The effects of lithium, rubidium, cesium and magnesium ions on the close packing of persistence-length DNA fragments

By application of scaled particle theory to persistence-length DNA fragments in sedimentation-equilibrium at speeds high enough to maintain close packing, the range of interhelical electrostatic repulsion was evaluated with LiCl, RbCl, CsCl, and MgCl2 as supporting electrolytes. Analysis of the data in terms of the Zimm cluster function confirmed that the net interaction between helices is purely repulsive in all cases. At constant ionic strength the electrostatic radius of the rod-like DNA decreases as the counterion changes from Li+ to Rb+ to Cs+. In contrast to univalent counterions, electrostatic radius increases with Mg2+ concentration, except at very low (mM) MgCl2 concentrations. All solutions undergo a reversible transition to a turbid, optically anisotropic phase at a slightly salt-dependent, critical DNA concentration, as observed previously for NaDNA.     

Incomplete ion dissociation underlies the weakened attraction between DNA helices at high spermidine concentrations

We have investigated the salt sensitivity of the hexagonal-to-cholesteric phase transition of spermidine-condensed DNA. This transition precedes the resolubilization of precipitated DNA that occurs at high spermidine concentration. The sensitivity of the critical spermidine concentration at the transition point to the anion species and the NaCl concentration indicates that ion pairing of this trivalent ion underlies this unusual transition. Osmotic pressure measurements of spermidine salt solutions are consistent with this interpretation. Spermidine salts are not fully dissociated at higher concentrations. The competition for DNA binding among the fully charged trivalent ion and the lesser charged complex species at higher concentrations significantly weakens attraction between DNA helices in the condensed state. This is contrary to the suggestion that the binding of spermidine at higher concentrations causes DNA overcharging and consequent electrostatic repulsion.     

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.     

Scaling of the equilibrium sedimentation distribution in dense DNA solutions

DNA molecules, several persistence lengths long in sedimentation equilibrium at speeds high enough to maintain fairly close packing, show a dense, sharply-bounded turbid phase and an isotropic phase (as with shorter fragments) and also an intermediate, somewhat turbid region. The concentration distribution in the isotropic phase is in satisfactory agreement with a simple extension of scaled particle theory in which semiflexible chains are equivalent to straight rods of the same length. The net intermolecular interactions, as inferred from the Zimm cluster integral, are purely repulsive. As in our previous study with short fragments, the results are compatible with a hard-core electrostatic radius, decreasing with increasing salt concentration. However, for the longer fragments it is necessary to infer either a slightly greater mass per unit length or a slightly smaller electrostatic radius for closest agreement with scaled particle theory. The properties of the solution at the boundary with the turbid, presumably strongly ordered phase are consistent with those found for shorter fragments and with theoretical scaling expectation for a hard, asymmetric particle.     

The osmotic pressure of chondroitin sulphate solutions: experimental measurements and theoretical analysis

We used equilibrium dialysis to measure the osmotic pressure of chondroitin sulphate (CS) solutions as a function of their concentration and fixed charge density (FCD) and the ionic strength and composition of the solution. Osmotic pressure varied nonlinearly with the concentration of chondroitin sulphate and in 0.15 M NaCl at FCDs typical of uncompressed cartilage (approximately 0.4 mmol/g extrafibrillar H2O) was approximately 3 atmospheres. Osmotic pressure fell by 60% as solution ionic strength increased up to about 1 M, but remained relatively constant at higher ionic strengths. The ratio of Ca2+ to Na+ in the medium was a minor determinant of osmotic pressure. The data are compared with a theoretical model of the electrostatic contribution to osmotic pressure calculated from the Poisson-Boltzmann equation using a rod-in-cell model for CS. The effective radius of the polyelectrolyte rod is taken as a free parameter. The model qualitatively reproduces the non-linear concentration dependence, but underestimates the osmotic pressure by an amount that is independent of ionic strength. This difference, presumably arising from oncotic and entropic effects, is approximately 1/3 of the total osmotic pressure at physiological polymer concentrations and ionic strength.     

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.     

