Electrostatic free energy landscapes for DNA helix bending

Effect of ethanol on the elasticities of double-stranded RNA and DNA revealed by magnetic tweezers and simulations

The elasticities of double-stranded (ds) DNA and RNA, which are critical to their biological functions and applications in materials science, can be significantly modulated by solution conditions such as ions and temperature. However, there is still a lack of a comprehensive understanding of the role of solvents in the elasticities of dsRNA and dsDNA in a comparative way. In this work, we explored the effect of ethanol solvent on the elasticities of dsRNA and dsDNA by magnetic tweezers and all-atom molecular dynamics simulations. We found that the bending persistence lengths and contour lengths of dsRNA and dsDNA decrease monotonically with the increase in ethanol concentration. Furthermore, the addition of ethanol weakens the positive twist-stretch coupling of dsRNA, while promotes the negative twist-stretch coupling of dsDNA. Counter-intuitively, the lower dielectric environment of ethanol causes a significant re-distribution of counterions and enhanced ion neutralization, which overwhelms the enhanced repulsion along dsRNA/dsDNA, ultimately leading to the softening in bending for dsRNA and dsDNA. Moreover, for dsRNA, ethanol causes slight ion-clamping across the major groove, which weakens the major groove-mediated twist-stretch coupling, while for dsDNA, ethanol promotes the stretch-radius correlation due to enhanced ion binding and consequently enhances the helical radius-mediated twist-stretch coupling.

The origin of different bending stiffness between double-stranded RNA and DNA revealed by magnetic tweezers and simulations

The subtle differences in the chemical structures of double-stranded (ds) RNA and DNA lead to significant variations in their biological roles and medical implications, largely due to their distinct biophysical properties, such as bending stiffness. Although it is well known that A-form dsRNA is stiffer than B-form dsDNA under physiological salt conditions, the underlying cause of this difference remains unclear. In this study, we employ high-precision magnetic-tweezer experiments along with molecular dynamics simulations and reveal that the relative bending stiffness between dsRNA and dsDNA is primarily determined by the structure- and salt-concentration-dependent ion distribution around their helical structures. At near-physiological salt conditions, dsRNA shows a sparser ion distribution surrounding its phosphate groups compared to dsDNA, causing its greater stiffness. However, at very high monovalent salt concentrations, phosphate groups in both dsRNA and dsDNA become fully neutralized by excess ions, resulting in a similar intrinsic bending persistence length of approximately 39 nm. This similarity in intrinsic bending stiffness of dsRNA and dsDNA is coupled to the analogous fluctuations in their total groove widths and further coupled to the similar fluctuation of base-pair inclination, despite their distinct A-form and B-form helical structures.

Temperature dependence of DNA elasticity: An all-atom molecular dynamics simulation study

We used all-atom molecular dynamics simulation to investigate the elastic properties of double-stranded DNA (dsDNA). We focused on the influences of temperature on the stretch, bend, and twist elasticities, as well as the twist-stretch coupling, of the dsDNA over a wide range of temperature. The results showed that the bending and twist persistence lengths, together with the stretch and twist moduli, decrease linearly with temperature. However, the twist-stretch coupling behaves in a positive correction and enhances as the temperature increases. The potential mechanisms of how temperature affects dsDNA elasticity and coupling were investigated by using the trajectories from atomistic simulation, in which thermal fluctuations in structural parameters were analyzed in detail. We analyzed the simulation results by comparing them with previous simulation and experimental data, which are in good agreement. The prediction about the temperature dependence of dsDNA elastic properties provides a deeper understanding of DNA elasticities in biological environments and potentially helps in the further development of DNA nanotechnology.

Transcriptional control of mycobacterial DNA damage response by sigma adaptation

Transcriptional activator PafBC is the key regulator of the mycobacterial DNA damage response and controls around 150 genes, including genes involved in the canonical SOS response, through an unknown molecular mechanism. Using a combination of biochemistry and cryo–electron microscopy, we demonstrate that PafBC in the presence of single-stranded DNA activates transcription by reprogramming the canonical −10 and −35 promoter specificity of RNA polymerase associated with the housekeeping sigma subunit. We determine the structure of this transcription initiation complex, revealing a unique mode of promoter recognition, which we term “sigma adaptation.” PafBC inserts between DNA and sigma factor to mediate recognition of hybrid promoters lacking the −35 but featuring the canonical −10 and a PafBC-specific −26 element. Sigma adaptation may constitute a more general mechanism of transcriptional control in mycobacteria.

