Competition between supercoils and toroids in single molecule DNA condensation

The condensation of free DNA into toroidal structures in the presence of multivalent ions and polypeptides is well known. Recent single molecule experiments have shown that condensation into toroids occurs even when the DNA molecule is subjected to tensile forces. Here we show that the combined tension and torsion of DNA in the presence of condensing agents dramatically modifies this picture by introducing supercoiled DNA as a competing structure in addition to toroids. We combine a fluctuating elastic rod model of DNA with phenomenological models for DNA interaction in the presence of condensing agents to compute the minimum energy configuration for given tension and end-rotations. We show that for each tension there is a critical number of end-rotations above which the supercoiled solution is preferred and below which toroids are the preferred state. Our results closely match recent extension rotation experiments on DNA in the presence of spermine and other condensing agents. Motivated by this, we construct a phase diagram for the preferred DNA states as a function of tension and applied end-rotations and identify a region where new experiments or simulations are needed to determine the preferred state.     

Polymer- and salt-induced toroids of hexagonal DNA.

A model is proposed for polymer- and salt-induced toroidal condensates of DNA, based on a recent theory of the undulation enhancement of the electrostatic interaction in the bulk hexagonal phase of semiflexible polyions. In a continuum approximation, the thermodynamic potential of a monomolecular toroid may be split up in bulk, surface, and curvature contributions. With the help of an approximate analytical minimization procedure, the optimal torus dimensions are calculated as a function of the concentrations of inert polymer and added salt. The stability of the torus is analyzed in terms of its surface tension and a bulk melting criterion. The theory should be applicable to psi-toroids that are not too thick.     

The possibility of intrinsic local curvature in DNA toroids

A variety of solution conditions are known to induce collapse of linear DNA into a compact configuration without dramatic change of local structure. When visualized, these compact forms frequently have a toroidal appearance. We ask whether the molecular basis of the toroidal shape can be a stable curvature of isolated rodlike DNA segments. Application of the classical Euler-Lagrange theory for the buckling of elastic rods provides us with an affirmative answer. Specifically, we see that, in principle, sufficient addition of inert polymer to DNA solutions can induce buckling of DNA segments. However, no attempt is made to quantitate the Euler-Lagrange condition for sufficiency in terms of added polymer concentration. We find also that complete neutralization of the phosphate charge is more than sufficient to induce buckling of DNA segments of length comparable to a Kuhn segment. The quantitative argument involves comparison of buckling forces provided by polyelectrolyte theory with the Euler-Lagrange criterion. Knowledge of the ionic-strength dependence of DNA bending stiffness (persistence length) is not required.     

Local structure of DNA toroids reveals curvature-dependent intermolecular forces

In viruses and cells, DNA is closely packed and tightly curved thanks to polyvalent cations inducing an effective attraction between its negatively charged filaments. Our understanding of this effective attraction remains very incomplete, partly because experimental data is limited to bulk measurements on large samples of mostly uncurved DNA helices. Here we use cryo electron microscopy to shed light on the interaction between highly curved helices. We find that the spacing between DNA helices in spermine-induced DNA toroidal condensates depends on their location within the torus, consistent with a mathematical model based on the competition between electrostatic interactions and the bending rigidity of DNA. We use our model to infer the characteristics of the interaction potential, and find that its equilibrium spacing strongly depends on the curvature of the filaments. In addition, the interaction is much softer than previously reported in bulk samples using different salt conditions. Beyond viruses and cells, our characterization of the interactions governing DNA-based dense structures could help develop robust designs in DNA nanotechnologies.     

Protein-DNA interactions determine the shapes of DNA toroids condensed in virus capsids

DNA toroids that form inside the bacteriophage capsid present different shapes according to whether they are formed by the addition of spermine or polyethylene glycol to the bathing solution. Spermine-DNA toroids present a convex, faceted section with no or minor distortions of the DNA interstrand spacing with respect to those observed in the bulk, whereas polyethylene glycol-induced toroids are flattened to the capsid inner surface and show a crescent-like, nonconvex shape. By modeling the energetics of the DNA toroid using a free-energy functional composed of energy contributions related to the elasticity of the wound DNA, exposed surface DNA energy, and adhesion between the DNA and the capsid, we established that the crescent shape of the toroidal DNA section comes from attractive interactions between DNA and the capsid. Such attractive interactions seem to be specific to the PEG condensation process and are not observed in the case of spermine-induced DNA condensation.     

