Dielectric increment and dielectric dispersion of solutions containing simple charged linear macromolecules. I. Theory

A theory is derived for the static and frequency dependent value of the electric permittivity for model systems representing a solution of a macromolecule bearing a large number of identical charges. The polyion is represented either as a charged rigid rod (A) or as a sequence of charged rodlike subunits in an arbitrary but fixed configuration (B) and it is assumed that a certain fraction of the counterions is closely associated to the macromolecule. The dielectric properties are described in terms of fluctuations in the distribution of the associated counterions along the polyion. These fluctuations can occur locally between potential barriers marking the ends of the subunits (if considered) but can also extend over the whole molecule. Neglecting correlations between different associated counterions expressions for the static value of the dielectric increment are obtained which reveal its dependence on the fraction of bound ions, on the charge of the counterions and on the length of the molecule for model A or the radius of gyration for model B. The dynamic behaviour of A is distinguishable from that of B as the former will present one single dispersion curve of the frequency dependent electric permittivity while the latter may give rise to two different dispersion regions. This will be the case if both the exchange between bound and free ions and the rotation of the complete molecule are relatively slow in comparison to the local bound counterion density fluctuations and if these fluctuations occur on a much shorter time scale than the ion density fluctuations extending over the complete macromolecule.     

Plasmon interpretation of 25 cm-1 mode in DNA.

An extension of the effective field approach for the normal mode dynamics of dissolved DNA polymers has been applied to study the vibrational modes of DNA-hydration sheath-counterion system, to include the effect of site bound counterions on the system dynamics. An alternative interpretation has been suggested for a 25 cm-1 mode recently observed in DNA samples and interpreted earlier as an interhelical mode. Analysing the eigenvectors this mode is found to possess a large electric dipole moment with longitudinal collective oscillations of the system. These characteristics identify this mode as a collective plasmon mode. Possible physical reasons for the existence of this character have been presented.     

Theoretical evaluation of dielectric absorption of microwave energy at the scale of nucleic acids

A theoretical model is proposed for the evaluation of dielectric properties of the cell nucleus between 0.3 and 3 GHz, as a function of its nucleic acids (NA) concentration (CNA). It is based on literature data on dielectric properties of DNA solutions and nucleoplasm. In skeletal muscle cells, the specific absorption rate (SAR) ratio between nucleoplasm and cytoplasm is found to be larger than one for CNA above 30 mg/ml. A nearly linear relationship is found between CNA and this nucleocytoplasmic SAR ratio. Considering the nanoscale of the layer of condensed counterions and bound water molecules at the NA-solution interface, the power absorption per unit volume is evaluated at this precise location. It is found to be between one and two orders of magnitude above that in muscle tissue as a whole. Under realistic microwave (MW) exposure conditions, however, these SAR inhomogeneities do not generate any significant thermal gradient at the scale considered here. Nevertheless, the question arises of a possible biological relevance of nonnegligible and preferential heat production at the location of the cell nucleus and of the NA molecules.     

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 behavior of polyelectrolytes II. The cylinder

The dipolar correlation function for a system of coupterions diffusing on the surface of a polyelectrolyte cylinder is computed. The influence of screened coulombic repulsions on the dielectric increment is determined. Dissociation and reassociation of the counterions to the cylinder is treated microscopically and the coupled bulk diffusion is solved in the presence of the Poisson-Boltzmann potential. It is found that the correlation function contains a small, fast decaying, molecular weight independent part arising from diffusion around the cylinder and a large, slowly decaying, molecular weight dependent part arising from diffusion along the cylinder axis. The dissociation-reassociation kinetics can play a large, possible dominant, role in determining the relaxation rates.     

Counterion diffusion in heparin solutions

The physiological importance of heparin is due to its strong interaction with bivalent counterions, especially Ca2+. A diffusional approach of this property is presented in this article: the observable is the self-diffusion coefficient of the counterions, as a function of the ratio of the polyelectrolyte over the added salt concentrations. All the results are in agreement with a simple "quasi-chemical model" in which two different states are assumed for the counterions: "free" or "bound." The proportions of these two types of ions are calculated according to the distribution function of the counterions around the polyion. We assume that those of counterions located at a distance closer than a, the characteristic distance, are bound; the others are free. The ionic distribution function is evaluated by a numerical integration of a cell model Poisson-Boltzmann equation. Finally, this model leads to a very good agreement with the experimental results, if the radius of heparin polyion is assumed to be 6 and 10 A.     