Radial distribution function of semiflexible oligomers with stretching flexibility

The radial distribution of the end-to-end distance R_ee is crucial for quantifying the global size and flexibility of a linear polymer. For semiflexible polymers, several analytical formulas have been derived for the radial distribution of R_ee ignoring the stretching flexibility. However, for semiflexible oligomers, such as DNA or RNA, the stretching flexibility can be rather pronounced and can significantly affect the radial distribution of R_ee. In this study, we obtained an extended formula that includes the stretch modulus to describe the distribution of R_ee for semiflexible oligomers on the basis of previous formulas for semiflexible polymers without stretching flexibility. The extended formula was validated by extensive Monte Carlo simulations over wide ranges of the stretch modulus and persistence length, as well as all-atom molecular dynamics simulations of short DNAs and RNAs. Additionally, our analyses showed that the effect of stretching flexibility on the distribution of R_ee becomes negligible for DNAs longer than ∼130 base pairs and RNAs longer than ∼240 base pairs.

Electrostatic bending response of a charged helix

We explore the electrostatic bending response of a chain of charged particles confined on a finite helical filament. We analyze how the energy difference ΔE between the bent and the unbent helical chain scales with the length of the helical segment and the radius of curvature and identify features that are not captured by the standard notion of the bending rigidity, normally used as a measure of bending tendency in the linear response regime. Using ΔE to characterize the bending response of the helical chain we identify two regimes with qualitatively different bending behaviors for the ground state configuration: the regime of small and the regime of large radius-to-pitch ratio, respectively. Within the former regime, ΔE changes smoothly with the variation of the system parameters. Of particular interest are its oscillations with the number of charged particles encountered for commensurate fillings which yield length-dependent oscillations in the preferred bending direction of the helical chain. We show that the origin of these oscillations is the nonuniformity of the charge distribution caused by the long-range character of the Coulomb interactions and the finite length of the helix. In the second regime of large values of the radius-to-pitch ratio, sudden changes in the ground state structure of the charges occur as the system parameters vary, leading to complex and discontinuous variations in the ground state bending response ΔE.

A pH-induced conformational switch in a tyrosine kinase inhibitor identified by electronic spectroscopy and quantum chemical calculations

Tyrosine kinase inhibitors (TKIs) are a major class of drug utilised in the clinic. During transit to their cognate kinases, TKIs will encounter different pH environments that could have a major influence on TKI structure. To address this, we report UV-Vis spectroscopic and computational studies of the TKI, AG1478, as a function of pH. The electronic absorption spectrum of AG1478 shifted by 10 nm (from 342 nm to 332 nm) from acid to neutral pH and split into two peaks (at 334 nm and 345 nm) in highly alkaline conditions. From these transitions, the pKa value was calculated as 5.58 ± 0.01. To compute structures and spectra, time-dependent density functional theory (TD-DFT) calculations were performed along with conductor-like polarizable continuum model (CPCM) to account for implicit solvent effect. On the basis of the theoretical spectra, we could assign the AG1478 experimental spectrum at acidic pH to a mixture of two twisted conformers (71% AG1478 protonated at quinazolyl nitrogen N(1) and 29% AG1478 protonated at quinazolyl nitrogen N(3)) and at neutral pH to the neutral planar conformer. The AG1478 absorption spectrum (pH 13.3) was fitted to a mixture of neutral (70%) and NH-deprotonated species (30%). These studies reveal a pH-induced conformational transition in a TKI.

