Role of DNA-DNA interactions on the structure and thermodynamics of bacteriophages Lambda and P4

Electrostatic interactions play an important role in both packaging of DNA inside bacteriophages and its release into bacterial cells. While at physiological conditions DNA strands repel each other, the presence of polyvalent cations such as spermine and spermidine in solutions leads to the formation of DNA condensates. In this study, we discuss packaging of DNA into bacteriophages P4 and Lambda under repulsive and attractive conditions using a coarse-grained model of DNA and capsids. Packaging under repulsive conditions leads to the appearance of the coaxial spooling conformations; DNA occupies all available space inside the capsid. Under the attractive potential both packed systems reveal toroidal conformations, leaving the central part of the capsids empty. We also present a detailed thermodynamic analysis of packaging and show that the forces required to pack the genomes in the presence of polyamines are significantly lower than those observed under repulsive conditions. The analysis reveals that in both the repulsive and attractive regimes the entropic penalty of DNA confinement has a significant non-negligible contribution into the total energy of packaging. Additionally we report the results of simulations of DNA condensation inside partially packed Lambda. We found that at low densities DNA behaves as free unconfined polymer and condenses into the toroidal structures; at higher densities rearrangement of the genome into toroids becomes hindered, and condensation results in the formation of non-equilibrium structures. In all cases packaging in a specific conformation occurs as a result of interplay between bending stresses experienced by the confined polymer and interactions between the strands.     

短DNA片段缩合结构的比较研究

本文利用透射式电镜对四种短DNA片段(500、1100、1500、2700 bP)的缩合结构进行了比较研究得出很有意义的结果。定量研究证实短至500 bP的DNA分子仍可形成复曲面,且分子量相差5倍多的DNA片段缩合形成的复曲面尺度大小一致。复曲面外径为400A左右。从而进一步证实作者与Arscott及Bloomfield关于复曲面尺度独立于DNA分子量,及短DNA片段的缩合是多分子缩合的结论。此外,观测到缩合中间结构的尺度依DNA分子量大小不同而变化,同时分子量愈小的DNA片段产生另一种缩合结构—棒体的几率愈大。     

Visualizing the Formation and Collapse of DNA Toroids

In living organisms, DNA is generally confined into very small volumes. In most viruses, positively charged multivalent ions assist the condensation of DNA into tightly packed toroidal structures. Interestingly, such cations can also induce the spontaneous formation of DNA toroids in vitro. To resolve the condensation dynamics and stability of DNA toroids, we use a combination of optical tweezers and fluorescence imaging to visualize in real-time spermine-induced (de)condensation in single DNA molecules. By actively controlling the DNA extension, we are able to follow (de)condensation under tension with high temporal and spatial resolution. We show that both processes occur in a quantized manner, caused by individual DNA loops added onto or removed from a toroidal condensate that is much smaller than previously observed in similar experiments. Finally, we present an analytical model that qualitatively captures the experimentally observed features, including an apparent force plateau.     

Time study of DNA condensate morphology: implications regarding the nucleation, growth, and equilibrium populations of toroids and rods

It is well known that multivalent cations cause free DNA in solution to condense into nanometer-scale particles with toroidal and rod-like morphologies. However, it has not been shown to what degree kinetic factors (e.g., condensate nucleation) versus thermodynamic factors (e.g., DNA bending energy) determine experimentally observed relative populations of toroids and rods. It is also not clear how multimolecular DNA toroids and rods interconvert in solution. We have conducted a series of condensation studies in which DNA condensate morphology statistics were measured as a function of time and DNA structure. Here, we show that in a typical in vitro DNA condensation reaction, the relative rod population 2 min after the initiation of condensation is substantially greater than that measured after morphological equilibrium is reached (ca. 20 min). This higher population of rods at earlier time points is consistent with theoretical studies that have suggested a favorable kinetic pathway for rod nucleation. By using static DNA loops to alter the kinetics and thermodynamics of condensation, we further demonstrate that reported increases in rod populations associated with decreasing DNA length are primarily due to a change in the thermodynamics of DNA condensation, rather than a change in the kinetics of condensate nucleation or growth. The results presented also reveal that the redistribution of DNA from rods to toroids is mediated through the exchange of DNA strands with solution.     

