Coulombic free energy and salt ion association per phosphate of all-atom models of DNA oligomer: dependence on oligomer size.

We investigate how the coulombic Gibbs free energy and salt ion association per phosphate charge of DNA oligomers vary with oligomer size ( number of charged residues ∣∣) at 0.15 M univalent salt by non-linear Poisson Boltzmann (NLPB) analysis of all-atom DNA models. Calculations of these quantities ([Formula: see text], [Formula: see text]) are performed for short and long double-stranded (ds) and single-stranded (ss) DNA oligomers, ranging from 4 to 118 phosphates (ds) and from 2 to 59 phosphates (ss). Behaviors of [Formula: see text] and [Formula: see text] as functions of ∣∣ provide a measure of the range of the coulombic end effect and determine the size of an oligomer at which an interior region with the properties (per charge) of the infinite-length polyelectrolyte first appears. This size (10-11 phosphates at each end for ds DNA and 6-9 for ss DNA at 0.15 M salt) is in close agreement with values obtained previously by Monte Carlo and NLPB calculations for cylindrical models of polyions, and by analysis of binding of oligocations to DNA oligomers. Differences in [Formula: see text] and in [Formula: see text] between ss and ds DNA are used to predict effects of oligomeric size and salt concentration on duplex stability in the vicinity of 0.15 M salt. Results of all-atom calculations are compared with results of less structurally detailed models and with experimental data.