Importance of oligoelectrolyte end effects for the thermodynamics of conformational transitions of nucleic acid oligomers: a grand canonical Monte Carlo analysis.

Effects of salt concentration on the stabilities of oligonucleotide helices are analyzed directly in terms of delta gamma N----yN identical to gamma denyN - gamma natN, the difference in the salt-nucleotide phosphate preferential interaction coefficients for the denatured state, having yN phosphate charges, and for the native state, having N phosphate charges (y = 1 for hairpin denaturation and y = 0.5 for dimer denaturation). Previous experimental studies of the denaturation of hairpin oligonucleotides (having 18 less than N less than 44) indicate significant differences between delta gamma N----N and delta gamma infinity, the value determined for the denaturation of the corresponding polynucleotide. These differences are thermodynamic manifestations of the oligoelectrolyte end effect. In contrast, the available data on the denaturation of oligonucleotide dimer helices (N less than or equal to 22) imply that differences between delta gamma infinity and delta gamma N----0.5N, and hence oligoelectrolyte end effects, are small or negligible. To determine the origin of these apparently conflicting implications concerning the importance of oligoelectrolyte end effects, we have calculated the N dependence of gamma N from grand canonical Monte Carlo simulations for an idealized model of the structure and charge distribution of each oligomer conformation. Our calculations are in quantitative agreement with the experimental finding for d(TA) hairpin oligomers that -delta gamma N----N decreases linearly as N-1 increases, and with the extant experimental determinations of delta gamma N----0.5N. These results provide an illustration of how the large electrostatic end effects exhibited by the hairpin denaturation data are masked when delta gamma infinity is compared with values of delta gamma N----0.5N for short dimer helices (N less than or equal to 22). For 0.5N greater than 24, -delta gamma N----0.5N is predicted to be a linear function of N-1 whose slope has the opposite sign from, and is more salt-concentration dependent than, the corresponding slope of -delta gamma N----N as a function of N-1. Our calculations also yield predictions about the N dependences of the individual values of gamma N that can be tested by determining Donnan coefficients from membrane dialysis equilibrium experiments. For long enough hairpin and dimer oligonucleotides (yN greater than or equal to 24), in either native or denatured forms, we predict that the (positive) difference gamma infinity - gamma N increases linearly with increasing N-1. For smaller values of N the difference gamma infinity - gamma N continues to increase with increasing N-1.