Ion distributions around left- and right-handed DNA and RNA duplexes: a comparative study

Competitive Influence of Alkali Metals in the Ion Atmosphere on Nucleic Acid Duplex Stability

The nonspecific atmosphere around nucleic acids, often termed the ion atmosphere, encompasses a collection of weak ion-nucleic acid interactions. Although nonspecific, the ion atmosphere has been shown to influence nucleic acid folding and structural stability. Studies investigating the composition of the ion atmosphere have shown competitive occupancy of the atmosphere between metal ions in the same solution. Many studies have investigated single ion effects on nucleic acid secondary structure stability; however, no comprehensive studies have investigated how the competitive occupancy of mixed ions in the ion atmosphere influences nucleic acid secondary structure stability. Here, six oligonucleotides were optically melted in buffers containing molar quantities, or mixtures, of either XCl (X = Li, K, Rb, or Cs) or NaCl. A correction factor was developed to better predict RNA duplex stability in solutions containing mixed XCl/NaCl. For solutions containing a 1:1 mixture of XCl/NaCl, one alkali metal chloride contributed more to duplex stability than the other. Overall, there was a 54% improvement in predictive capabilities with the correction factor compared with the standard 1.0 M NaCl nearest-neighbor models. This correction factor can be used in models to better predict RNA secondary structure in solutions containing mixed XCl/NaCl.

Structure and Dynamics of DNA and RNA Double Helices Formed by d(CTG), d(GTC), r(CUG), and r(GUC) Trinucleotide Repeats and Associated DNA-RNA Hybrids

Myotonic dystrophy type 1 is the most frequent form of muscular dystrophy in adults caused by an abnormal expansion of the CTG trinucleotide. Both the expanded DNA and the expanded CUG RNA transcript can fold into hairpins. Co-transcriptional formation of stable RNA·DNA hybrids can also enhance the instability of repeat tracts. We performed molecular dynamics simulations of homoduplexes associated with the disease, d(CTG)n and r(CUG)n, and their corresponding r(CAG)n:d(CTG)n and r(CUG)n:d(CAG)n hybrids that can form under bidirectional transcription and of non-pathological d(GTC)n and d(GUC)n homoduplexes. We characterized their conformations, stability, and dynamics and found that the U·U and T·T mismatches are dynamic, favoring anti-anti conformations inside the helical core, followed by anti-syn and syn-syn conformations. For DNA, the secondary minima in the non-expanding d(GTC)n helices are deeper, wider, and longer-lived than those in d(CTG)n, which constitutes another biophysical factor further differentiating the expanding and non-expanding sequences. The hybrid helices are closer to A-RNA, with the A-T and A-U pairs forming two stable Watson-Crick hydrogen bonds. The neutralizing ion distribution around the non-canonical pairs is also described.

Sensitivity of the RNA Structure to Ion Conditions as Probed by Molecular Dynamics Simulations of Common Canonical RNA Duplexes

RNA molecules play a key role in countless biochemical processes. RNA interactions, which are of highly diverse nature, are determined by the fact that RNA is a highly negatively charged polyelectrolyte, which leads to intimate interactions with an ion atmosphere. Although RNA molecules are formally single-stranded, canonical (Watson-Crick) duplexes are key components of folded RNAs. A double-stranded (ds) RNA is also important for the design of RNA-based nanostructures and assemblies. Despite the fact that the description of canonical dsRNA is considered the least problematic part of RNA modeling, the imperfect shape and flexibility of dsRNA can lead to imbalances in the simulations of larger RNAs and RNA-containing assemblies. We present a comprehensive set of molecular dynamics (MD) simulations of four canonical A-RNA duplexes. Our focus was directed toward the characterization of the influence of varying ion concentrations and of the size of the solvation box. We compared several water models and four RNA force fields. The simulations showed that the A-RNA shape was most sensitive to the RNA force field, with some force fields leading to a reduced inclination of the A-RNA duplexes. The ions and water models played a minor role. The effect of the box size was negligible, and even boxes with a small fraction of the bulk solvent outside the RNA hydration sphere were sufficient for the simulation of the dsRNA.

Structure and Formation of Z-DNA and Z-RNA

Despite structural differences between the right-handed conformations of A-RNA and B-DNA, both nucleic acids adopt very similar, left-handed Z-conformations. In contrast to their structural similarities and sequence preferences, RNA and DNA exhibit differences in their ability to adopt the Z-conformation regarding their hydration shells, the chemical modifications that promote the Z-conformation, and the structure of junctions connecting them to right-handed segments. In this review, we highlight the structural and chemical properties of both Z-DNA and Z-RNA and delve into the potential factors that contribute to both their similarities and differences. While Z-DNA has been extensively studied, there is a gap of knowledge when it comes to Z-RNA. Where such information is lacking, we try and extend the principles of Z-DNA stability and formation to Z-RNA, considering the inherent differences of the nucleic acids.

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

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

RNA as a Major-Groove Ligand: RNA-RNA and RNA-DNA Triplexes Formed by GAA and UUC or TTC Sequences

Friedreich's ataxia is associated with noncanonical nucleic acid structures that emerge when GAA:TTC repeats in the first intron of the FXN gene expand beyond a critical number of repeats. Specifically, the noncanonical repeats are associated with both triplexes and R-loops. Here, we present an in silico investigation of all possible triplexes that form by attaching a third RNA strand to an RNA:RNA or DNA:DNA duplex, complementing previous DNA-based triplex studies. For both new triplexes results are similar. For a pyridimine UUC⁺ third strand, the parallel orientation is stable while its antiparallel counterpart is unstable. For a neutral GAA third strand, the parallel conformation is stable. A protonated GA⁺A third strand is stable in both parallel and antiparallel orientations. We have also investigated Na⁺ and Mg²⁺ ion distributions around the triplexes. The presence of Mg²⁺ ions helps stabilize neutral, antiparallel GAA triplexes. These results (along with previous DNA-based studies) allow for the emergence of a complete picture of the stability and structural characteristics of triplexes based on the GAA and TTC/UUC sequences, thereby contributing to the field of trinucleotide repeats and the associated unusual structures that trigger expansion.

