Comparison of different approaches for calculation of polyelectrolyte free energy

We consider the problem of the mean field (Poisson-Boltzmann) calculation of the electrostatic free energy for a strongly charged polyelectrolyte such as DNA in a salt solution. We compare two approaches to calculate the free energy: (i) direct one starting from the statistical-mechanical expression for the electrostatic free energy and (ii) the polyion charge variation method. In the infinite dilution limit (in respect to polyion) and in excess salt (IDLES) the two approaches are fully equivalent. This is shown by straight forward algebra. We have performed specific calculations of the free energy difference for the case of B-Z transition in DNA as a function of ionic strength. As expected, the two approaches led to identical results. The ionic strength dependence of the B-to-Z free energy proves to be concaved up and as a result Z-DNA is stabilized at low ionic concentration as well as at high salt, in full agreement with our previous results (M.D.Frank-Kamenetskii et al., J. Biomol. Struct. Dyn. 3, 35-42 (1985]. Our data quantitatively agree with the results of Soumpasis (D.M.Soumpasis, J. Biomol. Struct. Dyn. 6, 563-574 (1988]. However, his claim about the absence of the effect of stabilization of Z-DNA at low salt proves to be groundless, and the criticism of our earlier approach seems to be irrelevant.