Application of the Poisson Boltzmann polyelectrolyte model for analysis of thermal denaturation of DNA in the presence of Na+ and polyamine cations

The Poisson Boltzmann (PB) cell model of polyelectrolyte solution has been used for calculation of the electrostatic free energy difference, Delta G(el), between double- and single-stranded DNA. The calculations have been performed for conditions relevant to describe the DNA helix-coil transition in NaCl solution in the presence of the natural polyamines putrescine(2+), spermidine(3+), spermine(4+) and their synthetic homologs with different spacing between the charged amino groups, for which experimental values of the DNA 'melting' transition temperature (T(m)) are available. Using the PB theory and the polyamine ion radius as an adjusting parameter provides quantitative agreement between experimental and theoretical T(m)--salt concentration dependencies only by using physically unreasonable radii for the polyamine. Thus, modeling the linear and flexible polyamines as charged spheres within the PB cell model is an implausible oversimplification. We propose another explanation for the experimental observations, still within the frame of the 'primitive' PB polyelectrolyte theory. This explanation is based on an analysis of the Delta G(el) dependence on the stoichiometry of polyamine-polyanion binding to double- and single-stranded DNA.     

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.     

The influence of salt on the structure and energetics of supercoiled DNA.

We present a detailed computational study of the influence of salt on the configurations, energies, and dynamics of supercoiled DNA. A potential function that includes both elastic and electrostatic energy components is employed. Specifically, the electrostatic term, with salt-dependent coefficients, is modeled after Stigter's pioneering work on the effective diameter of DNA as a function of salt concentration. Because an effective charge per unit length is used, the electrostatic formulation does not require explicit modeling of phosphates and can be used to study long DNAs at any desired resolution of charge. With explicit consideration of the electrostatic energy, an elastic bending constant corresponding to the nonelectrostatic part of the bending contribution to the persistence length is used. We show, for a series of salt concentrations ranging from 0.005 to 1.0 M sodium, how configurations and energies of supercoiled DNA (1000 and 3000 base pairs) change dramatically with the simulated salt environment. At high salt, the DNA adopts highly compact and bent interwound states, with the bending energy dominating over the other components, and the electrostatic energy playing a minor role in comparison to the bending and twisting terms. At low salt, the DNA supercoils are much more open and loosely interwound, and the electrostatic components are dominant. Over the range of three decades of salt examined, the electrostatic energy changes by a factor of 10. The buckling transition between the circle and figure-8 is highly sensitive to salt concentration: this transition is delayed as salt concentration decreases, with a particularly sharp increase below 0.1 M. For example, for a bending-to-twisting force constant ratio of A/C = 1.5, the linking number difference (delta LK) corresponding to equal energies for the circle and figure-8 increases from 2.1 to 3.25 as salt decreases from 1.0 to 0.005 M. We also present in detail a family of three-lobed supercoiled DNA configurations that are predicted by elasticity theory to be stable at low delta Lk. To our knowledge, such three-dimensional structures have not been previously presented in connection with DNA supercoiling. These branched forms have a higher bending energy than the corresponding interwound configurations at the same delta Lk but, especially at low salt, this bending energy difference is relatively small in comparison with the total energy, which is dominated by the electrostatic contributions. Significantly, the electrostatic energies of the three-lobed and (straight) interwound forms are comparable at each salt environment.(ABSTRACT TRUNCATED AT 400 WORDS)     

Exclusion of alcohols from spermidine-DNA assemblies: probing the physical basis of preferential hydration

