DNA like-charge attraction and overcharging by divalent counterions in the presence of divalent co-ions

Strongly correlated electrostatics of DNA systems has drawn the interest of many groups, especially the condensation and overcharging of DNA by multivalent counterions. By adding counterions of different valencies and shapes, one can enhance or reduce DNA overcharging. In this paper, we focus on the effect of multivalent co-ions, specifically divalent co-ions such as SO\(_{4}^{2-}\). A computational experiment of DNA condensation using Monte Carlo simulation in grand canonical ensemble is carried out where the DNA system is in equilibrium with a bulk solution containing a mixture of salt of different valency of co-ions. Compared to systems with purely monovalent co-ions, the influence of divalent co-ions shows up in multiple aspects. Divalent co-ions lead to an increase of monovalent salt in the DNA condensate. Because monovalent salts mostly participate in linear screening of electrostatic interactions in the system, more monovalent salt molecules enter the condensate leads to screening out of short-range DNA–DNA like charge attraction and weaker DNA condensation free energy. The overcharging of DNA by multivalent counterions is also reduced in the presence of divalent co-ions. Strong repulsions between DNA and divalent co-ions and among divalent co-ions themselves lead to a depletion of negative ions near the DNA surface as compared to the case without divalent co-ions. At large distances, the DNA–DNA repulsive interaction is stronger in the presence of divalent co-ions, suggesting that divalent co-ions’ role is not only that of simple stronger linear screening.     

Dependence of DNA condensation on the correlation distance between condensed counterions

Based on the ground state of counterions condensed on a DNA molecule, a model has been developed to successfully detect the process of DNA condensation. Through further investigation, the process of DNA condensation strongly depends on the correlation distance between condensed counterions on DNA molecules. Generally, there are two routes. The process of DNA condensation with the correlation distance between condensed counterions being 2 nm or 4 nm is different from the one with the correlation distance between condensed counterions being 3 nm or 5 nm. Effects of ionic strength on the diameter of toroidal condensates originate from the increase of correlation distance between condensed counterions.     

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     

Osmotic pressure and packaging structure of caged DNA

We present a theoretical model for aqueous solutions of double-stranded (ds) DNA with explicit consideration of electrostatic interactions, excluded-volume effects, van der Waals attractions, and salt ions. With reasonable parameters estimated from the DNA structure and experimental data for electrolytes, we are able to reproduce the DNA osmotic pressure in the bulk in good agreement with experiment. The predicted DNA osmotic pressure in λ-bacteriophages is found to coincide with that of the PEG8000 solution that inhibits DNA ejection as reported in recent experiments. Based on the radial distributions of DNA segments and of counterions at different degrees of packaging, we find that in the presence of Mg²⁺, DNA forms a multilayer structure near the inner surface of a fully loaded bacteriophage, but at low packing density the DNA segments are depleted from the surface owing to the local condensation of DNA induced by the divalent counterions. By contrast, the multilayer DNA structure is less distinctive in the presence of Na⁺ despite the increase of the DNA density at contact, and the depletion near the capsid surface is not found at low packing density.     

Toroid formation in charge neutralized flexible or semi-flexible biopolymers: potential pathway for assembly of DNA carriers

BACKGROUND: The theoretical state diagram for semi-flexible macromolecules such as DNA predicts that a tightly wound toroid can be a stable structure. Experimentally, toroids roughly 100 nm in diameter are routinely observed for DNA in the presence of multivalent cations at low DNA concentration. Theory also predicts toroids can form between non-DNA semi-flexible polymers and multivalent counterions. This phenomenon provides a means to co-package DNA with functionalized anionic polymers to create gene delivery systems. METHODS AND RESULTS: We show using electron microscopy that non-DNA polymers (polylysine, polyglutamic acid, and dextran sulfate) form toroids when mixed with multi- or polyvalent ions of opposite charge. The non-DNA toroids are similar in diameter to ones made with DNA. The results using dextran sulfate, a semi-flexible polymer, are explained by current theory. However, theory predicts that high flexibility in polypeptides should discourage their incorporation into stable toroids. To explain these latter observations we propose that charge neutralization facilitates secondary structure formation, which confers stiffness, thereby allowing stable toroids for the polypeptides studied. We measured the secondary structure of the toroid-forming polypeptides using circular dichroism (CD). The CD spectrum indicates the polypeptides undergo transitions from non-ordered structures (random coil) to ordered secondary structures (either alpha-helix or beta-sheet) upon charge neutralization which supports the hypothesis. The type of secondary structure is dependent on the type of multivalent counterion used to form the toroids. Formation of the polypeptide toroids confers resistance to heat denaturation of the resulting polypeptide secondary structure. The CD spectrum of DNA in a toroid also is changed from that of uncomplexed DNA, but all of the counterions used to form DNA toroids created structures with similar CD spectra in the DNA region (250-290 nm). CONCLUSIONS: The toroid structure obtained using DNA is observed in other semi-flexible non-DNA polymers such as dextran sulfate, and also in flexible polymers such as polylysine and polyglutamic acid upon charge neutralization with multivalent counterions. In the flexible polymers we propose that this phenomenon is due to induction of secondary structure upon charge neutralization, which decreases polymer flexibility, i.e. increases polymer stiffness, to enable toroid formation. These results have significant implications for the co-assembly of non-DNA anionic polymers with DNA to create nanoscopic gene carriers.     

