Interhelical spacing in liquid crystalline spermine and spermidine-DNA precipitates

Physics of DNA: unravelling hidden abilities encoded in the structure of ‘the most important molecule’

A comprehensive article “Structure and Interactions of Biological Helices”, published in 2007 in Reviews of Modern Physics, overviewed various aspects of the effect of DNA structure on DNA–DNA interactions in solution and related phenomena, with a thorough analysis of the theory of these effects. Here, an updated qualitative account of this area is presented without any sophisticated ‘algebra’. It overviews the basic principles of the structure-specific interactions between double-stranded DNA and focuses on the physics behind several related properties encoded in the structure of DNA. Among them are (i) DNA condensation and aptitude to pack into small compartments of cells or viral capcids, (ii) the structure of DNA mesophases, and (iii) the ability of homologous genes to recognize each other prior to recombination from a distance. Highlighted are some of latest developments of the theory, including the shape of the ‘recognition well’. The article ends with a brief discussion of the first experimental evidence of the protein-free homology recognition in a ‘test tube’.

Salt-dependent DNA-DNA spacings in intact bacteriophage λ reflect relative importance of DNA self-repulsion and bending energies

Using solution synchrotron x-ray scattering, we measure the variation of DNA-DNA d spacings in bacteriophage λ with mono-, di-, and polyvalent salt concentrations, for wild-type [48.5×10(3) base pairs (bp)] and short-genome-mutant (37.8 kbp) strains. From the decrease in d spacings with increasing salt, we deduce the relative contributions of DNA self-repulsion and bending to the energetics of packaged phage genomes. We quantify the DNA-DNA interaction energies within the intact phage by combining the measured d spacings in the capsid with measurements of osmotic pressure in DNA assemblies under the same salt conditions in bulk solution. In the commonly used Tris-Mg buffer, the DNA-DNA interaction energies inside the phage capsids are shown to be about 1kT/bp, an order of magnitude larger than the bending energies.

Conformations of semiflexible charged chains: an extended bundle versus repulsive coils

We consider two interacting semiflexible charged chains of length L(c) under shape fluctuations, where the interplay of electric and mechanical properties is found to yield rigidity-sensitive charge modulation and interdistance-dependent persistence length ℓ(p). The resulting conformation is characterized by equilibrium force between the chains and their fractal dimensions. It turns out that ℓ(p) and L(c) emerge as critical factors to determine the force nature as well as chain shapes. We show that conformational fluctuations cause the repulsion of nonsteric origin, and its competition with charge fluctuation effects yields the interchain force modulated by the length scales and counterion valence. As a result, it is predicted that flexible short chains can be more strongly repulsive than rigid long chains, although they carry smaller amount of net charges.

Divalent counterion-induced condensation of triple-strand DNA

Understanding and manipulation of the forces assembling DNA/RNA helices have broad implications for biology, medicine, and physics. One subject of significance is the attractive force between dsDNA mediated by polycations of valence ≥ 3. Despite extensive studies, the physical origin of the "like-charge attraction" remains unsettled among competing theories. Here we show that triple-strand DNA (tsDNA), a more highly charged helix than dsDNA, is precipitated by alkaline-earth divalent cations that are unable to condense dsDNA. We further show that our observation is general by examining several cations (Mg(2+), Ba(2+), and Ca(2+)) and two distinct tsDNA constructs. Cation-condensed tsDNA forms ordered hexagonal arrays that redissolve upon adding monovalent salts. Forces between tsDNA helices, measured by osmotic stress, follow the form of hydration forces observed with condensed dsDNA. Probing a well-defined system of point-like cations and tsDNAs with more evenly spaced helical charges, the counterintuitive observation that the more highly charged tsDNA (vs. dsDNA) is condensed by cations of lower valence provides new insights into theories of polyelectrolytes and the biological and pathological roles of tsDNA. Cations and tsDNAs also hold promise as a model system for future studies of DNA-DNA interactions and electrostatic interactions in general.

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.

