Polarization of Counterions in a Strongly Coupled Coulombic System: DNA

Abstract

Stellwagen, Elias and Eden and Diekmann et al. have used transient electric birefringence and electric dichroism to analyze the characteristics of DNA fragments as a function of salt concentrations and field strengths. At low field strengths, the Kerr law is satisfied, and for short fragments the polarizability is proportional to the square of the length of DNA. Elias and Eden find the polarizability to scale, instead, as the chain length cubed. Diekmann et al. find that for small numbers of base-pairs, the orientation can be explained by an induced dipole moment mechanism, and in low fields, the polarizability goes as L2.3 To describe the orientation data for larger DNA fragments, a constant dipole moment mechanism is needed. Experimental data on the polarization of DNA is usually interpreted via a classic model due to Mandel. In this approach, a DNA is viewed as a charged cylinder with counterions bound to it. The charges come from the phosphate groups only. Electrostatic interactions between the counterions and between the counterions and the negative phosphate charges are assumed negligible. The fluctuations of the bound counterions and the phenomenon of counterion condensation have been taken into account by Oosawa and Manning, respectively. As a result of the external field, the counterions along the contour length of the DNA are not distributed in a homogeneous way. This was implemented based on the assumption that the total number of counterions that are bound to the DNA does not change with variations in the electric field. However, the response of the counterions and the DNA due to the Debye atmosphere was ignored. In both models, the dipole moment is proportional to at low fields. Fixman-Jagannathan analyzed the effects due to the ion atmosphere and the hydrodynamic interactions on the polarizability of short rods. 8 The analysis shows that the polarized counterions lead to relaxation of the Debye atmosphere. 8 By solving a steady state non-linear diffusion equation with an approximate coupling between the Debye atmosphere and the delocalized condensed counterions, Rau and Charney argued that the dipole moment attains a maximum and then decreases with increasing electric field.