The interaction of the alcohols 2-methyl-2,4-pentanediol (MPD) and 2-propanol and of glycerol with condensed spermidine(3+)-DNA arrays are investigated with direct force measurements using osmotic stress coupled with X-ray scattering. Thermodynamic forces between DNA helices are measured from the dependence of helical interaxial spacings on the osmotic pressure applied by poly(ethylene glycol) solutions in equilibrium with the DNA phase. The sensitivity of these forces to solute concentration can be transformed into a change in the number of excess or deficit solutes or waters in the DNA phase by applying the Gibbs-Duhem equation. The alcohols examined are excluded from the condensed DNA array and strongly affect the osmotic stress force curves. DNA is preferentially hydrated. MPD is significantly more excluded than 2-propanol. The exclusion of these alcohols, however, is not due to a steric repulsion since glycerol that is intermediate in size between MPD and 2-propanol does not observably affect DNA force curves. As the distance between DNA helices varies, the change in the number of excess waters is independent of alcohol concentration for each alcohol. These solutes are acting osmotically on the condensed array. The distance dependence of exclusion indicates that repulsive water structuring forces dominate the interaction of alcohols with the DNA surface. The exclusion measured for these condensed arrays can quantitatively account for the effect of these alcohols on the precipitation of DNA from dilute solution by spermidine(3+).     

Light-scattering study of DNA condensation: Competition between collapse and aggregation

Light-scattering studies were done to investigate the DNA collapse transition, a large and discontinuous reduction in the radius of gyration. Of particular concern was differentiating the compaction of a single DNA molecule from aggregation. Solutions of RK2 plasmid DNA (M_r = 37 × 10⁶) or bacteriophage T7 DNA (M_r = 25 × 10⁶) were titrated with the condensing reagents spermidine in aqueous solvent or magnesium ion in ethanol–water solvent. The transition was followed by the change in scattering at a single angle or by the change in the angular dependence of scattering. At concentrations below 1 μg/mL, only aggregation could be detected by observation at a single angle; therefore, to study the collapse transition, it was necessary to measure the angular dependence of scattering. The intensities measured between the angles 30° and 60° were fit to known scattering functions. At low concentrations of the condensing reagent, the data were consistent with the scattering function of a random coil. On the other hand, during the transition at higher reagent concentrations, the curve that fit the data required two components—the scattering function for a random coil with a large radius of gyration, plus that for a sphere with a radius about one-fifth of that of the coil. The fractional concentration of the sphere increased with increasing condensing-reagent concentration. This two-component behavior is in apparent contrast to the situation with a more flexible polymer such as polystyrene, in accord with theoretical predictions. At still higher reagent concentrations, aggregation was apparent. Condensation to a collapsed state was reversible without hysteresis, while dissolution of the aggregated state nearly always occurred with hysteresis. Qualitative agreement between the observed DNA collapse transition and the theoretical phase diagram presented in the preceding paper was found, although the light-scattering results did not show quantitative agreement with the simple theoretical model.     

Direct measurement of temperature-dependent solvation forces between DNA double helices.

The assembly of double stranded DNA helices with divalent manganese ion is favored by increasing temperature. Direct force measurements, obtained from the osmotic stress technique coupled with x-ray diffraction, show that the force characteristics of spontaneously precipitated Mn(2+)-DNA closely resemble those observed previously by us for other counterion condensed DNA assemblies. At temperatures below the critical one for spontaneous assembly, we have quantitated the changes in entropy and manganese ion binding associated with the transition from repulsive to attractive interactions between helices mediated by osmotic stress. The release of structured water surrounding the DNA helix to the bulk solution is the most probable source of increased entropy after assembly. Increasing the water entropy of the bulk solution by changing the manganese salt anion from CI- to ClO4- predictably and quantitatively increases the transition entropy. This is further evidence for the dominating role of water in the close interaction of polar surfaces.     

Two-phase formation in solutions of tobacco mosaic virus and the problem of long-range forces

