Abrupt transition from a free, repulsive to a condensed, attractive DNA phase, induced by multivalent polyamine cations

Condensation Goes Viral: A Polymer Physics Perspective

The past decade has seen a revolution in our understanding of how the cellular environment is organized, where an incredible body of work has provided new insights into the role played by membraneless organelles. These rapid advancements have been made possible by an increasing awareness of the peculiar physical properties that give rise to such bodies and the complex biology that enables their function. Viral infections are not extraneous to this. Indeed, in host cells, viruses can harness existing membraneless compartments or, even, induce the formation of new ones. By hijacking the cellular machinery, these intracellular bodies can assist in the replication, assembly, and packaging of the viral genome as well as in the escape of the cellular immune response. Here, we provide a perspective on the fundamental polymer physics concepts that may help connect and interpret the different observed phenomena, ranging from the condensation of viral genomes to the phase separation of multicomponent solutions. We complement the discussion of the physical basis with a description of biophysical methods that can provide quantitative insights for testing and developing theoretical and computational models.

Locally Denatured DNA Compaction by Divalent Cations

The denaturation of DNA is a critical process in biology and has many biotechnological applications. We investigated the compaction of locally denatured DNA by a chemical denaturation agent, dimethyl sulfoxide (DMSO), using magnetic tweezers (MTs), atomic force microscopy (AFM), and dynamic light scattering (DLS). Our results show that DMSO not only is capable of denaturing DNA but also able to compact DNA directly. When the DMSO concentration is above 10%, DNA condensation occurs due to the reduction in the persistence length of DNA and excluded volume interactions. Meanwhile, locally denatured DNA is easily condensed by divalent cations, such as magnesium ions (Mg²⁺), contrasting with no native DNA condensation by the classical divalent cations. Specifically, the addition of more than 3 mM Mg²⁺ to a 5% DMSO solution leads to DNA condensation. The critical condensing force (F_C) increases from 6.4 to 9.5 pN when the Mg²⁺ concentration grows from 3 to 10 mM. However, F_C decreases gradually with a further increase in Mg²⁺ concentration. For 3% DMSO solution, above 30 mM Mg²⁺ is needed to compact DNA and a weaker condensing force was measured. With increasing Mg²⁺ concentration, the morphology of the DMSO partially denatured DNA complex changes from loosely random coils to a dense network structure, even forming a spherical condensation nucleus, and finally to a partially disintegrated network. These findings show that the elasticity of DNA plays an important role in its denaturation and condensation behavior.

Electrostatic Interactions in the Formation of DNA Complexes with Cis- and Trans-Isomers of Azobenzene-Containing Surfactants in Solutions with Di- and Trivalent Metal Ions

The effect of the presence of divalent and trivalent metal ions in solutions upon DNA packaging induced by the photosensitive azobenzene-containing surfactant is considered. It has been shown that the addition of divalent and trivalent metal ions does not affect the DNA-surfactant interaction for both the cis- and the trans-isomers of the surfactant. At the same time, the ionic strength of the solution, which is provided by a certain concentration of the salt, has a huge impact. It affects the association of surfactant molecules with each other and their binding to DNA. It has been shown by computer simulation that cobalt hexamine is attracted to the N7 atom of guanine in the major groove of DNA and does not penetrate into grooves near the AT base pairs.

Redox-sensitive CDC-42 clustering promotes wound closure in C. elegans

Tissue damage induces immediate-early signals, activating Rho small GTPases to trigger actin polymerization essential for later wound repair. However, how tissue damage is sensed to activate Rho small GTPases locally remains elusive. Here, we found that wounding the C. elegans epidermis induces rapid relocalization of CDC-42 into plasma membrane-associated clusters, which subsequently recruits WASP/WSP-1 to trigger actin polymerization to close the wound. In addition, wounding induces a local transient increase and subsequent reduction of H₂O₂, which negatively regulates the clustering of CDC-42 and wound closure. CDC-42 CAAX motif-mediated prenylation and polybasic region-mediated cation-phospholipid interaction are both required for its clustering. Cysteine residues participate in intermolecular disulfide bonds to reduce membrane association and are required for negative regulation of CDC-42 clustering by H₂O₂. Collectively, our findings suggest that H₂O₂-regulated fine-tuning of CDC-42 localization can create a distinct biomolecular cluster that facilitates rapid epithelial wound repair after injury.

