Dielectric behavior of linear polyelectrolytes

The dipolar correlation function for a system of counterions diffusing on the surface of a polyelectrolyte cylinder is computed. Repulsive coulombic interactions between the counterions are taken into account. Lateral dissociation and reassociation to the cylinder is treated microscopically. Numerical calculations needed to obtain quantitative results for the long time behavior are presented. The model dependence on its parameters is interpreted with special emphasis on parameter values typical of DNA.     

Dielectric behavior of polyelectrolytes. III. The role of counterion interactions

The role of the Coulomb forces between the counterions on the surface of polyelectrolytes on the dielectric response is analyzed. An estimate of the maximum dielectric increment (as a function of the number of counterions) is found as a function of the molecular length. The minimum-energy configuration of the counterions on a cylinder is found to be a double helix, suggesting the fundamental importance of electrostatic interactions in determining structure. Solutions of the dynamical equations for a few counterions indicate that a single mode dominates the relaxation which is enhanced by the inter-ion repulsions. A lower bound is found for this mode based on analysis of the system response for short lengths. Sum rules for the rates and amplitudes of the dipolar correlation function are derived and lead to an upper bound for the rate of the dominant mode. These bounds approach one another for the parameters characteristic of restriction fragments of DNA. This permits a prediction of the magnitude and time scale of the dielectric response.     

Dielectric behavior of DNA--dye complex. II

The dielectric relaxation of native DNA and the effect of aminoacridine dyes, such as acridine orange (AO), proflavine (PF), and ethidium bromide (EB) have been investigated at different molar DNA phosphate (P) to dye (D) ratios in the frequency range 100 Hz–100 kHz. The static dielectric constant was observed to decrease with increasing binding of aminoacridines. This was interpreted as arising from the neutralization of the surface changes of the DNA molecules as a result of dye binding. At any P/D ratio the extent of charge neutralization was greatest for AO and least for the EB–DNA complex. The relaxation time (τ) for dye-bound DNA was greater compared to that for native DNA. This increase in τ was ascribed to the increase in the length of the dye-bound DNA. The maximum value of τ occurred at P/D = 20, 10, and 2 for AO-, PF-, and EB-treated DNA, respectively. The variation of τ at various levels of binding gave a qualitative idea about the conformational changes of DNA due to its binding with the dyes.     

Dielectric behavior of polyelectrolytes. IV. Electric polarizability of rigid biopolymers in electric fields

The equilibrium Kerr effect of a system of mobile charges constrained to the surface of biomacromolecules is calculated. Cylindrical and spherical geometries are considered. For the cylinder we determine the anisotropy of electric polarizability as a function of length, temperature, and number of charged species in the low-field regime, and the fraction of the maximum induced dipole in the field direction for higher electric fields. The results are compared to experimental data for DNA oligomers taken from the literature. With spherical geometry we calculate the fractional induced dipole moment as a function of electric field strength and from this deduce the orientation function. The field dependence of the orientation function is compared to experimental data in the literature for bovine disk membrane vesicles.     

Dielectric behavior of polyelectrolytes. VI. Dynamic response of cylindrical biopolymers to electric fields

The time dependence of the orientation of a cylindrical biopolymer and the configuration of its counterion complement in the presence of an external electric field is found by solving a model forced diffusion equation. The solution is a high temperature expansion in the external field strength and is used to predict the nature of the dielectric relaxation and the dynamic Kerr effect for such systems. Specific application is made to the dynamic Kerr effect of a DNA oligomer for which experimental data appear in the literature. The analysis yields a value for the surface diffusion coefficient of a sodium ion on DNA at 20 degrees C of 3.8 x 10(-10) m2 s-1.     

Dielectric properties of polyelectrolytes. V. Dielectric dispersion of heavy meromyosin

Dielectric constant and dielectric loss of heavy meromyosin (HMM) were measured with varying pH. HMM showed a broader dispersion pattern than that with a single relaxation time especially on the high-frequencey side. The dielectric increment increased sharply with pH, above p^{H 6}, whereas the mean relaxation time and whole dispersion pattern were unchanged in the same region. The values of the increment and the mean relaxation time were much larger than those of usual globular proteins. The dispersion profile, pH dependence, and values of the increment are well explained by Oosawa's counterion fluctuation theory. Other mechanisms are more or less inadequate to our results. In the low pH region below the isoelectric precipitation region, both the increment and the mean relaxation time decreased; this is probably due to partial denaturation and suppression of the dissociation of carboxyl groups. An experiment on a urea-denatured sample supports this assumption. The biological significance of the pH dependence is discussed.     

