On the application of polyelectrolyte limiting laws to the helix-coil transition of DNA. IV. Depedence of helix stability on the concentration of divalent metal ions.

The molecular theory of the previous paper in this series is extended to determine the effect of divalent metal ions on helix stability relative to coil at fixed ionic strength and nucleotide phosphate concentration. Specification of the state of condensed counterions, as well as their concentration, is essential for the solution of this problem, and it is assumed that they translate freely within a thin cylindrical shell close to the polynucleotide. As a function of divalent counterion concentration m the relative stability of the helix is highly nonlinear. Although the overall trend is that the helix stability increases with addition of divalent metal ion, there is a narrow concentration range for which it decreases slightly. The behavior of the relative stability as a function of m is determined by the translational degrees of freedom of the counterions, both univalent and divalent, both condensed and uncondensed. Detailed comparison of the theory with data is not given here, but it is pointed out that the calculated values of the relative stability are consistent with the order of magnitude of the observed effect Mg²⁺ on the melting temperature.     

On the application of polyelectrolyte “limiting laws” to the helix-coil transition of DNA. I. Excess univalent cations

A general theory of polyelectrolyte solutions is here used to calculate the differences in Gibbs free energy, enthalpy, and entropy between the coil and helix forms of DNA at any temperature and salt concentration. The salt has univalent cations and is assumed present in excess over the base concentration. The results are restricted to sufficiently dilute solutions. It is shown that the salt concentrations effect is entirely entropic in origin. When applied to the melting temperature, the calculations yield a relation between the enthalpy difference at the melting temperature and the slope of the plot of melting temperature vs. the logarithm of the salt concentration. In accord with observation, both the Gibbs free energy difference at any fixed temperature and the melting temperature are predicted to be linear functions of the log of the salt concentration. However, the theory is not in quantitative agreement with enthalpy data. Data on various colligative and transport properties of both helix and coil forms are reviewed in the text and in Appendix B, and good agreement is found with theory for both forms. No attempt is made to explain why the theory is quantitative for these properties but not for heat measurements. Finally, in Appendix A, an approximate calculation is made of the free energy contributions due to ionic effects not associated with the salt concentration.     

Cation radius effects on the helix-coil transition of DNA. Cryptates and other large cations.

Most polyelectrolyte theories of the effect of ions on the thermal melting of DNA assume that the predominant influence of the cations comes through their charge. Ion size and structure are treated, for analytic convenience, as negligible variables. We have examined the validity of this assumption by measuring the melting temperature of calf thymus DNA as a function of salt concentration with four univalent cations of different hydrated radii. These are K+ (3.3 A), (n-Pr)4N+ (4.5 A), (EtOH)4N+ (4.5 A), and C222-K+ (5 A). C222-K+ is a complex of cryptand C222 with K+. With K+ as the sole cation, Tm varies linearly with the log of ionic strength over the range 0.001-0.1 M. With all the K+ sequestered by an equimolar amount of C222, Tm is depressed by 10-20 degrees C and the slope of Tm vs. ionic strength is lower. At low ionic strength, an even greater reduction in Tm is achieved with (n-Pr)4N+; but the similar-sized (EtOH)4N+ gives a curve more similar to K+. Theoretical modeling, taking into account cation size through the Poisson-Boltzmann equation for cylindrical polyelectrolytes, predicts that larger cations should be less effective in stabilizing the double helix; but the calculated effect is less than observed experimentally. These results show that valence, cation size, and specific solvation effects are all important in determining the stability of the double-helical form of DNA.     

A configurational interpretation of the axial phosphate spacing in polynucleotide helices and random coils

The structural implications arising from the observation (set forth in the preceding paper) that the charge density of a single-stranded randomly coiling polynucleotide chain is approximately equal to that of one strand of the familiar double helix are here examined. A computational scheme is described to obtain (using bond lengths, valence bond angles, and internal rotation angles) the mean phosphate–phosphate spacing parameter b along the chain axes of any single-stranded polynucleotide molecule. Attention is then focused upon the computed interphosphate spacing associated with both the theoretical randomly coiling polynucleotide that reproduces the observed experimental unperturbed dimensions and the familiar single-stranded helix. The calculations clearly demonstrate that the parameter b only weakly reflects the spatial configuration of the chain. The approximate equivalence of the b values associated with the single-stranded helix and the unperturbed randomly coiling polynucleotide is not indicative of strong configurational similarities between the two forms. The familiar helix is composed of a sequence of identically conformed compact structural residues while the random coil is characterized by a variety of chain-repeating residues of which a large proportion are extended units.     