Dynamic effects of the spine of hydrated magnesium on viral RNA pseudoknot structure

In the cellular environment, a viral RNA Pseudoknot (PK) structure is responsive to its prevailing ion atmosphere created by a mixture of monovalent and divalent cations. We investigate the influence of such a mixed-salt environment on RNA-PK structure at an atomic resolution through three sets of 1.5 μs explicit solvent molecular dynamics (MD) simulations and also by building a dynamic counterion-condensation (DCC) model at varying divalent Mg²⁺ concentrations. The DCC model includes explicit interaction of the ligand and adjacent chelated Mg²⁺ by extending the recently developed generalized Manning condensation model. Its implementation within an all-atom structure-based molecular dynamics framework bolsters its opportunity to explore large-length scale and long-timescale phenomena associated with complex RNA systems immersed in its dynamic ion environment. In the present case of RNA-PK, both explicit MD and DCC simulations reveal a spine of hydrated-Mg²⁺ to induce stem-I and stem-II closure where the minor groove between these stems is akin to breathing. Mg²⁺ mediated minor-groove narrowing is coupled with local base-flipping dynamics of a base triple and quadruple, changing the stem structure of such RNA. Contrary to the conversational view of the indispensable need for Mg²⁺ for the tertiary structure of RNA, the study warns about the plausible detrimental effect of specific Mg²⁺-phosphate interactions on the RNA-PK structure beyond a certain concentration of Mg²⁺.

Electrostatic free energies carry structural information on nucleic acid molecules in solution

Over the last several decades, a range of experimental techniques from x-ray crystallography and atomic force microscopy to nuclear magnetic resonance and small angle x-ray scattering have probed nucleic acid structure and conformation with high resolution both in the condensed state and in solution. We present a computational study that examines the prospect of using electrostatic free energy measurements to detect 3D conformational properties of nucleic acid molecules in solution. As an example, we consider the conformational difference between A- and B-form double helices whose structures differ in the values of two key parameters—the helical radius and rise per basepair. Mapping the double helix onto a smooth charged cylinder reveals that electrostatic free energies for molecular helices can, indeed, be described by two parameters: the axial charge spacing and the radius of a corresponding equivalent cylinder. We show that electrostatic free energies are also sensitive to the local structure of the molecular interface with the surrounding electrolyte. A free energy measurement accuracy of 1%, achievable using the escape time electrometry (ET e) technique, could be expected to offer a measurement precision on the radius of the double helix of approximately 1 Å. Electrostatic free energy measurements may, therefore, not only provide information on the structure and conformation of biomolecules but could also shed light on the interfacial hydration layer and the size and arrangement of counterions at the molecular interface in solution.

Nonalternating purine pyrimidine sequences can form stable left-handed DNA duplex by strong topological constraint

In vivo, left-handed DNA duplex (usually refers to Z-DNA) is mainly formed in the region of DNA with alternating purine pyrimidine (APP) sequence and plays significant biological roles. It is well known that d(CG)_n sequence can form Z-DNA most easily under negative supercoil conditions, but its essence has not been well clarified. The study on sequence dependence of Z-DNA stability is very difficult without modification or inducers. Here, by the strong topological constraint caused by hybridization of two complementary short circular ssDNAs, left-handed duplex part was generated for various sequences, and their characteristics were investigated by using gel-shift after binding to specific proteins, CD and T_m analysis, and restriction enzyme cleavage. Under the strong topological constraint, non-APP sequences can also form left-handed DNA duplex as stable as that of APP sequences. As compared with non-APP sequences, the thermal stability difference for APP sequences between Z-form and B-form is smaller, which may be the reason that Z-DNA forms preferentially for APP ones. This result can help us to understand why nature selected APP sequences to regulate gene expression by transient Z-DNA formation, as well as why polymer with chirality can usually form both duplexes with left- or right-handed helix.

Contact pairs of RNA with magnesium ions-electrostatics beyond the Poisson-Boltzmann equation

The electrostatic interaction of RNA with its aqueous environment is most relevant for defining macromolecular structure and biological function. The attractive interaction of phosphate groups in the RNA backbone with ions in the water environment leads to the accumulation of positively charged ions in the first few hydration layers around RNA. Electrostatics of this ion atmosphere and the resulting ion concentration profiles have been described by solutions of the nonlinear Poisson-Boltzmann equation and atomistic molecular dynamics (MD) simulations. Much less is known on contact pairs of RNA phosphate groups with ions at the RNA surface, regarding their abundance, molecular geometry, and role in defining RNA structure. Here, we present a combined theoretical and experimental study of interactions of a short RNA duplex with magnesium (Mg2+) ions. MD simulations covering a microsecond time range give detailed hydration geometries as well as electrostatics and spatial arrangements of phosphate-Mg2+ pairs, including both pairs in direct contact and separated by a single water layer. The theoretical predictions are benchmarked by linear infrared absorption and nonlinear two-dimensional infrared spectra of the asymmetric phosphate stretch vibration which probes both local interaction geometries and electric fields. Contact pairs of phosphate groups and Mg2+ ions are identified via their impact on the vibrational frequency position and line shape. A quantitative analysis of infrared spectra for a range of Mg2+-excess concentrations and comparison with fluorescence titration measurements shows that on average 20-30% of the Mg2+ ions interacting with the RNA duplex form contact pairs. The experimental and MD results are in good agreement. In contrast, calculations based on the nonlinear Poisson-Boltzmann equation fail in describing the ion arrangement, molecular electrostatic potential, and local electric field strengths correctly. Our results underline the importance of local electric field mapping and molecular-level simulations to correctly account for the electrostatics at the RNA-water interface.

