Measurement of the effect of monovalent cations on RNA hairpin stability

Markedly Different Effects of Monovalent Cations on the Efficiency of Gene Expression

The effect of monovalent cations on a cell-free transcription-translation (TX-TL) system is examined using a luciferase assay. It is found that the potency for all ions analyzed here is in the order Rb⁺  > K⁺  > Cs⁺  > Na⁺  ≈ Li⁺  > (CH₃ )₄ N⁺ , where Rb⁺ is most efficient at promoting TX-TL and the ions of Li⁺ , Na⁺ , and (CH₃ )₄ N⁺ exhibit an inhibitory effect. Similar promotion/inhibition effects are observed for cell-free TL alone with an mRNA template.

Thermodynamic determination of RNA duplex stability in magnesium solutions

The prediction of RNA secondary structure and thermodynamics from sequence relies on free energy minimization and nearest neighbor parameters. Currently, algorithms used to make these predictions are based on parameters from optical melting studies performed in 1 M NaCl. However, many physiological and biochemical buffers containing RNA include much lower concentrations of monovalent cations and the presence of divalent cations. In order to improve these algorithms, thermodynamic data was previously collected for RNA duplexes in solutions containing 71, 121, 221, and 621 mM Na+. From this data, correction factors for free energy (ΔG°37) and melting temperature (Tm) were derived. Despite these newly derived correction factors for sodium, the stabilizing effects of magnesium have been ignored. Here, the same RNA duplexes were melted in solutions containing 0.5, 1.5, 3.0, and 10.0 mM Mg2+ in the absence of monovalent cations. Correction factors for Tm and ΔG°37 were derived to scale the current parameters to a range of magnesium concentrations. The Tm correction factor predicts the melting temperature within 1.2°C, and the ΔG°37 correction factor predicts the free energy within 0.30 kcalmol. These newly derived magnesium correction factors can be incorporated into algorithms that predict RNA secondary structure and stability from sequence.

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

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

Differences in ion-RNA binding modes due to charge density variations explain the stability of RNA in monovalent salts

The stability of RNA increases as the charge density of the alkali metal cations increases. The molecular mechanism for this phenomenon remains elusive. To fill this gap, we performed all-atom molecular dynamics pulling simulations of HIV-1 trans-activation response RNA. We first established that the free energy landscape obtained in the simulations is in excellent agreement with the single-molecule optical tweezer experiments. The origin of the stronger stability in sodium compared to potassium is found to be due to the differences in the charge density-related binding modes. The smaller hydrated sodium ion preferentially binds to the highly charged phosphates that have high surface area. In contrast, the larger potassium ions interact with the major grooves. As a result, more cations condense around phosphate groups in the case of sodium ions, leading to the reduction of electrostatic repulsion. Because the proposed mechanism is generic, we predict that the same conclusions are valid for divalent alkaline earth metal cations.

Twisting DNA by salt

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

Na+ and K+ Ions Differently Affect Nucleosome Structure, Stability, and Interactions with Proteins

Inorganic ions are essential factors stabilizing nucleosome structure; however, many aspects of their effects on DNA transactions in chromatin remain unknown. Here, differential effects of K+ and Na+ on the nucleosome structure, stability, and interactions with protein complex FACT (FAcilitates Chromatin Transcription), poly(ADP-ribose) polymerase 1, and RNA polymerase II were studied using primarily single-particle Förster resonance energy transfer microscopy. The maximal stabilizing effect of K+ on a nucleosome structure was observed at ca. 80–150 mM, and it decreased slightly at 40 mM and considerably at >300 mM. The stabilizing effect of Na+ is noticeably lower than that of K+ and progressively decreases at ion concentrations higher than 40 mM. At 150 mM, Na+ ions support more efficient reorganization of nucleosome structure by poly(ADP-ribose) polymerase 1 and ATP-independent uncoiling of nucleosomal DNA by FACT as compared with K+ ions. In contrast, transcription through a nucleosome is nearly insensitive to K+ or Na+ environment. Taken together, the data indicate that K+ environment is more preserving for chromatin structure during various nucleosome transactions than Na+ environment.

The nucleotide addition cycle of the SARS-CoV-2 polymerase

Coronaviruses have evolved elaborate multisubunit machines to replicate and transcribe their genomes. Central to these machines are the RNA-dependent RNA polymerase subunit (nsp12) and its intimately associated cofactors (nsp7 and nsp8). We use a high-throughput magnetic-tweezers approach to develop a mechanochemical description of this core polymerase. The core polymerase exists in at least three catalytically distinct conformations, one being kinetically consistent with incorporation of incorrect nucleotides. We provide evidence that the RNA-dependent RNA polymerase (RdRp) uses a thermal ratchet instead of a power stroke to transition from the pre- to post-translocated state. Ultra-stable magnetic tweezers enable the direct observation of coronavirus polymerase deep and long-lived backtracking that is strongly stimulated by secondary structures in the template. The framework we present here elucidates one of the most important structure-dynamics-function relationships in human health today and will form the grounds for understanding the regulation of this complex.

The nucleotide addition cycle of the SARS-CoV-2 polymerase

Coronaviruses have evolved elaborate multisubunit machines to replicate and transcribe their genomes. Central to these machines are the RNA-dependent RNA polymerase subunit (nsp12) and its intimately associated cofactors (nsp7 and nsp8). We have used a high-throughput magnetic-tweezers approach to develop a mechanochemical description of this core polymerase. The core polymerase exists in at least three catalytically distinct conformations, one being kinetically consistent with incorporation of incorrect nucleotides. We provide the first evidence that an RdRp uses a thermal ratchet instead of a power stroke to transition from the pre- to post-translocated state. Ultra-stable magnetic tweezers enables the direct observation of coronavirus polymerase deep and long-lived backtrack that are strongly stimulated by secondary structure in the template. The framework presented here elucidates one of the most important structure-dynamics-function relationships in human health today, and will form the grounds for understanding the regulation of this complex.

