Divalent counterion-induced condensation of triple-strand DNA

Reprogramming Filamentous fd Viruses to Capture Copper Ions

C-terminal truncated variants (A, VA, NVA, ANVA, FANVA and GFANVA) of our recently identified Cu(II) specific peptide "HGFANVA" were displayed on filamentous fd phages. Wild type fd-tet and engineered virus variants were treated with 100 mM Cu(II) solution at a final phage concentration of 1011 vir/ml and 1012 vir/ml. Scanning electron microscopy (SEM) and atomic force microscopy (AFM) imaging before Cu(II) exposure showed ≈6-8 nm thick filamentous virus layer formation. Cu(II) treatment resulted in aggregated bundle-like assemblies with mineral deposition. HGFANVA phage formed aggregates with an excessive mineral coverage. As the virus concentration was 10-fold decreased, nanowire-like assemblies were observed for shorter peptide variants A, NVA and ANVA. Wild type fd phages did not show any mineral formation. Energy dispersive X-ray spectroscopy (EDX) analyses revealed the presence of C and N peaks on phage organic material. Cu peak was only detected for engineered viruses. Metal ion binding of viruses was next investigated by enzyme-linked immunosorbent assay (ELISA) analyses. Engineered viruses were able to bind Cu(II) forming mineralized intertwined structures although no His (H) unit was displayed. Such genetically reprogrammed virus based biological materials can be further applied for bioremediation studies to achieve a circular economy.

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.

Sequence-Dependent Orientational Coupling and Electrostatic Attraction in Cation-Mediated DNA-DNA Interactions

Condensation of DNA is vital for its biological functions and controlled nucleic acid assemblies. However, the mechanisms of DNA condensation are not fully understood due to the inability of experiments to access cation distributions and the complex interplay of energetic and entropic forces during assembly. By constructing free energy surfaces using exhaustive sampling and detailed analysis of cation distributions, we elucidate the mechanism of DNA condensation in different salt conditions and with different DNA sequences. We found that DNA condensation is facilitated by the correlated dynamics of the localized cations at the grooves of DNA helices. These dynamics are strongly dependent on the salt conditions and DNA sequences. In the presence of magnesium ions, major groove binding facilitates attraction. In contrast, in the presence of polyvalent cations, minor groove binding serves to create charge patterns, leading to condensation. Our findings present a novel advancement in the field and have broad implications for understanding and controlling nucleic acid complexes in vivo and in vitro.

Effect of mono- and multi-valent ionic environments on the in-lattice nanoparticle-grafted single-stranded DNA

Polyelectrolyte (PE) chains respond in a complex manner to multivalent salt environments, and this behavior depends on pH, temperature, and the presence of specific counter ions. Although much work has been done to understand the behaviour of free PE chains, it is important to reveal their behaviour on a nanoparticle's surface, where surface constraints, particle geometry, and multi-chain environment can affect their behaviour and contribute to particles' assembly states. Our work investigates, using in situ small-angle X-ray scattering (SAXS), the morphology of PE (single-stranded DNA) chains grafted onto the surface of spherical gold nanoparticles assembled in a lattice in the presence of monovalent, divalent and trivalent salts. For divalent salts, the DNA brush length was found to decrease at a faster rate with salt concentration than in the monovalent salt environment, while trivalent salts led to chain collapse. Using a power law analysis and the modified Daoud-Cotton model, we have obtained insight into the mechanism of a nanoparticle-grafted chain's response to ionic environments. Our analysis suggests that the decrease in brush length is due to the conventional electrostatic screening for monovalent systems, whereas for divalent systems both electrostatic screening and divalent ion bridging must be considered.

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.