The mutual interactions of RNA, counterions and water - quantifying the electrostatics at the phosphate-water interface

The structure and dynamics of polyanionic biomolecules, like RNA, are decisively determined by their electric interactions with the water molecules and the counterions in the environment. The solvation dynamics of the biomolecules involves a subtle balance of non-covalent and many-body interactions with structural fluctuations due to thermal motion occurring in a femto- to subnanosecond time range. This complex fluctuating many particle scenario is crucial in defining the properties of biological interfaces with far reaching significance for the folding of RNA structures and for facilitating RNA-protein interactions. Given the inherent complexity, suited model systems, carefully calibrated and benchmarked by experiments, are required to quantify the relevant interactions of RNA with the aqueous environment. In this feature article we summarize our recent progress in the understanding of the electrostatics at the biological interface of double stranded RNA (dsRNA) and transfer RNA (tRNA). Dimethyl phosphate (DMP) is introduced as a viable and rigorously accessible model system allowing the interaction strength with water molecules and counterions, their relevant fluctuation timescales and the spatial reach of interactions to be established. We find strong (up to ≈90 MV cm-1) interfacial electric fields with fluctuations extending up to ≈20 THz and demonstrate how the asymmetric stretching vibration νAS(PO2)- of the polarizable phosphate group can serve as the most sensitive probe for interfacial interactions, establishing a rigorous link between simulations and experiment. The approach allows for the direct interfacial observation of interactions of biologically relevant Mg2+ counterions with phosphate groups in contact pair geometries via the rise of a new absorption band imposed by exchange repulsion interactions at short interatomic distances. The systematic extension to RNA provides microscopic insights into the changes of the hydration structure that accompany the temperature induced melting of the dsRNA double helix and quantify the ionic interactions in the folded tRNA. The results show that pairs of negatively charged phosphate groups and Mg2+ ions represent a key structural feature of RNA embedded in water. They highlight the importance of binding motifs made of contact pairs in the electrostatic stabilization of RNA structures that have a strong impact on the surface potential and enable the fine tuning of the local electrostatic properties which are expected to be relevant for mediating the interactions between biomolecules.

Phosphate Vibrations Probe Electric Fields in Hydrated Biomolecules: Spectroscopy, Dynamics, and Interactions

Electric interactions have a strong impact on the structure and dynamics of biomolecules in their native water environment. Given the variety of water arrangements in hydration shells and the femto- to subnanosecond time range of structural fluctuations, there is a strong quest for sensitive noninvasive probes of local electric fields. The stretching vibrations of phosphate groups, in particular the asymmetric (PO₂)⁻ stretching vibration ν_AS(PO₂)⁻, allow for a quantitative mapping of dynamic electric fields in aqueous environments via a field-induced redshift of their transition frequencies and concomitant changes of vibrational line shapes. We present a systematic study of ν_AS(PO₂)⁻ excitations in molecular systems of increasing complexity, including dimethyl phosphate (DMP), short DNA and RNA duplex structures, and transfer RNA (tRNA) in water. A combination of linear infrared absorption, two-dimensional infrared (2D-IR) spectroscopy, and molecular dynamics (MD) simulations gives quantitative insight in electric-field tuning rates of vibrational frequencies, electric field and fluctuation amplitudes, and molecular interaction geometries. Beyond neat water environments, the formation of contact ion pairs of phosphate groups with Mg²⁺ ions is demonstrated via frequency upshifts of the ν_AS(PO₂)⁻ vibration, resulting in a distinct vibrational band. The frequency positions of contact geometries are determined by an interplay of attractive electric and repulsive exchange interactions.

Systematic Approach to Find the Global Minimum of Relaxation Dispersion Data for Protein-Induced B-Z Transition of DNA

Carr-Purcell-Meiboom-Gill (CPMG) relaxation dispersion spectroscopy is commonly used for quantifying conformational changes of protein in μs-to-ms timescale transitions. To elucidate the dynamics and mechanism of protein binding, parameters implementing CPMG relaxation dispersion results must be appropriately determined. Building an analytical model for multi-state transitions is particularly complex. In this study, we developed a new global search algorithm that incorporates a random search approach combined with a field-dependent global parameterization method. The robust inter-dependence of the parameters carrying out the global search for individual residues (GSIR) or the global search for total residues (GSTR) provides information on the global minimum of the conformational transition process of the Zα domain of human ADAR1 (hZαADAR1)-DNA complex. The global search results indicated that a α-helical segment of hZαADAR1 provided the main contribution to the three-state conformational changes of a hZαADAR1-DNA complex with a slow B-Z exchange process. The two global exchange rate constants, kex and kZB, were found to be 844 and 9.8 s-1, respectively, in agreement with two regimes of residue-dependent chemical shift differences-the "dominant oscillatory regime" and "semi-oscillatory regime". We anticipate that our global search approach will lead to the development of quantification methods for conformational changes not only in Z-DNA binding protein (ZBP) binding interactions but also in various protein binding processes.