Thermodynamics of polyelectrolyte solutions. An empirical extension of the manning theory to finite salt concentrations

The range of application of the Manning theory of polyelectrolyte solutions (J. Chem. Phys., 51 , 924 (1969)) is extended to finite concentrations of simple electrolyte by the empirical superposition of excess free energies arising from (i) interactions between mobile ions and polyions and (ii) mutual interactions between mobile ions. A comparison of published results with the modified theory shows excellent agreement over a wide range of concentrations. Results for a polyelectrolyte of low charge density suggest that the effective inter-charge spacing may be less than that of the fully extended polyion.     

Dielectric saturation of the aqueous boundary layers adjacent to charged bilayer membranes

Summary The surface charge density resulting from the adsorption of hydrophobic anions of dipicrylamine onto dioleyl-lecithin bilayer membranes has been measured directly using a high field pulse method. The surface charge density increases linearly with adsorbate concentration in the water until electrostatic repulsion of impinging hydrophobic ions by those already adsorbed becomes appreciable. Then Gouy-Chapman theory predicts that surface charge density will increase sublinearly, with the power [z ⁺/(z ⁺+2)] of the adsorbate concentration, wherez ⁺ is the cation valence of the indifferent electrolyte screening the negatively charged membrane surface. The predicted 1/3 and 1/2 power laws for univalent and divalent cations, respectively, have been observed in these experiments using Na⁺, Mg⁺⁺, and Ba⁺⁺ ions. Gouy-Chapman theory predicts further that the change from linear to sublinear dependence takes place at a surface charge density governed by the static dielectric constant of water and the concentration of indifferent electrolyte. Quantitative agreement with experiment is obtained at electrolyte concentrations of 10^–4 m and 10^–3 m, but can be maintained at higher concentrations only if the aqueous dielectric constant is decreased. A transition field model is proposed in which the Gouy-Chapman theory is modified to take account of dielectric saturation of water in the intense electric fields adjacent to charged membrane surfaces.     

Monte Carlo and Poisson–Boltzmann calculations of the fraction of counterions bound to DNA

The counterion density and the condensation region around DNA have been examined as functions of both ion size and added-salt concentration using Metropolis Monte Carlo (MC) and Poisson–Boltzmann (PB) methods. Two different definitions of the “bound” and “free” components of the electrolyte ion atmosphere were used to compare these approaches. First, calculation of the ion density in different spatial regions around the polyelectrolyte molecule indicates, in agreement with previous work, that the PB equation does not predict an invariance of the surface concentration of counterions as electrolyte is added to the system. Further, the PB equation underestimates the counterion concentration at the DNA surface, compared to the MC results, the difference being greatest in the grooves, where ionic concentrations are highest. If counterions within a fixed radius of the helical axis are considered to be bound, then the fraction of polyelectrolyte charge neutralized by counterions would be predicted to increase as the bulk electrolyte concentration increases. A second categorization—one in which monovalent cations in regions where the average electrostatic potential is ledd than ?kT are considered to be bound—provides an informative basis for comparison of MC and PB with each other and with counterion-condensation theory. By this criterion, PB calculations on the B from of DNA indicate that the amount of bound counterion charge per phosphate group is about .67 and is independent of salt concentration. A particularly provocative observatiob is that when this binding criterion is used, MC calculations quantitatively reproduce the bound fraction predicated by counterion-condensation theory for all-atom models of B-DNA and A-DNA as well as for charged cylindera of varying lineat charge densities. For example, for B-DNA and A-DNA, the fractions of phosphate groups neutralized by 2 Å hard sphere counterions are 0.768 and .817, respectively. For theoretical studies, the rediys enclosing the region in which the electrostatic potential is calculated studies, the radius enclosing the region in which the electrostatic potential is calculated to be less than ?kT is advocated s a more suitable binding or condensation radius that enclosing the fraction of counterions given by (1 – ξ^?1). A comparsion of radii calculated using both of these definitions is presented. © 1994 John Wiley & Sons, Inc.     