Aggregation of nucleosomes by divalent cations.

Conditions of precipitation of nucleosome core particles (NCP) by divalent cations (Ca(2+) and Mg(2+)) have been explored over a large range of nucleosome and cation concentrations. Precipitation of NCP occurs for a threshold of divalent cation concentration, and redissolution is observed for further addition of salt. The phase diagram looks similar to those obtained with DNA and synthetic polyelectrolytes in the presence of multivalent cations, which supports the idea that NCP/NCP interactions are driven by cation condensation. In the phase separation domain the effective charge of the aggregates was determined by measurements of their electrophoretic mobility. Aggregates formed in the presence of divalent cations (Mg(2+)) remain negatively charged over the whole concentration range. They turn positively charged when aggregation is induced by trivalent (spermidine) or tetravalent (spermine) cations. The higher the valency of the counterions, the more significant is the reversal of the effective charge of the aggregates. The sign of the effective charge has no influence on the aspect of the phase diagram. We discuss the possible reasons for this charge reversal in the light of actual theoretical approaches.     

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.     

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.     

Simple simulations of DNA condensation

Molecular dynamics simulations of a simple, bead-spring model of semiflexible polyelectrolytes such as DNA are performed. All charges are explicitly treated. Starting from extended, noncondensed conformations, condensed structures form in the simulations with tetravalent or trivalent counterions. No condensates form or are stable for divalent counterions. The mechanism by which condensates form is described. Briefly, condensation occurs because electrostatic interactions dominate entropy, and the favored coulombic structure is a charge-ordered state. Condensation is a generic phenomenon and occurs for a variety of polyelectrolyte parameters. Toroids and rods are the condensate structures. Toroids form preferentially when the molecular stiffness is sufficiently strong.     

Interactions of DNA with divalent metal ions. III. Extent of metal binding: Experiment and theory

DNA with Mn²⁺ as the only counterion has been prepared, and the extent of the Mn²⁺ binding was determined under a variety of conditions through measurements of the proton relaxation enhancement of water. The total extent of Mn²⁺ binding per DNA phosphate is found to be 0.43 ± 0.04, independent of the metal ion concentration in the experimental range of 2.8 × 10^?5 to 2.1 × 10^?3M. The predictions of Manning's condensation theory and those obtained from solution of the generalized Poisson-Boltzmann equation regarding the extent of divalent ion binding to polyelectrolytes, in the presence and absence of monovalent counterions, are compared with one another and with the experimental results. Good agreement between the two theoretical approaches is found, with less than 14% variance in the predicted extent of binding over a large range of mono- and divalent ion concentrations. While the predictions of both theoretical approaches generally agree with the experimental results, some discrepancies are noted and their possible origins discussed.     

Onset of DNA aggregation in presence of monovalent and multivalent counterions

We address theoretically aggregation of DNA segments by multivalent polyamines such as spermine and spermidine. In experiments, the aggregation occurs above a certain threshold concentration of multivalent ions. We demonstrate that the dependence of this threshold on the concentration of DNA has a simple form. When the DNA concentration c(DNA) is smaller than the monovalent salt concentration, the threshold multivalent ion concentration depends linearly on c(DNA), having the form alphac(DNA) + beta. The coefficients alpha and beta are related to the density profile of multivalent counterions around isolated DNA chains, at the onset of their aggregation. This analysis agrees extremely well with recent detailed measurements on DNA aggregation in the presence of spermine. From the fit to the experimental data, the number of condensed multivalent counterions per DNA chain can be deduced. A few other conclusions can then be reached: 1), the number of condensed spermine ions at the onset of aggregation decreases with the addition of monovalent salt; 2), the Poisson-Boltzmann theory overestimates the number of condensed multivalent ions at high monovalent salt concentrations; and 3), our analysis of the data indicates that the DNA charge is not overcompensated by spermine at the onset of aggregation.     