Thermodynamics of cation-induced DNA condensation.

An estimation of the various free energy contributions to DNA collapse into toroidal particles is made, considering DNA bending and segment mobility, electrostatic repulsions between DNA chains, and attractive forces resulting from correlated counterion fluctuations. It is shown that the process of DNA condensation becomes spontaneous in the presence of divalent cations in methanol, and in the presence of tri- or tetravalent cations in water media. This is a consequence of the large decrease in the electrostatic repulsion between charged DNA segments, allowing the attractive force resulting from correlated fluctuations of bound counterions to become dominant. Our calculations indicate that short DNA fragments would condense into multimolecular particles in order to maximize the attractive force due to counterion fluctuations.     

Cationic silanes stabilize intermediates in DNA condensation.

In vitro condensation of DNA has been widely studied to gain insight into the mechanisms of DNA compaction in biological systems such as chromosomes and phage heads and has been used to produce nanostructured particles with novel material and functional properties. Here we report on the condensation of DNA in aqueous solutions by cationic silanes, which combine the condensing properties of polyamines with the cross-linking chemistry of silanes. DNA can be reversibly condensed into classical toroidal and rod-shaped structures with these agents. At low silane concentrations DNA forms a variety of looped structures with well-defined characteristics, including flower- and sausage-shaped forms. These structures suggest that at low silane concentrations a DNA-DNA contact in which the strands are at very large angles to each other is stabilized. Changes in these structures observed as a function of silane concentration suggest possible pathways for the formation of toroids and rods.     

Brownian dynamics simulation of DNA condensation.

DNA condensation observed in vitro with the addition of polyvalent counterions is due to intermolecular attractive forces. We introduce a quantitative model of these forces in a Brownian dynamics simulation in addition to a standard mean-field Poisson-Boltzmann repulsion. The comparison of a theoretical value of the effective diameter calculated from the second virial coefficient in cylindrical geometry with some experimental results allows a quantitative evaluation of the one-parameter attractive potential. We show afterward that with a sufficient concentration of divalent salt (typically approximately 20 mM MgCl(2)), supercoiled DNA adopts a collapsed form where opposing segments of interwound regions present zones of lateral contact. However, under the same conditions the same plasmid without torsional stress does not collapse. The condensed molecules present coexisting open and collapsed plectonemic regions. Furthermore, simulations show that circular DNA in 50% methanol solutions with 20 mM MgCl(2) aggregates without the requirement of torsional energy. This confirms known experimental results. Finally, a simulated DNA molecule confined in a box of variable size also presents some local collapsed zones in 20 mM MgCl(2) above a critical concentration of the DNA. Conformational entropy reduction obtained either by supercoiling or by confinement seems thus to play a crucial role in all forms of condensation of DNA.     

DNA packaging induced by micellar aggregates: a novel in vitro DNA condensation system.

Evidence for a conceptually novel DNA packaging process is presented. X-ray scattering, electron microscopy, and circular dichroism measurements indicate that in the presence of positively charged micellar aggregates and flexible anionic polymers, such as negatively charged polypeptides or single-stranded RNA species, a complex is formed in which DNA molecules are partially embedded within a micellar scaffold and partially condensed into highly packed chiral structures. Based on studies of micelle-DNA and micelle-flexible anionic polymer systems, as well as on the known effects of a high charge density upon the micellar organization, a DNA packaging model is proposed. According to this model, the DNA induces the elongation of the micelles into rodlike aggregates, forming a closely packed matrix in which the DNA molecules are immobilized. In contrast, the flexible anionic polymers stabilize clusters of spherical micelles which are proposed to effect a capping of the rodlike micelles, thus arresting their elongation and creating surfactant-free segments of the DNA that are able to converge and collapse. Thus, unlike other in vitro DNA packaging systems, in which condensation follows encounters between charge-neutralized DNA molecules, a prepackaging phase where the DNA is immobilized within a matrix is proposed in this case. Cellular and nuclear membranes have been implicated in DNA packaging processes in vivo, and negatively charged polyelectrolytes were shown to be involved in the processes. These observations, combined with the basic tenets of the DNA condensation system described here, allow for the progression to the study of more elaborate model systems and thus might lead to insights into the nature and roles of the intricate in vivo DNA-membrane complexes.     

