The Significance of Cooperative Interactions in Biochemical Control Systems
In classical enzyme kinetics a hyperbolic relationship between the initial rate and the initial substrate concentration does not depend upon whether or not the rate of turnover of the enzyme-substrate compound is slow compared to the reverse of the enzyme and substrate binding reaction. However, in enzyme mechanisms involving ternary or higher order compounds it is sometimes possible to obtain non-hyperbolic relationships only if the type of quasi-equilibrium described above is not maintained. We examined the effect on the sigmoidal relationship expected from the classical “allosteric” model when the context is an enzyme that turns over rapidly (rather than a protein that simply binds a ligand). The results indicate that the sigmoidal shape of the relationship between the initial rate and the initial substrate concentration can be destroyed under certain general circumstances: 1) If the rate of turnover of the enzyme-substrate compounds formed from the favored form of the free enzyme is less than the rate of turnover of the other enzyme compounds, a hyperbolic relationship (with slight or no substrate inhibition) rather than a sigmoidal relationship can result whether or not quasi-equilibrium is maintained. 2) If the rate of the reverse of the enzyme and the substrate binding reactions for the favored form of the enzyme is considerably faster than the rate of the reverse binding reaction for the other form of the enzyme, a hyperbolic rather than a sigmoidal relationship can result provided quasi-equilibrium is not maintained.