Magnesium Contact Ions Stabilize the Tertiary Structure of Transfer RNA: Electrostatics Mapped by Two-Dimensional Infrared Spectra and Theoretical Simulations

Ions interacting with hydrated RNA play a central role in defining its secondary and tertiary structure. While spatial arrangements of ions, water molecules, and phosphate groups have been inferred from X-ray studies, the role of electrostatic and other noncovalent interactions in stabilizing compact folded RNA structures is not fully understood at the molecular level. Here, we demonstrate that contact ion pairs of magnesium (Mg²⁺) and phosphate groups embedded in local water shells stabilize the tertiary equilibrium structure of transfer RNA (tRNA). Employing dialyzed tRNA^Phe from yeast and tRNA from Escherichia coli, we follow the population of Mg²⁺ sites close to phosphate groups of the ribose-phosphodiester backbone step by step, combining linear and nonlinear infrared spectroscopy of phosphate vibrations with molecular dynamics simulations and ab initio vibrational frequency calculations. The formation of up to six Mg²⁺/phosphate contact pairs per tRNA and local field-induced reorientations of water molecules balance the phosphate–phosphate repulsion in nonhelical parts of tRNA, thus stabilizing the folded structure electrostatically. Such geometries display limited sub-picosecond fluctuations in the arrangement of water molecules and ion residence times longer than 1 μs. At higher Mg²⁺ excess, the number of contact ion pairs per tRNA saturates around 6 and weakly interacting ions prevail. Our results suggest a predominance of contact ion pairs over long-range coupling of the ion atmosphere and the biomolecule in defining and stabilizing the tertiary structure of tRNA.

Use of Ionic Liquids in Protein and DNA Chemistry

Ionic liquids (ILs) have been receiving much attention as solvents in various areas of biochemistry because of their various beneficial properties over the volatile solvents and ILs availability in myriad variants (perhaps as many as 108) owing to the possibility of paring one cation with several anions and vice-versa as well as formulations as zwitterions. Their potential as solvents lies in their tendency to offer both directional and non-directional forces toward a solute molecule. Because of these forces, ionic liquids easily undergo intermolecular interactions with a range of polar/non-polar solutes, including biomolecules such as proteins and DNA. The interaction of genomic species in aqueous/non-aqueous states assists in unraveling their structure and functioning, which have implications in various biomedical applications. The charge density of ionic liquids renders them hydrophilic and hydrophobic, which retain intact over long-range of temperatures. Their ability in stabilizing or destabilizing the 3D-structure of a protein or the double-helical structure of DNA has been assessed superior to the water and volatile organic solvents. The aptitude of an ion in influencing the structure and stability of a native protein depends on their ranking in the Hofmeister series. However, at several instances, a reverse Hofmeister ordering of ions and specific ion-solute interaction has been observed. The capability of an ionic liquid in terms of the tendency to promote the coiling/uncoiling of DNA structure is noted to rely on the basicity, electrostatic interaction, and hydrophobicity of the ionic liquid in question. Any change in the DNA's double-helical structure reflects a change in its melting temperature (T m), compared to a standard buffer solution. These changes in DNA structure have implications in biosensor design and targeted drug-delivery in biomedical applications. In the current review, we have attempted to highlight various aspects of ionic liquids that influence the structure and properties of proteins and DNA. In short, the review will address the issues related to the origin and strength of intermolecular interactions, the effect of structural components, their nature, and the influence of temperature, pH, and additives on them.

Modeling the effect of ion-induced shock waves and DNA breakage with the reactive CHARMM force field

Ion-induced DNA damage is an important effect underlying ion beam cancer therapy. This article introduces the methodology of modeling DNA damage induced by a shock wave caused by a projectile ion. Specifically it is demonstrated how single- and double strand breaks in a DNA molecule could be described by the reactive CHARMM (rCHARMM) force field implemented in the program MBN Explorer. The entire workflow of performing the shock wave simulations, including obtaining the crucial simulation parameters, is described in seven steps. Two exemplary analyses are provided for a case study simulation serving to: (a) quantify the shock wave propagation and (b) describe the dynamics of formation of DNA breaks. The article concludes by discussing the computational cost of the simulations and revealing the possible maximal computational time for different simulation set-ups.

Protein-induced B-Z transition of DNA duplex containing a 2'-OMe guanosine

Structural transformation of the canonical right-handed helix, B-DNA, to the non-canonical left-handed helix, Z-DNA, can be induced by the Zα domain of the human RNA editing enzyme ADAR1 (hZα_ADAR1). To characterize the site-specific preferences of binding and structural changes in DNA containing the 2'-O-methyl guanosine derivative (_mG), titration of the imino proton spectra and chemical shift perturbations were performed on hZα_ADAR1 upon binding to Z-DNA. The structural transition between B-Z conformation as the changing ratio between DNA and protein showed a binding affinity of the modified DNA onto the Z-DNA binding protein similar to wild-type DNA or RNA. The chemical shift perturbation results showed that the overall structure and environment of the modified DNA revealed DNA-like properties rather than RNA-like characteristics. Moreover, we found evidence for two distinct regimes, "Z-DNA Sensing" and "Modification Sensing", based on the site-specific chemical shift perturbation between the DNA (or RNA) binding complex and the modified DNA-hZα_ADAR1 complex. Thus, we propose that modification of the sugar backbone of DNA with 2'-O-methyl guanosine promotes the changes in the surrounding α3 helical structural segment as well as the non-perturbed feature of the β-hairpin region.

Opposite Effects of High-Valent Cations on the Elasticities of DNA and RNA Duplexes Revealed by Magnetic Tweezers

We report that trivalent cobalt hexammine cations decrease the persistence length, stretching modulus, helical density, and size of plectonemes formed under torque of DNA but increase those of RNA. Divalent magnesium cations, however, decrease the persistence lengths, contour lengths, and sizes of plectonemes while increasing the helical densities of both DNA and RNA. The experimental results are explained by different binding modes of the cations on DNA and RNA in our all-atom molecular dynamics simulations. The significant variations of the helical densities and structures of DNA and RNA duplexes induced by high-valent cations may affect interactions of the duplexes with proteins.

