Kinetics of allosteric conformational transition of a macromolecule prior to ligand binding: Analysis of stopped-flow kinetic experiments

Two fundamentally different mechanisms of ligand binding are commonly encountered in biological kinetics. One mechanism is a sequential multistep reaction in which the bimolecular binding step is followed by first-order steps. The other mechanism includes the conformational transition of the macromolecule, before the ligand binding, followed by the ligand binding process to one of the conformational states. In stopped-flow kinetic studies, the reaction mechanism is established by examining the behavior of relaxation times and amplitudes as a function of the reactant concentrations. A major diagnostic tool for detecting the presence of a conformational equilibrium of the macromolecule, before the ligand binding, is the decreasing value of one of the reciprocal relaxation times with the increasing [ligand]. The sequential mechanism cannot generate this behavior for any of the relaxation times. Such dependence is intuitively understood on the basis of approximate expressions for the relaxation times that can be comprehensively derived, using the characteristic equation of the coefficient matrix and polynomial theory. Generally, however, the used approximations may not be fulfilled. On the other hand, the two kinetic mechanisms can always be distinguished, using the approach based on the combined application of pseudo-first-order conditions, with respect to the ligand and the macromolecule. The two experimental conditions differ profoundly in the extent of the effect of the ligand on the protein conformational equilibrium. In a large excess of the ligand, the conformational equilibrium of the macromolecule, before the ligand binding, is strongly affected by the binding process. However, in a large excess of the macromolecule, ligand binding does not perturb the internal equilibrium of the macromolecule. As a result, the normal mode, affected by the conformational transition, is absent in the observed relaxation process. In the case of a sequential mechanism, the number of relaxation times is not altered by different pseudo-first-order conditions. Thus, the approach provides a strong diagnostic criterion for detecting the presence of the conformational transition of the macromolecule and establishing the correct mechanism. Application of this approach is illustrated for the binding of 3′-O-(N-methylantraniloyl)- 5′-diphosphate to the E. coli DnaC protein.