Validity of quasi-steady-state and transfer-function representations for input-output relation in a Michaelis-Menten...

In relation to the input-output characteristics of enzymatic reactions in the cellular metabolism and biochemical reactors, the validity of the quasi-steady-state and transfer-function representations of reaction velocity has been examined for a basic Michaelis-Menten reaction employing computer simulation, that is, numerical integration of the rate equation. The well-known S-v relationship (relationship between substrate concentration and reaction velocity)derived on the quasi-steady-state assumption is found to be in general a good approximation to the actual velocity throughout the temporal progress of the reaction. The validity of the approximation depends on a ratio of the Michaelis constant to the total enzyme concentration in the reaction system rather than on the individual rate constants. A transfer-function representation is derived on assuming an exponential change in the reaction velocity for the indicial response to the substrate influx rate. The representation has a wider valid region with a decrease in influx rate than with an increase in the influx rate. The validity is most dependent on a ratio of total enzyme concentration to the steady-state concentration of the substrate. The analysis of the linear sensitivity of the reaction velocity to rate constants reveals that the characteristics of these valid representations in systems analysis change according to the phase of the reaction.