DNA condensations on mica surfaces induced collaboratively by alcohol and hexammine cobalt

We performed systematic studies of λ-DNA condensation on mica surfaces induced by alcohol and hexammine cobalt (III) [Co(NH(3))(6)(3+)] using atomic force microscopy (AFM). The critical condensation concentration for [Co(NH(3))(6)(3+)] was found to be about 10 microM; the DNA molecules extended freely on mica when the concentration was below the critical value. The morphology of condensed DNA became more compact with increasing concentration. At about 500 microM [Co(NH(3))(6)(3+)] concentration, no condensation patterns could be observed due to charge inversion of the compact structures resulting in failure of adhesion to the positively charged surfaces. The critical concentration for alcohol was about 15% (v/v). At this concentration, a few intramolecular loops could be observed in the AFM images. With increasing ethanol concentration the condensation pattern became more complicated ranging from flower-like to pancake-like. When the solution contained both alcohol and hexammine cobalt (III), DNA condensation patterns could be observed even when the concentrations of the two condensation agents were lower than their critical values. We observed this phenomenon by adding mixtures of 10% alcohol and 8 microM hexammine cobalt (III) to DNA solutions. The condensation patterns were more compact than those of the condensation agents separately. Typical toroids were found at an appropriate alcohol and hexammine cobalt (III) concentration. The collaborative condensation phenomenon was analyzed by electrostatic interaction and charge neutralization.

Finite-width bundle is most stable in a solution with salt

We applied the mean-field approach to a columnar bundle assembled by the parallel arrangement of stiff polyelectrolyte rods in a salt bath. The electrostatic potential can be divided into two regions: inside the bundle for condensed counterions and outside the bundle for free small ions. To determine the distribution of condensed counterions inside the bundle, we use a local self-consistent condition that depends on the charge density, the electrostatic potential, and the net polarization. The results showed that, upon bundle formation, the electric charge of polyelectrolytes, even those inside the bundle, tends to survive in an inhomogeneous manner, and thus their width remains finite under thermal equilibrium because of the long-range effect of charge instability.

Cation-induced polyelectrolyte-polyelectrolyte attraction in solutions of DNA and nucleosome core particles

The paper reviews our current studies on the experimentally induced cation compaction and aggregation in solutions of DNA and nucleosome core particles and the theoretical modelling of these processes using coarse-grained continuum models with explicit mobile ions and with all-atom molecular dynamics (MD) simulations. Recent experimental results on DNA condensation by cationic oligopeptides and the effects of added salt are presented. The results of MD simulations modelling DNA-DNA attraction due to the presence of multivalent ions including the polyamine spermidine and fragments of histone tails, which exhibit bridging between adjacent DNA molecules, are discussed. Experimental data on NCP aggregation, using recombinantly prepared systems are summarized. Literature data and our results of studying of the NCP solutions are compared with predictions of coarse-grained MD simulations, including the important ion correlation as well as bridging mechanisms. The importance of the results to chromatin folding and aggregation is discussed.

Confined nematic polymers: order and packing in a nematic drop

We investigate the tight packing of nematic polymers inside a confining hard sphere. We model the polymer via the continuum Frank elastic free energy augmented by a simple density dependent part as well as by taking proper care of the connectivity of the polymer chains when compared with simple nematics. The free energy ansatz is capable of describing an orientational ordering transition within the sample between an isotropic polymer solution and a polymer nematic phase. We solve the Euler-Lagrange equations numerically with the appropriate boundary conditions for the director and density field and investigate the orientation and density profile within a sphere. Two important parameters of the solution are the exact locations of the beginning and the end of the polymer chain. Pending on their spatial distribution and the actual size of the hard sphere enclosure we can get a plethora of various configurations of the chain exhibiting different defect geometry.

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.

Differential stability of DNA crossovers in solution mediated by divalent cations

The assembly of DNA duplexes into higher-order structures plays a major role in many vital cellular functions such as recombination, chromatin packaging and gene regulation. However, little is currently known about the molecular structure and stability of direct DNA–DNA interactions that are required for such functions. In nature, DNA helices minimize electrostatic repulsion between double helices in several ways. Within crystals, B-DNA forms either right-handed crossovers by groove–backbone interaction or left-handed crossovers by groove–groove juxtaposition. We evaluated the stability of such crossovers at various ionic concentrations using large-scale atomistic molecular dynamics simulations. Our results show that right-handed DNA crossovers are thermodynamically stable in solution in the presence of divalent cations. Attractive forces at short-range stabilize such crossover structures with inter-axial separation of helices less than 20 Å. Right-handed crossovers, however, dissociate swiftly in the presence of monovalent ions only. Surprisingly, left-handed crossovers, assembled by sequence-independent juxtaposition of the helices, appear unstable even at the highest concentration of Mg²⁺studied here. Our study provides new molecular insights into chiral association of DNA duplexes and highlights the unique role divalent cations play in differential stabilization of crossover structures. These results may serve as a rational basis to understand the role DNA crossovers play in biological processes.