Salt-Dependent RNA Pseudoknot Stability: Effect of Spatial Confinement

Macromolecules, such as RNAs, reside in crowded cell environments, which could strongly affect the folded structures and stability of RNAs. The emergence of RNA-driven phase separation in biology further stresses the potential functional roles of molecular crowding. In this work, we employed the coarse-grained model that was previously developed by us to predict 3D structures and stability of the mouse mammary tumor virus (MMTV) pseudoknot under different spatial confinements over a wide range of salt concentrations. The results show that spatial confinements can not only enhance the compactness and stability of MMTV pseudoknot structures but also weaken the dependence of the RNA structure compactness and stability on salt concentration. Based on our microscopic analyses, we found that the effect of spatial confinement on the salt-dependent RNA pseudoknot stability mainly comes through the spatial suppression of extended conformations, which are prevalent in the partially/fully unfolded states, especially at low ion concentrations. Furthermore, our comprehensive analyses revealed that the thermally unfolding pathway of the pseudoknot can be significantly modulated by spatial confinements, since the intermediate states with more extended conformations would loss favor when spatial confinements are introduced.

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.

Structure-guided DNA-DNA attraction mediated by divalent cations

Probing the role of surface structure in electrostatic interactions, we report the first observation of sequence-dependent dsDNA condensation by divalent alkaline earth metal cations. Disparate behaviors were found between two repeating sequences with 100% AT content, a poly(A)-poly(T) duplex (AA-TT) and a poly(AT)-poly(TA) duplex (AT-TA). While AT-TA exhibits non-distinguishable behaviors from random-sequence genomic DNA, AA-TT condenses in all alkaline earth metal ions. We characterized these interactions experimentally and investigated the underlying principles using computer simulations. Both experiments and simulations demonstrate that AA-TT condensation is driven by non-specific ion–DNA interactions. Detailed analyses reveal sequence-enhanced major groove binding (SEGB) of point-charged alkali ions as the major difference between AA-TT and AT-TA, which originates from the continuous and close stacking of nucleobase partial charges. These SEGB cations elicit attraction via spatial juxtaposition with the phosphate backbone of neighboring helices, resulting in an azimuthal angular shift between apposing helices. Our study thus presents a distinct mechanism in which, sequence-directed surface motifs act with cations non-specifically to enact sequence-dependent behaviors. This physical insight allows a renewed understanding of the role of repeating sequences in genome organization and regulation and offers a facile approach for DNA technology to control the assembly process of nanostructures.

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.

Salt effect on thermodynamics and kinetics of a single RNA base pair

Due to the polyanionic nature of RNAs, the structural folding of RNAs are sensitive to solution salt conditions, while there is still lack of a deep understanding of the salt effect on the thermodynamics and kinetics of RNAs at a single base-pair level. In this work, the thermodynamic and the kinetic parameters for the base-pair AU closing/opening at different salt concentrations were calculated by 3-µsec all-atom molecular dynamics (MD) simulations at different temperatures. It was found that for the base-pair formation, the enthalpy change [Formula: see text] is nearly independent of salt concentration, while the entropy change [Formula: see text] exhibits a linear dependence on the logarithm of salt concentration, verifying the empirical assumption based on thermodynamic experiments. Our analyses revealed that such salt concentration dependence of the entropy change mainly results from the dependence of ion translational entropy change for the base pair closing/opening on salt concentration. Furthermore, the closing rate increases with the increasing of salt concentration, while the opening rate is nearly independent of salt concentration. Additionally, our analyses revealed that the free energy surface for describing the base-pair opening and closing dynamics becomes more rugged with the decrease of salt concentration.

Stability prediction of canonical and non-canonical structures of nucleic acids in various molecular environments and cells

This review provides the biophysicochemical background and recent advances in stability prediction of canonical and non-canonical structures of nucleic acids in various molecular environments and cells.

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.

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.