Quantitative Studies of an RNA Duplex Electrostatics by Ion Counting

RNAs are one of the most charged polyelectrolytes in nature, and understanding their electrostatics is fundamental to their structure and biological functions. An effective way to characterize the electrostatic field generated by nucleic acids is to quantify interactions between nucleic acids and ions that surround the molecules. These ions form a loosely associated cloud referred to as an ion atmosphere. Although theoretical and computational studies can describe the ion atmosphere around RNAs, benchmarks are needed to guide the development of these approaches, and experiments to date that read out RNA-ion interactions are limited. Here, we present ion counting studies to quantify the number of ions surrounding well-defined model systems of RNA and DNA duplexes. We observe that the RNA duplex attracts more cations and expels fewer anions compared to the DNA duplex, and the RNA duplex interacts significantly stronger with the divalent cation Mg²⁺, despite their identical total charge. These experimental results suggest that the RNA duplex generates a stronger electrostatic field than DNA, as is predicted based on the structural differences between their helices. Theoretical calculations using a nonlinear Poisson-Boltzmann equation give excellent agreement with experiments for monovalent ions but underestimate Mg²⁺-DNA and Mg²⁺-RNA interactions by 20%. These studies provide needed stringent benchmarks to use against other all-atom theoretical models of RNA-ion interactions, interactions that likely must be accurately accounted for in structural, dynamic, and energetic terms to confidently model RNA structure, interactions, and function.

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.

Symmetry breaking and functional incompleteness in biological systems

Symmetry-based explanations using symmetry breaking (SB) as the key explanatory tool have complemented and replaced traditional causal explanations in various domains of physics. The process of spontaneous SB is now a mainstay of contemporary explanatory accounts of large chunks of condensed-matter physics, quantum field theory, nonlinear dynamics, cosmology, and other disciplines. A wide range of empirical research into various phenomena related to symmetries and SB across biological scales has accumulated as well. Led by these results, we identify and explain some common features of the emergence, propagation, and cascading of SB-induced layers across the biosphere. These features are predicated on the thermodynamic openness and intrinsic functional incompleteness of the systems at stake and have not been systematically analyzed from a general philosophical and methodological perspective. We also consider possible continuity of SB across the physical and biological world and discuss the connection between Darwinism and SB-based analysis of the biosphere and its history.

Nucleobase carbonyl groups are poor Mg2+ inner-sphere binders but excellent monovalent ion binders-a critical PDB survey

Precise knowledge of Mg²⁺ inner-sphere binding site properties is vital for understanding the structure and function of nucleic acid systems. Unfortunately, the PDB, which represents the main source of Mg²⁺ binding sites, contains a substantial number of assignment issues that blur our understanding of the functions of these ions. Here, following a previous study devoted to Mg²⁺ binding to nucleobase nitrogens, we surveyed nucleic acid X-ray structures from the PDB with resolutions ≤2.9 Å to classify the Mg²⁺ inner-sphere binding patterns to nucleotide carbonyl, ribose hydroxyl, cyclic ether, and phosphodiester oxygen atoms. From this classification, we derived a set of "prior-knowledge" nucleobase Mg²⁺ binding sites. We report that crystallographic examples of trustworthy nucleobase Mg²⁺ binding sites are fewer than expected since many of those are associated with misidentified Na⁺ or K⁺ We also emphasize that binding of Na⁺ and K⁺ to nucleic acids is much more frequent than anticipated. Overall, we provide evidence derived from X-ray structures that nucleobases are poor inner-sphere binders for Mg²⁺ but good binders for monovalent ions. Based on strict stereochemical criteria, we propose an extended set of guidelines designed to help in the assignment and validation of ions directly contacting nucleobase and ribose atoms. These guidelines should help in the interpretation of X-ray and cryo-EM solvent density maps. When borderline Mg²⁺ stereochemistry is observed, alternative placement of Na⁺, K⁺, or Ca²⁺ must be considered. We also critically examine the use of lanthanides (Yb³⁺, Tb³⁺) as Mg²⁺ substitutes in crystallography experiments.

Dependence of DNA Persistence Length on Ionic Strength and Ion Type

Even though the persistence length L_{P} of double-stranded DNA plays a pivotal role in cell biology and nanotechnologies, its dependence on ionic strength I lacks a consensual description. Using a high-throughput single-molecule technique and statistical physics modeling, we measure L_{P} in the presence of monovalent (Li^{+}, Na^{+}, K^{+}) and divalent (Mg^{2+}, Ca^{2+}) metallic and alkyl ammonium ions, over a large range 0.5  mM≤I≤5  M. We show that linear Debye-Hückel-type theories do not describe even part of these data. By contrast, the Netz-Orland and Trizac-Shen formulas, two approximate theories including nonlinear electrostatic effects and the finite DNA radius, fit our data with divalent and monovalent ions, respectively, over the whole I range. Furthermore, the metallic ion type does not influence L_{P}(I), in contrast to alkyl ammonium monovalent ions at high I.

An intricate balance of hydrogen bonding, ion atmosphere and dynamics facilitates a seamless uracil to cytosine substitution in the U-turn of the neomycin-sensing riboswitch

The neomycin sensing riboswitch is the smallest biologically functional RNA riboswitch, forming a hairpin capped with a U-turn loop-a well-known RNA motif containing a conserved uracil. It was shown previously that a U→C substitution of the eponymous conserved uracil does not alter the riboswitch structure due to C protonation at N3. Furthermore, cytosine is evolutionary permitted to replace uracil in other U-turns. Here, we use molecular dynamics simulations to study the molecular basis of this substitution in the neomycin sensing riboswitch and show that a structure-stabilizing monovalent cation-binding site in the wild-type RNA is the main reason for its negligible structural effect. We then use NMR spectroscopy to confirm the existence of this cation-binding site and to demonstrate its effects on RNA stability. Lastly, using quantum chemical calculations, we show that the cation-binding site is altering the electronic environment of the wild-type U-turn so that it is more similar to the cytosine mutant. The study reveals an amazingly complex and delicate interplay between various energy contributions shaping up the 3D structure and evolution of nucleic acids.