Electrostatic effects on the stability of condensed DNA in the presence of divalent cations.

Cylindrical cell model Poisson-Boltzmann (P-B) calculations are used to evaluate the electrostatic contributions to the relative stability of various DNA conformations (A, B, C, Z, and single-stranded (ss) with charge spacings of 3.38 and 4.2 A) as a function of interhelix distance in a concentrated solution of divalent cations. The divalent ion concentration was set at 100 mM, to compare with our earlier reports of spectroscopic and calorimetric experiments, which demonstrate substantial disruption of B-DNA geometry. Monovalent cations neutralize the DNA phosphates in two ways, corresponding to different experimental situations: 1) There is no significant contribution to the ionic strength from the neutralizing cations, corresponding to DNA condensation from dilute solution and to osmotic stress experiments in which DNA segments are brought into close proximity to each other in the presence of a large excess of buffer. 2) The solution is uniformly concentrated in DNA, so that the neutralizing cations add significantly to those in the buffer at close DNA packing. In case 1), conformations with lower charge density (Z and ssDNA) have markedly lower electrostatic free energies than B-DNA as the DNA molecules approach closely, due largely to ionic entropy. If the divalent cations bind preferentially to single-stranded DNA or a distorted form of B-DNA, as is the case with transition metals, the base pairing and stacking free energies that stabilize the double helix against electrostatic denaturation may be overcome. Strong binding to the bases is favored by the high concentration of divalent cations at the DNA surface arising from the large negative surface potential; the surface concentration increases sharply as the interhelical distance decreases. In case 2), the concentration of neutralizing monovalent cations becomes very large and the electrostatic free energy difference between secondary structures becomes small as the interhelical spacing decreases. Such high ionic concentrations will be expected to modify the stability of DNA by changing water activity as well as by screening electrostatic interactions. This may be the root of the decreased thermal stability of DNA in the presence of high concentrations of magnesium ions.     

Immobilization and phytoavailability of cadmium in variable charge soils. I. Effect of phosphate addition

The effect of phosphate on the surface charge and cadmium (Cd) adsorption was examined in seven soils that varied in their variable-charge components. The effect of phosphate on immobilization and phytoavailability of Cd from one of the soils, treated with various levels of Cd (0–10 mg Cd kg^–1 soil), was further evaluated using mustard (Brassica juncea L.) plants. Cadmium immobilization in soil was evaluated by a chemical fractionation scheme. Addition of phosphate, as KH₂PO₄, increased the pH, negative charge and Cd adsorption by the soils. Of the seven soils examined, the three allophanic soils (i.e., Egmont, Patua and Ramiha) exhibited greater increases in phosphate-induced pH, negative charge and Cd²⁺ adsorption over the other four non-allophanic soils (i.e., Ballantrae, Foxton, Manawatu ad Tokomaru). Increasing addition of Cd enhanced Cd concentration in plants, resulting in decreased plant growth (i.e., phytotoxicity). Addition of phosphate effectively reduced the phytotoxicity of Cd. There was a significant inverse relationship between dry matter yield and Cd concentration in soil solution. Addition of phosphate decreased the concentration of the soluble + exchangeable Cd fraction but increased the concentration of inorganic-bound Cd fraction in soil. The phosphate-induced alleviation of Cd phytotoxicity can be attributed primarily to Cd immobilization due to increases in pH and surface charge.     

The effect of neutral salts on the conformational transition of poly-alpha-amino acids. I. Potentiometric titration and optical rotatory dispersion studies

The effect of salts on the coil-to-helix transition of poly-α-amino acids was investigated by optical rotatory dispersion and potentiometric titration techniques. Both charge-dependent and charge-independent contributions to the free energy were considered. The free energy of formation ΔF° of the uncharged α-helix from the uncharged random coil for poly-L -glutamic acid (PGA) decreases very rapidly in the limit of zero added salt concentration. This effect probably depends on the uncertainty affecting the choice of the extrapolation of the apparent pK for the random coil at low ionic strength. Above 0.1 M salt, where the free energy determination becomes meaningful, the anions and cations investigated do not affect the value of ΔF°, with the exception of Li⁺. Our data support the point of view that this cation binds to the peptide group. A class of salts produces an increase of the helical content of poly-L -ornithine (PO) both at low and high degree of ionization. This effect appears to be anion dependent. It is shown that (1) no change of ΔF° is involved; (2) recent theories of polyelectrolyte solutions cannot account for our results. We suggest that a true site binding of the anions to the charged amino groups occurs. The role of electrostatic binding in determining the conformational stability of proteins in the presence of some anions is stressed, and a general treatment for the electrostatic binding equilibria is outlined.     