Cis-Isomers of Photosensitive Cationic Azobenzene Surfactants in DNA Solutions at Different NaCl Concentrations: Experiment and Modeling

The DNA interaction with cis-isomers of photosensitive azobenzene-containing surfactants was studied by both experimental methods and computer simulation. It was shown that before the organization of micelles, such surfactants in the cis-conformation form associates of only a single type with a disordered orientation of molecules. In contrast, for trans-isomers, there exist two types of associates with head-to-head or head-to-tail orientations of molecules in dependence on salt concentration in a solution. The comparison of cis- and trans-isomer binding to DNA and the influence of salt concentration on the formation of their complexes with DNA were studied. It was shown that cis-isomers interact with phosphate groups of DNA and that their molecules were also located along the minor groove of DNA.

Dynamics of K+ counterions around DNA double helix in the external electric field: A molecular dynamics study

The structure of DNA double helix is stabilized by metal counterions condensed to a diffuse layer around the macromolecule. The dynamics of counterions in real conditions is governed by the electric fields from DNA and other biological macromolecules. In the present work the molecular dynamics study was performed for the system of DNA double helix with neutralizing K⁺ counterions and for the system of KCl salt solution in an external electric field of different strength (up to 32mV/Å). The analysis of ionic conductivities of these systems has shown that the counterions around the DNA double helix are slowed down compared with the KCl salt solution. The calculated values of ion mobility are within (0.05-0.4)mS/cm depending on the orientation of the external electric field relatively to the double helix. Under the electric field parallel to the macromolecule K⁺ counterions move along the grooves of the double helix staying longer in the places with narrower minor groove. Under the electric field perpendicular to the macromolecule the dynamics of counterions is less affected by DNA atoms, and starting with the electric field values about 30mV/Å the double helix undergoes a phase transition from a double-stranded to a single-strand state.

Some Features of Surfactant Organization in DNA Solutions at Various NaCl Concentrations

The photosensitive azobenzene-containing surfactant C₄-Azo-OC₆TMAB is a promising agent for reversible DNA packaging in a solution. The simulation of the trans-isomer surfactant organization into associates in a solution with and without salt as well as its binding to DNA at different NaCl concentrations was carried out by molecular dynamics. Experimental data obtained by spectral and hydrodynamic methods were used to verify the results of simulation. It was shown that head-to-tail aggregates with close to antiparallel orientation of surfactant molecules were formed at certain NaCl and surfactant concentrations (below critical micelle concentration). Such aggregates have two positively charged ends, and therefore, they can be attracted to negatively charged DNA phosphates far located along the chain, as well as those that belong to different molecules. This contributes to the formation of intermolecular DNA-DNA contacts, and this way, the experimentally observed precipitation of DNA can be explained.

Pattern preferences of DNA nucleotide motifs by polyamines putrescine2+, spermidine3+ and spermine4

The interactions of natural polyamines (putrescine2+, spermidine3+ and spermine4+) with DNA double helix are studied to characterize their nucleotide sequence pattern preference. Atomistic Molecular Dynamics simulations have been carried out for three systems consisting of the same DNA fragment d(CGCGAATTCGCGAATTCGCG) with different polyamines. The results show that polyamine molecules are localized with well-recognized patterns along the double helix with different residence times. We observed a clear hierarchy in the residence times of the polyamines, with the longest residence time (ca 100ns) in the minor groove. The analysis of the sequence dependence shows that polyamine molecules prefer the A-tract regions of the minor groove - in its narrowest part. The preferable localization of putrescine2+, spermidine3+ and spermine4+ in the minor groove with A-tract motifs is correlated with modulation of the groove width by a specific nucleotide sequences. We did develop a theoretical model pointing to the electrostatic interactions as the main driving force in this phenomenon, making it even more prominent for polyamines with higher charges. The results of the study explain the specificity of polyamine interactions with A-tract region of the DNA double helix which is also observed in experiments.