Understanding the Relative Flexibility of RNA and DNA Duplexes: Stretching and Twist-Stretch Coupling

The flexibility of double-stranded (ds) RNA and dsDNA is crucial for their biological functions. Recent experiments have shown that the flexibility of dsRNA and dsDNA can be distinctively different in the aspects of stretching and twist-stretch coupling. Although various studies have been performed to understand the flexibility of dsRNA and dsDNA, there is still a lack of deep understanding of the distinctive differences in the flexibility of dsRNA and dsDNA helices as pertains to their stretching and twist-stretch coupling. In this work, we have explored the relative flexibility in stretching and twist-stretch coupling between dsRNA and dsDNA by all-atom molecular dynamics simulations. The calculated stretch modulus and twist-stretch coupling are in good accordance with the existing experiments. Our analyses show that the differences in stretching and twist-stretch coupling between dsRNA and dsDNA helices are mainly attributed to their different (A- and B-form) helical structures. Stronger basepair inclination and slide in dsRNA is responsible for the apparently weaker stretching rigidity versus that of dsDNA, and the opposite twist-stretch coupling for dsRNA and dsDNA is also attributed to the stronger basepair inclination in dsRNA than in dsDNA. Our calculated macroscopic elastic parameters and microscopic analyses are tested and validated by different force fields for both dsRNA and dsDNA.

Predicting 3D Structure, Flexibility, and Stability of RNA Hairpins in Monovalent and Divalent Ion Solutions

A full understanding of RNA-mediated biology would require the knowledge of three-dimensional (3D) structures, structural flexibility, and stability of RNAs. To predict RNA 3D structures and stability, we have previously proposed a three-bead coarse-grained predictive model with implicit salt/solvent potentials. In this study, we further develop the model by improving the implicit-salt electrostatic potential and including a sequence-dependent coaxial stacking potential to enable the model to simulate RNA 3D structure folding in divalent/monovalent ion solutions. The model presented here can predict 3D structures of RNA hairpins with bulges/internal loops (<77 nucleotides) from their sequences at the corresponding experimental ion conditions with an overall improved accuracy compared to the experimental data; the model also makes reliable predictions for the flexibility of RNA hairpins with bulge loops of different lengths at several divalent/monovalent ion conditions. In addition, the model successfully predicts the stability of RNA hairpins with various loops/stems in divalent/monovalent ion solutions.

Predicting Molecular Crowding Effects in Ion-RNA Interactions

We develop a new statistical mechanical model to predict the molecular crowding effects in ion-RNA interactions. By considering discrete distributions of the crowders, the model can treat the main crowder-induced effects, such as the competition with ions for RNA binding, changes of electrostatic interaction due to crowder-induced changes in the dielectric environment, and changes in the nonpolar hydration state of the crowder-RNA system. To enhance the computational efficiency, we sample the crowder distribution using a hybrid approach: For crowders in the close vicinity of RNA surface, we sample their discrete distributions; for crowders in the bulk solvent away from the RNA surface, we use a continuous mean-field distribution for the crowders. Moreover, using the tightly bound ion (TBI) model, we account for ion fluctuation and correlation effects in the calculation for ion-RNA interactions. Applications of the model to a variety of simple RNA structures such as RNA helices show a crowder-induced increase in free energy and decrease in ion binding. Such crowding effects tend to contribute to the destabilization of RNA structure. Further analysis indicates that these effects are associated with the crowder-ion competition in RNA binding and the effective decrease in the dielectric constant. This simple ion effect model may serve as a useful framework for modeling more realistic crowders with larger, more complex RNA structures.

Flexibility of short DNA helices with finite-length effect: From base pairs to tens of base pairs

Flexibility of short DNA helices is important for the biological functions such as nucleosome formation and DNA-protein recognition. Recent experiments suggest that short DNAs of tens of base pairs (bps) may have apparently higher flexibility than those of kilo bps, while there is still the debate on such high flexibility. In the present work, we have studied the flexibility of short DNAs with finite-length of 5-50 bps by the all-atomistic molecular dynamics simulations and Monte Carlo simulations with the worm-like chain model. Our microscopic analyses reveal that short DNAs have apparently high flexibility which is attributed to the significantly strong bending and stretching flexibilities of ∼6 bps at each helix end. Correspondingly, the apparent persistence length lp of short DNAs increases gradually from ∼29 nm to ∼45 nm as DNA length increases from 10 to 50 bps, in accordance with the available experimental data. Our further analyses show that the short DNAs with excluding ∼6 bps at each helix end have the similar flexibility with those of kilo bps and can be described by the worm-like chain model with lp ∼ 50 nm.