The effect of temperature on DNA structural transitions under the action of Cu2+ and Ca2+ ions in aqueous solutions

The work examines the structural transitions of DNA under the action of Cu2+ and Ca2+ ions in aqueous solution at temperatures of 29 and 45 degrees C by ir spectroscopy. Upon binding to the divalent ions studied, DNA transits into the compact state both at 29 and 45 degrees C. In the compact state DNA remains in B-form limits. The compaction process is of high positive cooperativity. As temperature increases the divalent metal ion concentration required to induce DNA compaction decreases in the case of Cu(2+)-induced compaction and increases in the case of Ca(2+)-induced compaction. It is suggested that the mechanism of the temperature effect on DNA compaction in the presence of Cu2+ ions possessing higher affinity for DNA bases differs from that of the temperature influence on Ca(2+)-induced DNA compaction. In the case of copper ions the determining factor is the increase of binding constants of the Cu2+ ions interacting with the denatured parts formed on DNA while in the case of calcium ions it is the decreased screening action of counterions upon the increase of their hydration with temperature. The efficiency of divalent metal ions studied in inducing DNA compaction depends on hydration of counterions. DNA compaction occurs in a narrow interval of Cu2+ concentrations. As the Cu2+ ion concentration increases, DNA compaction is replaced with Cu(2+)-induced DNA aggregation. At elevated temperatures Cu(2+)-induced DNA compaction could acquire a phase transition character.     

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.     

Thermodynamic characterization of viral procapsid expansion into a functional capsid shell

The assembly of "complex" DNA viruses such as the herpesviruses and many tailed bacteriophages includes a DNA packaging step where the viral genome is inserted into a preformed procapsid shell. Packaging triggers a remarkable capsid expansion transition that results in thinning of the shell and an increase in capsid volume to accept the full-length genome. This transition is considered irreversible; however, here we demonstrate that the phage λ procapsid can be expanded with urea in vitro and that the transition is fully reversible. This provides an unprecedented opportunity to evaluate the thermodynamic features of this fascinating and essential step in virus assembly. We show that urea-triggered expansion is highly cooperative and strongly temperature dependent. Thermodynamic analysis indicates that the free energy of expansion is influenced by magnesium concentration (3-13?kcal/mol in the presence of 0.2-10?mM Mg(2+)) and that significant hydrophobic surface area is exposed in the expanded shell. Conversely, Mg(2+) drives the expanded shell back to the procapsid conformation in a highly cooperative transition that is also temperature dependent and strongly influenced by urea. We demonstrate that the gpD decoration protein adds to the urea-expanded capsid, presumably at hydrophobic patches exposed at the 3-fold axes of the expanded capsid lattice. The decorated capsid is biologically active and sponsors packaging of the viral genome in vitro. The roles of divalent metal and hydrophobic interactions in controlling packaging-triggered expansion of the procapsid shell are discussed in relation to a general mechanism for DNA-triggered procapsid expansion in the complex double-stranded DNA viruses.     

Limiting-laws of polyelectrolyte solutions. Ionic distribution in mixed-valency counterions systems. II. A comparison of conductometric data and theoretical predictions

The competitive binding of monovalent and divalent counterions (M+ and M2+, respectively) has been studied by a conductometric procedure as described by De Jong et al. (Biophysical Chemistry 27 (1987) 173) for aqueous solutions of alkali metal polymethacrylates in the presence of Ca (NO3)2 or Mg(NO3)2. The experimentally obtained fractions of conductometrically free counterions are compared with theoretical values computed according to a new thermodynamic model recently developed by Paoletti et al. (Biophysical Chemistry, 41 (1991) 73). For the systems studied, the fractions of free monovalent and divalent counterions can be fairly well described by the theory. In fact, the results support the assumption that under the present conditions the conductometrically obtained distribution parameters (l) and (2) approximate the equilibrium fractions of free monovalent and divalent counterions. For a degree of neutralization of 0.8 and a molar concentration ratio of divalent counterions and charged groups on the polyion up to 0.25, the mean M+/M2+, exchange ratio nu has been found to be 1.39 +/- 0.03 and 1.33 +/- 0.03 for the alkali metal/Ca/PMA and alkali metal/Mg/PMA systems, respectively. These values agree well with the theoretical value, which for this particular case is 1.38.     

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.     

Comparison of polyelectrolyte theories of the binding of cations to DNA.

Predictions of the binding of counterions to DNA made using the counterion condensation theory developed by Manning are compared with those made using the Poisson-Boltzmann equation, solved numerically by the Runge-Kutta procedure. Ions are defined as territorially or atmospherically bound if they fall within a given distance, defined by counterion condensation theory, from the DNA surface. Two types of experimental situations are considered. The first is the delocalized binding of a single type of counterion to DNA. In this case the Poisson-Boltzmann treatment predicts somewhat lower extents of binding TO DNA, modeled as a 10-A radius cylinder, than does Manning theory. The two theories converge as the radius decreases. The second type of experiment is the competition of ions of different valence for binding to DNA. The theories are compared with literature values of binding constants of divalent ions in the presence of monovalent ions, and of spermidine 3+ in the presence of Na+ or Mg2+. Both predict with fair accuracy the salt dependence of the equilibrium constants.     