Single-Molecule Studies of Protein Folding with Optical Tweezers

Manipulation of individual molecules with optical tweezers provides a powerful means of interrogating the structure and folding of proteins. Mechanical force is not only a relevant quantity in cellular protein folding and function, but also a convenient parameter for biophysical folding studies. Optical tweezers offer precise control in the force range relevant for protein folding and unfolding, from which single-molecule kinetic and thermodynamic information about these processes can be extracted. In this review, we describe both physical principles and practical aspects of optical tweezers measurements and discuss recent advances in the use of this technique for the study of protein folding. In particular, we describe the characterization of folding energy landscapes at high resolution, studies of structurally complex multidomain proteins, folding in the presence of chaperones, and the ability to investigate real-time cotranslational folding of a polypeptide.

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.

Environment-dependent single-chain mechanics of synthetic polymers and biomacromolecules by atomic force microscopy-based single-molecule force spectroscopy and the implications for advanced polymer materials

"The Tao begets the One. One begets all things of the world." This quote from Tao Te Ching is still inspiring for scientists in chemistry and materials science: The "One" can refer to a single molecule. A macroscopic material is composed of numerous molecules. Although the relationship between the properties of the single molecule and macroscopic material is not well understood yet, it is expected that a deeper understanding of the single-chain mechanics of macromolecules will certainly facilitate the development of materials science. Atomic force microscopy-based single-molecule force spectroscopy (AFM-SMFS) has been exploited extensively as a powerful tool to study the single-chain behaviors of macromolecules. In this review, we summarize the recent advances in the emerging field of environment-dependent single-chain mechanics of synthetic polymers and biomacromolecules by means of AFM-SMFS. First, the single-chain inherent elasticities of several typical linear macromolecules are introduced, which are also confirmed by one of three polymer models with theoretical elasticities of the corresponding macromolecules obtained from quantum mechanical (QM) calculations. Then, the effects of the external environments on the single-chain mechanics of synthetic polymers and biomacromolecules are reviewed. Finally, the impacts of single-chain mechanics of macromolecules on the development of polymer science especially polymer materials are illustrated.

Specific Nucleic Acid Chaperone Activity of HIV-1 Nucleocapsid Protein Deduced from Hairpin Unfolding

RNA and DNA hairpin formation and disruption play key regulatory roles in a variety of cellular processes. The 59-nucleotide transactivation response (TAR) RNA hairpin facilitates the production of full-length transcripts of the HIV-1 genome. Yet the stability of this long, irregular hairpin becomes a liability during reverse transcription as 24 base pairs must be disrupted for strand transfer. Retroviral nucleocapsid (NC) proteins serve as nucleic acid chaperones that have been shown to both destabilize the TAR hairpin and facilitate strand annealing with its complementary DNA sequence. Yet it has remained difficult to elucidate the way NC targets and dramatically destabilizes this hairpin while only weakly affecting the annealed product. In this work, we used optical tweezers to measure the stability of TAR and found that adding NC destabilized the hairpin and simultaneously caused a distinct change in both the height and location of the energy barrier. This data was matched to an energy landscape predicted from a simple theory of definite base pair destabilization. Comparisons revealed the specific binding sites found by NC along the irregular TAR hairpin. Furthermore, specific binding explained both the unusual shift in the transition state and the much weaker effect on the annealed product. These experiments illustrate a general method of energy landscape transformation that exposes important physical insights.

A Universal Assay for Making DNA, RNA, and RNA-DNA Hybrid Configurations for Single-Molecule Manipulation in Two or Three Steps without Ligation

Despite having a great variety of topologies, most DNA, RNA, and RNA-DNA hybrid (RDH) configurations for single-molecule manipulation are composed of several single-stranded (ss) DNA and ssRNA strands, with functional labels at the two ends for surface tethering. On this basis, we developed a simple, robust, and universal amplification-annealing (AA) assay for making all these configurations in two or three steps without inefficient digestion and ligation reactions. As examples, we made ssDNA, short ssDNA with double-stranded (ds) DNA handles, dsDNA with ssDNA handles, replication-fork shaped DNA/RDH/RNA, DNA holiday junction, three-site multiple-labeled and nicked DNA, torsion-constrained RNA/RDH, and short ssRNA with RDH handles. In addition to single-molecule manipulation techniques including optical tweezers, magnetic tweezers, and atomic force microscopy, these configurations can be applied in other surface-tethering techniques as well.

Constructing Free Energy Landscapes of Nucleic Acid Hairpin Unfolding

Single nucleic acid molecules form hairpins that may stabilize secondary and tertiary structures as well as perform enzymatic and other chemical functions. Considerable progress has been made in the effort to understand the contributions of various factors to the stability of a given hairpin sequence. For a given sequence, it is possible to compute both the most likely structural arrangements and their associated free energies over a range of experimental conditions. However, there are many observed hairpin irregularities for which the energies and function are not well understood. Here we examine the irregular RNA Transactivation Response (TAR) hairpin from the HIV-1 genome. Using single molecule optical tweezers, the hairpin is force unfolded, revealing the overall unfolding free energy and the character of the transition state. These measurements allow the construction of a simple energy landscape from unfolding measurements, which can be directly compared to a theoretical landscape. This method is easily adapted to other structures, including the effects of noncanonical bases and even ligand binding.

