Electrostatic persistence length of a smoothly bending polyion computed by numerical counterion condensation theory

Using numerical counterion condensation theory, we compute the electrostatic component of the persistence length of DNA for three models. In the line model, the phosphate charges are represented as points uniformly distributed on a line of zero radius. In the helical model, the phosphates are given the three-dimensional coordinates deduced from X-ray fiber diffraction; the helical model is considered with and without the dielectric saturation effect. For each model, the free energy of bending smoothly to a specified radius of curvature is calculated. All models exhibit strong end effects for finite-length DNA. Our most reliable model is the helical model with dielectric saturation. Persistence lengths calculated for it are linearly correlated, to good numerical approximation, with the inverse concentration of salt. Comparison with experimental data suggests that real thermal bending fluctuations of DNA in solution may not be describable as the smooth length-invariant bending postulated by any of the models.