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 (i.e. number of charged residues |ZD|) at 0.15 M univalent salt by non-linear Poisson Boltzmann (NLPB) analysis of all-atom DNA models. Calculations of these quantities (Gcoulu, ncoulu) 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 Gcoulu and ncoulu as functions of |ZD| 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 Gcoulu and in ncoulu 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.