Ion-mediated nucleic acid helix-helix interactions

Effects of monovalent and divalent cations on the rheology of entangled DNA

In this paper we investigate the effects of varying cation valency and concentration on the rheology of entangled λDNA solutions. We show that monovalent cations moderately increase the viscoelasticty of the solutions mainly by stabilising linear concatenation of λDNA "monomers" via hybridisation of their sticky ends. On the contrary, divalent cations have a far more complex and dramatic effect on the rheology of the solution and we observe evidence of inter-molecular DNA-DNA bridging by Mg2+. We argue that these results may be interesting in the context of dense solutions of single and double stranded DNA, e.g. in vivo or in biotechnology applications such as DNA origami and DNA hydrogels.

Why Na+ has higher propensity than K+ to condense DNA in a crowded environment

Experimentally, in the presence of the crowding agent polyethylene glycol (PEG), sodium ions compact double-stranded DNA more readily than potassium ions. Here, we have used molecular dynamics simulations and the "ion binding shells model" of DNA condensation to provide an explanation for the observed variations in condensation of short DNA duplexes in solutions containing different monovalent cations and PEG; several predictions are made. According to the model we use, externally bound ions contribute the most to the ion-induced aggregation of DNA duplexes. The simulations reveal that for two adjacent DNA duplexes, the number of externally bound Na+ ions is larger than the number of K+ ions over a wide range of chloride concentrations in the presence of PEG, providing a qualitative explanation for the higher propensity of sodium ions to compact DNA under crowded conditions. The qualitative picture is confirmed by an estimate of the corresponding free energy of DNA aggregation that is at least 0.2kBT per base pair more favorable in solution with NaCl than with KCl at the same ion concentration. The estimated attraction free energy of DNA duplexes in the presence of Na+ depends noticeably on the DNA sequence; we predict that AT-rich DNA duplexes are more readily condensed than GC-rich ones in the presence of Na+. Counter-intuitively, the addition of a small amount of a crowding agent with high affinity for the specific condensing ion may lead to the weakening of the ion-mediated DNA-DNA attraction, shifting the equilibrium away from the DNA condensed phase.

Multivalent Ion-Mediated Attraction between Like-Charged Colloidal Particles: Nonmonotonic Dependence on the Particle Charge

Ion-mediated effective interactions are important for the structure and stability of charged particles such as colloids and nucleic acids. It has been known that the intrinsic electrostatic repulsion between like-charged particles can be modulated into effective attraction by multivalent ions. In this work, we examined the dependence of multivalent ion-mediated attraction between like-charged colloidal particles on the particle charge in a wide range by extensive Monte Carlo simulations. Our calculations show that for both divalent and trivalent salts, the effective attraction between like-charged colloidal particles becomes stronger with the increase of the particle charge, whereas it gradually becomes weakened when the particle charge exceeds a "critical" value. Correspondingly, as the particle charge is increased, the driving force for such effective attraction transits from an attractive electrostatic force to an attractive depletion force, and the attraction weakening by high particle charges is attributed to the transition of electrostatic force from attraction to repulsion. Our analyses suggest that the attractive depletion force and the repulsive electrostatic force at high particle charges result from the Coulomb depletion which suppresses the counterion condensation in the limited region between two like-charged colloidal particles. Moreover, our extensive calculations indicate that the "critical" particle charge decreases apparently for larger ions and smaller colloidal particles due to stronger Coulomb depletion and decreases slightly at higher salt concentrations due to the slightly enhanced Coulomb depletion in the intervening space between colloidal particles. Encouragingly, we derived an analytical formula for the "critical" particle charge based on the Lindemann melting law.

Ion-mediated interactions between like-charged polyelectrolytes with bending flexibility

Ion-mediated interactions between polyelectrolytes (PEs) are crucial to the properties of flexible biopolymers such as nucleic acids and proteins but the effect of PE flexibility on such interactions has not been explicitly addressed until now. In this work, the potentials of mean force (PMFs) between like-charged PEs with different bending flexibility have been investigated by Monte Carlo simulations and a cylindrical confinement around each PE was involved to model two PEs in an array. We found that in the absence of trivalent salt, the PMFs between like-charged PEs in an array are apparently repulsive while the bending flexibility can visibly decrease the repulsive PMFs. With the addition of high trivalent salt, the PMFs become significantly attractive whereas the attractive PMFs can be apparently weakened by the bending flexibility. Our analyses reveal that the effect of bending flexibility is attributed to the increased PE conformational space, which allows the PEs to fluctuate away to decrease the monovalent ion-mediated repulsion or to weaken the trivalent ion-mediated attraction through disrupting trivalent ion-bridging configuration. Additionally, our further calculations show that the effect of bending flexibility on the ion-mediated interactions is less apparent for PEs without cylindrical confinement.