Poliovirus-associated protein kinase: destabilization of the virus capsid and stimulation of the phosphorylation reaction by Zn2+.

The previously described poliovirus-associated protein kinase activity phosphorylates viral proteins VP0 and VP2 as well as exogenous proteins in the presence of Mg2+. In this paper, the effect of Zn2+ on the phosphorylation reaction and the stability of the poliovirus capsid has been studied in detail and compared to that of Mg2+. Phosphorylation patterns of viral and other proteins depend on the divalent cation present. In the presence of Zn2+, phosphorylation of capsid proteins VP2 and VP4 is significantly higher while phosphorylation of VP0 and exogenous phosphate acceptor proteins is not detected. Our results indicate the activation of more than one virus-associated protein kinase by Zn2+. The ion-dependent behavior of the enzyme activities is observed independently of whether the virus was obtained from HeLa or green monkey kidney cells. The poliovirus capsid is destabilized by Zn2+. The destabilization leads to a substantially increased permeability of virus particles to ethidium bromide and RNase, concomitant with decreased infectivity of the sample. This alteration of the poliovirus capsid structure is a prerequisite for effective phosphorylation of viral capsid proteins. The increased level of phosphorylation of viral capsid proteins results in further destabilization of the viral capsid. As a result of the conformational changes, poliovirus-associated protein kinase activities dissociate from the virus particle. High-performance liquid chromatography-purified viral protein VP2 is phosphorylated by the released enzymes on serine, threonine, and tyrosine in the presence of Zn2+. We suggest that the destabilizing effect of phosphorylation on the viral capsid plays a role in uncoating of poliovirus.     

Study of the DNA/ethidium bromide interactions on mica surface by atomic force microscope: influence of the surface friction

The influence of mica surface on DNA/ethidium bromide interactions is investigated by atomic force microscopy (AFM). We describe the diffusion mechanism of a DNA molecule on a mica surface by using a simple analytical model. It appears that the DNA diffusion on a mica surface is limited by the surface friction due to the counterion correlations between the divalent counterions condensed on both mica and DNA surfaces. We also study the structural changes of linear DNA adsorbed on mica upon ethidium bromide binding by AFM. It turns out that linear DNA molecules adsorbed on a mica surface are unable to relieve the topological constraint upon ethidium bromide binding. In particular, strongly adsorbed molecules tend to be highly entangled, while loosely bound DNA molecules appear more extended with very few crossovers. Adsorbed DNA molecules cannot move freely on the surface because of the surface friction. Therefore, the topological constraint increases due to the ethidium bromide binding. Moreover, we show that ethidium bromide has a lower affinity for strongly bound molecules due to the topological constraint induced by the surface friction.     

Modeling and simulation of the mechanical response from nanoindentation test of DNA-filled viral capsids

Viruses can be described as biological objects composed mainly of two parts: a stiff protein shell called a capsid, and a core inside the capsid containing the nucleic acid and liquid. In many double-stranded DNA bacterial viruses (aka phage), the volume ratio between the liquid and the encapsidated DNA is approximately 1:1. Due to the dominant DNA hydration force, water strongly mediates the interaction between the packaged DNA strands. Therefore, water that hydrates the DNA plays an important role in nanoindentation experiments of DNA-filled viral capsids. Nanoindentation measurements allow us to gain further insight into the nature of the hydration and electrostatic interactions between the DNA strands. With this motivation, a continuum-based numerical model for simulating the nanoindentation response of DNA-filled viral capsids is proposed here. The viral capsid is modeled as large- strain isotropic hyper-elastic material, whereas porous elasticity is adopted to capture the mechanical response of the filled viral capsid. The voids inside the viral capsid are assumed to be filled with liquid, which is modeled as a homogenous incompressible fluid. The motion of a fluid flowing through the porous medium upon capsid indentation is modeled using Darcy’s law, describing the flow of fluid through a porous medium. The nanoindentation response is simulated using three-dimensional finite element analysis and the simulations are performed using the finite element code Abaqus. Force-indentation curves for empty, partially and completely DNA-filled capsids are directly compared to the experimental data for bacteriophage λ. Material parameters such as Young’s modulus, shear modulus, and bulk modulus are determined by comparing computed force-indentation curves to the data from the atomic force microscopy (AFM) experiments. Predictions are made for pressure distribution inside the capsid, as well as the fluid volume ratio variation during the indentation test.