Ions and RNAs: Free Energies of Counterion-Mediated RNA Fold Stabilities

Nucleic acid folding simulations using a physics-based atomistic free energy model

Performing full-resolution atomistic simulations of nucleic acid folding has remained a challenge for biomolecular modeling. Understanding how nucleic acids fold and how they transition between different folded structures as they unfold and refold has important implications for biology. This paper reports a theoretical model and computer simulation of the ab initio folding of DNA inverted repeat sequences. The formulation is based on an all-atom conformational model of the sugar-phosphate backbone via chain closure, and it incorporates three major molecular-level driving forces-base stacking, counterion-induced backbone self-interactions, and base pairing-via separate analytical theories designed to capture and reproduce the effects of the solvent without requiring explicit water and ions in the simulation. To accelerate computational throughput, a mixed numerical/analytical algorithm for the calculation of the backbone conformational volume is incorporated into the Monte Carlo simulation, and special stochastic sampling techniques were employed to achieve the computational efficiency needed to fold nucleic acids from scratch. This paper describes implementation details, benchmark results, and the advantages and technical challenges with this approach.

RNA-ligand molecular docking: advances and challenges

With rapid advances in computer algorithms and hardware, fast and accurate virtual screening has led to a drastic acceleration in selecting potent small molecules as drug candidates. Computational modeling of RNA-small molecule interactions has become an indispensable tool for RNA-targeted drug discovery. The current models for RNA-ligand binding have mainly focused on the docking-and-scoring method. Accurate docking and scoring should tackle four crucial problems: (1) conformational flexibility of ligand, (2) conformational flexibility of RNA, (3) efficient sampling of binding sites and binding poses, and (4) accurate scoring of different binding modes. Moreover, compared with the problem of protein-ligand docking, predicting ligand binding to RNA, a negatively charged polymer, is further complicated by additional effects such as metal ion effects. Thermodynamic models based on physics-based and knowledge-based scoring functions have shown highly encouraging success in predicting ligand binding poses and binding affinities. Recently, kinetic models for ligand binding have further suggested that including dissociation kinetics (residence time) in ligand docking would result in improved performance in estimating in vivo drug efficacy. More recently, the rise of deep-learning approaches has led to new tools for predicting RNA-small molecule binding. In this review, we present an overview of the recently developed computational methods for RNA-ligand docking and their advantages and disadvantages.

A Deep Dive into DNA Base Pairing Interactions Under Water

Base pairing plays a pivotal role in DNA functions and replication fidelity. But while the complementarity between Watson-Crick matched bases is generally believed to arise from the different number of hydrogen bonds in G|C pairs versus A|T, the energetics of these interactions are heavily renormalized by the aqueous solvent. Employing large-scale Monte Carlo simulations, we have extracted the solvent contribution to the free energy for canonical and some noncanonical and stacked base pairs. For all of them, the solvent's contribution to the base pairing free energy is exclusively destabilizing. While the direct hydrogen bonding interactions in the G|C pair is much stronger than A|T, the thermodynamic resistance produced by the solvent also pushes back much stronger against G|C compared to A|T, generating an only ∼1 kcal/mol free energy difference between them. We have profiled the density of water molecules in the solvent adjacent to the bases and observed a "freezing" behavior where waters are recruited into the gap between the bases to compensate for the unsatisfied hydrogen bonds between them. A very small number of water molecules that are associated with the Watson-Crick donor/acceptor atoms turn out to be responsible for the majority of the solvent's thermodynamic resistance to base pairing. The absence or presence of these near-field waters can be used to enhance fidelity during DNA replication.

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.

Topological Constraints and Their Conformational Entropic Penalties on RNA Folds

Functional RNAs can fold into intricate structures using a number of different secondary and tertiary structural motifs. Many factors contribute to the overall free energy of the target fold. This study aims at quantifying the entropic costs coming from the loss of conformational freedom when the sugar-phosphate backbone is subjected to constraints imposed by secondary and tertiary contacts. Motivated by insights from topology theory, we design a diagrammatic scheme to represent different types of RNA structures so that constraints associated with a folded structure may be segregated into mutually independent subsets, enabling the total conformational entropy loss to be easily calculated as a sum of independent terms. We used high-throughput Monte Carlo simulations to simulate large ensembles of single-stranded RNA sequences in solution to validate the assumptions behind our diagrammatic scheme, examining the entropic costs for hairpin initiation and formation of many multiway junctions. Our diagrammatic scheme aids in the factorization of secondary/tertiary constraints into distinct topological classes and facilitates the discovery of interrelationships among multiple constraints on RNA folds. This perspective, which to our knowledge is novel, leads to useful insights into the inner workings of some functional RNA sequences, demonstrating how they might operate by transforming their structures among different topological classes.