Divalent metal ions and intermolecular interactions facilitate DNA network formation

The interactions between divalent metal ions and DNA are crucial for basic life processes. These interactions are also important in advanced technological products such as DNA-based ion sensors. Current polyelectrolyte theories cannot describe these interactions well and do not consider the corresponding dynamics. In this study, we report the single-molecule dynamics of the binding of divalent metal ions to a single DNA molecule and the morphology characterization of the complex. We found that most of the divalent metal ions (Mn²⁺, Zn²⁺, Co²⁺, Ni²⁺, and Cd²⁺), except Mg²⁺ and Ca²⁺, could cause monomolecular DNA condensation. For transition metal ions, different ionic strengths were required to induce the compaction, and different shortening speeds were displayed in the dynamics, indicating ionic specificity. Atomic force microscopy revealed that the morphologies of the metal ion-DNA complexes were affected by the ionic strength of the metal ion, DNA chain length, and DNA concentration. At low metal ion concentration, DNA tended to adopt a random coil conformation. Increasing the ionic strength led to network-like condensed structures, suggesting that divalent metal ions can induce attraction between DNA molecules. Furthermore, higher DNA concentration and longer chain length enhanced intermolecular interactions and consequently resulted in network structures with a higher degree of interconnectivity.

Additive Modulation of DNA-DNA Interactions by Interstitial Ions

Quantitative understanding of biomolecular electrostatics, particularly involving multivalent ions and highly charged surfaces, remains lacking. Ion-modulated interactions between nucleic acids provide a model system in which electrostatics plays a dominant role. Using ordered DNA arrays neutralized by spherical cobalt³⁺ hexammine and Mg²⁺ ions, we investigate how the interstitial ions modulate DNA-DNA interactions. Using methods of ion counting, osmotic stress, and x-ray diffraction, we systematically determine thermodynamic quantities, including ion chemical potentials, ion partition, DNA osmotic pressure and force, and DNA-DNA spacing. Analyses of the multidimensional data provide quantitative insights into their interdependencies. The key finding of this study is that DNA-DNA forces are observed to linearly depend on the partition of interstitial ions, suggesting the dominant role of ion-DNA coupling. Further implications are discussed in light of physical theories of electrostatic interactions and like-charge attraction.

Characterisation of aptamer-anchored poly(EDMA-co-GMA) monolith for high throughput affinity binding

Immobilisation of aptameric ligands on solid stationary supports for effective binding of target molecules requires understanding of the relationship between aptamer-polymer interactions and the conditions governing the mass transfer of the binding process. Herein, key process parameters affecting the molecular anchoring of a thrombin-binding aptamer (TBA) onto polymethacrylate monolith pore surface, and the binding characteristics of the resulting macroporous aptasensor were investigated. Molecular dynamics (MD) simulations of the TBA-thrombin binding indicated enhanced Guanine 4 (G4) structural stability of TBA upon interaction with thrombin in an ionic environment. Fourier-transform infrared spectroscopy and thermogravimetric analyses were used to characterise the available functional groups and thermo-molecular stability of the immobilised polymer generated with Schiff-base activation and immobilisation scheme. The initial degradation temperature of the polymethacrylate stationary support increased with each step of the Schiff-base process: poly(Ethylene glycol Dimethacrylate-co-Glycidyl methacrylate) or poly(EDMA-co-GMA) [196.0 °C (±1.8)]; poly(EDMA-co-GMA)-Ethylenediamine [235.9 °C (±6.1)]; poly(EDMA-co-GMA)-Ethylenediamine-Glutaraldehyde [255.4 °C (±2.7)]; and aptamer-modified monolith [273.7 °C (±2.5)]. These initial temperature increments reflected in the associated endothermic energies were determined with differential scanning calorimetry. The aptameric ligand density obtained after immobilisation was 480 pmol/μL. Increase in pH and ionic concentration affected the surface charge distribution and the binding characteristics of the aptamer-modified disk-monoliths, resulting in the optimum binding pH and ionic concentration of 8.0 and 5 mM Mg²⁺, respectively. These results are critical in understanding and setting parametric constraints indispensable to develop and enhance the performance of aptasensors.