In a nearly salt-free medium, a dilute tobacco mosaic virus solution of rod-shaped virus particles of uniform length forms two phases; the bottom optically anisotropic phase has a greater virus concentration than has the top optically isotropic phase. For a sample containing particles of various lengths, the bottom phase contains longer particles than does the top and the concentrations top and bottom are nearly equal. The longer the particles the less the minimum concentration necessary for two-phase formation. Increasing the salt concentration increases the minimum concentration. The formation of two phases is explained in terms of geometrical considerations without recourse to the concept of long-range attractive forces. The minimum concentration for two-phase formation is that concentration at which correlation in orientation between the rod-shaped particles begins to take place. This concentration is determined by the thermodynamically effective size and shape of the particles as obtained from the concentration dependence of the osmotic pressure of the solutions measured by light scattering. The effective volume of the particles is introduced into the theory of Onsager for correlation of orientation of uniform size rods and good agreement with experiment is obtained. The theory is extended to a mixture of non-uniform size rods and to the case in which the salt concentration is varied, and agreement with experiment is obtained. The thermodynamically effective volume of the particles and its dependence on salt concentration are explained in terms of the shape of the particles and the electrostatic repulsion between them. Current theories of the hydration of proteins and of long-range forces are critically discussed. The bottom layer of freshly purified tobacco mosaic virus samples shows Bragg diffraction of visible light. The diffraction data indicate that the virus particles in solution form three-dimensional crystals approximately the size of crystalline inclusion bodies found in the cells of plants suffering from the disease.     

Energetics of a hexagonal-lamellar-hexagonal-phase transition sequence in dioleoylphosphatidylethanolamine membranes.

The phase diagram of DOPE/water dispersions was investigated by NMR and X-ray diffraction in the water concentration range from 2 to 20 water molecules per lipid and in the temperature range from -5 to +50 degrees C. At temperatures above 22 degrees C, the dispersions form an inverse (HII) phase at all water concentrations. Below 25 degrees C, an HII phase occurs at high water concentrations, an L alpha phase is formed at intermediate water concentrations, and finally the system switches back to an HII phase at low water concentrations. The enthalpy of the L alpha-HII-phase transition is +0.3 kcal/mol as measured by differential scanning calorimetry. Using 31P and 2H NMR and X-ray diffraction, we measured the trapped water volumes in HII and L alpha phases as a function of osmotic pressure. The change of the HII-phase free energy as a function of hydration was calculated by integrating the osmotic pressure vs trapped water volume curve. The phase diagram calculated on the basis of the known enthalpy of transition and the osmotic pressure vs water volume curves is in good agreement with the measured one. The HII-L alpha-HII double-phase transition at temperatures below 22 degrees C can be shown to be a consequence of (i) the greater degree of hydration of the HII phase in excess water and (ii) the relative sensitivities with which the lamellar and hexagonal phases dehydrate with increasing osmotic pressure. These results demonstrate the usefulness of osmotic stress measurements to understand lipid-phase diagrams.     

Measurement of intercolumnar forces between parallel guanosine four-stranded helices.

The deoxyguanosine-5'-monophosphate in aqueous solution self-associates into stable structures, which include hexagonal and cholesteric columnar phases. The structural unit is a four-stranded helix, composed of a stacked array of Hoogsteen-bonded guanosine quartets. We have measured by osmotic stress method the force per unit length versus interaxial distance between helices in the hexagonal phase under various ionic conditions. Two contributions have been recognized: the first one is purely electrostatic, is effective at large distances, and shows a strong dependence on the salt concentration of the solution. The second contribution is short range, dominates at interaxial separations smaller than about 30-32 A, and rises steeply as the columns approach each other, preventing the coalescence of the helices. This repulsion has an exponential nature and shows a magnitude and a decay length insensitive to the ionic strength of the medium. Because these features are distinctive of the hydration force detected between phospholipid bilayers or between several linear macromolecules (DNA, polysaccharides, collagen), we conclude that the dominant force experienced by deoxyguanosine helices approaching contact is hydration repulsion. The observed decay length of about 0.7 A has been rationalized to emerge from the coupling between the 3-A decay length of water solvent and the helically ordered structure of the hydrophilic groups on the opposing surfaces. The present results agree with recent measurements, also showing the dependence of the hydration force decay on the structure of interacting surfaces and confirm the correlations between force and structure.     