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.

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.

Role of microscopic flexibility in tightly curved DNA

The genetic material in living cells is organized into complex structures in which DNA is subjected to substantial contortions. Here we investigate the difference in structure, dynamics, and flexibility between two topological states of a short (107 base pair) DNA sequence in a linear form and a covalently closed, tightly curved circular DNA form. By employing a combination of all-atom molecular dynamics (MD) simulations and elastic rod modeling of DNA, which allows capturing microscopic details while monitoring the global dynamics, we demonstrate that in the highly curved regime the microscopic flexibility of the DNA drastically increases due to the local mobility of the duplex. By analyzing vibrational entropy and Lipari–Szabo NMR order parameters from the simulation data, we propose a novel model for the thermodynamic stability of high-curvature DNA states based on vibrational untightening of the duplex. This novel view of DNA bending provides a fundamental explanation that bridges the gap between classical models of DNA and experimental studies on DNA cyclization, which so far have been in substantial disagreement.

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.

DNA conformational flexibility study using phosphate backbone neutralization model

Due to the critical role of DNA in the processes of the cell cycle, the structural and physicochemical properties of DNA have long been of concern. In the present work, the effect of interplay between the DNA duplex and metal ions in solution on the DNA structure and conformational flexibility is studied by comparing the structure and dynamic conformational behavior of a duplex in a normal form and its “null isomer” using molecular dynamics methods. It was found that the phosphate neutralization changes the cation atmosphere around the DNA duplex greatly, increases the major groove width, decreases the minor groove width, and reduces the global bending direction preference. We also noted that the probability of BI phosphate linkages increases significantly because of the charge reduction in the backbone phosphate groups. More importantly, we found that the electrostatic effect on the DNA conformational flexibility is dependent on the sequence; that is, the phosphate backbone neutralization induces the global dynamic bending to be less flexible for GC-rich sequences but more flexible for AT-rich sequences.

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.

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.

Probe Position-Dependent Counterion Dynamics in DNA: Comparison of Time-Resolved Stokes Shift of Groove-Bound to Base-Stacked Probes in the Presence of Different Monovalent Counterions

Time-resolved fluorescence Stokes shifts (TRFSS) of 4',6-diamidino-2-phenylindole (DAPI) inside the minor groove of DNA are measured in the presence of three different monovalent counterions: sodium (Na(+)), rubidium (Rb(+)), and tetrabutylammonium (TBA(+)). Fluorescence up-conversion and time-correlated single photon counting are combined to obtain the time-resolved emission spectra (TRES) of DAPI in DNA from 100 fs to 10 ns. Time-resolved Stokes shift data suggest that groove-bound DAPI can not sense the counterion dynamics because the ions are displaced by DAPI far from the probe-site. However, when these results are compared to the earlier base-stacked coumarin data, the same ions are found to affect the nanosecond dynamics significantly. This suggests that the ions come close to the probe-site, such that they can affect the dynamics when measured by base-stacked coumarin. These results support previous molecular dynamics (MD) simulation data of groove-bound and base-stacked probes inside DNA.

Do we have to explicitly model the ions in brownian dynamics simulations of proteins?

Brownian dynamics (BD) is a very efficient coarse-grained simulation technique which is based on Einstein's explanation of the diffusion of colloidal particles. On these length scales well beyond the solvent granularity, a treatment of the electrostatic interactions on a Debye-Hückel (DH) level with its continuous ion densities is consistent with the implicit solvent of BD. On the other hand, since many years BD is being used as a workhorse simulation technique for the much smaller biological proteins. Here, the assumption of a continuous ion density, and therefore the validity of the DH electrostatics, becomes questionable. We therefore investigated for a few simple cases how far the efficient DH electrostatics with point charges can be used and when the ions should be included explicitly in the BD simulation. We find that for large many-protein scenarios or for binary association rates, the conventional continuum methods work well and that the ions should be included explicitly when detailed association trajectories or protein folding are investigated.

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.