Metal cation controls phosphate release in the myosin ATPase

Myosin is an enzyme that utilizes ATP to produce a conformational change generating a force. The kinetics of the myosin reverse recovery stroke depends on the metal cation complexed with ATP. The reverse recovery stroke is slow for MgATP and fast for MnATP. The metal ion coordinates the γ phosphate of ATP in the myosin active site. It is accepted that the reverse recovery stroke is correlated with the phosphate release; therefore, magnesium “holds” phosphate tighter than manganese. Magnesium and manganese are similar ions in terms of their chemical properties and the shell complexation; hence, we propose to use these ions to study the mechanism of the phosphate release. Analysis of octahedral complexes of magnesium and manganese show that the partial charge of magnesium is higher than that of manganese and the slightly larger size of manganese ion makes its ionic potential smaller. We hypothesize that electrostatics play a role in keeping and releasing the abstracted γ phosphate in the active site, and the stronger electric charge of magnesium ion holds γ phosphate tighter. We used stable myosin–nucleotide analog complex and Raman spectroscopy to examine the effect of the metal cation on the relative position of γ phosphate analog in the active site. We found that in the manganese complex, the γ phosphate analog is 0.01 nm further away from ADP than in the magnesium complex. We conclude that the ionic potential of the metal cation plays a role in the retention of the abstracted phosphate.     

Interactions des ions métalliques avec le DNA. I. Comportement de polyélectrolyte et liaison des ions compensateurs

The theory of polyelectrolyte solution of Alexandrowicz: and Katchalsky is used to calculate the electrostatic potential of single stranded polynucleotides for different ionic strength. We have considered the potential of double stranded DNA as the superposition of the different potentials produced by each chain, provided the average distance between the strands is higher than an ionic strength-dependent parameter b. For ionic strength lower than 5 × 10^?2M, the assumption is no longer valid, and a cylindrical model with a uniform charge density must be used. The continuity between the two models was tested, and thus we can calculate the electrical potential at the vicinity of a phosphate group in the whole range of ionic-strength where the double helix is stable. It was therefore possible to determine the theoretical number of ions bound electrostatically to DNA and we found an increase of ion binding with a decrease of ionic strength. Such a model was further applied to the change of specific volume in different salt solutions. Comparison is made with recent pycnometric data on Na^? and Cs^? salts of DNA. Agreement is good in the case of Cs⁺, but for Na⁺, cation binding is likely to be accompanied by a change of the hydration of DNA, which depends on ionic strength. With the same model we can see easily the ion-trapping properties of DNA which play an important role in any formation of complex between heavy ions and bases.     

Limiting laws and counterion condensation in polyelectrolyte solutions: IV. The approach to the limit and the extraordinary stability of the charge fraction

The limiting laws for polyelectrolyte solutions developed in previous papers of this series have been amply confirmed by measurement. A surprising result of the accumulated data is that the limiting polyelectrolyte charge fraction (fraction of fixed charges uncompensated by condensed counterions in the limit of zero concentration), persists up to concentrations of 0.1 M or even higher. Here the theory is extended in a simple manner to finite concentrations, and the stability of the charge fraction is found to be firmly based on consequences of the long-range polyelectrolyte field. The associated counterions are assumed to translate freely in a region centered on the contour axis of the polyion. The numerical value of the free volume is determined self-consistently from the axial charge density of the polyelectrolyte and is used as the general framework within which specific binding effects are treated.     