Molecular Simulations of Ion Effects on the Thermodynamics of RNA Folding

How ions affect RNA folding thermodynamics and kinetics is an important but a vexing problem that remains unsolved. Experiments have shown that the free-energy change, Δ G( c), of RNA upon folding varies with the salt concentration ( c) as, Δ G( c) = k _c ln  c + const, where the coefficient k _c is proportional to the difference in the ion preferential coefficient, ΔΓ. We performed simulations of a coarse-grained model, by modeling electrostatic interactions implicitly and with explicit representation of ions, to elucidate the molecular underpinnings of the relationship between Δ G and ΔΓ. The simulations quantitatively reproduce the heat capacity for a pseudoknot, thus validating the model. We show that Δ G( c), calculated directly from ΔΓ, varies linearly with ln  c ( c < 0.2 M), for a hairpin and the pseudoknot, demonstrating a molecular link between the two quantities. Explicit ion simulations also show the linear dependence of Δ G( c) on ln  c at all c with k _c = 2 k_B T, except that Δ G( c) values are shifted by ∼2 kcal/mol higher than experiments. The discrepancy is due to an underestimation of Γ for both the folded and unfolded states while giving accurate values for ΔΓ. The predictions for the salt dependence of ΔΓ are amenable to test using single-molecule pulling experiments. The framework provided here can be used to obtain accurate thermodynamics for other RNA molecules as well.

Why Does RNA Collapse? The Importance of Water in a Simulation Study of Helix-Junction-Helix Systems

Using computer simulations, we consider the balance of thermodynamic forces that collapse RNA. A model helix-junction-helix (HJH) construct is used to investigate the transition from an extended to a collapsed conformation. Conventional Molecular Dynamics and Milestoning Simulations are used to study the free energy profile of the process for two ion concentrations. We illustrate that HJH folds to a collapsed state with two types of counterions (Mg²⁺ and K⁺). By dissecting the free energy landscape into energetic and entropic contributions, we illustrate that the electrostatic forces between the RNA and the mobile ions do not drive the RNA to a collapsed state. Instead, entropy gains from water expulsion near the neighborhood of the RNA provide the stabilization free energy that tilt HJH into more compact structures. Further simulations of a three-helix hammerhead ribozyme show a similar behavior and support the idea of collapse due to increased gain in water entropy.

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

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

Monovalent ions modulate the flux through multiple folding pathways of an RNA pseudoknot

The assembly mechanism of RNA, vital to describing its functions, depends on both the sequence and the metal ion concentration. How the latter influences the folding trajectories remains an important unsolved problem. Here, we examine the folding pathways of an RNA pseudoknot (PK) with key functional roles in transcription and translation, using a combination of experiments and simulations. We demonstrate that the PK, consisting of two hairpins with differing stabilities, folds by parallel pathways. Surprisingly, the flux between them is modulated by monovalent salt concentration. Our work shows that the order of assembly of PKs is determined by the relative stability of the hairpins, implying that the folding landscape can be controlled by sequence and ion concentration.

The functions of RNA pseudoknots (PKs), which are minimal tertiary structural motifs and an integral part of several ribozymes and ribonucleoprotein complexes, are determined by their structure, stability, and dynamics. Therefore, it is important to elucidate the general principles governing their thermodynamics/folding mechanisms. Here, we combine laser temperature-jump experiments and coarse-grained simulations to determine the folding/unfolding pathways of VPK, a variant of the mouse mammary tumor virus (MMTV) PK involved in ribosomal frameshifting. Fluorescent nucleotide analogs (2-aminopurine and pyrrolocytidine) placed at different stem/loop positions in the PK serve as local probes allowing us to monitor the order of assembly of VPK that has two constituent hairpins with different intrinsic stabilities. We show that at 50 mM KCl, the dominant folding pathway populates only the more stable hairpin intermediate; as the salt concentration is increased, a parallel folding pathway emerges involving the less stable hairpin as an alternate intermediate. Notably, the flux between the pathways is modulated by the ionic strength. Our findings support the principle that the order of PK structure formation is determined by the relative stabilities of the hairpins, which can be altered by sequence variations or salt concentrations. The experimental results of salt effects on the partitioning between the two folding pathways are in remarkable agreement with simulations that were performed with no adjustable parameters. Our study not only unambiguously demonstrates that VPK folds by parallel pathways but also showcases the power of combining experiments and simulations for a more enriched description of RNA self-assembly.

Single-Molecule Mechanical Folding and Unfolding of RNA Hairpins: Effects of Single A-U to A·C Pair Substitutions and Single Proton Binding and Implications for mRNA Structure-Induced -1 Ribosomal Frameshifting

A wobble A·C pair can be protonated at near physiological pH to form a more stable wobble A⁺·C pair. Here, we constructed an RNA hairpin (rHP) and three mutants with one A-U base pair substituted with an A·C mismatch on the top (near the loop, U22C), middle (U25C), and bottom (U29C) positions of the stem, respectively. Our results on single-molecule mechanical (un)folding using optical tweezers reveal the destabilization effect of A-U to A·C pair substitution and protonation-dependent enhancement of mechanical stability facilitated through an increased folding rate, or decreased unfolding rate, or both. Our data show that protonation may occur rapidly upon the formation of an apparent mechanical folding transition state. Furthermore, we measured the bulk -1 ribosomal frameshifting efficiencies of the hairpins by a cell-free translation assay. For the mRNA hairpins studied, -1 frameshifting efficiency correlates with mechanical unfolding force at equilibrium and folding rate at around 15 pN. U29C has a frameshifting efficiency similar to that of rHP (∼2%). Accordingly, the bottom 2-4 base pairs of U29C may not form under a stretching force at pH 7.3, which is consistent with the fact that the bottom base pairs of the hairpins may be disrupted by ribosome at the slippery site. U22C and U25C have a similar frameshifting efficiency (∼1%), indicating that both unfolding and folding rates of an mRNA hairpin in a crowded environment may affect frameshifting. Our data indicate that mechanical (un)folding of RNA hairpins may mimic how mRNAs unfold and fold in the presence of translating ribosomes.