Apparent repulsion between equally and oppositely charged spherical polyelectrolytes in symmetrical salt solutions

Ion-mediated interactions are very important for the properties of colloids and biomacromolecules such as nucleic acids and proteins. In this work, the ion-mediated interactions between equally and oppositely charged spherical polyelectrolytes (SPEs) in symmetrical divalent electrolytes have been investigated by Monte Carlo simulations, and an unexpected apparent repulsion was observed at high divalent salt concentration. Our investigations also show that the effective repulsion becomes more pronounced for SPEs with higher charge densities and for counterions with larger sizes and was found to be tightly accompanied with the over-neutralization to SPEs by condensed counterions and their release upon the approach of SPEs. Such attractive interaction can be reproduced by our proposed modified Poisson-Boltzmann model and is mainly attributed to the increase in the electrostatic repulsion between on charged SPE and the over-neutralized counterions around the other oppositely SPE with the approach of the two SPEs.

Rapid and reagentless detection of thrombin in clinic samples via microfluidic aptasensors with multiple target-binding sites

A reusable and straightforward aptasensor with the implementation of open-ended porous silicon (OEPSi) membranes was introduced for thrombin detection. When passing through the nanochannels of OEPSi integrated in a microfluidic cell, thrombin in sample solution could be captured by thrombin-binding aptamers (TBA) immobilized along the inner walls. The formation of thrombin-aptamer complex causes refractive index changes which can be measured by reflective interferometric Fourier transform spectroscopy (RIFTS). And this flow-through configuration with OEPSi has proven more efficient in capturing thrombin than the flow-over configuration with closed-ended PSi. For higher sensitivity, we investigated how the pore size, ionic strength, pH and aptamers affected the thrombin-aptamer interaction in nanopores. Under optimized conditions, the limits of detection (LOD) for thrombin detection in the buffer and serum were ∼6.70 nM and ∼8.21 nM respectively and a wide linear detection range (10-1000 nM) was observed. More importantly, this work reveals the sensitivity of the label-free biosensor can be significantly improved by attaching newly designed aptamers with two thrombin-binding sites. This phenomenon also indicates the potential of aptamer probes in adjusting effective pore size and enhancing the interaction between aptamers and targets through meticulous sequence design. Furthermore, the proposed strategy has been applied in thrombin detection in clinic samples successfully, which was verified by Enzyme-Linked Immunosorbent Assays (ELISA).

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.

Direct Demonstration of DNA Compaction Mediated by Divalent Counterions

We unambiguously demonstrated DNA attraction and its regulation mediated by divalent cations Mg²⁺ and Ca²⁺ by tethering a DNA single chain at various pH solutions. It is found that DNA is compacted when the pH of the solution containing these divalent counterions is decreased below 5. When the pH of the medium is ∼4, DNA is in an unstable transition state, being able to switch between compact and extensible states. We can also regulate the DNA attraction through a cyclic process of DNA compaction and unraveling by alternating the pH of the solution between 3 and 8. The corresponding change of morphology of DNA modulated by pH is also confirmed by atomic force microscopy (AFM). In the theoretical aspect, the present experimental finding is consistent with the coarse-grained simulation of Langevin dynamics on the effect of pH on DNA in a solution of divalent counterions.

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.

Potential of mean force between oppositely charged nanoparticles: A comprehensive comparison between Poisson-Boltzmann theory and Monte Carlo simulations

Ion-mediated interactions between like-charged polyelectrolytes have been paid much attention, and the Poisson-Boltzmann (PB) theory has been shown to fail in qualitatively predicting multivalent ion-mediated like-charge attraction. However, inadequate attention has been paid to the ion-mediated interactions between oppositely charged polyelectrolytes. In this work, the potentials of mean force (PMF) between oppositely charged nanoparticles in 1:1 and 2:2 salt solutions were investigated by Monte Carlo simulations and the PB theory. Our calculations show that the PMFs between oppositely charged nanoparticles are generally attractive in 1:1 and 2:2 salt solutions and that such attractive PMFs become weaker at higher 1:1 or 2:2 salt concentrations. The comprehensive comparisons show that the PB theory can quantitatively predict the PMFs between oppositely charged nanoparticles in 1:1 salt solutions, except for the slight deviation at very high 1:1 salt concentration. However, for 2:2 salt solutions, the PB theory generally overestimates the attractive PMF between oppositely charged nanoparticles, and this overestimation becomes more pronounced for nanoparticles with higher charge density and for higher 2:2 salt concentration. Our microscopic analyses suggest that the overestimation of the PB theory on the attractive PMFs for 2:2 salt solutions is attributed to the underestimation of divalent ions bound to nanoparticles.