Counterion-Dependent Mechanisms of DNA Origami Nanostructure Stabilization Revealed by Atomistic Molecular Simulation

The DNA origami technique has proven to have tremendous potential for therapeutic and diagnostic applications like drug delivery, but the relatively low concentrations of cations in physiological fluids cause destabilization and degradation of DNA origami constructs preventing in vivo applications. To reveal the mechanisms behind DNA origami stabilization by cations, we performed atomistic molecular dynamics simulations of a DNA origami rectangle in aqueous solvent with varying concentrations of magnesium and sodium as well as polyamines like oligolysine and spermine. We explored the binding of these ions to DNA origami in detail and found that the mechanism of stabilization differs between ion types considerably. While sodium binds weakly and quickly exchanges with the solvent, magnesium and spermine bind close to the origami with spermine also located in between helices, stabilizing the crossovers characteristic for DNA origami and reducing repulsion of parallel helices. In contrast, oligolysine of length ten prevents helix repulsion by binding to adjacent helices with its flexible side chains, spanning the gap between the helices. Shorter oligolysine molecules with four subunits are weak stabilizers as they lack both the ability to connect helices and to prevent helix repulsion. This work thus shows how the binding modes of ions influence the stabilization of DNA origami nanostructures on a molecular level.

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.

Direct Demonstration of DNA Compaction Mediated by Divalent Counterions

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

Opposite effect of polyamines on In vitro gene expression: Enhancement at low concentrations but inhibition at high concentrations

Background

Polyamines have various biological functions including marked effects on the structure and function of genomic DNA molecules. Changes in the higher-order structure of DNA caused by polyamines are expected to be closely related to genetic activity. To clarify this issue, we examined the relationship between gene expression and the higher-order structure of DNA under different polyamine concentrations.

Principal findings

We studied the effects of polyamines, spermidine SPD(3+) and spermine SP(4+), on gene expression by a luciferase assay. The results showed that gene expression is increased by ca. 5-fold by the addition of SPD(3+) at 0.3 mM, whereas it is completely inhibited above 2 mM. Similarly, with SP(4+), gene expression is maximized at 0.08 mM and completely inhibited above 0.6 mM. We also performed atomic force microscopy (AFM) observations on DNA under different polyamine concentrations. AFM revealed that a flower-like conformation is generated at polyamine concentrations associated with maximum expression as measured by the luciferase assay. On the other hand, DNA molecules exhibit a folded compact conformation at polyamine concentrations associated with the complete inhibition of expression. Based on these results, we discuss the plausible mechanism of the opposite effect, i.e., enhancement and inhibition, of polyamines on gene expression.

Conclusion and significance

It was found that polyamines exert opposite effect, enhancement and inhibition, on gene expression depending on their concentrations. Such an opposite effect is argued in relation to the conformational change of DNA: enhancement is due to the parallel ordering of DNA segments that is accompanied by a decrease in the negative charge of double-stranded DNA, and inhibition is caused by the compaction of DNA into a tightly packed state with almost perfect charge-neutralization.

Predicting Ion Effects in an RNA Conformational Equilibrium

We develop a partial charge-based tightly bound ion (PCTBI) model for the ion effects in RNA folding. On the basis of the Monte Carlo tightly bound ion (MCTBI) approach, the model can account for ion fluctuation and correlation effects, and can predict the ion distribution around the RNA. Furthermore, unlike the previous coarse-grained RNA charge models, where negative charges are placed on the phosphates only, the current new model considers the detailed all-atom partial charge distribution on the RNA. Thus, the model not only keeps the advantage of the MCTBI model, but also has the potential to provide important detailed information unattainable by the previous MCTBI models. For example, the model predicts the reduction in ion binding upon protein binding and ion-induced conformational switches. For hepatitis C virus genomic RNA, the model predicts a Mg²⁺-induced stabilization of a kissing motif for a cis-acting regulatory element in the genomic RNA. Extensive theory-experiment comparisons support the reliability of the theoretical predictions. Therefore, the model may serve as a robust starting point for further development of an accurate method for ion effects in an RNA conformational equilibrium and RNA-cofactor interactions.