Evidence that both kinetic and thermodynamic factors govern DNA toroid dimensions: effects of magnesium(II) on DNA condensation by hexammine cobalt(III)

Millimolar concentrations of divalent cations are shown to affect the size of toroids formed when DNA is condensed by multivalent cations. The origins of this effect were explored by varying the order in which MgCl(2) was added to a series of DNA condensation reactions with hexammine cobalt chloride. The interplay between Mg(II), temperature, and absolute cation concentration on DNA condensation was also investigated. These studies reveal that DNA condensation is extremely sensitive to whether Mg(II) is associated with DNA prior to condensation or Mg(II) is added concurrently with hexammine cobalt(III) at the time of condensation. It was also found that, in the presence of Mg(II), temperature and dilution can have opposite effects on the degree of DNA condensation. A systematic comparison of DNA condensates observed in this study clearly illustrates that, under our low-salt conditions, toroid size is determined by the kinetics of toroid nucleation and growth. However, when Mg(II) is present during condensation, toroid size can also be limited by a thermodynamic parameter (e.g., undercharging). The path dependence of DNA condensation presented here illustrates that regardless of which particular factors limit toroid growth, toroids formed under the various conditions of this study are largely nonequilibrium structures.     

Atomic force microscopy analysis of intermediates in cobalt hexammine-induced DNA condensation

The packaging pathway of cobalt hexammine-induced DNA condensation on the surface of mica was examined by varying the concentration of Co(NH3)6(3+) in a dilute DNA solution and visualizing the condensates by atomic force microscopy (AFM). Images reveal that cobalt hexammine-induced DNA condensation on mica involves well-defined structures. At 30 microM Co(NH3)6(3+), prolate ellipsoid condensates composed of relatively shorter rods with linkages between them are formed. At 80 microM Co(NH3)6(3+), the condensed features include toroids with average diameter of approximately 240 nm as well as U-shaped and rod-like condensates with nodular appearances. The results imply that the condensates, whether toroids, U-shaped or rod-like structures have similar intermediate state which includes relatively shorter rod-like segments. The average size of the condensed toroids after incubated at room temperature for 5 h (approximately 240 nm) is much larger than that incubated for 0.5 h (approximately 100 nm). The results indicate that the condensation of DNA by Co(NH3)6(3+) is a kinetic-controlled process.     

Influence of DNA length on spermine-induced condensation. Importance of the bending and stiffening of DNA

Using DNA restriction fragments of 258 to 4362 base-pairs, we have investigated the influence of the DNA length on the condensation process induced by spermine, with the aid of electric dichroism measurements. The 258- and 436 bp fragments condensed into rod-like particles, while the fragments of 748 bp or more condensed into torus-shaped particles. Our results suggest that a DNA molecule longer than the circumference of the toroids observed previously (680 bp) is required to serve as a nucleus for the growth of the condensed particles. The toroids were more stable in the electric field than the rod-shaped particles, suggesting that rapid fluctuations of the bound spermine counterions can provide one of the main attractive forces yielding to the condensation process. Relaxation time data for the 436 bp fragment revealed that the structure of DNA was altered at a spermine concentration as low as one-tenth of that required for condensation: the DNA became bent in the presence of spermine. Moreover, the field strength dependence of the relaxation times, as well as the fitting of the decay curves at 12.5 kV/cm, showed an increase of the stiffness of the DNA double helix upon spermine addition. We estimated that, in the case of DNA condensation by spermine, a decrease in the measured persistence length may occur, irrespective of the DNA flexibility, owing to the bending of the DNA molecule.     

Influence of DNA length on spermine-induced condensation: Importance of the bending and stiffening of DNA

Using DNA restriction fragments of 258 to 4362 base-pairs, we have investigated the influence of the DNA length on the condensation process induced by spermine, with the aid of electric dichroism measurements. The 258- and 436 bp fragments condensed into rod-like particles, while the fragments of 748 bp or more condensed into torus-shaped particles. Our results suggest that a DNA molecule longer than the circumference of the toroids observed previously (680 bp) is required to serve as a nucleus for the growth of the condensed particles. The toroids were more stable in the electric field than the rod-shaped particles, suggesting that rapid fluctuations of the bound spermine counterions can provide one of the main attractive forces yielding to the condensation process. Relaxation time data for the 436 bp fragment revealed that the structure of DNA was altered at a spermine concentration as low as one-tenth of that required for condensation: the DNA became bent in the presence of spermine. Moreover, the field strength dependence of the relaxation times, as well as the fitting of the decay curves at 12.5 kV/cm, showed an increase of the stiffness of the DNA double helix upon spermine addition. We estimated that, in the case of DNA condensation by spermine, a decrease in the measured persistence length may occur, irrespective of the DNA flexibility, owing to the bending of the DNA molecule.     

