An analytical method for determining very high binding constants at equilibrium for reactions requiring an effector is proposed and applied to study the interaction of tetracycline with the repressor of the tetracycline resistance gene from Tn10. In this method complex formation is limited by low concentrations of the effector, which is Mg2+ for the interaction of tetracycline and Tet repressor. The binding of Mg2+ to tetracycline and subsequent formation of the ternary repressor-Mg(2+)-tetracycline complex are coupled reactions yielding a dependence of repressor-tetracycline-Mg2+ complex formation on the concentration of free Mg2+. The binding constants can be determined from the quantitative analysis of ternary complex formation with increasing Mg2+ concentrations. This method allows the determination of very high association constants at equilibrium in a large range of protein concentrations. In the case of repressor and tetracycline, the same affinity constant of 3 +/- 2 x 10(9) M-1 was found in the range of 0.1 to 5 microM of repressor. This result indicates that no association or dissociation of the repressor subunits occurs upon binding of tetracycline. Furthermore, the results show that a repressor dimer binds two effector molecules without significant cooperativity.