Competitive Binding of Mg2+ and Na+ Ions to Nucleic Acids: From Helices to Tertiary Structures

Nucleic acids generally reside in cellular aqueous solutions with mixed divalent/monovalent ions, and the competitive binding of divalent and monovalent ions is critical to the structures of nucleic acids because of their polyanionic nature. In this work, we first proposed a general and effective method for simulating a nucleic acid in mixed divalent/monovalent ion solutions with desired bulk ion concentrations via molecular dynamics (MD) simulations and investigated the competitive binding of Mg²⁺/Na⁺ ions to various nucleic acids by all-atom MD simulations. The extensive MD-based examinations show that single MD simulations conducted using the proposed method can yield desired bulk divalent/monovalent ion concentrations for various nucleic acids, including RNA tertiary structures. Our comprehensive analyses show that the global binding of Mg²⁺/Na⁺ to a nucleic acid is mainly dependent on its structure compactness, as well as Mg²⁺/Na⁺ concentrations, rather than the specific structure of the nucleic acid. Specifically, the relative global binding of Mg²⁺ over Na⁺ is stronger for a nucleic acid with higher effective surface charge density and higher relative Mg²⁺/Na⁺ concentrations. Furthermore, the local binding of Mg²⁺/Na⁺ to a phosphate of a nucleic acid mainly depends on the local phosphate density in addition to Mg²⁺/Na⁺ concentrations.

Hexahydrated Mg2+ Binding and Outer-Shell Dehydration on RNA Surface

The interaction between metal ions, especially Mg²⁺ ions, and RNA plays a critical role in RNA folding. Upon binding to RNA, a metal ion that is fully hydrated in bulk solvent can become dehydrated. Here we use molecular dynamics simulation to investigate the dehydration of bound hexahydrated Mg²⁺ ions. We find that a hydrated Mg²⁺ ion in the RNA groove region can involve significant dehydration in the outer hydration shell. The first or innermost hydration shell of the Mg²⁺ ion, however, is retained during the simulation because of the strong ion-water electrostatic attraction. As a result, water-mediated hydrogen bonding remains an important form for Mg²⁺-RNA interaction. Analysis for ions at different binding sites shows that the most pronounced water deficiency relative to the fully hydrated state occurs at a radial distance of around 11 Å from the center of the ion. Based on the independent 200 ns molecular dynamics simulations for three different RNA structures (Protein Data Bank: 1TRA, 2TPK, and 437D), we find that Mg²⁺ ions overwhelmingly dominate over monovalent ions such as Na⁺ and K⁺ in ion-RNA binding. Furthermore, application of the free energy perturbation method leads to a quantitative relationship between the Mg²⁺ dehydration free energy and the local structural environment. We find that ΔΔG_hyd, the change of the Mg²⁺ hydration free energy upon binding to RNA, varies linearly with the inverse distance between the Mg²⁺ ion and the nearby nonbridging oxygen atoms of the phosphate groups, and ΔΔG_hyd can reach -2.0 kcal/mol and -3.0 kcal/mol for an Mg²⁺ ion bound to the surface and to the groove interior, respectively. In addition, the computation results in an analytical formula for the hydration ratio as a function of the average inverse Mg²⁺-O distance. The results here might be useful for further quantitative investigations of ion-RNA interactions in RNA folding.

Energetics, Ion, and Water Binding of the Unfolding of AA/UU Base Pair Stacks and UAU/UAU Base Triplet Stacks in RNA

Triplex formation occurs via interaction of a third strand with the major groove of double-stranded nucleic acid, through Hoogsteen hydrogen bonding. In this work, we use a combination of temperature-dependent UV spectroscopy and differential scanning calorimetry to determine complete thermodynamic profiles for the unfolding of polyadenylic acid (poly(rA))·polyuridylic acid (poly(rU)) (duplex) and poly(rA)·2poly(rU) (triplex). Our thermodynamic results are in good agreement with the much earlier work of Krakauer and Sturtevant using only UV melting techniques. The folding of these two helices yielded an uptake of ions, Δ n_Na⁺ = 0.15 mol Na⁺/mol base pair (duplex) and 0.30 mol Na⁺/mole base triplet (triplex), which are consistent with their polymer behavior and the higher charge density parameter of triple helices. The osmotic stress technique yielded a release of structural water, Δ n_W = 2 mol H₂O/mol base pair (duplex unfolding into single strands) and an uptake of structural water, Δ n_W = 2 mol H₂O/mole base pair (triplex unfolding into duplex and a single strand). However, an overall release of electrostricted waters is obtained for the unfolding of both complexes from pressure perturbation calorimetric experiments. In total, the Δ V values obtained for the unfolding of triplex into duplex and a single strand correspond to an immobilization of two structural waters and a release of three electrostricted waters. The Δ V values obtained for the unfolding of duplex into two single strands correspond to the release of two structural waters and the immobilization of four electrostricted water molecules.