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.     

Condensation of DNA by trivalent cations. 1. Effects of DNA length and topology on the size and shape of condensed particles

In vitro condensation of DNA by multivalent cations can provide useful insights into the physical factors governing folding and packaging of DNA in vivo. We have made a detailed study of hexammine cobalt (III) induced condensation of 2700 and 1350 base pair (bp) fragments of plasmid pUC12 DNA by electron microscopy and laser light scattering. The condensed DNA takes the form of toroids and rods. Both are present in all condensates, but the proportion of toroids is higher with the larger fragments. The intact, closed circular plasmid produces smaller particles than the linear fragments. The size of a particle is independent of DNA fragment length. Two hours after adding the condensing agent, a typical toroid is about 800 A in diameter; the outer radius (R1) is approximately 400 A, and the inner radius (R2) is approximately 140 A for both sets of fragments. These dimensions are relatively stable, but there is sufficient change in both R1 and R2 to produce approximately 50% increase in volume from 2 to 24 h. A typical rod at 2 h is about 1800 A long and 300 A wide. The distribution of rod lengths is similar to that of mean toroid circumferences pi (R1 + R2), and the distribution of rod widths is similar to that of toroidal widths (R1-R2). The 2700-bp fragments show a significantly higher ratio of toroids to rods than the 1350-bp fragments. Both types of particle are multimolecular. The average number of molecules/particle, calculated from the above dimensions, assuming hexagonally packed B-form DNA with a center-to-center spacing of 27 A, is 13 +/- 4 for condensates of 2700-bp fragments and 26 +/- 11 for those of 1350-bp fragments. Monomolecular condensates of much larger DNAs have similar dimensions, suggesting that size is governed primarily by the balance of attractive and repulsive intermolecular forces rather than by the entropic factors associated with incorporation of a number of small particles into a larger one. The similar dimensions and volumes of toroids and rods indicate that the free energy cost of continual bending in toroids, minus that gained by extra net attraction in a cyclic particle, is comparable to that of abrupt bending or kinking in rods. Although the condensed particles are multimeric, their distinct toroidal or rodlike shapes distinguish them from the random aggregates that would be generally expected from the multimolecular association of large, flexible polymers.     

Bacterial protein HU dictates the morphology of DNA condensates produced by crowding agents and polyamines

Controlling the size and shape of DNA condensates is important in vivo and for the improvement of nonviral gene delivery. Here, we demonstrate that the morphology of DNA condensates, formed under a variety of conditions, is shifted completely from toroids to rods if the bacterial protein HU is present during condensation. HU is a non-sequence-specific DNA binding protein that sharply bends DNA, but alone does not condense DNA into densely packed particles. Less than one HU dimer per 225 bp of DNA is sufficient to completely control condensate morphology when DNA is condensed by spermidine. We propose that rods are favored in the presence of HU because rods contain sharply bent DNA, whereas toroids contain only smoothly bent DNA. The results presented illustrate the utility of naturally derived proteins for controlling the shape of DNA condensates formed in vitro. HU is a highly conserved protein in bacteria that is implicated in the compaction and shaping of nucleoid structure. However, the exact role of HU in chromosome compaction is not well understood. Our demonstration that HU governs DNA condensation in vitro also suggests a mechanism by which HU could act as an architectural protein for bacterial chromosome compaction and organization in vivo.     

DNA toroids: stages in condensation.

The effects of polylysine (PLL) and PLL-asialoorosomucoid (AsOR) on DNA condensation have been analyzed by AFM. Different types of condensed DNA structures were observed, which show a sequence of conformational changes as circular plasmid DNA molecules condense progressively. The structures range from circular molecules with the length of the plasmid DNA to small toroids and short rods with approximately 1/6 to 1/8 the contour length of the uncondensed circular DNA. Single plasmid molecules of 6800 base pairs (bp) condense into single toroids of approximately 110 nm diameter, measured center-to-center. The results are consistent with a model for DNA condensation in which circular DNA molecules fold several times into progressively shorter rods. Structures intermediate between toroids and rods suggest that at least some toroids may form by the opening up of rods as proposed by Dunlap et al. [(1997) Nucleic Acids Res. 25, 3095]. Toroids and rods formed at lysine:nucleotide ratios of 5:1 and 6:1. This high lysine:nucleotide ratio is discussed in relation to entropic considerations and the overcharging of macroions. PLL-AsOR is much more effective than PLL alone for condensing DNA, because several PLL molecules are attached to a single AsOR molecule, resulting in an increased cation density.     

