Analytical expressions are derived to describe the ionic strength dependence of the electrostatic interaction energy between two macromolecules (proteins). Not only the monopole-monopole interactions are considered but also the monopole-dipole interactions are taken into account. The interaction energy is used to calculate the ionic strength dependence of the rate constant of a reaction between two macromolecules. It is found that a complex formation between the reactants can drastically change the ionic strength dependence of the rate constant, especially at low ionic strength. The ionic strength dependence of a diffusion-controlled rate constant is also considered. The ionic strength dependence of the rate constant of a reaction between two macromolecules as derived in this paper is compared with the Debye-Huckel equation and the equation derived by Wherland and Gray (Proc. Natl. Acad. Sci. U.S.A. (1976), 73, 2950–2954). The dipole moments of the reactants can cause an appreciable deviation in the ionic strength dependence. This deviation is strongly dependent on the direction of the dipole moment relative to the active site on the molecule. At ionic strengths higher than 0.1 M the ionic strength dependence of the rate constant is determined mainly by the monopole-dipole interactions. From measurements at I > 0.1 M an estimate of the dipole moment can be made. The theory derived in this paper is applied to the interactions cytochrome c -cytochrome b 5 and cytochrome c -cytochrome c oxidase. If one assumes that the net charge of cytochrome c is +7 ant its dipole moment is 325 debye, then good fits are obtained if the net charge and the dipole moment for cytochrome b 5 are −8 and 570 debye, respectively. The net charge and dipole moment obtained for cytochrome c oxidase are −21 and 2130 debye, respectively. Using these values it is calculated that the dissociation constant between ferricytochrome c -cytochrome c oxidase is K ( I = 0.044 M) = 0.12 μ M and that between ferrocytochrome c - cytochrome c oxidase K ( I = 0.044 M) = 0.33 μ M. These values agree remarkably well with data reported in the literature (0.13 μ M and 0.35 μM). Dissociation constants at other ionic strengths and for other ions are also reported.