Toward Understanding Liposome-Based siRNA Delivery Vectors: Atomic-Scale Insight into siRNA-Lipid Interactions

Liposome carriers for delivering small interfering RNA (siRNA) into target cells are of tremendous importance because the siRNA-based therapy offers a completely new approach for treating a wide range of diseases, including cancer and viral infections. In this paper, we employ the state-of-the-art computer simulations to get an atomic-scale insight into the interactions of siRNA with zwitterionic (neutral) lipids. Our computational findings clearly demonstrate that siRNA does adsorb on the surface of a neutral lipid bilayer. The siRNA adsorption, being rather weak and unstable, is driven by attractive interactions of overhanging unpaired nucleotides with choline moieties of lipid molecules. It is the presence of the unpaired terminal nucleotides that underlies a drastic difference between siRNA and DNA; the latter is not able to bind to the zwitterionic lipid bilayer. We also show that adding divalent Ca ions leads to the formation of stable siRNA-lipid system complexes; these complexes are stabilized by Ca-mediated aggregates of siRNA and lipid molecules rather than by the overhanging siRNA nucleotides. Furthermore, the molecular mechanism of interactions between siRNA and the lipid bilayer in the presence of divalent cations seems to involve exchange of Ca ions between the outer mouth of the major groove of siRNA and the lipid/water interface. Overall, our findings contribute significantly to a deeper understanding of the structure and function of liposome carriers used for siRNA delivery and can be used as a theoretical basis for further development of siRNA-based therapeutics.

Structural and Dynamical Characterization of DNA and RNA Quadruplexes Obtained from the GGGGCC and GGGCCT Hexanucleotide Repeats Associated with C9FTD/ALS and SCA36 Diseases

A (GGGGCC) hexanucleotide repeat (HR) expansion in the C9ORF72 gene has been considered the major cause behind both frontotemporal dementia and amyotrophic lateral sclerosis, while a (GGGCCT) is associated with spinocerebellar ataxia 36. Recent experiments involving NMR, CD, optical melting and 1D 1H NMR spectroscopy, suggest that the r(GGGGCC) HR can adopt a hairpin structure with G-G mismatches in equilibrium with a G-quadruplex structure. G-Quadruplexes have also been identified for d(GGGGCC). As these experiments lack molecular resolution, we have used molecular dynamics microsecond simulations to obtain a structural characterization of the G-quadruplexes associated with both HRs. All DNA G-quadruplexes, parallel or antiparallel, with or without loops are stable, while only parallel and one antiparallel (stabilized by diagonal loops) RNA G-quadruplexes are stable. It is known that antiparallel G-quadruplexes require alternating guanines to be in a syn conformation that is hindered by the C3'-endo pucker preferred by RNA. Initial RNA antiparallel quadruplexes built with C2'-endo sugars evolve such that the transition (C2'-endo)-to-(C3'-endo) triggers unwinding and buckling of the flat G-tetrads, resulting in the unfolding of the RNA antiparallel quadruplex. Finally, a parallel G-quadruplex stabilizes an adjacent C-tetrad in both DNA and RNA (thus effectively becoming a mixed quadruplex of 5 layers). The C-tetrad is stabilized by the stacking interactions with the preceding G-tetrad, by cyclical hydrogen bonds C(N4)-(O2), and by an ion between the G-tetrad and the C-tetrad. In addition, antiparallel DNA G-quadruplexes also stabilize flat C-layers at the ends of the quadruplexes.

RNA Structural Dynamics As Captured by Molecular Simulations: A Comprehensive Overview

With both catalytic and genetic functions, ribonucleic acid (RNA) is perhaps the most pluripotent chemical species in molecular biology, and its functions are intimately linked to its structure and dynamics. Computer simulations, and in particular atomistic molecular dynamics (MD), allow structural dynamics of biomolecular systems to be investigated with unprecedented temporal and spatial resolution. We here provide a comprehensive overview of the fast-developing field of MD simulations of RNA molecules. We begin with an in-depth, evaluatory coverage of the most fundamental methodological challenges that set the basis for the future development of the field, in particular, the current developments and inherent physical limitations of the atomistic force fields and the recent advances in a broad spectrum of enhanced sampling methods. We also survey the closely related field of coarse-grained modeling of RNA systems. After dealing with the methodological aspects, we provide an exhaustive overview of the available RNA simulation literature, ranging from studies of the smallest RNA oligonucleotides to investigations of the entire ribosome. Our review encompasses tetranucleotides, tetraloops, a number of small RNA motifs, A-helix RNA, kissing-loop complexes, the TAR RNA element, the decoding center and other important regions of the ribosome, as well as assorted others systems. Extended sections are devoted to RNA-ion interactions, ribozymes, riboswitches, and protein/RNA complexes. Our overview is written for as broad of an audience as possible, aiming to provide a much-needed interdisciplinary bridge between computation and experiment, together with a perspective on the future of the field.