The bacteriophage genome undergoes a succession of intracapsid phase transitions upon DNA ejection

Double-stranded DNA bacteriophage genomes are densely packaged into capsids until the ejection is triggered upon interaction of the tail with the bacterial receptor. Using cryo-electron microscopy, we describe the organization of the genome in the full capsid of T5 and show how it undergoes a series of phase transitions upon progressive ejection when the encapsidated DNA length decreases. Monodomains of hexagonally crystallized DNA segments initially form a three-dimensional lattice of defects. The structure turns liquid crystalline (two-dimensional hexagonal and then cholesteric) and finally isotropic. These structures suggest a mechanism in which defects of the full capsid would initiate the ejection and introduce the necessary fluidity to relax the constrained mosaic crystal to let the genome start flowing out of the capsid.

Electrostatics and optimal arrangement of ionic triangular lattices confined to cylindrical fibers

We study the optimal packing of triangular ionic lattices on the surface of nanofibers. We compute the favored orientation of the lattice with respect to the axis of the cylindrical fiber, and we determine the effects of the surface curvature. Electrostatic interactions prefer chiral arrangements only for special families of lattices that depend on the fiber diameter. However, there are families of lattices that energetically promote achiral configurations. Besides the long-range Coulomb interactions we consider the behavior of short-range elastic forces, represented by interconnected springs between neighboring ions. In this case a different family of achiral lattices is always preferred. We also show that varying the stoichiometric composition of charges, as well as including higher-order curvature effects, does not significantly modify such a scenario.

Structure of toroidal DNA collapsed inside the phage capsid

The structure of DNA toroids made of individual DNA molecules of various lengths (3,000 to 55,000 bp) was studied, by using partially filled bacteriophage capsids in conjunction with cryoelectron microscopy. The tetravalent cation spermine was diffused through the capsid to condense the DNA under conditions that were chosen to produce a hexagonal packing. Our results demonstrate that the frustration arising between chirality and hexagonal packing leads to the formation of twist walls; the correlation between helices combined with their strong curvature impose variations of the DNA helical pitch.

Generalized Poisson-Fermi formalism for investigating size correlation effects with multiple ions

We establish a generalized Poisson-Fermi formalism to compute the electrostatic potential next to charged surfaces in the presence of multiple ion species with different sizes. A generalized Fermi-like ion distribution is deduced from the excess free energy, after expansion of the functional entropy of free space in which the ions have all the same size. The ion distribution is expressed in terms of the bulk volume fractions of each ion species rather than their bulk concentrations so as to account for the excluded volumes. We present size correlations effects such as underscreening and ion stratification, which have not been investigated before with such a simple theory. The change of dielectric properties across the space, arising from the finite spatial occupancy of ions, can be solved self-consistently through the Bruggeman model. The generalized Poisson-Fermi formalism is anticipated to be useful for interpreting electrophoretic mobility measurements and for computing the electrostatic potential over the surface of biomolecules in ionic solutions.

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

We have investigated the energetics of DNA condensation by multivalent polyamine cations. Solution small angle x-ray scattering was used to monitor interactions between short 25 base pair dsDNA strands in the free supernatant DNA phase that coexists with the condensed DNA phase. Interestingly, when tetravalent spermine is used, significant inter-DNA repulsion is observed in the free phase, in contrast with the presumed inter-DNA attraction in the coexisting condensed phase. DNA condensation thus appears to be a discrete, first-order-like, transition from a repulsive gaseous to an attractive condensed solid phase, in accord with the reported all-or-none condensation of giant DNA. We further quantify the electrostatic repulsive potentials in the free DNA phase and estimate the number of additional spermine cations that bind to DNA upon condensation.

Applied chemistry of natural DNA

Recently, natural DNA has emerged as an appealing biomacromolecule for functional materials. It is abundant and renewable, and possesses the well known double helix structure that promises many unique properties difficult to find in other polymers. Natural DNA has been applied in electronic, optical and biomaterials, as a catalyst for enantioselective reactions, and as a material for cleaning the environment. Most of the applications are based on combining DNA with other chemicals or nanoparticles by electrostatic binding, intercalation or groove binding. In this critical review article, recent developments in utilizing natural DNA are reviewed by focusing on three basic properties of DNA: the electrostatic property as a polyelectrolyte, selective affinity for small molecules, and biocompatibility (128 references).