DNA condensation by multivalent cations

In the presence of multivalent cations, high molecular weight DNA undergoes a dramatic condensation to a compact, usually highly ordered toroidal structure. This review begins with an overview of DNA condensation : condensing agents, morphology, kinetics, and reversibility, and the minimum size required to form orderly condensates. It then summarizes the statistical mechanics of the collapse of stiff polymers, which shows why DNA condensation is abrupt and why toroids are favored structures. Various ways to estimate or measure intermolecular forces in DNA condensation are discussed, all of them agreeing that the free energy change per base pair is very small, on the order of 1% of thermal energy. Experimental evidence is surveyed showing that DNA condensation occurs when about 90% of its charge is neutralized by counterions. The various intermolecular forces whose interplay gives rise to DNA condensation are then reviewed. The entropy loss upon collapse of the expanded wormlike coil costs free energy, and stiffness sets limits on tight curvature. However, the dominant contributions seem to come from ions and water. Electrostatic repulsions must be overcome by high salt concentrations or by the correlated fluctuations of territorially bound multivalent cations. Hydration must be adjusted to allow a cooperative accommodation of the water structure surrounding surface groups on the DNA helices as they approach. Undulations of the DNA in its confined surroundings extend the range of the electrostatic forces. The condensing ions may also subtly modify the local structure of the double helix. © 1998 John Wiley & Sons, Inc. Biopoly 44: 269–282, 1997     

Strongly correlated electrostatics of viral genome packaging

The problem of viral packaging (condensation) and ejection from viral capsid in the presence of multivalent counterions is considered. Experiments show divalent counterions strongly influence the amount of DNA ejected from bacteriophage. In this paper, the strong electrostatic interactions between DNA molecules in the presence of multivalent counterions is investigated. It is shown that experiment results agree reasonably well with the phenomenon of DNA reentrant condensation. This phenomenon is known to cause DNA condensation in the presence of tri- or tetra-valent counterions. For divalent counterions, the viral capsid confinement strongly suppresses DNA configurational entropy, therefore the correlation between divalent counterions is strongly enhanced causing similar effect. Computational studies also agree well with theoretical calculations.     

Influence of charged surfaces on the morphology of DNA condensed with multivalent ions

DNA in solution can be condensed into dense aggregates by multivalent counterions. Here we investigate the effect of a nearby surface on the morphology of DNA condensates. We show that, contrary to what has often been assumed, interactions between DNA condensates and the surface can strongly influence the observed morphology. This limits the usefulness of surface probes such as atomic force microscopy for studying the morphology of condensates in bulk solution. Surprisingly, we find that the most negatively charged surface disturbs the condensate morphology most, suggesting that the microscopic mechanism resulting in DNA condensation is also responsible for the attractive force between DNA and the surface.     

Condensation of DNA by multivalent cations: considerations on mechanism.

DNA is generally found within viruses and cells in a tightly packaged state, typically occupying only 10(-4)-10(-6) of the volume of the uncondensed DNA wormlike coil. Condensation can be induced in vitro at low salt by the naturally occurring polyamines spermidine3+ and spermine4+, by hexammine cobalt(III), and even by Mg2+ in methanol-water mixtures. These condensates generally have an orderly, toroidal, or rodlike shape and size similar to that of DNA gently lysed from phage heads. It is also striking that the condensate size distribution is independent of DNA molecular length from 400 to 40,000 base pairs (bp), but that shorter DNA molecules (e.g., 150-bp mononucleosomal DNA) cannot condense in this fashion. We have constructed a successive association equilibrium theory to attempt to explain these results, using an equation devised by Tanford for micelle formation. Most of the obvious attractive and repulsive free energy contributions (mixing, bending, hydration, and other nearest-neighbor interactions) are linear in the amount of DNA incorporated, but the net attractive delta G0 grows nonlinearly because of the increasing average number of nearest neighbors of each duplex as the particle grows. In order that the size distribution have a maximum, a quadratic repulsive free energy is also required, arising from the electrostatic self-energy of the incompletely neutralized particles. The net attractive free energy per base pair interaction is tiny, on the order of 10(-3) kT. Despite the apparent generally correct order of magnitude of the various free energy terms, the calculated size distribution is smaller and narrower than observed experimentally. It appears that the size distribution of condensed particles is determined kinetically rather than thermodynamically. Very short DNA molecules cannot nucleate stable aggregates because they cannot develop adequate overlap, either internally or intermolecularly. A substantial fraction of rodlike condensates is observed in aqueous solutions only with a rather inefficient condensing agent, permethylated spermidine. This suggests that slow condensation kinetics may be required to overcome the high activation energy of highly distorted DNA bends or kinks at the turning points of rods. Evidence is reviewed that condensation may be associated with localized helix structure distortion provoked by condensing agents.     