Spermine Condenses DNA, but Not RNA Duplexes

Interactions between the polyamine spermine and nucleic acids drive important cellular processes. Spermine condenses DNA and some RNAs, such as poly(rA):poly(rU). A large fraction of the spermine present in cells is bound to RNA but apparently does not condense it. Here, we study the effect of spermine binding to short duplex RNA and DNA, and compare our findings with predictions of molecular-dynamics simulations. When small numbers of spermine are introduced, RNA with a designed sequence containing a mixture of 14 GC pairs and 11 AU pairs resists condensation relative to DNA of an equivalent sequence or to 25 bp poly(rA):poly(rU) RNA. A comparison of wide-angle x-ray scattering profiles with simulation results suggests that spermine is sequestered deep within the major groove of mixed-sequence RNA. This prevents condensation by limiting opportunities to bridge to other molecules and stabilizes the RNA by locking it into a particular conformation. In contrast, for DNA, simulations suggest that spermine binds externally to the duplex, offering opportunities for intermolecular interaction. The goal of this study is to explain how RNA can remain soluble and available for interaction with other molecules in the cell despite the presence of spermine at concentrations high enough to precipitate DNA.

Monte Carlo Tightly Bound Ion Model: Predicting Ion-Binding Properties of RNA with Ion Correlations and Fluctuations

Experiments have suggested that ion correlation and fluctuation effects can be potentially important for multivalent ions in RNA folding. However, most existing computational methods for the ion electrostatics in RNA folding tend to ignore these effects. The previously reported tightly bound ion (TBI) model can treat ion correlation and fluctuation but its applicability to biologically important RNAs is severely limited by the low computational efficiency. Here, on the basis of Monte Carlo sampling for the many-body ion distribution, we develop a new computational model, the Monte Carlo tightly bound ion (MCTBI) model, for ion-binding properties around an RNA. Because of an enhanced sampling algorithm for ion distribution, the model leads to a significant improvement in computational efficiency. For example, for a 160-nt RNA, the model causes a more than 10-fold increase in the computational efficiency, and the improvement in computational efficiency is more pronounced for larger systems. Furthermore, unlike the earlier model that describes ion distribution using the number of bound ions around each nucleotide, the current MCTBI model is based on the three-dimensional coordinates of the ions. The higher efficiency of the model allows us to treat the ion effects for medium to large RNA molecules, RNA-ligand complexes, and RNA-protein complexes. This new model together with proper RNA conformational sampling and the energetics model may serve as a starting point for further development for the ion effects in RNA folding and conformational changes and for large nucleic acid systems.

Multi-shell model of ion-induced nucleic acid condensation

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

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.

Ion competition in condensed DNA arrays in the attractive regime

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

The effect of polyamines on the binding of anti-DNA antibodies from patients with SLE and normal human subjects

Antibodies to DNA (anti-DNA) are the serological hallmark of systemic lupus erythematosus (SLE). To elucidate specificity further, the effect of polyamines on the binding of anti-DNA antibodies from patients with lupus was tested by ELISA to calf thymus (CT) DNA; we also assessed the binding of plasmas of patients and normal human subjects (NHS) to Micrococcus luteus (MC) DNA. As these studies showed, spermine can dose-dependently inhibit SLE anti-DNA binding to CT DNA and can promote dissociation of preformed immune complexes. With MC DNA as antigen, spermine failed to inhibit the NHS anti-DNA binding. Studies using plasmas adsorbed to a CT DNA cellulose affinity indicated that SLE plasmas are mixtures of anti-DNA that differ in inhibition by spermine and binding to conserved and non-conserved determinants. Together, these studies demonstrate that spermine can influence the binding of anti-DNA autoantibodies and may contribute to the antigenicity of DNA.