Biophysics of viral infectivity: matching genome length with capsid size

In this review, we discuss recent advances in biophysical virology, presenting experimental and theoretical studies on the physical properties of viruses. We focus on the double-stranded (ds) DNA bacteriophages as model systems for all of the dsDNA viruses both prokaryotic and eukaryotic. Recent studies demonstrate that the DNA packaged into a viral capsid is highly pressurized, which provides a force for the first step of passive injection of viral DNA into a bacterial cell. Moreover, specific studies on capsid strength show a strong correlation between genome length, and capsid size and robustness. The implications of these newly appreciated physical properties of a viral particle with respect to the infection process are discussed.

Mono- and trivalent ions around DNA: a small-angle scattering study of competition and interactions

The presence of small numbers of multivalent ions in DNA-containing solutions results in strong attractive forces between DNA strands. Despite the biological importance of this interaction, e.g., DNA condensation, its physical origin remains elusive. We carried out a series of experiments to probe interactions between short DNA strands as small numbers of trivalent ions are included in a solution containing DNA and monovalent ions. Using resonant (anomalous) and nonresonant small angle x-ray scattering, we coordinated measurements of the number and distribution of each ion species around the DNA with the onset of attractive forces between DNA strands. DNA-DNA interactions occur as the number of trivalent ions increases. Surprisingly good agreement is found between data and size-corrected numerical Poisson-Boltzmann predictions of ion competition for non- and weakly interacting DNAs. We also obtained an estimate for the minimum number of trivalent ions needed to initiate DNA-DNA attraction.

Molecular dynamics simulation of multivalent-ion mediated attraction between DNA molecules

All atom molecular dynamics simulations with explicit water were done to study the interaction between two parallel double-stranded DNA molecules in the presence of the multivalent counterions putrescine (2+), spermidine (3+), spermine (4+) and cobalt hexamine (3+). The inter-DNA interaction potential is obtained with the umbrella sampling technique. The attractive force is rationalized in terms of the formation of ion bridges, i.e., multivalent ions which are simultaneously bound to the two opposing DNA molecules. The lifetime of the ion bridges is short on the order of a few nanoseconds.

Attractive forces between cation condensed DNA double helices

By combining single-molecule magnetic tweezers and osmotic stress on DNA assemblies, we separate attractive and repulsive components of the total intermolecular interaction between multivalent cation condensed DNA. Based on measurements of several different cations, we identify two invariant properties of multivalent cation-mediated DNA interactions: repulsive forces decay exponentially with a 2.3 +/- 0.1 A characteristic decay length and the attractive component of the free energy is always 2.3 +/- 0.2 times larger than the repulsive component of the free energy at force-balance equilibrium. These empirical constraints are not consistent with current theories that attribute DNA-DNA attractions to a correlated lattice of counterions. The empirical constraints are consistent with theories for Debye-Hückel interactions between helical line charges and with the order-parameter formalism for hydration forces. Each of these theories posits exponentially decaying attractions and, if we assume this form, our measurements indicate a cation-independent, 4.8 +/- 0.5 A characteristic decay length for intermolecular attractions between condensed DNA molecules.

A geometrical template for toroidal aggregates of chiral macromolecules

The formation of toroidal aggregates by long chiral molecules of biological origin, as collagen, f-actin and DNA, or by chiral synthetic polypeptides has been observed in specific ionic environments. Such aggregates have received considerable attention in order to identify the various physical factors susceptible to contribute to this original morphogenesis, particularly in the case of those formed by DNA. We consider here the eventual role of a spontaneous uniform twist of micrometric pitch whose possible occurrence is suggested by some observations and by recent studies of DNA dense phases exhibiting cholesteric and "blue" phase structures. Following an approach inspired by the geometry and topology of fiber bundles, we show that the necessity to propagate such a twist in a dense bundle of fibers leads to the formation of aggregates having a toroidal shape and, in the case of the nanometric aggregates of DNA, characteristic sizes similar to those observed.