Physics-based all-atom modeling of RNA energetics and structure

The database of RNA sequences is exploding, but knowledge of energetics, structures, and dynamics lags behind. All-atom computational methods, such as molecular dynamics, hold promise for closing this gap. New algorithms and faster computers have accelerated progress in improving the reliability and accuracy of predictions. Currently, the methods can facilitate refinement of experimentally determined nuclear magnetic resonance and x-ray structures, but are 'unreliable' for predictions based only on sequence. Much remains to be discovered, however, about the many molecular interactions driving RNA folding and the best way to approximate them quantitatively. The large number of parameters required means that a wide variety of experimental results will be required to benchmark force fields and different approaches. As computational methods become more reliable and accessible, they will be used by an increasing number of biologists, much as x-ray crystallography has expanded. Thus, many fundamental physical principles underlying the computational methods are described. This review presents a summary of the current state of molecular dynamics as applied to RNA. It is designed to be helpful to students, postdoctoral fellows, and faculty who are considering or starting computational studies of RNA. WIREs RNA 2017, 8:e1422. doi: 10.1002/wrna.1422.

Oligonucleotide-Peptide Complexes: Phase Control by Hybridization

When oppositely charged polymers are mixed, counterion release drives phase separation; understanding this process is a key unsolved problem in polymer science and biophysical chemistry, particularly for nucleic acids, polyanions whose biological functions are intimately related to their high charge density. In the cell, complexation by basic proteins condenses DNA into chromatin, and membraneless organelles formed by liquid-liquid phase separation of RNA and proteins perform vital functions and have been linked to disease. Electrostatic interactions are also the primary method used for assembly of nanoparticles to deliver therapeutic nucleic acids into cells. This work describes complexation experiments with oligonucleotides and cationic peptides spanning a wide range of polymer lengths, concentrations, and structures, including RNA and methylphosphonate backbones. We find that the phase of the complexes is controlled by the hybridization state of the nucleic acid, with double-stranded nucleic acids forming solid precipitates while single-stranded oligonucleotides form liquid coacervates, apparently due to their lower charge density. Adding salt "melts" precipitates into coacervates, and oligonucleotides in coacervates remain competent for sequence-specific hybridization and phase change, suggesting the possibility of environmentally responsive complexes and nanoparticles for therapeutic or sensing applications.

Ionic Solution: What Goes Right and Wrong with Continuum Solvation Modeling

Solvent-mediated electrostatic interactions were well recognized to be important in the structure and function of molecular systems. Ionic interaction is an important component in electrostatic interactions, especially in highly charged molecules, such as nucleic acids. Here, we focus on the quality of the widely used Poisson-Boltzmann surface area (PBSA) continuum models in modeling ionic interactions by comparing with both explicit solvent simulations and the experiment. In this work, the molality-dependent chemical potentials for sodium chloride (NaCl) electrolyte were first simulated in the SPC/E explicit solvent. Our high-quality simulation agrees well with both the previous study and the experiment. Given the free-energy simulations in SPC/E as the benchmark, we used the same sets of snapshots collected in the SPC/E solvent model for PBSA free-energy calculations in the hope to achieve the maximum consistency between the two solvent models. Our comparative analysis shows that the molality-dependent chemical potentials of NaCl were reproduced well with both linear PB and nonlinear PB methods, although nonlinear PB agrees better with SPC/E and the experiment. Our free-energy simulations also show that the presence of salt increases the hydrophobic effect in a nonlinear fashion, in qualitative agreement with previous theoretical studies of Onsager and Samaras. However, the lack of molality-dependency in the nonelectrostatics continuum models dramatically reduces the overall quality of PBSA methods in modeling salt-dependent energetics. These analyses point to further improvements needed for more robust modeling of solvent-mediated interactions by the continuum solvation frameworks.

Direct Observation of Folding Energy Landscape of RNA Hairpin at Mechanical Loading Rates

By applying a controlled mechanical load using optical tweezers, we measured the diffusive barrier crossing in a 49 nt long P5ab RNA hairpin. We find that in the free-energy landscape the barrier height (G^‡) and transition distance (x^‡) are dependent on the loading rate (r) along the pulling direction, x, as predicted by Bell. The barrier shifted toward the initial state, whereas ΔG^‡ reduced significantly from 50 to 5 kT, as r increased from 0 to 32 pN/s. However, the equilibrium work (ΔG) during strand separation, as estimated by Crook's fluctuation theorem, remained unchanged at different rates. Previously, helix formation and denaturation have been described as two-state (F ↔ U) transitions for P5ab. Herein, we report three intermediate states I₁, I, and I₂ located at 4, 11, and 16 nm respectively, from the folded conformation. The intermediates were observed only when the hairpin was subjected to an optimal r, 7.6 pN/s. The results indicate that the complementary strands in P5ab can zip and unzip through complex routes, whereby mismatches act as checkpoints and often impose barriers. The study highlights the significance of loading rates in force-spectroscopy experiments that are increasingly being used to measure the folding properties of biomolecules.

Computational Assessment of Potassium and Magnesium Ion Binding to a Buried Pocket in GTPase-Associating Center RNA

An experimentally well-studied model of RNA tertiary structures is a 58mer rRNA fragment, known as GTPase-associating center (GAC) RNA, in which a highly negative pocket walled by phosphate oxygen atoms is stabilized by a chelated cation. Although such deep pockets with more than one direct phosphate to ion chelation site normally include magnesium, as shown in one GAC crystal structure, another GAC crystal structure and solution experiments suggest potassium at this site. Both crystal structures also depict two magnesium ions directly bound to the phosphate groups comprising this controversial pocket. Here, we used classical molecular dynamics simulations as well as umbrella sampling to investigate the possibility of binding of potassium versus magnesium inside the pocket and to better characterize the chelation of one of the binding magnesium ions outside the pocket. The results support the preference of the pocket to accommodate potassium rather than magnesium and suggest that one of the closely binding magnesium ions can only bind at high magnesium concentrations, such as might be present during crystallization. This work illustrates the complementary utility of molecular modeling approaches with atomic-level detail in resolving discrepancies between conflicting experimental results.