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.

Quantifying Coulombic and solvent polarization-mediated forces between DNA helices

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

Ion-mediated RNA structural collapse: effect of spatial confinement

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

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.

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

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

A universal description for the experimental behavior of salt-(in)dependent oligocation-induced DNA condensation

We report a systematic study of the condensation of plasmid DNA by oligocations with variation of the charge, Z, from +3 to +31. The oligocations include a series of synthetic linear ε-oligo(L-lysines), (denoted εKn, n = 3–10, 31; n is the number of lysines with the ligand charge Z = n+1) and branched α-substituted homologues of εK10: εYK10, εLK10 (Z = +11); εRK10, εYRK10 and εLYRK10 (Z = +21). Data were obtained by light scattering, UV absorption monitored precipitation assay and isothermal titration calorimetry in a wide range concentrations of DNA and monovalent salt (KCl, CKCl). The dependence of EC50 (ligand concentration at the midpoint of DNA condensation) on C(KCl) shows the existence of a salt-independent regime at low C(KCl) and a salt-dependent regime with a steep rise of EC50 with increase of C(KCl). Increase of the ligand charge shifts the transition from the salt-independent to salt-dependent regime to higher C(KCl). A novel and simple relationship describing the EC50 dependence on DNA concentration, charge of the ligand and the salt-dependent dissociation constant of the ligand–DNA complex is derived. For the ε-oligolysines εK6–εK10, the experimental dependencies of EC50 on C(KCl) and Z are well-described by an equation with a common set of parameters. Implications from our findings for understanding DNA condensation in chromatin are discussed.

Role of amino acid insertions on intermolecular forces between arginine peptide condensed DNA helices: implications for protamine-DNA packaging in sperm

In spermatogenesis, chromatin histones are replaced by arginine-rich protamines to densely compact DNA in sperm heads. Tight packaging is considered necessary to protect the DNA from damage. To better understand the nature of the forces condensing protamine-DNA assemblies and their dependence on amino acid content, the effect of neutral and negatively charged amino acids on DNA-DNA intermolecular forces was studied using model peptides containing six arginines. We have previously observed that the neutral amino acids in salmon protamine decrease the net attraction between protamine-DNA helices compared with the equivalent homo-arginine peptide. Using osmotic stress coupled with x-ray scattering, we have investigated the component attractive and repulsive forces that determine the net attraction and equilibrium interhelical distance as a function of the chemistry, position, and number of the amino acid inserted. Neutral amino acids inserted into hexa-arginine increase the short range repulsion while only slightly affecting longer range attraction. The amino acid content alone of salmon protamine is enough to rationalize the forces that package DNA in sperm heads. Inserting a negatively charged amino acid into hexa-arginine dramatically weakens the net attraction. Both of these observations have biological implications for protamine-DNA packaging in sperm heads.

Linker histone H1 stimulates DNA strand exchange between short oligonucleotides retaining high sensitivity to heterology

The interaction of human linker histone H1(0) with short oligonucleotides was characterized. The capability of the histone to promote DNA strand exchange in this system has been demonstrated. The reaction is reversible at saturating amounts of H1 corresponding to complete binding of the oligonucleotide substrates with the histone. In our conditions the complete saturation of DNA with the histone occurs at a ratio of one protein molecule per about 60 nucleotides irrespectively of DNA strandedness. In contrast to the DNA strand exchange promoted by RecA-like enzymes of homologous recombination the H1 promoted reaction exhibits low tolerance to interruptions of homology between oligonucleotide substrates comparable to those for the case of spontaneous strand exchange between free DNA molecules at elevated temperatures and the exchange promoted by some synthetic polycations.