The compaction of DNA helices into either continuous supercoils or folded-fiber rods and toroids.

We have investigated by electron microscopy the mechanism of DNA compaction and have found that the double helix has the intrinsic potential to direct its own packaging into two distinctly different and mutally exclusive modes. The mode of DNA packaging is determined by the electrostatic charge density and water activity of the immediate microenvironment of the helix. The two basic structures formed by both linear and covalently closed-circular DNA are: a left-handed supercoil characteristic of minimally charge-shielded DNA, and a smooth rod characteristic of fully charge-shielded DNA. We propose that in the supercoil, the double helix is overwound (increased turn-angle), while in the rod, the helix is folded back and forth on itself. Variation of these two basic structures are the beaded fiber of DNA obtained with partially charge-shielded DNA and the toroid formed by the bending of the DNA rod and fusion of its ends in the presence of certain cations. We compare the DNA packaging inside these in vitro generated structures to DNA packaging in chromatin and viral capsids, and conclude that the packaging of DNA brought about by the use of salts and alcohol closely mimics the packaging behavior of the DNA in vivo, where it is usually complexed with histones or polyamines.     

Chromosome condensation: DNA compaction in real time

Mitotic chromosomes must be organised into a highly ordered and compacted form to allow proper segregation of DNA during each round of cell division. Two new studies report observations of DNA compaction by eukaryotic and bacterial condensin molecules in real time using magnetic and optical trapping micromanipulation techniques.     

One-electron oxidation of condensed DNA toroids: injection-site dependent charge (radical cation) mobility

DNA condensates were formed by treating linear pUC19 plasmids ligated to an AQ-containing oligomer with spermidine. The condensates are toroid-shaped objects having a radius of 70 to 100 nm. Irradiation of the condensates with UV light (absorbed by the anthraquinone) causes the one-electron oxidation of the DNA and concomitant reaction at GG steps of the oligomer. Analysis of the distance dependence of the reaction at guanine in these condensates reveals a dependency on the position of the AQ. This observation is attributed to a reduction in the rate for trapping of the radical cation in the relatively dehydrated interior of the condensate.     

Ligand-induced DNA condensation: choosing the model

We test and compare different models for ligand-induced DNA condensation. Using 14C-labeled spermidine3+, we measure the binding to condensed DNA at micromolar to molar polyamine concentrations. DNA aggregates at a critical polyamine concentration. Spermidine3+ binding becomes highly cooperative at the onset of aggregation. At higher concentrations, spermidine3+ binding to condensed DNA reaches a plateau with the degree of binding equal to 0.7 (NH(4+)/PO3-). Condensed DNA exists in a wide range of spermidine concentrations with the roughly constant degree of ligand binding. At greater concentrations, the degree of binding increases again. Further spermidine penetration between the double helices causes DNA resolubilization. We show that a simple two-state model without ligand-ligand interactions qualitatively predicts the reentrant aggregation-resolubilization behavior and the dependence on the ligand, Na+, and DNA concentrations. However, such models are inconsistent with the cooperative ligand binding to condensed DNA. Including the contact or long-range ligand-ligand interactions improves the coincidence with the experiments, if binding to condensed DNA is slightly more cooperative than to the starting DNA. For example, in the contact interaction model it is equivalent to an additional McGhee-von Hippel cooperativity parameter of approximately 2. Possible physical mechanisms for the observed cooperativity of ligand binding are discussed.     

