effects. However, further application of the model to larger systems is limited by the low computational efficiency of the model. Here, we develop a new computational efficient TBI model using free energy landscape-guided sampling method. The method leads to drastic reduction in the computer time by a factor of 50 for RNAs of 50-100 nucleotides long. The improvement in the computational efficiency would be more significant for larger structures. To test the new method, we apply the model to predict the free energies and the number of bound ions for a series of RNA folding systems. The validity of this new model is supported by the nearly exact agreement with the results from the original TBI model and the agreement with the experimental data. The method may pave the way for further applications of the TBI model to treat a broad range of biologically significant systems such as tetraloop-receptor and riboswitches.

Magnesium Ion-Water Coordination and Exchange in Biomolecular Simulations

Magnesium ions have an important role in the structure and folding mechanism of ribonucleic acid systems. To properly simulate these biophysical processes, the applied molecular models should reproduce, among other things, the kinetic properties of the ions in water solution. Here, we have studied the kinetics of the binding of magnesium ions with water molecules and nucleic acid systems using molecular dynamics simulation in detail. We have validated the parameters used in biomolecular force fields, such as AMBER and CHARMM, for Mg(2+) ions and also for the biologically relevant ions Na(+), K(+), and Ca(2+) together with three different water models (TIP3P, SPC/E, and TIP5P). The results show that Mg(2+) ions have a slower exchange rate than Na(+), K(+), and Ca(2+) in agreement with the experimental trend, but the simulated value underestimates the experimentally observed Mg(2+)-water exchange rate by several orders of magnitude, irrespective of the force field and water model. A new set of parameters for Mg(2+) was developed to reproduce the experimental kinetic data. This set also leads to better reproduction of structural data than existing models. We have applied the new parameter set to Mg(2+) binding with a monophosphate model system and with the purine riboswitch, add A-riboswitch. In line with the Mg(2+)-water results, the newly developed parameters show a better description of the structure and kinetics of the Mg(2+)-phosphate binding than all other models. The characterization of the ion binding to the riboswitch system shows that the new parameter set does not affect the global structure of the ribonucleic acid system or the number of ions involved in direct or indirect binding. A slight decrease in the number of water-bridged contacts between A-riboswitch and the Mg(2+) ion is observed. The results support the ability of the newly developed parameters to improve the kinetic description of the Mg(2+) and phosphate ions and their applicability in nucleic acid simulation.

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.

The ionic atmosphere around A-RNA: Poisson-Boltzmann and molecular dynamics simulations

The distributions of different cations around A-RNA are computed by Poisson-Boltzmann (PB) equation and replica exchange molecular dynamics (MD). Both the nonlinear PB and size-modified PB theories are considered. The number of ions bound to A-RNA, which can be measured experimentally, is well reproduced in all methods. On the other hand, the radial ion distribution profiles show differences between MD and PB. We showed that PB results are sensitive to ion size and functional form of the solvent dielectric region but not the solvent dielectric boundary definition. Size-modified PB agrees with replica exchange molecular dynamics much better than nonlinear PB when the ion sizes are chosen from atomistic simulations. The distribution of ions 14 Å away from the RNA central axis are reasonably well reproduced by size-modified PB for all ion types with a uniform solvent dielectric model and a sharp dielectric boundary between solvent and RNA. However, this model does not agree with MD for shorter distances from the A-RNA. A distance-dependent solvent dielectric function proposed by another research group improves the agreement for sodium and strontium ions, even for shorter distances from the A-RNA. However, Mg(2+) distributions are still at significant variances for shorter distances.

Interactions of cations with RNA loop-loop complexes

RNA loop-loop interactions are essential in many biological processes, including initiation of RNA folding into complex tertiary shapes, promotion of dimerization, and viral replication. In this article, we examine interactions of metal ions with five RNA loop-loop complexes of unique biological significance using explicit-solvent molecular-dynamics simulations. These simulations revealed the presence of solvent-accessible tunnels through the major groove of loop-loop interactions that attract and retain cations. Ion dynamics inside these loop-loop complexes were distinctly different from the dynamics of the counterion cloud surrounding RNA and depend on the number of basepairs between loops, purine sequence symmetry, and presence of unpaired nucleotides. The cationic uptake by kissing loops depends on the number of basepairs between loops. It is interesting that loop-loop complexes with similar functionality showed similarities in cation dynamics despite differences in sequence and loop size.