Plasmon Interpretation of 25 cm−1 Mode in DNA

Abstract

An extension of the effective field approach for the normal mode dynamics of dissolved DNA polymers has been applied to study the vibrational modes of DNA-hydration sheath-counterion system, to include the effect of site bound counterions on the system dynamics. An alternative interpretation has been suggested for a 25 cm^?1 mode recently observed in DNA samples and interpreted earlier as an interhelical mode. Analysing the eigenvectors this mode is found to possess a large electric dipole moment with longitudinal collective oscillations of the system. These characteristics identify this mode as a collective plasmon mode. Possible physical reasons for the existence of this character have been presented.     

Dielectric studies of electrolytic poly(α-amino acid)s in aqueous solutions

The dependence of the dielectric constant and dielectric loss of aqueous solutions of poly-ε, N-succinyl-L -lysine on its degree of polymerization, degree of neutralization, concentration of the polymer, and counterion type was studied in a frequency range from 300 Hz to 5 MHz. Regardless of the conformation, a low-frequency dispersion in a frequency range lower than 10 kHz and a high-frequency dispersion in a range higher than 100 kHz were found. The large value of the dielectric increment, its nonlinear dependence on concentration, its remarkable dependence on counterion type, and its dependence on the degree of polymerization suggest that the low-frequency dispersion is mainly due to the polarization of loosely bound counterions. These data were found for both the helical and coiled forms. The rotational motion of the electric dipole on the molecule could not have been primarily responsible for these results. On the other hand, the high-frequency dispersions may be attributable to the Maxwell–Wagner-type effect. The results were compared with the dispersions of poly(L -glutamic acid), poly(L -lysine), and their salts reported previously.     

Counterion fluctuation and dielectric dispersion in linear polyelectrolytes

The thermal fluctuation in the concentration of counterions bound to a rodlike polyion was analyzed by expanding the fluctuation in a Fourier series along the rod. The amplitude and the relaxation time of fluctuations of various wave lengths were obtained as functions of the charge density and the length of the polyion. From these results the real and imaginary parts of the dielectric constant of the polyelectrolyte solution were derived as the sum of contributions of fluctuations of different modes. The dielectric dispersion curve or the Cole-Cole plot obtained was found to be in good agreement with experimental data.     

Limiting laws and counterion condensation in polyelectrolyte solutions: V. Further development of the chemical model

Counterion binding to polyelectrolyte chains is formulated as a chemical reaction M^z(free) → M^z(bound). Expressions for the chemical potentials of free and bound counterions are set equal to obtain the reaction equilibrium. The results are equivalent to those in the previous paper of this series. An additional result obtained here is that a polyion holds its bound counterion layer with a strength on the order of 100 $\text{kcal}\text{(mole cooperative unit)}$. The method is then applied to the calculation of the polarizability along the chain due to the bound (condensed) counterions.     

Electro-optical studies on synthetic polyelectrolytes: IV. Electric polarizability and conformation of poly-N-methyl-2-vinylpyridinium bromide in aqueous solution

Measurements of the relaxation time on aqueous solutions of the title polyelectrolyte as a function of the concentration and of the molecular weight show that its conformation at very high dilution can be better accounted for by a weakly bending rod or worndike chain model, with persistence length ranging from 200 to 400 Å. The analysis of the field strength dependence of the electric birefringence yields electric polarizability values which increase sharply with the dilution and are not significantly dependent upon the molecular weight. This has been tentatively interpreted on the basis of the theories derived by Oosawa and by Mendel and Van der Touw. The partially flexible model proposed by the latter authors allow to identify the electric polarizability calculated from electro-optical data to the specific dielectric increment measured in the high frequency range; both parameters appear to be molecular weight independent. The electric polarizability obtained from the Kerr effect would be originated in the induced dipoles caused by the delocalization of the bound counterions along rigid subunits whose length seems however to differ from the persistence length.     

On the mechanism of dielectric relaxation in aqueous DNA solutions.