Structure and Dynamics of DNA and RNA Double Helices Obtained from the CCG and GGC Trinucleotide Repeats

Expansions of both GGC and CCG sequences lead to a number of expandable, trinucleotide repeat (TR) neurodegenerative diseases. Understanding of these diseases involves, among other things, the structural characterization of the atypical DNA and RNA secondary structures. We have performed molecular dynamics simulations of (GCC) _n and (GGC) _n homoduplexes in order to characterize their conformations, stability, and dynamics. Each TR has two reading frames, which results in eight nonequivalent RNA/DNA homoduplexes, characterized by CpG or GpC steps between the Watson-Crick base pairs. Free energy maps for the eight homoduplexes indicate that the C-mismatches prefer anti-anti conformations, while G-mismatches prefer anti-syn conformations. Comparison between three modifications of the DNA AMBER force field shows good agreement for the mismatch free energy maps. The mismatches in DNA-GCC (but not CCG) are extrahelical, forming an extended e-motif. The mismatched duplexes exhibit characteristic sequence-dependent step twist, with strong variations in the G-rich sequences and the e-motif. The distribution of Na⁺ is highly localized around the mismatches, especially G-mismatches. In the e-motif, there is strong Na⁺ binding by two G(N7) atoms belonging to the pseudo GpC step created when cytosines are extruded and by extrahelical cytosines. Finally, we used a novel technique based on fast melting by means of an infrared laser pulse to classify the relative stability of the different DNA-CCG and -GGC homoduplexes.

Structure and Dynamics of DNA and RNA Double Helices of CAG and GAC Trinucleotide Repeats

CAG trinucleotide repeats are known to cause 10 late-onset progressive neurodegenerative disorders as the repeats expand beyond a threshold, whereas GAC repeats are associated with skeletal dysplasias and expand from the normal five to a maximum of seven repeats. The TR secondary structure is believed to play a role in CAG expansions. We have carried out free energy and molecular dynamics studies to determine the preferred conformations of the A-A noncanonical pairs in (CAG)_n and (GAC)_n trinucleotide repeats (n = 1, 4) and the consequent changes in the overall structure of the RNA and DNA duplexes. We find that the global free energy minimum corresponds to A-A pairs stacked inside the core of the helix with anti-anti conformations in RNA and (high-anti)-(high-anti) conformations in DNA. The next minimum corresponds to anti-syn conformations, whereas syn-syn conformations are higher in energy. Transition rates of the A-A conformations are higher for RNA than DNA. Mechanisms for these various transitions are identified. Additional structural and dynamical aspects of the helical conformations are explored, with a focus on contrasting CAG and GAC duplexes. The neutralizing ion distribution around the noncanonical pairs is described.

Unraveling Mg2+-RNA binding with atomistic molecular dynamics

Interaction with divalent cations is of paramount importance for RNA structural stability and function. We report here a detailed molecular dynamics study of all the possible binding sites for Mg2+ on an RNA duplex, including both direct (inner sphere) and indirect (outer sphere) binding. In order to tackle sampling issues, we develop a modified version of bias-exchange metadynamics, which allows us to simultaneously compute affinities with previously unreported statistical accuracy. Results correctly reproduce trends observed in crystallographic databases. Based on this, we simulate a carefully chosen set of models that allows us to quantify the effects of competition with monovalent cations, RNA flexibility, and RNA hybridization. Our simulations reproduce the decrease and increase of Mg2+ affinity due to ion competition and hybridization, respectively, and predict that RNA flexibility has a site-dependent effect. This suggests a nontrivial interplay between RNA conformational entropy and divalent cation binding.

Structure and Dynamics of DNA and RNA Double Helices Obtained from the GGGGCC and CCCCGG Hexanucleotide Repeats That Are the Hallmark of C9FTD/ALS Diseases

A (GGGGCC) hexanucleotide repeat (HR) expansion in the C9ORF72 gene, and its associated antisense (CCCCGG) expansion, are considered the major cause behind frontotemporal dementia and amyotrophic lateral sclerosis. We have performed molecular dynamics simulations to characterize the conformation and dynamics of the 12 duplexes that result from the three different reading frames in sense and antisense HRs for both DNA and RNA. These duplexes display atypical structures relevant not only for a molecular level understanding of these diseases but also for enlarging the repertoire of nucleic-acid structural motifs. G-rich helices share common features. The inner G-G mismatches stay inside the helix in Gsyn-Ganti conformations and form two hydrogen bonds (HBs) between the Watson-Crick edge of Ganti and the Hoogsteen edge of Gsyn. In addition, Gsyn in RNA forms a base-phosphate HB. Inner G-G mismatches cause local unwinding of the helix. G-rich double helices are more stable than C-rich helices due to better stacking and HBs of G-G mismatches. C-rich helix conformations vary wildly. C mismatches flip out of the helix in DNA but not in RNA. Least (most) stable C-rich RNA and DNA helices have single (double) mismatches separated by two (four) Watson-Crick basepairs. The most stable DNA structure displays an "e-motif" where mismatched bases flip toward the minor groove and point in the 5' direction. There are two RNA conformations, where the orientation and HB pattern of the mismatches is coupled to bending of the helix.

Types and concentrations of metal ions affect local structure and dynamics of RNA

The roles that metal ions play in the structure and dynamics of RNA molecules are long-standing problems that have been studied extensively but are still not well understood. Here we show that metal ions have distributions around RNA molecules that strongly depend on the types and concentrations of the metal ions and also the electrostatic surface of the molecule. In particular, the ion distributions may not balance all the local electronegativity of the molecule. These ion distributions do not only greatly affect local structures but also lead to different local dynamics of RNA. We studied the effects of different ion solutions on the structure and dynamics of RNA by taking the preQ_{1} riboswitch aptamer domain as an illustrative example and using molecular dynamics simulations. Since the local structures and dynamics of RNAs are important to their functions, our results also indicate that the selection of proper ion conditions is necessary to model them correctly, in contrast to the use of diverse ion solutions in current molecular dynamics simulations.

Does Cation Size Affect Occupancy and Electrostatic Screening of the Nucleic Acid Ion Atmosphere?