Effect of Cation-π Interaction on Macroionic Self-Assembly

A series of rod-shaped polyoxometalates (POMs) [Bu₄ N]₇ [Mo₆ O₁₈ NC(CH₂ O)₃ MnMo₆ O₁₈ (OCH₂ )₃ CNMo₆ O₁₈ ] and [Bu₄ N]₇ [ArNMo₆ O₁₇ NC(CH₂ O)₃ MnMo₆ O₁₈ (OCH₂ )₃ CNMo₆ O₁₇ NAr] (Ar=2,6-dimethylphenyl, naphthyl and 1-methylnaphthyl) were chosen to study the effects of cation-π interaction on macroionic self-assembly. Diffusion ordered spectroscopy (DOSY) and isothermal titration calorimetry (ITC) techniques show that the binding affinity between the POMs and Zn²⁺ ions is enhanced significantly after grafting aromatic groups onto the clusters, leading to the effective replacement of tetrabutylammonium counterions (TBAs) upon the addition of ZnCl₂ . The incorporation of aromatic groups results in the significant contribution of cation-π interaction to the self-assembly, as confirmed by the opposite trend of assembly size vs. ionic strength when compared with those without aromatic groups. The small difference between two aromatic groups toward the Zn²⁺ ions is amplified after combining with the clusters, which consequently triggers the self-recognition behavior between two highly similar macroanions.

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.

Directionally Interacting Spheres and Rods Form Ordered Phases

The structures formed by mixtures of dissimilarly shaped nanoscale objects can significantly enhance our ability to produce nanoscale architectures. However, understanding their formation is a complex problem due to the interplay of geometric effects (entropy) and energetic interactions at the nanoscale. Spheres and rods are perhaps the most basic geometrical shapes and serve as convenient models of such dissimilar objects. The ordered phases formed by each of these individual shapes have already been explored, however, when mixed, spheres and rods have demonstrated only limited structural organization to date. Here, we show using experiments and theory that the introduction of directional attractions between rod ends and isotropically interacting spherical nanoparticles (NPs) through DNA base pairing leads to the formation of ordered three-dimensional lattices. The spheres and rods arrange themselves in a complex alternating manner, where the spheres can form either a face-centered cubic (FCC) or hexagonal close-packed (HCP) lattice, or a disordered phase, as observed by in situ X-ray scattering. Increasing NP diameter at fixed rod length yields an initial transition from a disordered phase to the HCP crystal, energetically stabilized by rod-rod attraction across alternating crystal layers, as revealed by theory. In the limit of large NPs, the FCC structure is instead stabilized over the HCP by rod entropy. We, therefore, propose that directionally specific attractions in mixtures of anisotropic and isotropic objects offer insight into unexplored self-assembly behavior of noncomplementary shaped particles.

Improved model of hydrated calcium ion for molecular dynamics simulations using classical biomolecular force fields

Calcium ions (Ca(2+) ) play key roles in various fundamental biological processes such as cell signaling and brain function. Molecular dynamics (MD) simulations have been used to study such interactions, however, the accuracy of the Ca(2+) models provided by the standard MD force fields has not been rigorously tested. Here, we assess the performance of the Ca(2+) models from the most popular classical force fields AMBER and CHARMM by computing the osmotic pressure of model compounds and the free energy of DNA-DNA interactions. In the simulations performed using the two standard models, Ca(2+) ions are seen to form artificial clusters with chloride, acetate, and phosphate species; the osmotic pressure of CaAc2 and CaCl2 solutions is a small fraction of the experimental values for both force fields. Using the standard parameterization of Ca(2+) ions in the simulations of Ca(2+) -mediated DNA-DNA interactions leads to qualitatively wrong outcomes: both AMBER and CHARMM simulations suggest strong inter-DNA attraction whereas, in experiment, DNA molecules repel one another. The artificial attraction of Ca(2+) to DNA phosphate is strong enough to affect the direction of the electric field-driven translocation of DNA through a solid-state nanopore. To address these shortcomings of the standard Ca(2+) model, we introduce a custom model of a hydrated Ca(2+) ion and show that using our model brings the results of the above MD simulations in quantitative agreement with experiment. Our improved model of Ca(2+) can be readily applied to MD simulations of various biomolecular systems, including nucleic acids, proteins and lipid bilayer membranes. © 2016 Wiley Periodicals, Inc. Biopolymers 105: 752-763, 2016.