The observation of the local ordering characteristics of spermidine-condensed DNA: atomic force microscopy and polarizing microscopy studies.

Condensation of DNA by multivalent cations can provide useful insights into the physical factors governing the folding and packaging of DNA in vivo. In this work, local ordered structures of spermidine-DNA complexes prepared from different DNA concentrations have been examined by using atomic force microscopy (AFM) and polarizing microscopy (PM). Two types (I and II) of DNA condensates, significantly different in sizes, were observed. It was found that for extremely dilute solutions (DNA concentrations around 1 ng/microl or below), the DNA molecules would collapse into toroidal structures with a volume equivalent to a single lambda-DNA (type I). In relatively dilute solutions (DNA concentrations between 1 and 10 ng/microll), a significantly larger structure of multimolecular toroids (circular and elliptical, type II) were formed, which were constructed by many fine particles. Measurements show that the average diameter of these fine particles was similar to the outer diameter of the monomolecular toroids observed in extremely dilute solutions, and the thickness of the multimolecular toroids had a distribution of multi-layers with height increments of 11 nm, indicating that the multimolecular toroidal structures have lamellar characteristics. Moreover, by enriching the DNA-spermidine complexes in very diluted solution, branch-like structures constructed by subunits were observed by using AFM. The analysis of the pellets in polarizing microscopy reveals a liquid-crystal-like pattern. These observations suggest that DNA-spermidine condensation could have multiple stages, which are very sensitive to the DNA and spermidine concentrations.     

Packaging of genomes in bacteriophages: a comparison of ssRNA bacteriophages and dsDNA bacteriophages.

In complex DNA bacteriophages like lambda, T4, T7, P22, P2, the DNA is packaged into a preformed precursor particle which sometimes has a smaller size and often a shape different from that of the phage head. This packaging mechanism is different from the one suggested for the RNA phages, according to which RNA nucleates the shell formation. The different mechanisms could be understood by comparing the genomes to be packaged: single stranded fII RNA has a very compact structure with high helix content. It might easily form quasispherical structures in solution (as seen in the electron microscope by Thach & Thach (1973)) around which the capsid could assemble. Double stranded phage DNA, on the other hand, is a rigid molecule which occupies a large volume in solution and has to be concentrated 15-fold during packaging into the preformed capsid, and the change in the capsid structure observed hereby might provide the necessary DNA condensation energy.     

Ion-dependent DNA configuration in bacteriophage capsids

Bacteriophages densely pack their long double-stranded DNA genome inside a protein capsid. The conformation of the viral genome inside the capsid is consistent with a hexagonal liquid crystalline structure. Experiments have confirmed that the details of the hexagonal packing depend on the electrochemistry of the capsid and its environment. In this work, we propose a biophysical model that quantifies the relationship between DNA configurations inside bacteriophage capsids and the types and concentrations of ions present in a biological system. We introduce an expression for the free energy that combines the electrostatic energy with contributions from bending of individual segments of DNA and Lennard-Jones-type interactions between these segments. The equilibrium points of this energy solve a partial differential equation that defines the distributions of DNA and the ions inside the capsid. We develop a computational approach that allows us to simulate much larger systems than what is possible using the existing molecular-level methods. In particular, we are able to estimate bending and repulsion between the DNA segments as well as the full electrochemistry of the solution, both inside and outside of the capsid. The numerical results show good agreement with existing experiments and with molecular dynamics simulations for small capsids.