The complex dielectric response of calf thymus DNA in aqueous saline solutions has been measured from 1 MHz to 1 GHz. The results are presented in terms of the relaxation of the incremental contributions to the permittivity and conductivity from the condensed counterions surrounding the DNA molecules. Measurements of the low-frequency conductivity of the samples also lends support to the condensed counterion interpretation.     

Divalent paramagnetic counterions site binding in polyelectrolyte solutions. Analysis of the frequency dependence of the water protons magnetic relaxation and the characteristic parameters of "site binding"

Chemical shift and relaxation time measurements on the water protons in polyelectrolyte solutions containing divalent paramagnetic counterions have shown the existence of three types of counterions: - site bound with loss of water molecules and partial or complete release of the electrostriction in the first hydration sphere, - atmospherically trapped with no change in hydration, - free. The overall stoichiometry of the two former is in agreement with Manning's fraction of condensed counterions. A complete analysis of the frequency dependent contribution of site bound counterions to the water protons relaxation times leads us to interesting conclusions on the modifications of the first hydration shell and on the life time of site binding.     

Allowance for spatial dispersion of dielectric permittivity in polyelectrolyte model of DNA.

In order to allow for real dielectric properties of a solvent in calculating of electrostatic characteristics of strongly charged polyions such as DNA in salt solution we consider a simple model of linear dielectric response of a medium. The interactions between charged particles are treated in the framework of self-consistent-field approximation. The basic characteristic of the problem, electrostatic potential, can be found from the solution of non-linear integro-differential equation. Specifically we consider so-called quasimacroscopic model where dielectric response of a medium depends only on the distance from the polyion. Application of the approach for calculating of the B-to-Z free energy qualitatively retains the main conclusion obtained previously within the model with fixed dielectric constant: non-monotonous behavior of the free energy differences as a function of ionic strength. At the same time, essential sensitivity of the results to specific values of dielectric parameters is observed.     

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.     

Conductometric analysis of the competition between monovalent and divalent counterions in their interaction with polyelectrolytes

A procedure is described for the analysis of the conductivity of solutions of anionic polyelectrolytes in which both mono- and divalent counterions are present. The method is based on analysis of the relation between the overall conductivity of the system and the conductivity of the individual monovalent cations which are only electrostatically (non-specifically) bound. The system is described in terms of the two-state approach, implying that the counterions are considered to be either fully bound to the polyion or completely free. The potentialities of the proposed method are explored by studying solutions of alkali polyacrylates with and without added zinc nitrate at several alkali nitrate concentrations. The results give a picture of the composition of the counterionic atmosphere around the polyion in systems with both mono- and divalent counterions present. To a certain degree, the divalent ion Zn(II) was found to be bound quantitatively by the polyion. The composition of the counterionic atmosphere around the polyion was largely independent of alkali nitrate concentration when the latter was present in not too large an excess with respect to both Zn(II) and the charged monomers.     

Binding of non-intercalating antibiotics to B-DNA: a theoretical study taking into account nucleic acid flexibility

A detailed theoretical study has been made for five antibiotics which all bind selectively to AT sequences in the minor groove of B-DNA: SN-18071, NSC-101327, distamycin-2, distamycin-3 and netropsin. The optimal complexes were found for systems in which the flexibility of DNA, as well as that of the antibiotics, was taken into account. Explicit, mobile counterions and a dielectric function modelling aqueous solution were also included. The binding geometries of the most strongly interacting antibiotics, distamycin-3 and netropsin, are compared in considerable detail and it is shown that notable differences exist between them. The results for netropsin are also discussed in the light of recent disagreements concerning its exact binding location within DNA.     

Transport phenomena and ion binding in solutions of sodium polystyrenesulphonate

The results of transference and conductance measurements on solutions of sodium polystyrenesulpnonate, in the concentration range from 0.0025 to 0.075 monomolar, are presented. The fraction of free Counterions calculated from experimental data is found to he independent of molecular weight of the polyelectrolyte within the range of degree of polymerization from 200 to 2400. The experimental data, combined with the cell model, are used to calculate the electrostatic potential at a cylindrical surface Which surrounds the polyion and divides the counterions into bound and free. The same value for this potential is found for the whole concentration range investigated, which lends support to the assumption of cylindrical distribution of counterions in polyelectrolyte solutions.