Divalent Ion-Mediated DNA-DNA Interactions: A Comparative Study of Triplex and Duplex

Ion-mediated interaction between DNAs is essential for DNA condensation, and it is generally believed that monovalent and nonspecifically binding divalent cations cannot induce the aggregation of double-stranded (ds) DNAs. Interestingly, recent experiments found that alkaline earth metal ions such as Mg²⁺ can induce the aggregation of triple-stranded (ts) DNAs, although there is still a lack of deep understanding of the surprising findings at the microscopic level. In this work, we employed all-atom dynamic simulations to directly calculate the potentials of mean force (PMFs) between tsDNAs, between dsDNAs, and between tsDNA and dsDNA in Mg²⁺ solutions. Our calculations show that the PMF between tsDNAs is apparently attractive and becomes more strongly attractive at higher [Mg²⁺], although the PMF between dsDNAs cannot become apparently attractive even at high [Mg²⁺]. Our analyses show that Mg²⁺ internally binds into grooves and externally binds to phosphate groups for both tsDNA and dsDNA, whereas the external binding of Mg²⁺ is much stronger for tsDNA. Such stronger external binding of Mg²⁺ for tsDNA favors more apparent ion-bridging between helices than for dsDNA. Furthermore, our analyses illustrate that bridging ions, as a special part of external binding ions, are tightly and positively coupled to ion-mediated attraction between DNAs.

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.

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.

Evidence of protein-free homology recognition in magnetic bead force-extension experiments

Earlier theoretical studies have proposed that the homology-dependent pairing of large tracts of dsDNA may be due to physical interactions between homologous regions. Such interactions could contribute to the sequence-dependent pairing of chromosome regions that may occur in the presence or the absence of double-strand breaks. Several experiments have indicated the recognition of homologous sequences in pure electrolytic solutions without proteins. Here, we report single-molecule force experiments with a designed 60 kb long dsDNA construct; one end attached to a solid surface and the other end to a magnetic bead. The 60 kb constructs contain two 10 kb long homologous tracts oriented head to head, so that their sequences match if the two tracts fold on each other. The distance between the bead and the surface is measured as a function of the force applied to the bead. At low forces, the construct molecules extend substantially less than normal, control dsDNA, indicating the existence of preferential interaction between the homologous regions. The force increase causes no abrupt but continuous unfolding of the paired homologous regions. Simple semi-phenomenological models of the unfolding mechanics are proposed, and their predictions are compared with the data.

A review of immune amplification via ligand clustering by self-assembled liquid-crystalline DNA complexes

We examine how the interferon production of plasmacytoid dendritic cells is amplified by the self-assembly of liquid-crystalline antimicrobial peptide/DNA complexes. These specialized dendritic cells are important for host defense because they quickly release large quantities of type I interferons in response to infection. However, their aberrant activation is also correlated with autoimmune diseases such as psoriasis and lupus. In this review, we will describe how polyelectrolyte self-assembly and the statistical mechanics of multivalent interactions contribute to this process. In a more general compass, we provide an interesting conceptual corrective to the common notion in molecular biology of a dichotomy between specific interactions and non-specific interactions, and show examples where one can construct exquisitely specific interactions using non-specific interactions.

Salt contribution to the flexibility of single-stranded nucleic acid offinite length

Nucleic acids are negatively charged macromolecules and their structure properties are strongly coupled to metal ions in solutions. In this article, the salt effects on the flexibility of single-stranded (ss) nucleic acid chain ranging from 12 to 120 nucleotides are investigated systematically by the coarse-grained Monte Carlo simulations where the salt ions are considered explicitly and the ss chain is modeled with the virtual-bond structural model. Our calculations show that, the increase of ion concentration causes the structural collapse of ss chain and multivalent ions are much more efficient in causing such collapse, and both trivalent/small divalent ions can induce more compact state than a random relaxation state. We found that monovalent, divalent, and trivalent ions can all overcharge ss chain, and the dominating source for such overcharging changes from ion-exclusion-volume effect to ion Coulomb correlations. In addition, the predicted Na(+) and Mg(2+)-dependent persistence length l(p)'s of ss nucleic acid are in accordance with the available experimental data, and through systematic calculations, we obtained the empirical formulas for l(p) as a function of [Na(+)], [Mg(2+)] and chain length.