Contribution of nonlocal interactions to DNA elasticity

A nonlocal harmonic elastic rod model is proposed to describe the elastic behavior of short DNA molecules. We show that the nonlocal interactions contribute to effective bending energy of the molecule and affect its apparent persistence length. It is also shown that the anomalous behavior which has been observed in all-atom molecular dynamic simulations [A. K. Mazur, Biophys. J. 134, 4507 (2006)] can be a consequence of both nonlocal interactions between DNA base pairs and the intrinsic curvature of DNA.

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.

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.

Salt-dependent folding energy landscape of RNA three-way junction

RNAs are highly negatively charged chain molecules. Metal ions play a crucial role in RNA folding stability and conformational changes. In this work, we employ the recently developed tightly bound ion (TBI) model, which accounts for the correlation between ions and the fluctuation of ion distributions, to investigate the ion-dependent free energy landscape for the three-way RNA junction in a 16S rRNA domain. The predicted electrostatic free energy landscape suggests that 1), ion-mediated electrostatic interactions cause an ensemble of unfolded conformations narrowly populated around the maximally extended structure; and 2), Mg(2+) ion-induced correlation effects help bring the helices to the folded state. Nonelectrostatic interactions, such as noncanonical interactions within the junctions and between junctions and helix stems, might further limit the conformational diversity of the unfolded state, resulting in a more ordered unfolded state than the one predicted from the electrostatic effect. Moreover, the folded state is predominantly stabilized by the coaxial stacking force. The TBI-predicted folding stability agrees well with the experimental measurements for the different Na(+) and Mg(2+) ion concentrations. For Mg(2+) solutions, the TBI model, which accounts for the Mg(2+) ion correlation effect, gives more improved predictions than the Poisson-Boltzmann theory, which tends to underestimate the role of Mg(2+) in stabilizing the folded structure. Detailed control tests indicate that the dominant ion correlation effect comes from the charge-charge Coulombic correlation rather than the size (excluded volume) correlation between the ions. Furthermore, the model gives quantitative predictions for the ion size effect in the folding energy landscape and folding cooperativity.

Predicting electrostatic forces in RNA folding

Metal ion-mediated electrostatic interactions are critical to RNA folding. Although considerable progress has been made in mechanistic studies, the problem of accurate predictions for the ion effects in RNA folding remains unsolved, mainly due to the complexity of several potentially important issues such as ion correlation and dehydration effects. In this chapter, after giving a brief overview of the experimental findings and theoretical approaches, we focus on a recently developed new model, the tightly bound ion (TBI) model, for ion electrostatics in RNA folding. The model is unique because it can treat ion correlation and fluctuation effects for realistic RNA 3D structures. For monovalent ion (such as Na(+)) solutions, where ion correlation is weak, TBI and the Poisson-Boltzmann (PB) theory give the same results and the results agree with the experimental data. For multivalent ion (such as Mg(2+)) solutions, where ion correlation can be strong, however, TBI gives much improved predictions than the PB. Moreover, the model suggests an ion correlation-induced mechanism for the unusual efficiency of Mg(2+) ions in the stabilization of RNA tertiary folds. In this chapter, after introducing the theoretical framework of the TBI model, we will describe how to apply the model to predict ion-binding properties and ion-dependent folding stabilities.

Salt dependence of nucleic acid hairpin stability

Single-stranded junctions/loops are frequently occurring structural motifs in nucleic acid structures. Due to the polyanionic nature of the nucleic acid backbone, metal ions play a crucial role in the loop stability. Here we use the tightly bound ion theory, which can account for the possible ion correlation and ensemble (fluctuation) effects, to predict the ion-dependence of loop and stem-loop (hairpin) free energies. The predicted loop free energy is a function of the loop length, the loop end-to-end distance, and the ion (Na(+) and Mg(2+) in this study) concentrations. Based on the statistical mechanical calculations, we derive a set of empirical formulas for the loop thermodynamic parameters as functions of Na(+) and Mg(2+) concentrations. For three specific types of loops, namely, hairpin, bulge, and internal loops, the predicted free energies agree with the experimental data. Further applications of these empirical formulas to RNA and DNA hairpin stability lead to good agreements with the available experimental data. Our results indicate that the ion-dependent loop stability makes significant contribution to the overall ion-dependence of the hairpin stability.