The effect of salt on self-assembled actin-lysozyme complexes

We present a combined experimental and computational study of the bundling of F-actin filaments induced by lysozyme proteins. Synchrotron small-angle x-ray scattering results show that these bundles consist of close-packed columnar complexes in which the actin is held together by incommensurate, one-dimensional arrays of lysozyme macroions. Molecular dynamics simulations of a coarse-grained model confirm the arrangement of the lysozyme and the stability of this structure. In addition, we find that these complexes remain stable even in the presence of significant concentrations of monovalent salt. The simulations show that this arises from partitioning of the salt between the aqueous and the condensed phases. The osmotic pressure resulting from the excess concentration of the salt in the aqueous phase balances the osmotic pressure increase in the bundle. These results are relevant for a variety of biological and biomedical problems in which electrostatic complexation between anionic polyelectrolytes and cationic globular proteins takes place, such as the pathological self-assembly of endogenous antibiotic polypeptides and inflammatory polymers in cystic fibrosis.     

A semiempirical extension of polyelectrolyte theory to the treatment of oligoelectrolytes: Application to oligonucleotide helix-coil transitions

The interaction of counterions with a suitably long, charged oligomer appears susceptible to treatment in the context of polyelectrolyte theory by the introduction of an end-effect parameter that reflects the reduced association of counterions with the terminal regions of the oligo-ion. Use of a physically reasonable value for the end-effect parameter provides excellent agreement between theory and the experimental data of Elson, Scheffler, and Baldwin [J. Mol. Biol. 54 , 401–415 (1970)] on the dependences of melting temperature on salt concentration and chain length for a series of hairpin helices formed by d(TA) oligomers. The differences in behavior expected for hairpin, dimer, and oligomer-polymer helices are discussed. The salt dependence of the end-joining equilibrium investigated for λ DNA by Wang and Davidson [Cold Spring Harbor Symp. Quant. Biol. 33 , 409–415 (1968)] is treated as an oligomer–polymer interconversion. The dependence of equilibrium constant for this reaction on counterion concentration is in good agreement with that predicted by theory for an end-region totalling 24 nucleotides, the known length of the λ ends.     

Application of polyelectrolyte limiting laws to virial and asymptotic expansions for the Donnan equilibrium

We have applied a general polyelectrolyte theory to an analysis of the Donnan equilibrium. The polyelectrolyte concentration is measured by a dimensionless parameter x, equal to the ratio of the equivalent polyelectrolyte concentration to the concentration of salt in the external compartment. For small x, virial series - expansions in powers of x - are developed for the Donnan salt-exclusion, osmotic pressure, and electromotive force. For large x, asymptotic expansions for these effects are presented. Polyion-polyion interactions are explicitly neglected, so that the physical significance of the virial series differs from its meaning in neutral polymer chemistry. Numerical results illustrate large deviations from ideal Donnan behavior as well as satisfactory agreement with published data on the salt-exclusion and emf effects. However, results for the Donnan osmotic pressure disagree with the data, except in the case of zero salt concentration in the external compartment, for which agreement is almost exact.     

Compaction of a bacterial group I ribozyme coincides with the assembly of core helices

Counterions are critical to the self-assembly of RNA tertiary structure because they neutralize the large electrostatic forces which oppose the folding process. Changes in the size and shape of the Azoarcus group I ribozyme as a function of Mg(2+) and Na(+) concentration were followed by small angle neutron scattering. In low salt buffer, the RNA was expanded, with an average radius of gyration (R(g)) of 53 +/- 1 A. A highly cooperative transition to a compact form (R(g) = 31.5 +/- 0.5 A) was observed between 1.6 and 1.7 mM MgCl(2). The collapse transition, which is unusually sharp in Mg(2+), has the characteristics of a first-order phase transition. Partial digestion with ribonuclease T1 under identical conditions showed that this transition correlated with the assembly of double helices in the ribozyme core. Fivefold higher Mg(2+) concentrations were required for self-splicing, indicating that compaction occurs before native tertiary interactions are fully stabilized. No further decrease in R(g) was observed between 1.7 and 20 mM MgCl(2), indicating that the intermediates have the same dimensions as the native ribozyme, within the uncertainty of the data (+/-1 A). A more gradual transition to a final R(g) of approximately 33.5 A was observed between 0.45 and 2 M NaCl. This confirms the expectation that monovalent ions not only are less efficient in charge neutralization but also contract the RNA less efficiently than multivalent ions.