Dielectric disperison of linear polyelectrolytes

A three-dimensional (gaussian) model is formulated that permits evaluation of the one-dimensional fourier cosine transform of the counterion-counterion coulombic interaction energy ?_k. It is shown that ?_kis much larger for small k than was assumed by Oosawa; consequently, the magnitude of his dielectric increment, and also his relaxation time, must be drastically revised to smaller values. Evidently, the self-field of the fluctuation is large enough to seriously depress the amplitude of the spontaneous fluctuations, and to force Ohmic conduction of the ions at a rate far in excess of the rate of translational diffusion. Finally, it is noted that in highly conducting bulk solvents, where both positive and negative counterfoils coexist in the ion-atmosphere, one might expect to observe a low-frequency component of the dielectric relaxation arising from unequal rates of diffusion of the positive and negative species, in analogy with the situation for spherical colloidal particles. In such a circumstance, the basic counterfoil fluctuation mechanism proposed by Oosawa would acquire a new validity.     

Dielectric properties of polyelectrolytes. II. A theory of dielectric increment due to ion fluctuation by a matrix method

The mean square of dipole moment of a linear macromolecule which is responsible for dielectric increment of aqueous polyelectrolyte solutions is calculated by means of a matrix method in which ion binding at discrete sites and the nearest-neighbor interaction are taken into account. On the basis of the relationship between polarization of poly-ion and fluctuation of bound counterions the present theory indicates that the loosely bound ions result in larger increment and otherwise smaller increment. Also, the theory predicts that the dielectric increment has a maximum at an intermediate monovalent–divalent ion ratio when both species coexist. These results are consistent with experiments on polyacrylic acid neutralized with NaOH and Ca(OH)₂. At large contents of divalent ions the effect of chelation is also discussed.     

Dielectric increment and dielectric dispersion of solutions containing simple charged linear macromolecules. II. Experimental results with synthetic polyelectrolytes

The electric permittivity of aqueous solutions of different synthetic polyelectrolytes have been measured as a function of frequency in the range 5 kHz up to 100 MHz in the absence of added salt. Solutions of polymethacrylic acid and polyacrylic acid of different degrees of polymerization, both partially neutralized with NaOH, were investigated as well as solutions of Na-polystyrenesulphonate at different concentrations.For all systems a dispersion profile with two separated dispersion regions was obtained with a molecular weight dependent value of the static electric permittivity. The low frequency dispersion region was found to be characterized by a molecular weight dependent mean relaxation time while for the high frequency dispersion region both the mean relaxation time and the dielectric increment are molecular weight independent. It is shown that the reciprocal values of the specific increments and of the relaxation times depend linearly on the macromolecular concentration. Extrapolation of the corresponding quantities to infinite dilution was found to be possible. A comparison of these extrapolated values with calculated ones according to the previously derived theory also applicable to flexible macromolecules establishes that this theory describes satisfactorily the dielectric behaviour of the systems investigated.The conclusion is reached that the high frequency dispersion and relaxation can be attributed to fluctuations in the distribution of bound counterions along limited parts of the macromolecule. The relaxation time of the low frequency dispersion region seems to be essentially determined by the rotation of the complete molecule and the static electric permittivity can he explained in terms of fluctuations in the counterion density extending over the whole macromolecule.     

Dielectric properties of polyelectrolytes. I. A study on tetra-n-butyl ammonium polyacrylate

Dielectric constant and loss of aqueous solutions of tetra-n-butyl ammonium polyacrylate ((Bu)₄NPA) were measured in the frequency range from 300 Hz to 6 MHz as compared with sodium and other salts at various conditions. Our results show that there are two dispersions observed in the low-frequency range (LFD, several ten kHz to MHz), respectively, both of which are roughly expressed as the Cole-Cole dispersion formula with Cole parameters about 0.3. The large values of dielectric increment, its nonlinear concentration dependence, and other features suggest that both dispersions are explained by relaxations of two different ionic processes. For HFD, experimental results were qualitatively similar to those have been reported and compared with theories of the Maxwell-Wagner-type effect. On the other hand, LFD may be attributable to the polarization of loosely bound counterions. A model available for LFD was presented on the basis of counterion fluctuation.     

Dielectric properties of polyelectrolytes. III. Effect of divalent cations on dielectric increment of polyacids

Dielectric dispersion of polyacrylic acid (PAA) and polystyrene sulfonic acid (PSS) was measured in the presence of divalent cations. Effects of divalent ions were studied by neutralization with varying ratios of sodium hydroxide and divalent base concentration, addition of salts of divalent cations, and neutralization with divalent bases only. Two dispersion regions were observed in all cases, i.e., low-frequency dispersion (10²–10⁴ Hz) and high-frequency dispersion (10⁵–10⁶ Hz). The dielectric increment increases in the presence of sodium and alkaline earth metal ions together, but not with sodium and transition metal ions. This is due to the increment of low-frequency dispersion and is attributable to the fluctuation of bound counterions which is explained by our theory previously reported.¹ In the case of PAA neutralized with large fractions of divalent ions, or with divalent ions only, the increment is very small because of reduction of the fluctuation by interaction between bound ions at the neighboring sites and reduction of the effective length of polyion probably due to chelation by divalent ions. There are some differences among the effects of Mg⁺⁺, Ca⁺⁺, and Ba⁺⁺ on dielectric increment which may result from affinity or chelating ability of these ions.     