Interplay of ion binding and attraction in DNA condensed by multivalent cations

We have measured forces generated by multivalent cation-induced DNA condensation using single-molecule magnetic tweezers. In the presence of cobalt hexammine, spermidine, or spermine, stretched DNA exhibits an abrupt configurational change from extended to condensed. This occurs at a well-defined condensation force that is nearly equal to the condensation free energy per unit length. The multivalent cation concentration dependence for this condensation force gives the apparent number of multivalent cations that bind DNA upon condensation. The measurements show that the lower critical concentration for cobalt hexammine as compared to spermidine is due to a difference in ion binding, not a difference in the electrostatic energy of the condensed state as previously thought. We also show that the resolubilization of condensed DNA can be described using a traditional Manning–Oosawa cation adsorption model, provided that cation–anion pairing at high electrolyte concentrations is taken into account. Neither overcharging nor significant alterations in the condensed state are required to describe the resolubilization of condensed DNA. The same model also describes the spermidine³⁺/Na⁺ phase diagram measured previously.

Effects of salt concentrations and bending energy on the extent of ejection of phage genomes

Recent work has shown that pressures inside dsDNA phage capsids can be as high as many tens of atmospheres; it is this pressure that is responsible for initiation of the delivery of phage genomes to host cells. The forces driving ejection of the genome have been shown to decrease monotonically as ejection proceeds, and hence to be strongly dependent on the genome length. Here we investigate the effects of ambient salts on the pressures inside phage-lambda, for the cases of mono-, di-, and tetravalent cations, and measure how the extent of ejection against a fixed osmotic pressure (mimicking the bacterial cytoplasm) varies with cation concentration. We find, for example, that the ejection fraction is halved in 30 mM Mg(2+) and is decreased by a factor of 10 upon addition of 1 mM spermine. These effects are calculated from a simple model of genome packaging, using DNA-DNA repulsion energies as determined independently from x-ray diffraction measurements on bulk DNA solutions. By comparing the measured ejection fractions with values implied from the bulk DNA solution data, we predict that the bending energy makes the d-spacings inside the capsid larger than those for bulk DNA at the same osmotic pressure.

DNA ejection from bacteriophage: towards a general behavior for osmotic-suppression experiments

We present in this work in vitro measurements of the force ejecting DNA from two distinct bacteriophages (T5 and lambda using the osmotic-suppression technique. Our data are analyzed by revisiting the current theories of DNA packaging in spherical capsids. In particular we show that a simplified analytical model based on bending considerations only is able to account quantitatively for the experimental findings. Physical and biological consequences are discussed.

Polyamine-induced bundling of F-actin

To better understand the mechanism of actin filament (F-actin) bundling by polyamines, we have measured the onset of bundling as a function of polyamine concentration. Samples were centrifuged at low speeds to separate bundles from unbundled actin, and the relative amounts of actin in the pellet and supernatant were determined via gel electrophoresis, yielding a description of the bundling transition as a function of actin and polyamine concentrations. These experiments were carried out for two different polyamines, spermine (tetravalent) and spermidine (trivalent). We found that the threshold concentration of polyamine needed to bundle actin is independent of both actin concentration and Mg2+ concentration over a wide range in Mg2+ concentration. We also find that spermine in F-actin bundles is essentially invisible in solution-phase proton NMR, suggesting that it is bound so tightly to F-actin that it is immobilized.

Effects of condensing agent and nuclease on the extent of ejection from phage lambda

We have recently demonstrated, that DNA ejection from bacteriophage lambda can be partially or completely suppressed in vitro by external osmotic pressure. This suggests that DNA ejection from phage is driven by an internal mechanical force consisting of DNA bending and DNA-DNA electrostatic repulsion energies. In the present work we investigate the extent to which DNA ejection is incomplete at zero osmotic external pressure when phage is opened with its receptor in vitro. The DNA fragment remaining in the capsid and the tail that is no longer bent or compressed -and hence for which there is no internal driving force for ejection- is shown not to be ejected. We also demonstrate that DNA can be "pulled" out from the capsid by DNase I acting as a DNA binding protein or spermine acting as a DNA condensing agent. In particular, cryo electron microscopy and gel electrophoresis experiments show the following: (i) DNA ejection from bacteriophage lambda incubated in vitro with its receptor is incomplete at zero external osmotic force, with several persistence lengths of DNA remaining inside the phage capsid, if no nuclease (DNase I) or DNA condensing agent (spermine) is present in the host solution; (ii) in the presence of both DNase I and spermine in the host solution, 60% (approximately 29 kbp) of wild-type lambda DNA (48.5 kbp) remains unejected inside the phage capsid, in the form of an unconstrained toroidal condensate; (iii) with DNase I added, but no spermine, the ejection is complete; (iv) with spermine, but without DNase I added, all the DNA is again ejected, and organized as a toroidal condensate outside.