Beyond Poisson-Boltzmann: Numerical Sampling of Charge Density Fluctuations

We present a method aimed at sampling charge density fluctuations in Coulomb systems. The derivation follows from a functional integral representation of the partition function in terms of charge density fluctuations. Starting from the mean-field solution given by the Poisson-Boltzmann equation, an original approach is proposed to numerically sample fluctuations around it, through the propagation of a Langevin-like stochastic partial differential equation (SPDE). The diffusion tensor of the SPDE can be chosen so as to avoid the numerical complexity linked to long-range Coulomb interactions, effectively rendering the theory completely local. A finite-volume implementation of the SPDE is described, and the approach is illustrated with preliminary results on the study of a system made of two like-charge ions immersed in a bath of counterions.

X-ray characterization of mesophases of human telomeric G-quadruplexes and other DNA analogues

Observed in the folds of guanine-rich oligonucleotides, non-canonical G-quadruplex structures are based on G-quartets formed by hydrogen bonding and cation-coordination of guanosines. In dilute 5'-guanosine monophosphate (GMP) solutions, G-quartets form by the self-assembly of four GMP nucleotides. We use x-ray diffraction to characterize the columnar liquid-crystalline mesophases in concentrated solutions of various model G-quadruplexes. We then probe the transitions between mesophases by varying the PEG solution osmotic pressure, thus mimicking in vivo molecular crowding conditions. Using the GMP-quadruplex, built by the stacking of G-quartets with no covalent linking between them, as the baseline, we report the liquid-crystalline phase behaviors of two other related G-quadruplexes: (i) the intramolecular parallel-stranded G-quadruplex formed by the 22-mer four-repeat human telomeric sequence AG3(TTAG3)3 and (ii) the intermolecular parallel-stranded G-quadruplex formed by the TG4T oligonucleotides. Finally, we compare the mesophases of the G-quadruplexes, under PEG-induced crowding conditions, with the corresponding mesophases of the canonical duplex and triplex DNA analogues.

Determining the Locations of Ions and Water around DNA from X-Ray Scattering Measurements

Nucleic acids carry a negative charge, attracting salt ions and water. Interactions with these components of the solvent drive DNA to condense, RNA to fold, and proteins to bind. To understand these biological processes, knowledge of solvent structure around the nucleic acids is critical. Yet, because they are often disordered, ions and water evade detection by x-ray crystallography and other high-resolution methods. Small-angle x-ray scattering (SAXS) is uniquely sensitive to the spatial correlations between solutes and the surrounding solvent. Thus, SAXS provides an experimental constraint to guide or test emerging solvation theories. However, the interpretation of SAXS profiles is nontrivial because of the difficulty in separating the scattering signals of each component: the macromolecule, ions, and hydration water. Here, we demonstrate methods for robustly deconvoluting these signals, facilitating a more straightforward comparison with theory. Using SAXS data collected on an absolute intensity scale for short DNA duplexes in solution with Na(+), K(+), Rb(+), or Cs(+) counterions, we mathematically decompose the scattering profiles into components (DNA, water, and ions) and validate the decomposition using anomalous scattering measurements. In addition, we generate a library of physically motivated ion atmosphere models and rank them by agreement with the scattering data. The best-fit models have relatively compact ion atmospheres when compared to predictions from the mean-field Poisson-Boltzmann theory of electrostatics. Thus, the x-ray scattering methods presented here provide a valuable measurement of the global structure of the ion atmosphere that can be used to test electrostatics theories that go beyond the mean-field approximation.