Electrostatics are central to all aspects of nucleic acid behavior, including their folding, condensation, and binding to other molecules, and the energetics of these processes are profoundly influenced by the ion atmosphere that surrounds nucleic acids. Given the highly complex and dynamic nature of the ion atmosphere, understanding its properties and effects will require synergy between computational modeling and experiment. Prior computational models and experiments suggest that cation occupancy in the ion atmosphere depends on the size of the cation. However, the computational models have not been independently tested, and the experimentally observed effects were small. Here, we evaluate a computational model of ion size effects by experimentally testing a blind prediction made from that model, and we present additional experimental results that extend our understanding of the ion atmosphere. Giambasu et al. developed and implemented a three-dimensional reference interaction site (3D-RISM) model for monovalent cations surrounding DNA and RNA helices, and this model predicts that Na(+) would outcompete Cs(+) by 1.8-2.1-fold; i.e., with Cs(+) in 2-fold excess of Na(+) the ion atmosphere would contain an equal number of each cation (Nucleic Acids Res. 2015, 43, 8405). However, our ion counting experiments indicate that there is no significant preference for Na(+) over Cs(+). There is an ∼25% preferential occupancy of Li(+) over larger cations in the ion atmosphere but, counter to general expectations from existing models, no size dependence for the other alkali metal ions. Further, we followed the folding of the P4-P6 RNA and showed that differences in folding with different alkali metal ions observed at high concentration arise from cation-anion interactions and not cation size effects. Overall, our results provide a critical test of a computational prediction, fundamental information about ion atmosphere properties, and parameters that will aid in the development of next-generation nucleic acid computational models.

A bouquet of DNA structures: Emerging diversity

Structural polymorphism of DNA has constantly been evolving from the time of illustration of the double helical model of DNA by Watson and Crick. A variety of non-canonical DNA structures have constantly been documented across the globe. DNA attracted worldwide attention as a carrier of genetic information. In addition to the classical Watson–Crick duplex, DNA can actually adopt diverse structures during its active participation in cellular processes like replication, transcription, recombination and repair. Structures like hairpin, cruciform, triplex, G-triplex, quadruplex, i-motif and other alternative non-canonical DNA structures have been studied at length and have also shown their in vivo occurrence. This review mainly focuses on non-canonical structures adopted by DNA oligonucleotides which have certain prerequisites for their formation in terms of sequence, its length, number and orientation of strands along with varied solution conditions. This conformational polymorphism of DNA might be the basis of different functional properties of a specific set of DNA sequences, further giving some insights for various extremely complicated biological phenomena. Many of these structures have already shown their linkages with diseases like cancer and genetic disorders, hence making them an extremely striking target for structure-specific drug designing and therapeutic applications.

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DNA can adopt diverse range of structures other than classical Watson–Crick duplex.

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Discussion of alternate structures like hairpin, cruciform, triplex, quadruplex etc.

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This review gives some insights for the biological relevance of DNA structures.

Competitive interaction of monovalent cations with DNA from 3D-RISM

The composition of the ion atmosphere surrounding nucleic acids affects their folding, condensation and binding to other molecules. It is thus of fundamental importance to gain predictive insight into the formation of the ion atmosphere and thermodynamic consequences when varying ionic conditions. An early step toward this goal is to benchmark computational models against quantitative experimental measurements. Herein, we test the ability of the three dimensional reference interaction site model (3D-RISM) to reproduce preferential interaction parameters determined from ion counting (IC) experiments for mixed alkali chlorides and dsDNA. Calculations agree well with experiment with slight deviations for salt concentrations >200 mM and capture the observed trend where the extent of cation accumulation around the DNA varies inversely with its ionic size. Ion distributions indicate that the smaller, more competitive cations accumulate to a greater extent near the phosphoryl groups, penetrating deeper into the grooves. In accord with experiment, calculated IC profiles do not vary with sequence, although the predicted ion distributions in the grooves are sequence and ion size dependent. Calculations on other nucleic acid conformations predict that the variation in linear charge density has a minor effect on the extent of cation competition.

Physicochemical Properties of Ion Pairs of Biological Macromolecules

Ion pairs (also known as salt bridges) of electrostatically interacting cationic and anionic moieties are important for proteins and nucleic acids to perform their function. Although numerous three-dimensional structures show ion pairs at functionally important sites of biological macromolecules and their complexes, the physicochemical properties of the ion pairs are not well understood. Crystal structures typically show a single state for each ion pair. However, recent studies have revealed the dynamic nature of the ion pairs of the biological macromolecules. Biomolecular ion pairs undergo dynamic transitions between distinct states in which the charged moieties are either in direct contact or separated by water. This dynamic behavior is reasonable in light of the fundamental concepts that were established for small ions over the last century. In this review, we introduce the physicochemical concepts relevant to the ion pairs and provide an overview of the recent advancement in biophysical research on the ion pairs of biological macromolecules.

Elastic network models for RNA: a comparative assessment with molecular dynamics and SHAPE experiments

Elastic network models (ENMs) are valuable and efficient tools for characterizing the collective internal dynamics of proteins based on the knowledge of their native structures. The increasing evidence that the biological functionality of RNAs is often linked to their innate internal motions poses the question of whether ENM approaches can be successfully extended to this class of biomolecules. This issue is tackled here by considering various families of elastic networks of increasing complexity applied to a representative set of RNAs. The fluctuations predicted by the alternative ENMs are stringently validated by comparison against extensive molecular dynamics simulations and SHAPE experiments. We find that simulations and experimental data are systematically best reproduced by either an all-atom or a three-beads-per-nucleotide representation (sugar-base-phosphate), with the latter arguably providing the best balance of accuracy and computational complexity.