DNA condensation with polyamines I. Spectroscopic studies

The addition of polyamines with three or four positive charges to very dilute solutions of phage T7 DNA leads to a co-operative condensation. The reaction is very rapid and the DNA remains in the B-form as characterized by circular dichroism. The particles which are formed are roughly the size of a phage particle when they are prepared for electron microscopy. This aspect is discussed more completely in the accompanying paper (Chattoraj et al., 1978).Most of the experiments were performed at low ionic strength (roughly 0.002 m) with the triamine, spermidine. The reaction also occurs in 0.15 m-sodium chloride but here the experiments are accompanied by slow irreversible effects which are evidently due to aggregation since they are accompanied by a commensurate increase in turbidity. Consequently, most of the experiments have been done under the reversible low ionic strength conditions.Neither Mg²⁺ nor the diamine putrescine produce the reaction at concentrations similar to those found in bacterial cells. The tetramer spermine, on the other hand, which is not found in bacterial cells, is a very strong condensation agent in the μm region. The spermidine analog, bis-(3-aminopropyl)amine is very similar in behavior to spermidine.The role which polyamines might play in the condensation of DNA in phage heads is discussed.     

Dynamics of DNA condensation

The condensation of DNA induced by spermine and spermidine is investigated by equilibrium titrations and stopped-flow and field-jump experiments using scattered light detection. The spermine concentration required for the cooperative condensation process is measured at different DNA concentrations; these data are used to evaluate both the condensation threshold degree of spermine binding and the binding constant of spermine according to an excluded-site model. Stopped-flow measurements of the spermine-induced condensation demonstrate the existence of two processes: (1) A "fast" reaction is observed in the millisecond time range, when the reactant concentrations are around 1 microM; it is associated with a characteristic induction period and is assigned to the intramolecular condensation reaction. (2) A slow reaction with time constants of, e.g., 100 s strongly dependent upon both spermine and DNA concentrations is assigned to an intermolecular DNA association. The unusual time course of the intramolecular condensation reaction with the induction period provides evidence for a "threshold kinetics". During the induction period, spermine molecules are bound to DNA, but the degree of binding remains below the threshold value. As soon as the degree of ligand binding arrives at the threshold, the DNA is condensed in a relatively fast reaction. Model calculations of the spermine binding kinetics according to an excluded-site model demonstrate that the spermine molecules bound to DNA are mobile along the double helix. A comparison of the experimental data with the results of Monte Carlo simulations suggests a rate constant of approximately 200 s-1 for spermine movement by one nucleotide residue.(ABSTRACT TRUNCATED AT 250 WORDS)     