Multi-shell model of ion-induced nucleic acid condensation

We present a semi-quantitative model of condensation of short nucleic acid (NA) duplexes induced by trivalent cobalt(iii) hexammine (CoHex) ions. The model is based on partitioning of bound counterion distribution around single NA duplex into "external" and "internal" ion binding shells distinguished by the proximity to duplex helical axis. In the aggregated phase the shells overlap, which leads to significantly increased attraction of CoHex ions in these overlaps with the neighboring duplexes. The duplex aggregationfree energy is decomposed into attractive and repulsive components in such a way that they can be represented by simple analytical expressions with parameters derived from molecular dynamic simulations and numerical solutions of Poisson equation. The attractive term depends on the fractions of bound ions in the overlapping shells and affinity of CoHex to the "external" shell of nearly neutralized duplex. The repulsive components of the free energy are duplex configurational entropy loss upon the aggregation and the electrostatic repulsion of the duplexes that remains after neutralization by bound CoHex ions. The estimates of the aggregationfree energy are consistent with the experimental range of NA duplex condensation propensities, including the unusually poor condensation of RNA structures and subtle sequence effects upon DNAcondensation. The model predicts that, in contrast to DNA, RNA duplexes may condense into tighter packed aggregates with a higher degree of duplex neutralization. An appreciable CoHex mediated RNA-RNA attraction requires closer inter-duplex separation to engage CoHex ions (bound mostly in the "internal" shell of RNA) into short-range attractive interactions. The model also predicts that longer NA fragments will condense more readily than shorter ones. The ability of this model to explain experimentally observed trends in NAcondensation lends support to proposed NAcondensation picture based on the multivalent "ion binding shells."

Potential of mean force between like-charged nanoparticles: Many-body effect

Ion-mediated interaction is important for the properties of polyelectrolytes such as colloids and nucleic acids. The effective pair interactions between two polyelectrolytes have been investigated extensively, but the many-body effect for multiple polyelectrolytes still remains elusive. In this work, the many-body effect in potential of mean force (PMF) between like-charged nanoparticles in various salt solutions has been comprehensively examined by Monte Carlo simulation and the nonlinear Poisson-Boltzmann theory. Our calculations show that, at high 1:1 salt, the PMF is weakly repulsive and appears additive, while at low 1:1 salt, the additive assumption overestimates the repulsive many-body PMF. At low 2:2 salt, the pair PMF appears weakly repulsive while the many-body PMF can become attractive. In contrast, at high 2:2 salt, the pair PMF is apparently attractive while the many-body effect can cause a weaker attractive PMF than that from the additive assumption. Our microscopic analyses suggest that the elusive many-body effect is attributed to ion-binding which is sensitive to ion concentration, ion valence, number of nanoparticles and charges on nanoparticles.

The structural stability and catalytic activity of DNA and RNA oligonucleotides in the presence of organic solvents

Organic solvents and apolar media are used in the studies of nucleic acids to modify the conformation and function of nucleic acids, to improve solubility of hydrophobic ligands, to construct molecular scaffolds for organic synthesis, and to study molecular crowding effects. Understanding how organic solvents affect nucleic acid interactions and identifying the factors that dominate solvent effects are important for the creation of oligonucleotide-based technologies. This review describes the structural and catalytic properties of DNA and RNA oligonucleotides in organic solutions and in aqueous solutions with organic cosolvents. There are several possible mechanisms underlying the effects of organic solvents on nucleic acid interactions. The reported results emphasize the significance of the osmotic pressure effect and the dielectric constant effect in addition to specific interactions with nucleic acid strands. This review will serve as a guide for the selection of solvent systems based on the purpose of the nucleic acid-based experiments.

