SALT DEPENDENCE OF OLIGOION POLYION BINDING - A THERMODYNAMIC DESCRIPTION BASED ON PREFERENTIAL INTERACTION COEFFICIENTS

The binding of a ligand (such as an oligolysine) to a polyion (such as DNA) in aqueous solution is characterized by K(obs) = C(B)/C(F)C(L), the quotient of molar concentrations of the participants in the complexation equilibrium, L(ZL) + F(ZF) reversible B(ZB). The generally large power dependence of K(obs) on the concentration of salt, C3, is quantified experimentally by evaluating SK(obs) = (partial derivative ln K(obs)/partial derivative ln C3)T,P at constant temperature and pressure. Introducing approximations that can be justified under typical experimental conditions (C3 much greater than CB, CF, CL), we show that SK(obs) = DELTA(\Z(J)\ - 2GAMMA2J3), a stoichiometrically weighted combination of terms pertaining to the participants in the binding reaction (J = F, B, or L). Here GAMMA2J3 = (partial derivative In a2J/partial derivative In a3)T,P,m2J, a3 is the activity of uniunivalent sa It, and a2J (M2J) is the activity (molality) of an electroneutral component, 2J, that consists of an ionic species J, bearing Z(J) charges, and an equivalent number \Z(J)\ of oppositely charged univalent ions. We establish the conditions under which -GAMMA2J3 = GAMMA32J(MC) = (partial derivative C3/partial derivative C2J) T,a3, the form of the preferential interaction coefficient that can be evaluated from a series of grand canonical Monte Carlo (GCMC) simulations at constant T and a3. We also demonstrate the conditions under which -GAMMA2J3 = GAMMA32J = (partial derivative C3/partial derivative C2J)T,mu1,mu3' the preferential interaction coefficient that can be determined by membrane dialysis. For systems that exhibit a linear dependence of In K(obs) on in C3 over a wide range of C3, any salt dependences of the individual GAMMA2J3 must effectively cancel so that DELTA(\Z(J)\ - 2GAMMA2J3) is constant. Various salt-dependent corrections to this expression must be considered when C3 approaches the molar level. The rigorous thermodynamic relationship between SK(obs) and the coefficients GAMMA32J(MC) will enable the use of GCMC simulations to investigate the molecular determinants of the effect of salt on oligoion-polyion binding and on other equilibria involving polyions, including aggregation and conformational transitions.