Electrostatic effects on polynucleotide transitions. I. Behavior at neutral pH

An approximate analytical expression for the electrostatic free energy of a polynucleo-tide in any of its possible ordered or random conformations is derived by integration of the screened-Coulomb potential energy function over all charge pairs in the structure. The electrostatic free energy of any form is found to be a linear function of the logarithm of the monovalent counterion concentration, in the range of low salt concentrations. Hence the electrostatic free energy difference between ordered and disordered forms in a polynucleotide structural transition is a linear function of the logarithm of the monovalent counterion concentration. A free energy balance applied to a two-state model for the transition then yields a linear dependence of the transition temperature T_m upon the logarithm of the counterion concentration. Calculation of the quantity dT_m/d log M, where M is the monovalent counterion concentration, shows it to be a characteristic constant for a given transition, with a magnitude and sign proportional to the charge density difference between the ordered and disordered forms. Use of any one of several alternate, simple assumptions yields predicted dT_m/d log M values in good agreement with experimental data for various polynucleotide transitions.     

Solution properties of an exopolysaccharide from a Pseudomonas strain obtained using glycerol as sole carbon source

We report the solution properties of a new exopolysaccharide (EPS) obtained from a Pseudomonas strain fed with glycerol as the sole source of carbon. This high molecular mass (3 × 10⁶ g mol⁻¹) biopolymer is essentially made of galactose monomers with pyruvate and succinate groups imparting a polyelectrolyte character. The Smidsrod parameter B computed from the ionic strength dependence of the intrinsic viscosity indicates that the EPS backbone is rather flexible. In salt free aqueous solutions, the zero shear viscosity scaling with concentration follows a typical polyelectrolyte behavior in bad solvent, whereas at high ionic strength the rheological response is reminiscent from neutral polymers. Light scattering data indicate that the EPS adopts a globular conformation as a result of hydrophobic interactions. EPS solutions are stable within 4 days as particle sizing does not indicate EPS aggregation. Both globular conformation and stability against precipitation from solution are attributed to the low charge density of the polyelectrolyte.     

Thermal stability of lysozyme as a function of ion concentration: A reappraisal of the relationship between the Hofmeister series and protein stability

Anion and cation effects on the structural stability of lysozyme were investigated using differential scanning calorimetry. At low concentrations (<5 mM) anions and cations alter the stability of lysozyme but they do not follow the Hofmeister (or inverse Hofmeister) series. At higher concentrations protein stabilization follows the well‐established Hofmeister series. Our hypothesis is that there are three mechanisms at work. At low concentrations the anions interact with charged side chains where the presence of the ion can alter the structural stability of the protein. At higher concentrations the low charge density anions perchlorate and iodide interact weakly with the protein. Their presence however reduces the Gibbs free energy required to hydrate the core of the protein that is exposed during unfolding therefore destabilizing the structure. At higher concentrations the high charge density anions phosphate and sulfate compete for water with the protein as it unfolds increasing the Gibbs free energy required to hydrate the newly exposed core of the protein therefore stabilizing the structure.     

Approach to the limit of counterion condensation

According to counterion condensation theory, one of the contributions to the polyelectrolyte free energy is a pairwise sum of Debye-Hückel potentials between polymer charges that are reduced by condensed counterions. When the polyion model is taken as an infinitely long and uniformly spaced line of charges, a simple closed expression for the summation, combined with entropy-derived mixing contributions, leads to the central result of the theory, a condensed fraction of counterions dependent only on the linear charge density of the polyion and the valence of the counterion, stable against increases of salt up to concentrations in excess of 0.1 M. Here we evaluate the sum numerically for B-DNA models other than the infinite line of B-DNA charges. For a finite-length line there are end effects at low salt. The condensation limit is reached as a flat plateau by increasing the salt concentration. At a fixed salt concentration the condensation limit is reached by increasing the length of the line. At moderate salt even very short B-DNA line-model oligomers have condensed fractions not far from the infinite polymer limit. For a long double-helical array with charge coordinates at the phosphates of B-DNA, the limiting condensed fraction appears to be approached at low salt. In contrast to the results for the line of charges, however, the computed condensed fraction varies strongly with salt in the range of experimentally typical concentrations. Salt invariance is restored, in agreement with both the line model and experimental data, when dielectric saturation is considered by means of a distance-dependent dielectric function. For sufficiently long B-DNA line and helical models, as typical salt concentrations, the counterion binding fraction approaches the polymer limit as a linear function of 1/P, where P is the number of phosphate groups of B-DNA.     