Free energy landscape and multiple folding pathways of an H-type RNA pseudoknot

How RNA sequences fold to specific tertiary structures is one of the key problems for understanding their dynamics and functions. Here, we study the folding process of an H-type RNA pseudoknot by performing a large-scale all-atom MD simulation and bias-exchange metadynamics. The folding free energy landscapes are obtained and several folding intermediates are identified. It is suggested that the folding occurs via multiple mechanisms, including a step-wise mechanism starting either from the first helix or the second, and a cooperative mechanism with both helices forming simultaneously. Despite of the multiple mechanism nature, the ensemble folding kinetics estimated from a Markov state model is single-exponential. It is also found that the correlation between folding and binding of metal ions is significant, and the bound ions mediate long-range interactions in the intermediate structures. Non-native interactions are found to be dominant in the unfolded state and also present in some intermediates, possibly hinder the folding process of the RNA.

Multivalent ion-mediated nucleic acid helix-helix interactions: RNA versus DNA

Ion-mediated interaction is critical to the structure and stability of nucleic acids. Recent experiments suggest that the multivalent ion-induced aggregation of double-stranded (ds) RNAs and DNAs may strongly depend on the topological nature of helices, while there is still lack of an understanding on the relevant ion-mediated interactions at atomistic level. In this work, we have directly calculated the potentials of mean force (PMF) between two dsRNAs and between two dsDNAs in Co(NH3)6 (3+) (Co-Hex) solutions by the atomistic molecular dynamics simulations. Our calculations show that at low [Co-Hex], the PMFs between B-DNAs and between A-RNAs are both (strongly) repulsive. However, at high [Co-Hex], the PMF between B-DNAs is strongly attractive, while those between A-RNAs and between A-DNAs are still (weakly) repulsive. The microscopic analyses show that for A-form helices, Co-Hex would become 'internal binding' into the deep major groove and consequently cannot form the evident ion-bridge between adjacent helices, while for B-form helices without deep grooves, Co-Hex would exhibit 'external binding' to strongly bridge adjacent helices. In addition, our further calculations show that, the PMF between A-RNAs could become strongly attractive either at very high [Co-Hex] or when the bottom of deep major groove is fixed with a layer of water.

DNA under Force: Mechanics, Electrostatics, and Hydration

Quantifying the basic intra- and inter-molecular forces of DNA has helped us to better understand and further predict the behavior of DNA. Single molecule technique elucidates the mechanics of DNA under applied external forces, sometimes under extreme forces. On the other hand, ensemble studies of DNA molecular force allow us to extend our understanding of DNA molecules under other forces such as electrostatic and hydration forces. Using a variety of techniques, we can have a comprehensive understanding of DNA molecular forces, which is crucial in unraveling the complex DNA functions in living cells as well as in designing a system that utilizes the unique properties of DNA in nanotechnology.

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.

Why double-stranded RNA resists condensation

The addition of small amounts of multivalent cations to solutions containing double-stranded DNA leads to inter-DNA attraction and eventual condensation. Surprisingly, the condensation is suppressed in double-stranded RNA, which carries the same negative charge as DNA, but assumes a different double helical form. Here, we combine experiment and atomistic simulations to propose a mechanism that explains the variations in condensation of short (25 base-pairs) nucleic acid (NA) duplexes, from B-like form of homopolymeric DNA, to mixed sequence DNA, to DNA:RNA hybrid, to A-like RNA. Circular dichroism measurements suggest that duplex helical geometry is not the fundamental property that ultimately determines the observed differences in condensation. Instead, these differences are governed by the spatial variation of cobalt hexammine (CoHex) binding to NA. There are two major NA-CoHex binding modes--internal and external--distinguished by the proximity of bound CoHex to the helical axis. We find a significant difference, up to 5-fold, in the fraction of ions bound to the external surfaces of the different NA constructs studied. NA condensation propensity is determined by the fraction of CoHex ions in the external binding mode.