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.

Targeted binding of nucleocapsid protein transforms the folding landscape of HIV-1 TAR RNA

Retroviral nucleocapsid (NC) proteins are nucleic acid chaperones that play a key role in the viral life cycle. During reverse transcription, HIV-1 NC facilitates the rearrangement of nucleic acid secondary structure, allowing the transactivation response (TAR) RNA hairpin to be transiently destabilized and annealed to a cDNA hairpin. It is not clear how NC specifically destabilizes TAR RNA but does not strongly destabilize the resulting annealed RNA-DNA hybrid structure, which must be formed for reverse transcription to continue. By combining single-molecule optical tweezers measurements with a quantitative mfold-based model, we characterize the equilibrium TAR stability and unfolding barrier for TAR RNA. Experiments show that adding NC lowers the transition state barrier height while also dramatically shifting the barrier location. Incorporating TAR destabilization by NC into the mfold-based model reveals that a subset of preferential protein binding sites is responsible for the observed changes in the unfolding landscape, including the unusual shift in the transition state. We measure the destabilization induced at these NC binding sites and find that NC preferentially targets TAR RNA by binding to specific sequence contexts that are not present on the final annealed RNA-DNA hybrid structure. Thus, specific binding alters the entire RNA unfolding landscape, resulting in the dramatic destabilization of this specific structure that is required for reverse transcription.

A U⋅U Pair-to-U⋅C Pair Mutation-Induced RNA Native Structure Destabilisation and Stretching-Force-Induced RNA Misfolding

Little is known about how a non-Watson-Crick pair affects the RNA folding dynamics. We studied the effects of a U⋅U-to-U⋅C pair mutation on the folding of a hairpin in human telomerase RNA. The ensemble thermal melting of the hairpins shows an on-pathway intermediate with the disruption of the internal loop structure containing the U⋅U/U⋅C pairs. By using optical tweezers, we applied a stretching force on the terminal ends of the hairpins to probe directly the non-nearest-neighbour effects upon the mutations. The single U⋅U to U⋅C mutations are observed to 1) lower the mechanical unfolding force by approximately 1 picoNewton (pN) per mutation without affecting the unfolding reaction transition-state position (thus suggesting that removing a single hydrogen bond affects the structural dynamics at least two base pairs away), 2) result in more frequent misfolding into a small hairpin at approximately 10 pN and 3) shift the folding reaction transition-state position towards the native hairpin structure and slightly increase the mechanical folding kinetics (thus suggesting that untrapping from the misfolded state is not the rate-limiting step).

RNA folding: structure prediction, folding kinetics and ion electrostatics

Beyond the "traditional" functions such as gene storage, transport and protein synthesis, recent discoveries reveal that RNAs have important "new" biological functions including the RNA silence and gene regulation of riboswitch. Such functions of noncoding RNAs are strongly coupled to the RNA structures and proper structure change, which naturally leads to the RNA folding problem including structure prediction and folding kinetics. Due to the polyanionic nature of RNAs, RNA folding structure, stability and kinetics are strongly coupled to the ion condition of solution. The main focus of this chapter is to review the recent progress in the three major aspects in RNA folding problem: structure prediction, folding kinetics and ion electrostatics. This chapter will introduce both the recent experimental and theoretical progress, while emphasize the theoretical modelling on the three aspects in RNA folding.

Modeling of RNA nanotubes using molecular dynamics simulation

In this study, we construct novel RNA nanoclusters, RNA nanotubes made of several nanorings up to the size of 20 nm, utilizing the molecular dynamics simulation, and study their structural properties [i.e., the root mean square deviation, the radius of gyration and the radial distribution function (RDF)] in physiological solutions that can be used for drug delivery into the human body. The patterns of energy and temperature variations of the systems are also discussed. Furthermore, we study the concentration of ions around the tube as a function of time at a particular temperature. We have found that when the temperature increases, the number of ions increases within a certain distance of the tube. We report that the number of ions within this distance around the tubes decreases in quenched runs. This indicates that some ions evaporate with decrease in temperature, as has been observed in the case of the nanoring. RDF plots also demonstrate a similar trend with temperature, as was found in the case of RNA nanorings.

High efficiency acetylcholinesterase immobilization on DNA aptamer modified surfaces

We report here the in vitro selection of DNA aptamers for electric eel acetylcholinesterase (AChE). One selected aptamer sequence (R15/19) has a high affinity towards the enzyme (Kd=157±42 pM). Characterization of the aptamer showed its binding is not affected by low ionic strength (~20 mM), however significant reduction in affinity occurred at high ionic strength (~1.2 M). In addition, this aptamer does not inhibit the catalytic activity of AChE that we exploit through immobilization of the DNA on a streptavidin-coated surface. Subsequent immobilization of AChE by the aptamer results in a 4-fold higher catalytic activity when compared to adsorption directly on to plastic.

Single-molecule methods for ligand counting: linking ion uptake to DNA hairpin folding

Ligand associations play a significant role in biochemical processes, typically through stabilizing a particular conformation of a folded biomolecule. Here, we demonstrate the ability to measure the changes in the number of ligands associated with a single, stretched biomolecule as it undergoes a conformational change. We do this by combining thermodynamic theory with single-molecule measurements that directly track biomolecular conformation. We utilize this technique to determine the changes in the ionic atmosphere of a DNA hairpin undergoing a force-destabilized folding transition. We find that the number of counterions liberated upon DNA unfolding is a nonmonotonic function of the monovalent salt concentration of the solution, contrary to predictions from common nucleic acid models. This demonstrates that previously unobserved phenomena can be measured with our ligand counting approach.