Salt effects on condensed protamine-DNA assemblies: anion binding and weakening of attraction

Using osmotic stress coupled with X-ray scattering, we have directly examined the salt sensitivity of the intermolecular forces between helices in condensed protamine-DNA arrays. Thermodynamic forces are measured from the dependence of DNA helical interaxial spacings on external salt concentration or the osmotic pressure applied by neutral polymer solutions in equilibrium with the condensed phase. Force curves of salmon protamine-DNA condensates are highly dependent on salt species and concentration, indicating salt binding to protamine-DNA complexes. This dependence of the forces on salt species follows the Hofmeister series for anions. Chaotropic anions bind more tightly to protamine-DNA arrays than kosmotropic anions, thus more greatly disrupting the attractive thermodynamic forces. Variations with cation type are small compared with those observed for anions. Further, osmotic stress is used to estimate the number of ions bound in the condensed phase through a Gibbs-Duhem relationship. We estimate that at equilibrium, ∼1 Br(-) is bound per protamine molecule at 200 mM NaBr concentration. Remarkably, this one bound anion results in a change of ∼12% in the surface-to-surface distance between DNA helices. Potential biological implications of this attractive force salt sensitivity are discussed.

SAXS studies of ion-nucleic acid interactions

Positively charged ions, atoms, or molecules compensate the high negative charge of the nucleic acid backbone. Their presence is critical to the biological function of DNA and RNA. This review focuses on experimental studies probing (a) interactions between small ions and nucleic acids and (b) ion-mediated interactions between nucleic acid duplexes. Experimental results on these simple model systems can be compared with specific theoretical models to validate their predictions. Small angle X-ray scattering (SAXS) provides unique insight into these interactions. Anomalous SAXS reports the spatial correlations of condensed (e.g., locally concentrated) counterions to individual DNA or RNA duplexes. SAXS very effectively reports interactions between nucleic acid helices, which range from strongly repulsive to strongly attractive depending on the ionic species present. The sign and strength of interparticle interactions are easily deduced from dramatic changes in the scattering profiles of interacting duplexes.

Double-stranded RNA resists condensation

Much attention has been focused on DNA condensation because of its fundamental biological importance. The recent discovery of new roles for RNA duplexes demands efficient packaging of double-stranded RNA for therapeutics. Here we report measurements of short DNA and RNA duplexes in the presence of trivalent ions. Under conditions where UV spectroscopy indicates condensation of DNA duplexes into (insoluble) precipitates, RNA duplexes remain soluble. Small angle x-ray scattering results suggest that the differing surface topologies of RNA and DNA may be crucial in generating the attractive forces that result in precipitation.

Importance of diffuse metal ion binding to RNA

RNAs are highly charged polyanionic molecules. RNA structure and function are strongly correlated with the ionic condition of the solution. The primary focus of this article is on the role of diffusive ions in RNA folding. Due to the long-range nature of electrostatic interactions, the diffuse ions can contribute significantly to RNA structural stability and folding kinetics. We present an overview of the experimental findings as well as the theoretical developments on the diffuse ion effects in RNA folding. This review places heavy emphasis on the effect of magnesium ions. Magnesium ions play a highly efficient role in stabilizing RNA tertiary structures and promoting tertiary structural folding. The highly efficient role goes beyond the mean-field effect such as the ionic strength. In addition to the effects of specific ion binding and ion dehydration, ion-ion correlation for the diffuse ions can contribute to the efficient role of the multivalent ions such as the magnesium ions in RNA folding.

Predicting ion binding properties for RNA tertiary structures

Recent experiments pointed to the potential importance of ion correlation for multivalent ions such as Mg(2+) ions in RNA folding. In this study, we develop an all-atom model to predict the ion electrostatics in RNA folding. The model can treat ion correlation effects explicitly by considering an ensemble of discrete ion distributions. In contrast to the previous coarse-grained models that can treat ion correlation, this new model is based on all-atom nucleic acid structures. Thus, unlike the previous coarse-grained models, this new model allows us to treat complex tertiary structures such as HIV-1 DIS type RNA kissing complexes. Theory-experiment comparisons for a variety of tertiary structures indicate that the model gives improved predictions over the Poisson-Boltzmann theory, which underestimates the Mg(2+) binding in the competition with Na(+). Further systematic theory-experiment comparisons for a series of tertiary structures lead to a set of analytical formulas for Mg(2+)/Na(+) ion-binding to various RNA and DNA structures over a wide range of Mg(2+) and Na(+) concentrations.

