Three cases will illustrate how this equation behaves.
In this case [S] + Km = [S] (approximately), so (5) becomes: or:
This is the rate at large substrate concentration, the maximal rate for [E], which is called Vmax.
Substituting into (5) gives the Michaelis-Menten Equation as it is normally shown:
Remember, this equation is derived for Vo, when very little product has formed and the back-reaction can be ignored.
In this case [S] + Km = Km (approximately) so (5) becomes: or:
So, at low [S], Vo is linearly proportional to [S].
Km is defined as the [S] that results in half-maximal rate.