Light scattering,CD, and ligand binding studies of ferrihemoglobin–polyelectrolyte complexes

Quasi‐elastic light scattering (QELS), electrophoretic light scattering (ELS), CD spectroscopy, and azide binding titrations were used to study the complexation at pH 6.8 between ferrihemoglobin and three polyelectrolytes that varied in charge density and sign. Both QELS and ELS show that the structure of the soluble complex formed between ferrihemoglobin and poly(diallyldimethylammonium chloride) [PDADMAC] varies with protein concentration. At fixed 1.0 mg/mL polyelectrolyte concentration, protein addition increases complex size and decreases complex mobility in a tightly correlated manner. At 1.0 mg/mL or greater protein concentration, a stable complex is formed between one polyelectrolyte chain and many protein molecules (i.e., an intra‐polymer complex) with apparent diameter approximately 2.5 times that of the protein‐free polyelectrolyte. Under conditions of excess polyelectrolyte, each of the three ferrihemoglobin–polyelectrolyte solutions exhibits a single diffusion mode in QELS, which indicates that all protein molecules are complexed. CD spectra suggest little or no structural disruption of ferrihemoglobin upon complexation. Azide binding to the ferrihemoglobin–poly(2‐acrylamide‐2‐methylpropanesulfonate) [PAMPS] complex is substantially altered relative to the polyelectrolyte‐free protein, but minimal change is induced by complexation with an AMPS‐based copolymer of reduced linear charge density. The change in azide binding induced by PDADMAC is intermediate between that of PAMPS and its copolymer. © 1999 John Wiley & Sons, Inc. Biopoly 50: 153–161, 1999     

The Effect of Surface Charge on the Voltage-Dependent Conductance Induced in Thin Lipid Membranes by Monazomycin

Differences in the behavior of phosphatidylethanolamine (PE) and phosphatidylglycerol (PG) thin lipid membranes treated with monazomycin are shown to be due to the negative surface charge on PG membranes. We demonstrate that shifts of the conductance-voltage (g-V) characteristic of PG films produced by changes of univalent or divalent cation concentrations result from changes of the membrane surface potential on one or both sides. In particular, if divalent cations are added to the aqueous phase not containing monazomycin, the resulting asymmetry of the surface potentials results in an intramembrane potential difference not recordable by electrodes in the bulk phases. Nevertheless, this intramembrane potential difference is "seen" by the monazomycin, and consequently the g-V characteristic is shifted along the voltage axis. These changes are accounted for by diffuse double layer theory. Thus we find it unnecessary to invoke specific binding of Mg⁺⁺ or Ca⁺⁺ to the negative charges of PG membranes to explain the observation that concentrations of these ions some 100-fold lower than that of the univalent cation present produce large shifts of the g-V characteristic. We suggest that analogous shifts of g-V characteristics in axons produced by changes of divalent cation concentration are also best explained by diffuse double layer theory.     

Comparison of Different Approaches for Calculation of Polyelectrolyte Free Energy

Abstract

We consider the problem of the mean field (Poisson-Boltzmann) calculation of the electrostatic free energy for a strongly charged polyelectrolyte such as DNA in a salt solution. We compare two approaches to calculate the free energy: (i) direct one, starting from the statistical-mechanical expression for the electrostatic free energy and (ii) the polyion charge variation method. In the infinite dilution limit (in respect to polyion) and in excess salt (IDLES) the two approaches are fully equivalent. This is shown by straight forward algebra. We have performed specific calculations of the free energy difference for the case of B-Z transition in DNA as a function of ionic strength. As expected, the two approaches led to identical results. The ionic strength dependence of the B-to-Z free energy proves to be concaved up and as a result Z-DNA is stabilized at low ionic concentration as well as at high salt in full agreement with our previous results (M.D. Frank- Kamenetskii et al, J. Biomol. Struct. Dyn. 3, 35–42 (1985)). Our data quantitatively agree with the results of Soumpasis (D. M. Soumpasis, J. Biomol. Struct. Dyn. 6, 563–574 (1988)). However, his claim about the absence of the effect of stabilization of Z-DNA at low salt proves to be groundless, and the criticism of our earlier approach seems to be irrelevant.