Effects of salt, polyethylene glycol, and locked nucleic acids on the thermodynamic stabilities of consecutive terminal adenosine mismatches in RNA duplexes

Consecutive terminal mismatches add thermodynamic stability to RNA duplexes and occur frequently in microRNA-mRNA interactions. Accurate thermodynamic stabilities of consecutive terminal mismatches contribute to the development of specific, high-affinity siRNA therapeutics. Consecutive terminal adenosine mismatches (TAMS) are studied at different salt concentrations, with polyethylene glycol cosolutes, and with locked nucleic acid (LNA) substitutions. These measurements provide benchmarks for the application of thermodynamic predictions to different physiological or therapeutic conditions. The salt dependence for RNA duplex stability is similar for TAMS, internal loops, and Watson-Crick duplexes. A unified model for predicting the free energy of an RNA duplex with or without loops and mismatches at lower sodium concentrations is presented. The destabilizing effects of PEG 200 are larger for TAMS than internal loops or Watson-Crick duplexes, which may result from different base stacking conformations, dynamics, and water hydration. In contrast, LNA substitutions stabilize internal loops much more than TAMS. Surprisingly, the average per adenosine increase in stability for LNA substitutions in internal loops is -1.82 kcal/mol and only -0.20 kcal/mol for TAMS. The stabilities of TAMS and internal loops with LNA substitutions have similar favorable free energies. Thus, the unfavorable free energy of adenosine internal loops is largely an entropic effect. The favorable stabilities of TAMS result mainly from base stacking. The ability of RNA duplexes to form extended terminal mismatches in the absence of proteins such as argonaute and identifying the enthalpic contributions to terminal mismatch stabilities provide insight into the physical basis of microRNA-mRNA molecular recognition and specificity.

G-quadruplex DNA aptamers for zeatin recognizing

Zeatins, a major type of cytokinin, are ubiquitous in higher plants, and involve in regulating a wide range of developmental processes. The development of highly specific ligands to zeatins would be very useful in plant biological research. Here we describe a group of oligonucleotide ligands (aptamers) generated against trans-zeatin. The optimized aptamers possess strong affinity to trans-zeatin and trans-zeatin riboside (Kd=3-5 μM), and relatively weak affinity (Kd=27-30 μM) to cis-zeatin and dihydrozeatin. These aptamers adopt a hairpin-G-quadruplex structure for binding to zeatin. A fluorescence turn-on aptasensor based on graphene oxide (GO) was developed for the recognition of zeatins. The specificity assay of this aptasensor shows good response to zeatins, and no response to the adenine derivatives (analog of zeatins) abundantly existing in biological samples. These results show the great potential of these aptamers in chemical analysis and biological investigation of zeatins.

Dominant role of the 5' TAR bulge in dimerization of HIV-1 genomic RNA, but no evidence of TAR-TAR kissing during in vivo virus assembly

The 5' untranslated region of HIV-1 genomic RNA (gRNA) contains two stem-loop structures that appear to be equally important for gRNA dimerization: the 57-nucleotide 5' TAR, at the very 5' end, and the 35-nucleotide SL1 (nucleotides 243-277). SL1 is well-known for containing the dimerization initiation site (DIS) in its apical loop. The DIS is a six-nucleotide palindrome. Here, we investigated the mechanism of TAR-directed gRNA dimerization. We found that the trinucleotide bulge (UCU24) of the 5' TAR has dominant impacts on both formation of HIV-1 RNA dimers and maturation of the formed dimers. The ΔUCU trinucleotide deletion strongly inhibited the first process and blocked the other, thus impairing gRNA dimerization as severely as deletion of the entire 5' TAR, and more severely than deletion of the DIS, inactivation of the viral protease, or most severe mutations in the nucleocapsid protein. The apical loop of TAR contains a 10-nucleotide palindrome that has been postulated to stimulate gRNA dimerization by a TAR-TAR kissing mechanism analogous to the one used by SL1 to stimulate dimerization. Using mutations that strongly destabilize formation of the TAR palindrome duplex, as well as compensatory mutations that restore duplex formation to a wild-type-like level, we found no evidence of TAR-TAR kissing, even though mutations nullifying the kissing potential of the TAR palindrome could impair dimerization by a mechanism other than hindering of SL1. However, nullifying the kissing potential of TAR had much less severe effects than ΔUCU. By not uncovering a dimerization mechanism intrinsic to TAR, our data suggest that TAR mutations exert their effect 3' of TAR, yet not on SL1, because TAR and SL1 mutations have synergistic effects on gRNA dimerization.

Non-specific binding of Na+ and Mg2+ to RNA determined by force spectroscopy methods

RNA duplex stability depends strongly on ionic conditions, and inside cells RNAs are exposed to both monovalent and multivalent ions. Despite recent advances, we do not have general methods to quantitatively account for the effects of monovalent and multivalent ions on RNA stability, and the thermodynamic parameters for secondary structure prediction have only been derived at 1M [Na(+)]. Here, by mechanically unfolding and folding a 20 bp RNA hairpin using optical tweezers, we study the RNA thermodynamics and kinetics at different monovalent and mixed monovalent/Mg(2+) salt conditions. We measure the unfolding and folding rupture forces and apply Kramers theory to extract accurate information about the hairpin free energy landscape under tension at a wide range of ionic conditions. We obtain non-specific corrections for the free energy of formation of the RNA hairpin and measure how the distance of the transition state to the folded state changes with force and ionic strength. We experimentally validate the Tightly Bound Ion model and obtain values for the persistence length of ssRNA. Finally, we test the approximate rule by which the non-specific binding affinity of divalent cations at a given concentration is equivalent to that of monovalent cations taken at 100-fold concentration for small molecular constructs.