Exploring soft matter with x-rays: from the discovery of the DNA structure to the challenges of free electron lasers

X-rays have long been a precious tool for the study of the structure of matter. While the short wavelength makes them ideal for investigating materials down to the atomic scale, their high penetration power allows for the exploration of opaque samples at a multitude of length scales. We give an overview of the x-ray techniques suited for the characterization of soft matter and of their application to systems of current interest. We describe the advantages and limitations of existing x-ray methods and outline the possible developments following the introduction of a new kind of coherent source: the x-ray free electron laser.

Electrostatics of strongly charged biological polymers: ion-mediated interactions and self-organization in nucleic acids and proteins

Charges on biological polymers in physiologically relevant solution conditions are strongly screened by water and salt solutions containing counter-ions. However, the entropy of these counterions can result in surprisingly strong interactions between charged objects in water despite short screening lengths, via coupling between osmotic and electrostatic interactions. Widespread work in theory, experiment, and computation has been carried out to gain a fundamental understanding of the rich, yet sometimes counterintuitive, behavior of these polyelectrolyte systems. Examples of polyelectrolyte association in biology include DNA packaging and RNA folding, as well as aggregation and self-organization phenomena in different disease states.

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

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

Intensities of DNA ion-phosphate modes in the low-frequency Raman spectra

The Raman intensities of counterion vibrations with respect to the phosphate groups of the double-helix backbone (ion-phosphate modes) in the low-frequency spectra (< 200 cm(-1)) of B -DNA with different alkali metal counterions have been calculated using the model for DNA conformational vibrations and the valence-optic approach. The results have showed that the spectra of DNA with heavy counterions (Rb(+) and Cs(+)) differ from the spectra of DNA with light counterions (Na(+) and K(+)). The calculated spectra of DNA with heavy counterions are characterized by intensive modes of ion-phosphate vibrations that form one united band near 115 cm(-1). Ion-phosphate modes in the spectra of DNA with light counterions are characterized by higher frequencies (near 180 cm(-1)) and much lower intensity. Our calculations explain why the modes of ion-phosphate vibrations are observed in Cs-DNA spectra rather than in Na-DNA. The determined sensitivity of the intensities of DNA low-frequency spectra to the counterion type proves the existence of the ion-phosphate modes.

A universal description for the experimental behavior of salt-(in)dependent oligocation-induced DNA condensation

We report a systematic study of the condensation of plasmid DNA by oligocations with variation of the charge, Z, from +3 to +31. The oligocations include a series of synthetic linear epsilon-oligo(l-lysines), (denoted epsilonKn, n = 3-10, 31; n is the number of lysines equal to the ligand charge) and branched alpha-substituted homologues of epsilonK10: epsilonYK10, epsilonLK10 (Z = +10); epsilonRK10, epsilonYRK10 and epsilonLYRK10 (Z = +20). Data were obtained by light scattering, UV absorption monitored precipitation assay and isothermal titration calorimetry in a wide range concentrations of DNA and monovalent salt (KCl, C(KCl)). The dependence of EC(50) (ligand concentration at the midpoint of DNA condensation) on C(KCl) shows the existence of a salt-independent regime at low C(KCl) and a salt-dependent regime with a steep rise of EC(50) with increase of C(KCl). Increase of the ligand charge shifts the transition from the salt-independent to salt-dependent regime to higher C(KCl). A novel and simple relationship describing the EC(50) dependence on DNA concentration, charge of the ligand and the salt-dependent dissociation constant of the ligand-DNA complex is derived. For the epsilon-oligolysines epsilonK3-epsilonK10, the experimental dependencies of EC(50) on C(KCl) and Z are well-described by an equation with a common set of parameters. Implications from our findings for understanding DNA condensation in chromatin are discussed.