reactions catalysed per second. The Michaelis–Menten equation describes how the (initial) reaction rate v0 depends on the position of the substrate-binding equilibrium and the rate constant k2. (Michaelis–Menten equation) with the constants This Michaelis–Menten equation is the basis for most single-substrate enzyme kinetics. Two crucial assumptions underlie this equation (apart from the general assumption about the mechanism only involving no intermediate or product inhibition, and there is no allostericity or cooperativity). The first assumption is the so-called quasi-steady-state assumption (or pseudo-steady-state hypothesis), namely that the concentration of the substrate-bound enzyme (and hence also the unbound enzyme) changes much more slowly than those of the product and substrate and thus the change over time of the complex can be set to zero . The second assumption is that the total enzyme concentration does not change over time, thus . A complete derivation can be found here. The Michaelis constant KM is experimentally defined as the concentration at which the rate of the enzyme reaction is half Vmax, which can be verified by substituting [S] = KM into the Michaelis–Menten equation and can also be seen graphically. If the rate-determining enzymatic step is slow compared to substrate dissociation (), the Michaelis constant KM is roughly the dissociation constant KD of the ES complex. If [S] is small compared to then the term and also very little ES complex is formed, thus [E]_{\rm tot} \approx [E]. Therefore, the rate of product formation is Thus the product formation rate depends on the enzyme concentration as well as on the substrate concentration, the equation resembles a bimolecular reaction with a corresponding pseudo-second order rate constant . This constant is a measure of catalytic efficiency. The most efficient enzymes reach a in the range of . These enzymes are so efficient they effectively catalyse a reaction each time they encounter a substrate molecule and have thus reached an upper theoretical limit for efficiency (diffusion limit); and are sometimes referred to as kinetically perfect enzymes. But most enzymes are far from perfect: the average values of and are about and , respectively. Direct use of the Michaelis–Menten equation for time course kinetic analysis The observed velocities predicted by the Michaelis–Menten equation can be used to directly model the time course disappearance of substrate and the production of product through incorporation of the Michaelis–Menten equation into the equation for first order chemical kinetics. This can only be achieved