## Tuesday, February 19, 2013

### Michaelis-Menten

Two important characteristics of an enzymatic reaction are its Km and its Vmax. The Vmax is a theoretical fastest rate of conversion that can be achieved, while the Km is the concentration of substrate that causes the rate of conversion to be half of Vmax. This is important because it describes a relationship between a transitional state of the enzyme complex, Km = (Vq + Vr) / Vs, where Vq and Vr represent changes from the transitional state to the two final states of the enzyme, and Vs represents the change from the substrate to the transitional state.

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).