Electrostatic effects on polynucleotide transitions. I. Behavior at neutral pH

An approximate analytical expression for the electrostatic free energy of a polynucleo-tide in any of its possible ordered or random conformations is derived by integration of the screened-Coulomb potential energy function over all charge pairs in the structure. The electrostatic free energy of any form is found to be a linear function of the logarithm of the monovalent counterion concentration, in the range of low salt concentrations. Hence the electrostatic free energy difference between ordered and disordered forms in a polynucleotide structural transition is a linear function of the logarithm of the monovalent counterion concentration. A free energy balance applied to a two-state model for the transition then yields a linear dependence of the transition temperature Tm upon the logarithm of the counterion concentration. Calculation of the quantity dTm/d log M, where M is the monovalent counterion concentration, shows it to be a characteristic constant for a given transition, with a magnitude and sign proportional to the charge density difference between the ordered and disordered forms. Use of any one of several alternate, simple assumptions yields predicted dTm/d log M values in good agreement with experimental data for various polynucleotide transitions.