Quantitative analysis of the ion-dependent folding stability of DNA triplexes

A DNA triplex is formed through binding of a third strand to the major groove of a duplex. Due to the high charge density of a DNA triplex, metal ions are critical for its stability. We recently developed the tightly bound ion (TBI) model for ion-nucleic acids interactions. The model accounts for the potential correlation and fluctuations of the ion distribution. We now apply the TBI model to analyze the ion dependence of the thermodynamic stability for DNA triplexes. We focus on two experimentally studied systems: a 24-base DNA triplex and a pair of interacting 14-base triplexes. Our theoretical calculations for the number of bound ions indicate that the TBI model provides improved predictions for the number of bound ions than the classical Poisson-Boltzmann (PB) equation. The improvement is more significant for a triplex, which has a higher charge density than a duplex. This is possibly due to the higher ion concentration around the triplex and hence a stronger ion correlation effect for a triplex. In addition, our analysis for the free energy landscape for a pair of 14-mer triplexes immersed in an ionic solution shows that divalent ions could induce an attractive force between the triplexes. Furthermore, we investigate how the protonated cytosines in the triplexes affect the stability of the triplex helices.

Salt contribution to RNA tertiary structure folding stability

Accurate quantification of the ionic contribution to RNA folding stability could greatly enhance our ability to understand and predict RNA functions. Recently, motivated by the potential importance of ion correlation and fluctuation in RNA folding, we developed the tightly bound ion (TBI) model. Extensive experimental tests showed that the TBI model can lead to better treatment of multivalent ions than the Poisson-Boltzmann equation. In this study, we use the model to quantify the contribution of salt (Na(+) and Mg(2+)) to the RNA tertiary structure folding free energy. Folding of the RNA tertiary structure often involves intermediates. We focus on the folding transition from an intermediate state to the native state, and compute the electrostatic folding free energy of the RNA. Based on systematic calculations for a variety of RNA molecules, we derive a set of formulas for the electrostatic free energy for tertiary structural folding as a function of the sequence length and compactness of the RNA and the Na(+) and Mg(2+) concentrations. Extensive comparisons with experimental data suggest that our model and the extracted empirical formulas are quite reliable.

Functional role of ribosomal signatures

Although structure and sequence signatures in ribosomal RNA and proteins are defining characteristics of the three domains of life and instrumental in constructing the modern phylogeny, little is known about their functional roles in the ribosome. In this work, the largest coevolving RNA/protein signatures in the bacterial 30S ribosome are investigated both experimentally and computationally through all-atom molecular-dynamics simulations. The complex includes the N-terminal fragment of the ribosomal protein S4, which is a primary binding protein that initiates 30S small subunit assembly from the 5' domain, and helix 16 (h16), which is part of the five-way junction in 16S rRNA. Our results show that the S4 N-terminus signature is intrinsically disordered in solution, whereas h16 is relatively stable by itself. The dynamic disordered property of the protein is exploited to couple the folding and binding process to the five-way junction, and the results provide insight into the mechanism for the early and fast binding of S4 in the assembly of the ribosomal small subunit.

Predicting ion binding properties for RNA tertiary structures

Recent experiments pointed to the potential importance of ion correlation for multivalent ions such as Mg(2+) ions in RNA folding. In this study, we develop an all-atom model to predict the ion electrostatics in RNA folding. The model can treat ion correlation effects explicitly by considering an ensemble of discrete ion distributions. In contrast to the previous coarse-grained models that can treat ion correlation, this new model is based on all-atom nucleic acid structures. Thus, unlike the previous coarse-grained models, this new model allows us to treat complex tertiary structures such as HIV-1 DIS type RNA kissing complexes. Theory-experiment comparisons for a variety of tertiary structures indicate that the model gives improved predictions over the Poisson-Boltzmann theory, which underestimates the Mg(2+) binding in the competition with Na(+). Further systematic theory-experiment comparisons for a series of tertiary structures lead to a set of analytical formulas for Mg(2+)/Na(+) ion-binding to various RNA and DNA structures over a wide range of Mg(2+) and Na(+) concentrations.