Steady State Kinetics for Enzymes with Multiple Binding Sites Upstream of the Catalytic Site

Abstract

The Michaelis–Menten mechanism, which describes the binding of a substrate to an enzyme, is a simplification of the process on a molecular scale. A more detailed model should include the binding of the substrate to precatalytic binding sites (PCBSs) prior to the transition to the catalytic site. Our work shows that the incorporation of PCBSs, in steady-state conditions, generates a Michaelis–Menten-type expression, in which the kinetic parameters KM and Vmax adopt more complex expressions than in the model without PCBSs. The equations governing reaction kinetics can be seen as generalized symmetries, relative to time translation actions over the state space of the underlying chemical system. The study of their structure and defining parameters can be interpreted as looking for invariants associated with these time evolution actions. The expression of KM decreases as the number of PCBSs increases, while Vmax reaches a minimum when the first PCBSs are incorporated into the model. To evaluate the trend of the dynamic behavior of the system, numerical simulations were performed based on schemes with different numbers of PCBSs and six conditions of kinetic constants. From these simulations, with equal kinetic constants for the formation of the Substrate/PCBS complex, it is observed that KM and Vmax are lower than those obtained with the Michaelis–Menten model. For the model with PCBSs, the Vmax reaches a minimum at one PCBS and that value is maintained for all of the systems evaluated. Since KM decreases with the number of PCBSs, the catalytic efficiency increases for enzymes fitting this model. All of these observations are consistent with the general equation obtained. This study allows us to explain, on the basis of the PCBS to KM and Vmax ratios, the effect on enzyme parameters due to mutations far from the catalytic site, at sites involved in the first enzyme/substrate interaction. In addition, it incorporates a new mechanism of enzyme activity regulation that could be fundamental to search for new activity-modulating sites or for the design of mutants with modified enzyme parameters.