Dependence of Counterion Binding on DNA Shape as Determined By Counterion Condensation Theory

Electric dichroism transients of aqueous solutions of DNA

In this work we develop a theory of reduced electric linear dichroism transients of DNA fragments in aqueous solution. The DNA fragments are modelled as rigid 'bent-rod molecules' (BRM) with the following physical parameters: electric charge, electric polarizability tensors and hydrodynamical ones, and the average transition probability tensor per molecule. In order to study the growth and decay of electric dichroism transients, the orientational distribution function of the molecules is needed. This function is obtained by solving the time-dependent Fokker-Planck equation in the presence of a low electric field E, using a perturbation method and the Fourier method with time-dependent coefficients. In our calculations the origin of the coordinate system is the mass centre of the BRM. With respect to this centre, the electric dipole moment of the molecule is zero. The developed theory adequately explains the experimental results. We show that the theoretical approach used in this work is equivalent to the one applied in the Brownian dynamics simulation work performed by Porschke and co-workers. We also analyse the effect of a possible electric dipole moment on the transients of the reduced electric linear dichroism in DNA bent fragments.

Counterion condensation and shape within Poisson-Boltzmann theory

An analytical approximation to the nonlinear Poisson-Boltzmann (PB) equation is applied to charged macromolecules that possess one-dimensional symmetry and can be modeled by a plane, infinite cylinder, or sphere. A functional substitution allows the nonlinear PB equation subject to linear boundary conditions to be transformed into an approximate linear (Debye-Hückel-type) equation subject to nonlinear boundary conditions. A simple analytical result for the surface potential of such polyelectrolytes follows, leading to expressions for the amount of condensed (or renormalized) charge and the electrostatic Helmholtz energy for polyelectrolytes. Analytical high-charge/low-salt and low-charge/high-salt limits are shown to be similar to results obtained by others based on PB or counterion condensation theory. Several important general observations concerning polyelectrolytes treated within the context of PB theory can be made including: (1) all charged surfaces display some counterion condensation for finite electrolyte concentration, (2) the effect of surface geometry is described primarily by the sum of the Debye constant and the mean curvature of the surface, (3) two surfaces with the same surface charge density and mean curvature condense approximately identical fractions of counterions, (4) the amount of condensation is not determined by a predefined "condensation distance" although such a distance can be determined uniquely from it, and (5) substantial condensation occurs if the Debye constant of the electrolyte is much less than the mean curvature of a highly charged polyelectrolyte.