We are interested in finding the initial velocity (V0) of the reaction, the rate at which the enzyme can convert a substrate S as soon as the two are mixed together Given the Km and the Vmax, the reaction's V0 can be calculated using the Michaelis-Menten equation: V0 = Vmax * S / ( S+Km). This equation graphs a hyperbolic curve that approaches Vmax as S increases.

This equation takes on interesting characteristics in certain situations. If the concentration of S is much less than Km, S+Km becomes approximately Km, and the formula simplifies to Vmax * S / Km. Conversely, if S is much greater than Km, Km falls from the equation, yielding Vmax * S / S, or Vmax. (Of course, if S = Km, the equation becomes Vmax * S / (S+S), or Vmax / 2, which is the definition of Km).

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