Roles of the amino group of purine bases in the thermodynamic stability of DNA base pairing

The energetic aspects of hydrogen-bonded base-pair interactions are important for the design of functional nucleotide analogs and for practical applications of oligonucleotides. The present study investigated the contribution of the 2-amino group of DNA purine bases to the thermodynamic stability of oligonucleotide duplexes under different salt and solvent conditions, using 2'-deoxyriboinosine (I) and 2'-deoxyribo-2,6-diaminopurine (D) as non-canonical nucleotides. The stability of DNA duplexes was changed by substitution of a single base pair in the following order: G•C > D•T ≈ I•C > A•T > G•T > I•T. The apparent stabilization energy due to the presence of the 2-amino group of G and D varied depending on the salt concentration, and decreased in the water-ethanol mixed solvent. The effects of salt concentration on the thermodynamics of DNA duplexes were found to be partially sequence-dependent, and the 2-amino group of the purine bases might have an influence on the binding of ions to DNA through the formation of a stable base-paired structure. Our results also showed that physiological salt conditions were energetically favorable for complementary base recognition, and conversely, low salt concentration media and ethanol-containing solvents were effective for low stringency oligonucleotide hybridization, in the context of conditions employed in this study.

Conformation-dependent DNA attraction

Understanding how DNA molecules interact with other biomolecules is related to how they utilize their functions and is therefore critical for understanding their structure-function relationships. For a long time, the existence of Z-form DNA (a left-handed double helical version of DNA, instead of the common right-handed B-form) has puzzled the scientists, and the definitive biological significance of Z-DNA has not yet been clarified. In this study, the effects of DNA conformation in DNA-DNA interactions are explored by molecular dynamics simulations. Using umbrella sampling, we find that for both B- and Z-form DNA, surrounding Mg(2+) ions always exert themselves to screen the Coulomb repulsion between DNA phosphates, resulting in very weak attractive force. On the contrary, a tight and stable bound state is discovered for Z-DNA in the presence of Mg(2+) or Na(+), benefiting from their hydrophobic nature. Based on the contact surface and a dewetting process analysis, a two-stage binding process of Z-DNA is outlined: two Z-DNA first attract each other through charge screening and Mg(2+) bridges to phosphate groups in the same way as that of B-DNA, after which hydrophobic contacts of the deoxyribose groups are formed via a dewetting effect, resulting in stable attraction between two Z-DNA molecules. The highlighted hydrophobic nature of Z-DNA interaction from the current study may help to understand the biological functions of Z-DNA in gene transcription.

Ion competition in condensed DNA arrays in the attractive regime

Physical origin of DNA condensation by multivalent cations remains unsettled. Here, we report quantitative studies of how one DNA-condensing ion (Cobalt(3+) Hexammine, or Co(3+)Hex) and one nonDNA-condensing ion (Mg(2+)) compete within the interstitial space in spontaneously condensed DNA arrays. As the ion concentrations in the bath solution are systematically varied, the ion contents and DNA-DNA spacings of the DNA arrays are determined by atomic emission spectroscopy and x-ray diffraction, respectively. To gain quantitative insights, we first compare the experimentally determined ion contents with predictions from exact numerical calculations based on nonlinear Poisson-Boltzmann equations. Such calculations are shown to significantly underestimate the number of Co(3+)Hex ions, consistent with the deficiencies of nonlinear Poisson-Boltzmann approaches in describing multivalent cations. Upon increasing the concentration of Mg(2+), the Co(3+)Hex-condensed DNA array expands and eventually redissolves as a result of ion competition weakening DNA-DNA attraction. Although the DNA-DNA spacing depends on both Mg(2+) and Co(3+)Hex concentrations in the bath solution, it is observed that the spacing is largely determined by a single parameter of the DNA array, the fraction of DNA charges neutralized by Co(3+)Hex. It is also observed that only ∼20% DNA charge neutralization by Co(3+)Hex is necessary for spontaneous DNA condensation. We then show that the bath ion conditions can be reduced to one variable with a simplistic ion binding model, which is able to describe the variations of both ion contents and DNA-DNA spacings reasonably well. Finally, we discuss the implications on the nature of interstitial ions and cation-mediated DNA-DNA interactions.

Understanding nucleic acid-ion interactions

Ions surround nucleic acids in what is referred to as an ion atmosphere. As a result, the folding and dynamics of RNA and DNA and their complexes with proteins and with each other cannot be understood without a reasonably sophisticated appreciation of these ions' electrostatic interactions. However, the underlying behavior of the ion atmosphere follows physical rules that are distinct from the rules of site binding that biochemists are most familiar and comfortable with. The main goal of this review is to familiarize nucleic acid experimentalists with the physical concepts that underlie nucleic acid-ion interactions. Throughout, we provide practical strategies for interpreting and analyzing nucleic acid experiments that avoid pitfalls from oversimplified or incorrect models. We briefly review the status of theories that predict or simulate nucleic acid-ion interactions and experiments that test these theories. Finally, we describe opportunities for going beyond phenomenological fits to a next-generation, truly predictive understanding of nucleic acid-ion interactions.

