Cf. Anderson et Mt. Record, SALT DEPENDENCE OF OLIGOION POLYION BINDING - A THERMODYNAMIC DESCRIPTION BASED ON PREFERENTIAL INTERACTION COEFFICIENTS, Journal of physical chemistry, 97(27), 1993, pp. 7116-7126
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 comple
xation equilibrium, L(ZL) + F(ZF) reversible B(ZB). The generally larg
e power dependence of K(obs) on the concentration of salt, C3, is quan
tified experimentally by evaluating SK(obs) = (partial derivative ln K
(obs)/partial derivative ln C3)T,P at constant temperature and pressur
e. Introducing approximations that can be justified under typical expe
rimental conditions (C3 much greater than CB, CF, CL), we show that SK
(obs) = DELTA(\Z(J)\ - 2GAMMA2J3), a stoichiometrically weighted combi
nation 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, an
d 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 est
ablish the conditions under which -GAMMA2J3 = GAMMA32J(MC) = (partial
derivative C3/partial derivative C2J) T,a3, the form of the preferenti
al interaction coefficient that can be evaluated from a series of gran
d canonical Monte Carlo (GCMC) simulations at constant T and a3. We al
so demonstrate the conditions under which -GAMMA2J3 = GAMMA32J = (part
ial derivative C3/partial derivative C2J)T,mu1,mu3' the preferential i
nteraction coefficient that can be determined by membrane dialysis. Fo
r 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 mu
st effectively cancel so that DELTA(\Z(J)\ - 2GAMMA2J3) is constant. V
arious salt-dependent corrections to this expression must be considere
d when C3 approaches the molar level. The rigorous thermodynamic relat
ionship 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 equilib
ria involving polyions, including aggregation and conformational trans
itions.