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.

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.

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.

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.

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.

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.

Helical structure determines different susceptibilities of dsDNA, dsRNA, and tsDNA to counterion-induced condensation

Recent studies of counterion-induced condensation of nucleic acid helices into aggregates produced several puzzling observations. For instance, trivalent cobalt hexamine ions condensed double-stranded (ds) DNA oligomers but not their more highly charged dsRNA counterparts. Divalent alkaline earth metal ions condensed triple-stranded (ts) DNA oligomers but not dsDNA. Here we show that these counterintuitive experimental results can be rationalized within the electrostatic zipper model of interactions between molecules with helical charge motifs. We report statistical mechanical calculations that reveal dramatic and nontrivial interplay between the effects of helical structure and thermal fluctuations on electrostatic interaction between oligomeric nucleic acids. Combining predictions for oligomeric and much longer helices, we also interpret recent experimental studies of the role of counterion charge, structure, and chemistry. We argue that an electrostatic zipper attraction might be a major or even dominant force in nucleic acid condensation.

Effect of magnesium ions on dielectric relaxation in semidilute DNA aqueous solutions

The effect of magnesium ion Mg(2+) on the dielectric relaxation of semidilute DNA aqueous solutions has been studied by means of dielectric spectroscopy in the 100 Hz-100 MHz frequency range. de Gennes-Pfeuty-Dobrynin semidilute solution correlation length is the pertinent fundamental length scale for sufficiently low concentration of added salt, describing the collective properties of Mg-DNA solutions. No relaxation fingerprint of the DNA denaturation bubbles, leading to exposed hydrophobic core scaling, was detected at low DNA concentrations, thus indicating an increased stability of the double-stranded conformation in Mg-DNA solutions as compared to the case of Na-DNA solutions. Some changes are detected in the behavior of the fundamental length scale pertaining to the single molecule DNA properties, reflecting modified electrostatic screening effects of the Odijk-Skolnick-Fixman type. All results consistently demonstrate that Mg(2+) ions interact with DNA in a similar way as Na(1+) ions do, their effect being mostly describable through an enhanced screening.

Nanostructure-induced DNA condensation

The control of the DNA condensation process is essential for compaction of DNA in chromatin, as well as for biological applications such as nonviral gene therapy. This review endeavours to reflect the progress of investigations on DNA condensation effects of nanostructure-based condensing agents (such as nanoparticles, nanotubes, cationic polymer and peptide agents) observed by using atomic force microscopy (AFM) and other techniques. The environmental effects on structural characteristics of nanostructure-induced DNA condensates are also discussed.

Effective and reversible DNA condensation induced by a simple cyclic/rigid polyamine containing carbonyl moiety

The transfection of DNA in gene therapy largely depends on the possibility of obtaining its condensation. The details of nanoparticle formation are essential for functioning, as mediated by the diverse elements containing molecular structure, ionic strength in mediums, and condensing motivator. Here, we report two kinds of DNA condensing agents based on simple cyclic/rigid polyamine molecules, having evaluated their structural effect on nanoparticle formation. The reversible condensation-dissociation process was achieved by ion-switching, attributing to a possible condensing mechanism-competitive building of external hydrogen bonds. Using poly[(dA-dT)2] and poly[(dG-dC)2] as substrates, respectively, circular dichroism (CD) signals clearly presented dissimilar interactions between polyamines and both rich sequences, implying potential preference for G-C sequence. The presence of divalent ion Zn(2+) as an efficient motivator accelerated the achievement of DNA condensation, and an accessible schematic model was depicted to explain the promotion in detail. In addition, by comparison with the behaviors of linear polyamines, differences between condensation and aggregation were explicitly elucidated in aspects of morphology and surface charges, as well as induced condition. The present work may have the potential to reveal the precise mechanism of DNA nanoparticle formation and, in particular, be applied to gene delivery as an efficient nonviral vector.