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.

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.

Theory for RNA folding, stretching, and melting including loops and salt

Secondary structure formation of nucleic acids strongly depends on salt concentration and temperature. We develop a theory for RNA folding that correctly accounts for sequence effects, the entropic contributions associated with loop formation, and salt effects. Using an iterative expression for the partition function that neglects pseudoknots, we calculate folding free energies and minimum free energy configurations based on the experimentally derived basepairing free energies. The configurational entropy of loop formation is modeled by the asymptotic expression -clnm, where m is the length of the loop and c the loop exponent, which is an adjustable constant. Salt effects enter in two ways: first, we derive salt-induced modifications of the free energy parameters for describing basepairing, and second, we include the electrostatic free energy for loop formation. Both effects are modeled on the Debye-Hückel level including counterion condensation. We validate our theory for two different RNA sequences. For tRNA-phe, the resultant heat capacity curves for thermal denaturation at various salt concentrations accurately reproduce experimental results. For the P5ab RNA hairpin, we derive the global phase diagram in the three-dimensional space spanned by temperature, stretching force, and salt concentration and obtain good agreement with the experimentally determined critical unfolding force. We show that for a proper description of RNA melting and stretching, both salt and loop entropy effects are needed.

Importance of diffuse metal ion binding to RNA

RNAs are highly charged polyanionic molecules. RNA structure and function are strongly correlated with the ionic condition of the solution. The primary focus of this article is on the role of diffusive ions in RNA folding. Due to the long-range nature of electrostatic interactions, the diffuse ions can contribute significantly to RNA structural stability and folding kinetics. We present an overview of the experimental findings as well as the theoretical developments on the diffuse ion effects in RNA folding. This review places heavy emphasis on the effect of magnesium ions. Magnesium ions play a highly efficient role in stabilizing RNA tertiary structures and promoting tertiary structural folding. The highly efficient role goes beyond the mean-field effect such as the ionic strength. In addition to the effects of specific ion binding and ion dehydration, ion-ion correlation for the diffuse ions can contribute to the efficient role of the multivalent ions such as the magnesium ions in RNA folding.

Characterization and application of a DNA aptamer binding to L-tryptophan

DNA aptamers for specific recognition of L-tryptophan have been evolved by a SELEX (systematic evolution of ligands by exponential enrichment) technique. Truncation-mutation experiments suggest that a 34-mer sequence, Trp3a-1, possesses the strongest binding ability to L-tryptophan. Trp3a-1 is predicted to adopt a loop-stem secondary structure, in which the loop may further fold into a binding pocket for L-tryptophan with the help of the stem. The specificity investigation shows that Trp3a-1 strongly binds to L-tryptophan, has almost no binding to other amino acids, and weakly binds to some tryptophan analogs and peptides containing the L-tryptophan residue. The binding of Trp3a-1 to L-tryptophan is mainly contributed to by hydrogen bonds and precise stacking formed between the binding pocket of Trp3a-1 and all groups on L-tryptophan. This aptamer has also been proved to be an effective ligand for the chiral separation of D/L-tryptophan. L-tryptophan and its derivatives are known to play important biological roles; this aptamer ligand could be used as a tool for the analysis of tryptophan and other related studies.

Comparisons between chemical mapping and binding to isoenergetic oligonucleotide microarrays reveal unexpected patterns of binding to the Bacillus subtilis RNase P RNA specificity domain

Microarrays with isoenergetic pentamer and hexamer 2'-O-methyl oligonucleotide probes with LNA (locked nucleic acid) and 2,6-diaminopurine substitutions were used to probe the binding sites on the RNase P RNA specificity domain of Bacillus subtilis. Unexpected binding patterns were revealed. Because of their enhanced binding free energies, isoenergetic probes can break short duplexes, merge adjacent loops, and/or induce refolding. This suggests new approaches to the rational design of short oligonucleotide therapeutics but limits the utility of microarrays for providing constraints for RNA structure determination. The microarray results are compared to results from chemical mapping experiments, which do provide constraints. Results from both types of experiments indicate that the RNase P RNA folds similarly in 1 M Na(+) and 10 mM Mg(2+).

Nuclear magnetic resonance structure of the prohead RNA E-loop hairpin

The Bacillus subtilis phage phi29 packaging motor requires prohead RNA for genome encapsidation. The nuclear magnetic resonance structure of the prohead RNA E-loop hairpin, r(5'AUUGAGUU), is presented and compared to predictions from MC-SYM. The prohead RNA E-loop hairpins contain sequences similar to rRNA hairpins. Comparison of predicted and experimentally determined prohead and ribosomal hairpin structures reveals that sequence similarity is a stronger determinant of hairpin structural similarity than grouping similar types of RNA. All the hairpins contain a U-turn motif but differ in the first noncanonical pair and backbone orientation. These structures provide benchmarks for further improvements in RNA structure predictions from sequence.

Fluorescence competition assay measurements of free energy changes for RNA pseudoknots

RNA pseudoknots have important functions, and thermodynamic stability is a key to predicting pseudoknots in RNA sequences and to understanding their functions. Traditional methods, such as UV melting and differential scanning calorimetry, for measuring RNA thermodynamics are restricted to temperature ranges around the melting temperature for a pseudoknot. Here, we report RNA pseudoknot free energy changes at 37 °C measured by fluorescence competition assays. Sequence-dependent studies for the loop 1−stem 2 region reveal (1) the individual nearest-neighbor hydrogen bonding (INN-HB) model provides a reasonable estimate for the free energy change when a Watson−Crick base pair in stem 2 is changed, (2) the loop entropy can be estimated by a statistical polymer model, although some penalty for certain loop sequences is necessary, and (3) tertiary interactions can significantly stabilize pseudoknots and extending the length of stem 2 may alter tertiary interactions such that the INN-HB model does not predict the net effect of adding a base pair. The results can inform writing of algorithms for predicting and/or designing RNA secondary structures.