DNA condensation with polyamines. II. Electron microscopic studies

Approximately 75% of the wheat and rye genomes consist of repeated sequence DNA. Three-quarters of the non-repeated or few copy sequences in wheat are less than 1000 base-pairs long, whilst in rye approximately half of the non-repeated or few copy sequences are in this size class. Most of the remaining non-repeated or few copy sequences appear to be a few thousand base-pairs long.In this paper a somewhat novel approach has been used to quantitatively analyse the linear organisation of the large proportion of repeated sequence DNA as well as the non-repeated DNA in the wheat and rye genomes. Repeated sequences in the genomes of oats, barley, wheat and rye have been used as probes to distinguish and isolate four different groups of repeated sequences and their neighbouring sequences from the wheat and rye genomes. Radioactively labelled wheat or rye DNA fragments ranging from 200 to over 9000 nucleotides long were incubated separately with large excesses of denatured unlabelled oats, barley, wheat and rye DNAs to C_ot values which enable all the repeated sequences of the unlabelled DNA to renature. The following parameters were then determined from the proportions of total labelled DNA in fragments which had at least partially renatured. (1) The proportions of the repeated sequences in the labelled DNAs that were able to hybridise to each unlabelled DNA; (2) the mean distance apart of the hybridising sequences on the longer labelled fragments; and (3) the proportion of the genome in which the hybridising sequences were concentrated. Analysis of these results, together with those of separate experiments designed to quantitatively estimate the nature of sequences unable to reanneal with the repeated sequences of each of the probe DNAs, have enabled schematic maps to be drawn which show how the repeated and non-repeated sequences are arranged in the wheat and rye genomes.Both genomes are constructed from millions of relatively short sequences, most of them considerably shorter than 3000 base-pairs. This structure was recognised because adjacent sequences can be distinguished by their frequency of repetition (i.e. repeated or non-repeated) or by their evolutionary origin. Approximately 40 to 45% of the wheat genome and 30 to 35% of the rye genome consists of short non-repeated sequences interspersed between short repeated sequences. Approximately 50% of the wheat genome and 60% of the rye genome consists of tandemly arranged repeated sequences of different evolutionary origins. It is postulated that much of this complex repeated sequence DNA could have arisen from amplification of compound sequences, each containing repeated and non-repeated sequence DNA.Short repeated sequences with a number average length of around 200 base-pairs and which occupy about 20% of the wheat and rye genomes are related to repeated sequences also found in oats and barley. They are concentrated in 60 to 70% of the wheat and rye genomes, being interspersed with different short repeated sequences and a significant proportion of the short non-repeated sequences.Rye chromosomes contain more DNA than wheat chromosomes. This is principally, but not entirely, due to additional repeated sequence DNA. Many quantitative changes appear to have occurred in both genomes, possibly affecting most families of repeated sequences, since wheat and rye diverged from a common ancestor. Both species contain species-specific repeated sequences (24% of rye genome; 16% of wheat genome) but a large proportion of these are closely interspersed with repeated sequences found in both genomes.     

Exchange of counterions in DNA condensation

We measured the fluorescence intensity of DNA-bound fluorescent dyes YO-PRO-1 (oxazole yellow) and YOYO-1 (dimer of oxazole yellow) at various spermidine concentrations to determine how counterions on DNA are exchanged in the process of DNA condensation. A decrease of fluorescence intensity was observed with an increase of spermidine. Considering the chemical equilibrium under the competition between the dye and spermidine for counterion condensation on DNA, the theoretical curve well describes the decrease of the fluorescence intensity. These results indicate that dyes are exchanged for spermidine at the binding site on DNA; that is, the exchange of counterions occurs. The parameters associated with the decrease of the fluorescence intensity show that the relative affinity of the dye and spermidine for DNA depends on the state of DNA. Moreover, YOYO-1 prevents the DNA condensation, but the effect of YO-PRO-1 on the condensation is very slight, though both dyes intercalate for DNA; the high affinity of YOYO-1 compared to YO-PRO-1 enables prevention of the condensation.     

Structural effects of cobalt-amine compounds on DNA condensation.

Light scattering and electron microscopy have been used to investigate the structural effects of the trivalent complexes hexaammine cobalt (III) chloride (Cohex), tris(ethylenediamine) cobalt(III) chloride (Coen), and cobalt(III) sepulchrate chloride (Cosep) on DNA condensation. These cobalt-amine compounds have similar ligand coordination geometries but differ slightly in size. Their hydrophobicity is in the order Cosep > Coen > Cohex, according to the numbers of methylene groups in these ligands. All of these compounds effectively precipitate DNA at high concentrations; but despite a lower surface charge density, Cosep condenses DNA twice as effectively as Coen or Cohex. UV and CD measurements of the supernatants of cobalt-amine/DNA solutions reveal a preferential binding of Delta-Coen over Lambda-Coen to the precipitated DNA, but there is no chiral selectivity for Cosep. Competition experiments show that the binding strengths of these three cobalt-amine compounds to aggregated DNA are comparable. A charge neutralization of 88-90% is required for DNA condensation. Our data indicate that 1) electrostatic interaction is the main driving force for binding of multivalent cations to DNA; 2) DNA condensation is dependent on the structure of the condensing agent; and 3) the hydration pattern or polarization of water molecules on the surface of condensing agents plays an important role in DNA condensation and chiral recognition.