The titration curve of alpha-helical poly(L-lysine) with extended side chains in 95% methanol solution at 25 degrees C was studied. The relative free energy between ionized microstates was evaluated as the sum of the potentials of mean force (PMF) between pairs of charged lysine residues. The PMF of the interaction between different lys(+)-lys(+) pairs was calculated within the framework of the continuum electrostatic model by solving the nonlinear Poisson-Boltzmann equation. In a polar solvent with no added salt, the PMFs between the nearest neighbor pairs on an alpha-helix are well screened and, within a factor of 1.3-1.5, are equal to the value of the Coulombic potential obtained by using the dielectric constant of the solvent. The PMFs between lysines on opposite sides of the alpha-helix are weaker than would be predicted from the Coulombic potential alone. The calculated PMF of the lys(+)-lys(+) pair in a polar solution of a 1:1 salt depends strongly on the degree of ionization of the poly(L-lysine); it decreases or relaxes by a factor of 0.5-0.2 as the degree of ionization of poly(L-lysine) increases. This relaxation of the pair PMFs is due to the nonlinear effects of the interaction of the mobile ions with the background electrostatic potential of the charged solute. The nonlinear relaxation factor of the pair PMFs is a function of the net electrical potential near the helix solute and is very important for low and physiological salt concentrations; it facilitates proton binding by highly charged poly(L-lysine) and results in a weak dependence of the free energy of proton binding by poly(L-lysine) on the salt concentration. The calculated PMFs and nonlinear relaxation factors of lys(+)-lys(+) interactions reproduce the experimental titration curve of poly(L-lysine) in a 95% methanol solution that is 0.02 M in a 1:1 salt with an accuracy of 0.2 pH unit.