Structural diversity of triplet repeat RNAs

Tandem repeats of various trinucleotide motifs are present in the human transcriptome, but the functions of these regular sequences, which likely depend on the structures they form, are still poorly understood. To gain new insight into the structural and functional properties of triplet repeats in RNA, we have performed a biochemical structural analysis of the complete set of triplet repeat transcripts, each composed of a single sequence repeated 17 times. We show that these transcripts fall into four structural classes. The repeated CAA, UUG, AAG, CUU, CCU, CCA, and UAA motifs did not form any higher order structure under any analyzed conditions. The CAU, CUA, UUA, AUG, and UAG repeats are ordered according to their increasing tendency to form semistable hairpins. The repeated CGA, CGU, and all CNG motifs form fairly stable hairpins, whereas AGG and UGG repeats fold into stable G-quadruplexes. The triplet repeats that formed the most stable structures were characterized further by biophysical methods. UV-monitored structure melting revealed that CGG and CCG repeats form, respectively, the most and least stable hairpins of all CNG repeats. Circular dichroism spectra showed that the AGG and UGG repeat quadruplexes are formed by parallel RNA strands. Furthermore, we demonstrated that the different susceptibility of various triplet repeat transcripts to serum nucleases can be explained by the sequence and structural features of the tested RNAs. The results of this study provide a comprehensive structural foundation for the functional analysis of triplet repeats in transcripts.

Coarse-grained ions without charges: reproducing the solvation structure of NaCl in water using short-ranged potentials

A coarse-grained model of NaCl in water is presented where the ions are modeled without charge to avoid computationally challenging electrostatics. A monatomic model of water [V. Molinero and E. B. Moore, J. Phys. Chem. B 113, 4008 (2009)] is used as the basis for this coarse-grain approach. The ability of Na(+) to disrupt the native tetrahedral arrangement of water molecules, and of Cl(-) to integrate within this organization, is preserved in this mW-ion model through parametrization focused on water's solvation of these ions. This model successfully reproduces the structural effect of ions on water, referenced to observations from experiments and atomistic molecular dynamics simulations, while using extremely short-ranged potentials. Without Coulomb interactions the model replicates details of the ion-water structure such as distinguishing contact and solvent-separated ion pairs and the free energy barriers between them. The approach of mimicking ionic effects with short-ranged interactions results in performance gains of two orders of magnitude compared to Ewald methods. Explored over a broad range of salt concentration, the model reproduces the solvation structure and trends of diffusion relative to atomistic simulations and experimental results. The functional form of the mW-ion model can be parametrized to represent other electrolytes. With increased computational efficiency and reliable structural fidelity, this model promises to be an asset for accessing significantly longer simulation time scales with an explicit solvent in a coarse-grained system involving, for example, polyelectrolytes such as proteins, nucleic acids, and fuel-cell membranes.

Molecular dynamics study of the RNA ring nanostructure: a phenomenon of self-stabilization

We study mechanical and thermodynamic properties of RNA nanostructures focusing on a hexagonal nanoring discussed in Yingling and Shapiro (2007 Nano Lett. 7 2328). We are concerned with the following main issues: (i) the stability of the nanoring versus temperature; (ii) the effect of the environment (solvent, counterions) on its stability; (iii) conformations and dynamics under external force. The process of evaporation of the ions from the ring upon temperature drop has been found, demonstrating a surprising feature-the uptake of ions by the nanoring increases with the temperature. The connection of this behavior to the dielectric constant of water, hydration and structural changes in the nanoring is discussed. Several properties of the nanoring, such as elastic and transport coefficients, have been determined. A measure of the tensile elasticity of the ring against its uniform 2D in-plane compression has been given, as K(eff) < or = 0.01 GPa, which is a much lower value compared to typical values found for soft matter other than RNA.

Mechanical unfolding of two DIS RNA kissing complexes from HIV-1

An RNA kissing complex formed by the dimerization initiation site plays a critical role in the survival and infectivity of human immunodeficiency virus. Two dimerization initiation site kissing sequences, Mal and Lai, have been found in most human immunodeficiency virus 1 variants. Formation and stability of these RNA kissing complexes depend crucially on cationic conditions, particularly Mg 2+. Using optical tweezers, we investigated the mechanical unfolding of single RNA molecules with either Mal-type (GUGCAC) or Lai-type (GCGCGC) kissing complexes under various ionic conditions. The force required to disrupt the kissing interaction of the two structures, the rip force, is sensitive to concentrations of KCl and MgCl2; addition of 3 mM MgCl2 to 100 mM KCl changes the rip force of Mal from 21 +/- 4 to 46 +/- 3 pN. From the rip force distribution, the kinetics of breaking the kissing interaction is calculated as a function of force and cation concentration. The two kissing complexes have distinct unfolding transition states, as shown by different values of deltaX(++), which is the distance from the folded structure to the unfolding transition state. The deltaX(++) of Mal is approximately 0.6 nm smaller than that of Lai, suggesting that fewer kissing base pairs are broken at the transition state of the former, consistent with observations that the Lai-type kissing complex is more stable and requires significantly more force to unfold than the Mal type. More importantly, neither K+ nor Mg 2+ significantly changes the position of the transition state along the reaction coordinate. However, increasing concentrations of cations increase the kinetic barrier. We derived a cation-specific parameter, m, to describe how the height of the kinetic barrier depends on the concentration of cations. Our results suggest that Mg 2+ greatly slows down the unfolding of the kissing complex but has moderate effects on the formation kinetics of the structure.