Structure and phase diagram of nucleosome core particles aggregated by multivalent cations

The degree of compaction of the eukaryotic chromatin in vivo and in vitro is highly sensitive to the ionic environment. We address the question of the effect of multivalent ions on the interactions and mutual organization of the chromatin structural units, the nucleosome core particles (NCPs). Conditions of precipitation of NCPs in the presence of 10 mM Tris buffer and various amounts of either magnesium (Mg(2+)) or spermidine (Spd(3+)) are explored, compared, and discussed in relation to theoretical models. In addition, the structure of the aggregates is analyzed by complementary techniques: freeze-fracture electron microscopy, cryoelectron microscopy, and x-ray diffraction. In Mg(2+)-NCP aggregates, NCPs tend to stack on top of one another to form columns that are not long-range organized. In the presence of Spd(3+), NCPs precipitate to form a dense isotropic phase, a disordered phase of columns, a two-dimensional columnar hexagonal phase, or a three-dimensional crystal. The more ordered phases (two-dimensional or three-dimensional hexagonal) are found close to the precipitation line, where the number of positive charges carried by cations is slightly larger than the number of available negative charges of the NCPs. All ordered phases coexist with the dense isotropic phases. Formation of hexagonal and columnar phases is prevented by an excess of polycations.

Inter-DNA attraction mediated by divalent counterions

Can nonspecifically bound divalent counterions induce attraction between DNA strands? Here, we present experimental evidence demonstrating attraction between short DNA strands mediated by Mg2+ ions. Solution small angle x-ray scattering data collected as a function of DNA concentration enable model independent extraction of the second virial coefficient. As the [Mg2+] increases, this coefficient turns from positive to negative reflecting the transition from repulsive to attractive inter-DNA interaction. This surprising observation is corroborated by independent light scattering experiments. The dependence of the observed attraction on experimental parameters including DNA length provides valuable clues to its origin.

Liposome-induced DNA compaction and reentrant condensation investigated by dielectric relaxation spectroscopy and dynamic light scattering techniques

Interaction of DNA with oppositely charged objects, such as multivalent ions, cationic surfactants, cationic liposomes, basic proteins, and alcohols, up to nano- or mesoscopic particles, gives rise to a very interesting and fascinating phenomenology, where the shape, size, and stability of the resulting aggregates depend on a delicate balance between different driving forces, mainly of electrostatic origin. We have studied the cationic liposome-DNA complexes during the whole complexation process, below, close to, and above the isoelectric condition, where the number of cationic lipids equals the number of phosphate groups on the DNA chain. We took advantage of the combined use of dynamic light scattering, laser Doppler electrophoretic mobility, and radio-wave dielectric relaxation measurements in order to characterize both the structural parameters (hydrodynamic radius) and the electrical parameters (charge and counterion concentration) of the resulting structures. These structures are fundamentally of two types, clusters of liposomes stuck together by DNA chains (cluster phase in low-density colloidal suspension) and coexisting DNA coils and DNA globules, according to the procedure through which interactions occur (liposomes in excess DNA solution or DNA in excess liposome suspension).

Electrostatics of DNA Complexes with Cationic Lipid Membranes

We present the exact solutions of the linear Poisson-Boltzmann equation for several problems relevant to electrostatics of DNA complexes with cationic lipids. We calculate the electrostatic potential and electrostatic energy for lamellar and inverted hexagonal phases, concentrating on the effects of dielectric boundaries. We compare our results for the complex energy with the known results of numerical solution of the nonlinear Poisson-Boltzmann equation. Using the solution for the lamellar phase, we calculate the compressibility modulus and compare our findings with the experimental data available. Also, we treat charge-charge interactions across, along, and between two low-dielectric membranes. We obtain an estimate for the strength of electrostatic interactions of one-dimensional DNA smectic layers across the lipid membrane. We discuss in the end some aspects of two-dimensional DNA condensation and DNA-DNA attraction in the DNA-lipid lamellar phase in the presence of di- and trivalent cations. We analyze the equilibrium DNA-DNA separations in lamellar complexes using the recently developed theory of electrostatic interactions of DNA helical charge motifs.

