Interactions of Cationic Ligands and Proteins with Small Nucleic Acids: Analytic Treatment of the Large Coulombic End Effect on Binding Free Energy as a Function of Salt Concentration

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Abstract
For nonspecific binding of oligopeptides and other cationic ligands, including proteins, to nucleic acid oligomers, we develop a model capable of quantifying and predicting the salt concentration dependence of the binding free energy (Δ ) by way of an analytic treatment of the Coulombic end effect (CEE). Ligands, nucleic acids, and their complexes (species j of valence Zj) are modeled as finite lattices with |Zj| charged residues; the CEE is quantified by its characteristic length Ne (specified in charged residues) and its consequences for the free energy and ion association of the oligomer. Expressions are developed for the individual site binding constants Ki as a function of position (site number i) of a bound ligand on a nucleic acid and for the observed binding constant Kobs as an ensemble average of Ki. Analysis of Δ = −RT ln Kobs and SaKobs ≡ (∂ ln Kobs)/(∂ ln a±) for binding of the oligopeptide KWK6 (ZL = +8) to single-stranded (ss) dT(pdT)|ZD| oligomers (dT-mers) where ZD = {−6, −10, −11, −14, −15} in the range 0.1−0.25 M Na+ yields Ne = 9.0 ± 0.8 residues at each end, demonstrating that both KWK6 and the above dT-mers are sufficiently short so that the CEE extends over the entire molecule. The dependences of Kobs and of SaKobs on |ZD| for a given ZL are determined by the difference between 2Ne and the net number of charged residues Q in the complex (Q ≡ |ZD| − ZL). For Q < 2Ne, characteristic of complexes of KWK6 with this set of dT-mers, the distribution of binding free energies Δ = −RT ln Ki for sites along the DNA oligomer is parabolic, and Kobs and SaKobs are strongly dependent on |ZD|. For Q ≥ 2Ne, the distribution of binding free energies Δ is trapezoidal, and the dependence of Kobs and SaKobs on |ZD| is weaker. Application of the model to nonspecific binding of human DNA polymerase β to ssDNA demonstrates the significance of the CEE in determining Kobs and SaKobs of binding of a cationic site on a protein to a DNA oligomer.