Theoretical Model for Solvent-Induced Base Stacking Interactions in Solvent-Free DNA Simulations

Ultrahigh-throughput conformational sampling of biopolymers like nucleic acids are most effectively carried out without explicit solvents, but the physical origins of almost all inter- and intramolecular interactions controlling nucleic acid structures are rooted in water. Single-stranded (ss) DNAs or RNAs in water are characterized by ensembles of diverse conformations. To properly capture solvent-induced nucleobase stacking interactions in an otherwise solvent-free Monte Carlo algorithm, theoretical models are developed here to describe the solvent entropy and dispersion terms in base stacking free energies. To validate these models, equilibrium ensembles of ss (dA) _n and (dT) _n sequences ( n = 30, 40, and 50) were simulated, and they quantitatively reproduced experimental small-angle X-ray scattering (SAXS) data. Simulated dA ensembles show substantial stacking. While less prevalent, stacking in dT chains is not negligible. Analysis of SAXS profiles suggests that excess features between wavevector 0.03 and 0.18 Å^-1 correlate with stacking, and stacking in dA versus dT chains is chain length-dependent, where (dT)₃₀ and (dA)₃₀ chains have more similar structures, but longer dA chains show more stacking over dT. The average stack length in ss-dA chains is 5-10 nucleotides, yielding an estimate for the overall A|A stacking free energy at ∼1 kcal/mol.

Structure-Based Model of RNA Pseudoknot Captures Magnesium-Dependent Folding Thermodynamics

We develop a simple, coarse-grained approach for simulating the folding of the Beet Western Yellow Virus (BWYV) pseudoknot toward the goal of creating a transferable model that can be used to study other small RNA molecules. This approach combines a structure-based model (SBM) of RNA with an electrostatic scheme that has previously been shown to correctly reproduce ionic condensation in the native basin. Mg²⁺ ions are represented explicitly, directly incorporating ion-ion correlations into the system, and K⁺ is represented implicitly, through the mean-field generalized Manning counterion condensation theory. Combining the electrostatic scheme with a SBM enables the electrostatic scheme to be tested beyond the native basin. We calibrate the SBM to reproduce experimental BWYV unfolding data by eliminating overstabilizing backbone interactions from the molecular contact map and by strengthening base pairing and stacking contacts relative to other native contacts, consistent with the experimental observation that relative helical stabilities are central determinants of the RNA unfolding sequence. We find that this approach quantitatively captures the Mg²⁺ dependence of the folding temperature and generates intermediate states that better approximate those revealed by experiment. Finally, we examine how our model captures Mg²⁺ condensation about the BWYV pseudoknot and a U-tail variant, for which the nine 3' end nucleotides are replaced with uracils, and find our results to be consistent with experimental condensation measurements. This approach can be easily transferred to other RNA molecules by eliminating and strengthening the same classes of contacts in the SBM and including generalized Manning counterion condensation.

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.

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

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

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.

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

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

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

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

A New Method to Predict Ion Effects in RNA Folding

The strong interaction between metal ions in solution and highly charged RNA molecules is critical for RNA structure formation and stabilization. Metal ions binding to RNA can induce RNA structural changes that are important for RNA cellular functions. Therefore, quantitative modeling of the ion effects is essential for RNA structure prediction and RNA-based molecular design. Recently, inspired by the increasing experimental evidence that supports the importance of ion correlation and fluctuation in ion-RNA interactions, we developed a new computational model, Monte Carlo Tightly Bound Ion (MCTBI) model. The validity of the model is shown by the improved accuracy in the predictions for ion binding properties and ion-dependent free energies for RNA structures. In this chapter, using homodimeric tetraloop-receptor docking as an illustrative example, we showcase the MCTBI method for the computational prediction of the ion effects in RNA folding.

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.

Atomistic Free Energy Model for Nucleic Acids: Simulations of Single-Stranded DNA and the Entropy Landscape of RNA Stem-Loop Structures

While single-stranded (ss) segments of DNAs and RNAs are ubiquitous in biology, details about their structures have only recently begun to emerge. To study ssDNA and RNAs, we have developed a new Monte Carlo (MC) simulation using a free energy model for nucleic acids that has the atomisitic accuracy to capture fine molecular details of the sugar-phosphate backbone. Formulated on the basis of a first-principle calculation of the conformational entropy of the nucleic acid chain, this free energy model correctly reproduced both the long and short length-scale structural properties of ssDNA and RNAs in a rigorous comparison against recent data from fluorescence resonance energy transfer, small-angle X-ray scattering, force spectroscopy and fluorescence correlation transport measurements on sequences up to ∼100 nucleotides long. With this new MC algorithm, we conducted a comprehensive investigation of the entropy landscape of small RNA stem-loop structures. From a simulated ensemble of ∼10(6) equilibrium conformations, the entropy for the initiation of different size RNA hairpin loops was computed and compared against thermodynamic measurements. Starting from seeded hairpin loops, constrained MC simulations were then used to estimate the entropic costs associated with propagation of the stem. The numerical results provide new direct molecular insights into thermodynaimc measurement from macroscopic calorimetry and melting experiments.

Quantifying Coulombic and solvent polarization-mediated forces between DNA helices

One of the fundamental problems in nucleic acids biophysics is to predict the different forces that stabilize nucleic acid tertiary folds. Here we provide a quantitative estimation and analysis for the forces between DNA helices in an ionic solution. Using the generalized Born model and the improved atomistic tightly binding ions model, we evaluate ion correlation and solvent polarization effects in interhelix interactions. The results suggest that hydration, Coulomb correlation and ion entropy act together to cause the repulsion and attraction between nucleic acid helices in Mg(2+) and Mn(2+) solutions, respectively. The theoretical predictions are consistent with experimental findings. Detailed analysis further suggests that solvent polarization and ion correlation both are crucial for the interhelix interactions. The theory presented here may provide a useful framework for systematic and quantitative predictions of the forces in nucleic acids folding.