Phospholipid-based artificial viruses assembled by multivalent cations

Self-assembled DNA delivery systems based on cationic lipids are simple to produce and weakly hazardous in comparison with viral vectors, but possess a significant toxicity at high doses. Phospholipids are in contrast intrinsically safe; yet their association with DNA is problematic because of unfavorable electrostatic interactions. We achieve the phospholipid-DNA complexation through the like-charge attraction induced by cations. Monovalent cations are inappropriate due to their poor binding affinity with lipids as inferred from electrophoretic mobility, whereas x-ray diffractions reveal that with multivalent cations, DNA is complexed within an inverted hexagonal liquid-crystalline phase. Coarse-grained Monte Carlo simulations confirm the self-assembly of a DNA rod wrapped into a lipid layer with cations in between acting as molecular glue. Transfection experiments performed with Ca2+ and La3+ demonstrate efficiencies surpassing those obtained with optimized cationic DOTAP-based systems, while preserving the viability of cells. Inspired by bacteriophages that resort to polycations to compact their genetic materials, complexes assembled with tetravalent spermine achieve unprecedented transfection efficiencies for phospholipids. Influence of complex growth time, lipid/DNA mass ratio, and ion concentration are examined. These complexes may initiate new developments for nontoxic gene delivery and fundamental studies of biological self-assembly.

Electrostatic free energy landscapes for nucleic acid helix assembly

Metal ions are crucial for nucleic acid folding. From the free energy landscapes, we investigate the detailed mechanism for ion-induced collapse for a paradigm system: loop-tethered short DNA helices. We find that Na+ and Mg2+ play distinctive roles in helix-helix assembly. High [Na+] (>0.3 M) causes a reduced helix-helix electrostatic repulsion and a subsequent disordered packing of helices. In contrast, Mg2+ of concentration >1 mM is predicted to induce helix-helix attraction and results in a more compact and ordered helix-helix packing. Mg2+ is much more efficient in causing nucleic acid compaction. In addition, the free energy landscape shows that the tethering loops between the helices also play a significant role. A flexible loop, such as a neutral loop or a polynucleotide loop in high salt concentration, enhances the close approach of the helices in order to gain the loop entropy. On the other hand, a rigid loop, such as a polynucleotide loop in low salt concentration, tends to de-compact the helices. Therefore, a polynucleotide loop significantly enhances the sharpness of the ion-induced compaction transition. Moreover, we find that a larger number of helices in the system or a smaller radius of the divalent ions can cause a more abrupt compaction transition and a more compact state at high ion concentration, and the ion size effect becomes more pronounced as the number of helices is increased.

Are liquid crystalline properties of nucleosomes involved in chromosome structure and dynamics?

Nucleosome core particles correspond to the structural units of eukaryotic chromatin. They are charged colloids, 101 Angstrom in diameter and 55 Angstrom in length, formed by the coiling of a 146/147 bp DNA fragment (50 nm) around the histone protein octamer. Solutions of these particles can be concentrated, under osmotic pressure, up to the concentrations found in the nuclei of living cells. In the presence of monovalent cations (Na(+)), nucleosomes self-assemble into crystalline or liquid crystalline phases. A lamello-columnar phase is observed at 'low salt' concentrations, while a two-dimensional hexagonal phase and a three-dimensional quasi-hexagonal phase form at 'high salt' concentrations. We followed the formation of these phases from the dilute isotropic solutions to the ordered phases by combining cryoelectron microscopy and X-ray diffraction analyses. The phase diagram is presented as a function of the monovalent salt concentration and applied osmotic pressure. An alternative method to condense nucleosomes is to induce their aggregation upon addition of divalent or multivalent cations (Mg(2+), spermidine(3+) and spermine(4+)). Ordered phases are also found in the aggregates. We also discuss whether these condensed phases of nucleosomes may be relevant from a biological point of view.

Solubility and charge inversion of complexes of DNA and basic proteins

The basic proteins, protamines and histones H1, are known to condense DNA in vivo. We examine here their ability to condense and solubilize in vitro linear DNA [and a synthetic polyanion, Poly(Styrene-Sulfonate) or PSS] at low ionic concentrations by varying the charge concentration ratio. Phase separation is observed in a very narrow range of ratios for short DNA and PSS; on both sides of this range, polydisperse and charged complexes are formed. A charge inversion is detected. For long DNA chains however, a different behavior is observed: the complexes are not soluble in excess of proteins.