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.

Ionic microenvironmental effects on triplex DNA stabilization: cationic counterion effects on poly(dT)·poly(dA)·poly(dT)

The structure and conformation of nucleic acids are influenced by metal ions, polyamines, and the microenvironment. In poly(purine) · poly(pyrimidine) sequences, triplex DNA formation is facilitated by metal ions, polyamines and other ligands. We studied the effects of mono- and di-valent metal ions, and ammonium salts on the stability of triple- and double-stranded structures formed from poly(dA) and poly(dT) by measuring their respective melting temperatures. In the presence of metal ions, the absorbance versus temperature profile showed two transitions: Tm1 for triplex to duplex and single stranded DNA, and Tm2 for duplex DNA melting to single stranded DNA. Monovalent cations (Li(+), Na(+), K(+), Rb(+), Cs(+) and [Formula: see text] ) promoted triplex DNA at concentrations ≥150 mM. Tm1 varied from 49.8 °C in the presence of 150 mM Li(+) to 30.6 °C in the presence of 150 mM K(+). [Formula: see text] was very effective in stabilizing triplex DNA and its efficacy decreased with increasing substitution of the hydrogen atoms with methyl, ethyl, propyl and butyl groups. As in the case of monovalent cations, a concentration-dependent increase in Tm1 was observed with divalent ions and triplex DNA stabilization decreased in the order: Mg(2+) > Ca(2+) > Sr(2+) > Ba(2+). All positively charged cations increased the melting temperature of duplex DNA. Values of Δn (number of ions released) on triplex DNA melting were 0.46 ± 0.06 and 0.18 ± 0.02, respectively, for mono- and di-valent cations, as calculated from 1/Tm1 versus ln[M(+,2+)] plots. The corresponding values for duplex DNA were 0.25 ± 0.02 and 0.12 ± 0.02, respectively, for mono- and di-valent cations. Circular dichroism spectroscopic studies showed distinct conformational changes in triplex DNA stabilized by alkali metal and ammonium ions. Our results might be useful in developing triplex forming oligonucleotide based gene silencing techniques.

Biomolecular electrostatics and solvation: a computational perspective

An understanding of molecular interactions is essential for insight into biological systems at the molecular scale. Among the various components of molecular interactions, electrostatics are of special importance because of their long-range nature and their influence on polar or charged molecules, including water, aqueous ions, proteins, nucleic acids, carbohydrates, and membrane lipids. In particular, robust models of electrostatic interactions are essential for understanding the solvation properties of biomolecules and the effects of solvation upon biomolecular folding, binding, enzyme catalysis, and dynamics. Electrostatics, therefore, are of central importance to understanding biomolecular structure and modeling interactions within and among biological molecules. This review discusses the solvation of biomolecules with a computational biophysics view toward describing the phenomenon. While our main focus lies on the computational aspect of the models, we provide an overview of the basic elements of biomolecular solvation (e.g. solvent structure, polarization, ion binding, and non-polar behavior) in order to provide a background to understand the different types of solvation models.

Distribution of counterions and interaction between two similarly charged dielectric slabs: roles of charge discreteness and dielectric inhomogeneity

The distribution of counterions and the electrostatic interaction between two similarly charged dielectric slabs is studied in the strong coupling limit. Dielectric inhomogeneities and discreteness of charge on the slabs have been taken into account. It is found that the amount of dielectric constant difference between the slabs and the environment, and the discreteness of charge on the slabs have opposing effects on the equilibrium distribution of the counterions. At small interslab separations, increasing the amount of dielectric constant difference increases the tendency of the counterions toward the middle of the intersurface space between the slabs and the discreteness of charge pushes them to the surfaces of the slabs. In the limit of point charges, independent of the strength of dielectric inhomogeneity, counterions distribute near the surfaces of the slabs. The interaction between the slabs is attractive at low temperatures and its strength increases with the dielectric constant difference. At room temperature, the slabs may completely attract each other, reach to an equilibrium separation, or have two equilibrium separations with a barrier in between, depending on the system parameters.

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.