Relationship between enzyme concentration and Michaelis constant in enzyme assays

Abstract

The upper bound of enzyme concentration for accurately estimating the parameters in Michaelis-Menten (MM) equation is not completely determined and still under discussion, even though many researchers have investigated the equation’s validity for a long time. In the paper, we broadly investigated the correlation between the system of ordinary differential equations for monosubstrate irreversible enzyme reaction (HMM-system) and its derivative MM equation focusing on the relationship between initial enzyme concentration [E]0 and Michaelis constant Km by numerical simulation. According to the results, the initial reaction velocity v0 is still a function of initial substrate concentration [S]0 at [E]0<Km. The function is identical to the MM equation at [E]0≦0.01Km, while it is described as a new type of equation at 0.01Km≦[E]0<Km. This function is of great significance in enzyme assays as a comprehensive approximation for the HMM-system.