DNA acts as a nucleation site for transient cavitation in the ultrasonic nebulizer

Several new technologies based upon ultrasound technology have been proposed as a method to enhance the delivery of genetic therapeutics. Using ultrasonic nebulization and a well-established method to quantitatively monitor transient cavitation, this study investigates the extent and factors influencing the degradation of DNA. Results from our studies show that the presence of DNA greatly enhances cavitation, and that the number of transient cavitation events also increases with the hydrodynamic diameter and number of DNA molecules in solution. More importantly, removing saturated gases from the plasmid DNA solutions resulted in a decrease in transient cavitation events but not degradation rate, suggesting that the cavitation event responsible for degradation occurs locally at the DNA molecule. Finally, complexing plasmid DNA with the cationic polymer polyethylenimine protected the native structure by reducing the molecule's potential to act as a heterogeneous nucleation site for transient cavitation.

Overview of the structure of all-AT oligonucleotides: organization in helices and packing interactions

We present the crystalline organization of 33 all-AT deoxyoligonucleotide duplexes, studied by x-ray diffraction. Most of them have very similar structures, with Watson-Crick basepairs and a standard average twist close to 36 degrees. The molecules are organized as parallel columns of stacked duplexes in a helical arrangement. Such organization of duplexes is very regular and repetitive: all sequences show the same pattern. It is mainly determined by the stacking of the terminal basepairs, so that the twist in the virtual TA base step between neighbor duplexes is always negative, approximately -22 degrees. The distance between the axes of parallel columns is practically identical in all cases, approximately 26 A. Interestingly, it coincides with that found in DNA viruses and fibers in their hexagonal phase. It appears to be a characteristic distance for ordered parallel DNA molecules. This feature is due to the absence of short range intermolecular forces, which are usually due to the presence of CG basepairs at the end of the oligonucleotide sequence. The duplexes apparently interact only through their diffuse ionic atmospheres. The results obtained can thus be considered as intermediate between liquid crystals, fibers, and standard crystal structures. They provide new information on medium range DNA-DNA interactions.

Ion-mediated nucleic acid helix-helix interactions

Salt ions are essential for the folding of nucleic acids. We use the tightly bound ion (TBI) model, which can account for the correlations and fluctuations for the ions bound to the nucleic acids, to investigate the electrostatic free-energy landscape for two parallel nucleic acid helices in the solution of added salt. The theory is based on realistic atomic structures of the helices. In monovalent salt, the helices are predicted to repel each other. For divalent salt, while the mean-field Poisson-Boltzmann theory predicts only the repulsion, the TBI theory predicts an effective attraction between the helices. The helices are predicted to be stabilized at an interhelix distance approximately 26-36 A, and the strength of the attractive force can reach -0.37 k(B)T/bp for helix length in the range of 9-12 bp. Both the stable helix-helix distance and the strength of the attraction are strongly dependent on the salt concentration and ion size. With the increase of the salt concentration, the helix-helix attraction becomes stronger and the most stable helix-helix separation distance becomes smaller. For divalent ions, at very high ion concentration, further addition of ions leads to the weakening of the attraction. Smaller ion size causes stronger helix-helix attraction and stabilizes the helices at a shorter distance. In addition, the TBI model shows that a decrease in the solvent dielectric constant would enhance the ion-mediated attraction. The theoretical findings from the TBI theory agree with the experimental measurements on the osmotic pressure of DNA array as well as the results from the computer simulations.

Compaction of single-chain DNA by histone-inspired nanoparticles

We elaborated a versatile experimental model of chromatin which consists of a single chain of long duplex DNA that interacts with well-defined cationic nanoparticles of various sizes. We found that the DNA compaction by nanoparticles is stepwise and progressive at the single-chain level. It is controlled by the ability of DNA to wrap nanoparticles, which is more efficient for larger particles and, similar to DNA-histone interaction, is optimal at a physiological salt concentration.

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.

Effect of spermine and DNase on DNA release from bacteriophage T5

Bacterial viruses (bacteriophages) consist of nucleic acid protected by a protein envelope called capsid. At the start of infection, the phage genome is translocated into the bacterial cytoplasm. In vitro (and also in vivo), this DNA release can be triggered by binding a specific receptor protein to the phage tail. The force responsible for the release arises from energy stored in the capsid due to strong confinement of the DNA. We show that this force can be modified by adding molecules like spermine that affect DNA conformation. The tetravalent cation spermine can reduce the pressure inside the capsid and induce condensation of the released DNA. We examine the effect of spermine on DNA ejection from phage T5 by using light scattering and gel electrophoresis to measure the amount of DNA remaining in the capsid at the end of ejection. We discuss the results in terms of free energy minimization and we demonstrate that the presence of a DNA condensate outside the phage generates an additional force pulling passively on the DNA remaining inside the capsid.