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 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. 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 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.

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.