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.

Ion-mediated RNA structural collapse: effect of spatial confinement

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

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

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

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.

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.

Conformations of semiflexible charged chains: an extended bundle versus repulsive coils

We consider two interacting semiflexible charged chains of length L(c) under shape fluctuations, where the interplay of electric and mechanical properties is found to yield rigidity-sensitive charge modulation and interdistance-dependent persistence length ℓ(p). The resulting conformation is characterized by equilibrium force between the chains and their fractal dimensions. It turns out that ℓ(p) and L(c) emerge as critical factors to determine the force nature as well as chain shapes. We show that conformational fluctuations cause the repulsion of nonsteric origin, and its competition with charge fluctuation effects yields the interchain force modulated by the length scales and counterion valence. As a result, it is predicted that flexible short chains can be more strongly repulsive than rigid long chains, although they carry smaller amount of net charges.

Divalent counterion-induced condensation of triple-strand DNA

Understanding and manipulation of the forces assembling DNA/RNA helices have broad implications for biology, medicine, and physics. One subject of significance is the attractive force between dsDNA mediated by polycations of valence ≥ 3. Despite extensive studies, the physical origin of the "like-charge attraction" remains unsettled among competing theories. Here we show that triple-strand DNA (tsDNA), a more highly charged helix than dsDNA, is precipitated by alkaline-earth divalent cations that are unable to condense dsDNA. We further show that our observation is general by examining several cations (Mg(2+), Ba(2+), and Ca(2+)) and two distinct tsDNA constructs. Cation-condensed tsDNA forms ordered hexagonal arrays that redissolve upon adding monovalent salts. Forces between tsDNA helices, measured by osmotic stress, follow the form of hydration forces observed with condensed dsDNA. Probing a well-defined system of point-like cations and tsDNAs with more evenly spaced helical charges, the counterintuitive observation that the more highly charged tsDNA (vs. dsDNA) is condensed by cations of lower valence provides new insights into theories of polyelectrolytes and the biological and pathological roles of tsDNA. Cations and tsDNAs also hold promise as a model system for future studies of DNA-DNA interactions and electrostatic interactions in general.

Influence of organic ions on DNA damage induced by 1 eV to 60 keV electrons

We report the results of a study on the influence of organic salts on the induction of single strand breaks (SSBs) and double strand breaks (DSBs) in DNA by electrons of 1 eV to 60 keV. Plasmid DNA films are prepared with two different concentrations of organic salts, by varying the amount of the TE buffer (Tris-HCl and EDTA) in the films with ratio of 1:1 and 6:1 Tris ions to DNA nucleotide. The films are bombarded with electrons of 1, 10, 100, and 60 000 eV under vacuum. The damage to the 3197 base-pair plasmid is analyzed ex vacuo by agarose gel electrophoresis. The highest yields are reached at 100 eV and the lowest ones at 60 keV. The ratios of SSB to DSB are surprisingly low at 10 eV (∼4.3) at both salt concentrations, and comparable to the ratios measured with 100 eV electrons. At all characteristic electron energies, the yields of SSB and DSB are found to be higher for the DNA having the lowest salt concentration. However, the organic salts are more efficient at protecting DNA against the damage induced by 1 and 10 eV electrons. DNA damage and protection by organic ions are discussed in terms of mechanisms operative at each electron energy. It is suggested that these ions create additional electric fields within the groove of DNA, which modify the resonance parameter of 1 and 10 eV electrons, namely, by reducing the electron capture cross-section of basic DNA units and the lifetime of corresponding transient anions. An interstrand electron transfer mechanism is proposed to explain the low ratios for the yields of SSB to those of DSB produced by 10 eV electrons.

Compact intermediates in RNA folding

Large noncoding RNAs fold into their biologically functional structures via compact yet disordered intermediates, which couple the stable secondary structure of the RNA with the emerging tertiary fold. The specificity of the collapse transition, which coincides with the assembly of helical domains, depends on RNA sequence and counterions. It determines the specificity of the folding pathways and the magnitude of the free energy barriers to the ensuing search for the native conformation. By coupling helix assembly with nascent tertiary interactions, compact folding intermediates in RNA also play a crucial role in ligand binding and RNA-protein recognition.