Dielectric permittivity of quantum plasma. Part II

The transverse and longitudinal dielectric permittivities of isotropic quantum plasma are calculated in the quantum plasma models based on the Dirac and Pauli equations. The dispersion relations for transverse-longitudinal waves in quantum particle beams are derived. Relativistic longitudinal and transverse waves in cold isotropic quantum plasma in models based on the Klein-Gordon and Dirac equations, as well as spin waves in the model based on the Pauli equation, are considered. Conditions for wave-particle resonance interactions in relativistic quantum plasma are analyzed.     

Dielectric behavior of DNA-proflavine complex

The dielectric relaxation of namtive DNA and DNA–proflavine complexes at different DNA phosphate (P) to dye (D) ratios, were investigated in the frequency range 100 c/sec to 100 Kc/sec. The proflavine molecules were found to have a profound effect on the static dielectric constant and the relaxation time of the polymers. The static dielectric constant was oberserved to decrese with increasing level of added proflavine. At P/D = 1, the variation of dielectric constant with frequency was small. Relaxation time (τ) was greater for the DNA–proflavine complexes compared to that for free DNA, Maximum value of the relaxation time was obtained at P/D = 10. The increase in the relaxation time and decrease in the static dielectric constant were attributed to the increase in length and meutralization of surface charges of the DNA molecules, respectively, as aresult of proflavine binding.     

The ecology ofCarex oxyandra II. The behavior of seedlings and tillers

A study on the seedlings and tillers ofCarex oxyandra, a pioneer perennial, was carried out at Mt. Bandai, Fukushima Prefecture, Japan. A field experiment showed that seedlings had a rather low rate of growth, a small biomass and a high mortality rate. On the other hand, tillers in clones befan growth much earlier, had a rapid growth rate and grew to a larger body size. Furthermore, there was a considerable difference in growth pattern between tillers without flowers and those with flowers; tillers without flowers had a longer growing season and a larger amount of leaves, roots and new rhizomes. The numerical proportions of these two types of tillers in clones varied with clonal vigor.     

Dielectric behavior of aqueous solutions of plasmid DNA at microwave frequencies.

The relative permittivity and dielectric loss of aqueous solutions of plasmid (pUC8.c1 and pUC8.c2) DNA have been measured at 20 degrees C over the frequency range 100 MHz-10 GHz. The solutions had a concentration of 0.1% DNA, and were studied both in the relaxed and the supercoiled form. The dielectric measurements were made using a variety of techniques including frequency domain and time domain methods of operation. No evidence of any resonance absorption, nor of any other kind of enhanced absorption, was observed.     

Dielectric behavior and atomic structure of serum albumin

After 1946, serum albumin was available for studies. Its residue sequence and internal disulfide bonding was developed by 1976. We began to make dielectric dispersion studies and apply Perrin's equations for rotational relaxation times around the two axes of revolution in 1938. These data indicated that albumin should have an elongated shape. In 1992 atomic structure data indicated the molecule was heart-shaped. A similar 1998 study of albumin complexed with fatty acid showed that the molecule was substantially rearranged. We found that the dielectric constant of albumin solutions was sensitive to fatty acid content, making this property an attractive probe in stop–flow kinetic studies. Such studies show that the fatty acid reaction is a two-step process. The fatty acid first binds to exterior sites in a diffusion-limited second order reaction complete in 1 ms. Then a first order rearrangement reaction with 400 ms half-life follows. Thus the highly specialized serum albumin sequence of amino acid residues determines not only the structure of the unligated molecule, but also the distinctive structures of the numerous multiligated molecules.     

Limiting sedimentation and diffusion coefficients of polyelectrolytes. The charge effect

General expressions relating the sedimentation and diffusion constants of polyelectrolytes to the friction properties of ionic components in multicomponent systems have been derived. A quantitative explanation of the charge effect with respect to the addition of a low-molecular-weight salt is given; special attention is laid on limiting laws according to the salt-to-polymer concentration ratio. The theory is applied to a simple model, the infinitely long rod-like model, to illustrate the peculiar aspect of the charge effect in presence of salt.     

Binding of ionic ligands to polyelectrolytes.

Ionic ligands can bind to polyelectrolytes such as DNA or charged polysaccharides. We develop a Poisson-Boltzmann treatment to compute binding constants as a function of ligand charge and salt concentration in the limit of low ligand concentration. For flexible chain ligands, such as oligopeptides, we treat their conformations using lattice statistics. The theory predicts the salt dependence and binding free energies, of Mg(2+) ions to polynucleotides, of hexamine cobalt(III) to calf thymus DNA, of polyamines to T7 DNA, of oligolysines to poly(U) and poly(a), and of tripeptides to heparin, a charged polysaccharide. One parameter is required to obtain absolute binding constants, the distance of closest separation of the ligand to the polyion. Some, but not all, of the binding entropies and enthalpies are also predicted accurately by the model.