The Michaelis–Menten relation: Enzymes are proteins that act as catalysts converting one type of substance, the substrate, into another type. An example of an enzyme is invertase, an enzyme in your body, which converts sucrose into fructose and glucose. Enzymes can act very rapidly; under the right circumstances, a single molecule of an enzyme can convert millions of molecules of the substrate per minute. The Michaelis–Menten relation expresses the initial speed of the reaction as a rational function of the initial concentration of the substrate:
where v is the initial speed of the reaction (in moles per liter per second),s is the initial concentration of the substrate (in moles per liter), and V and Km areconstants that are important measures of the kinetic properties of the enzyme.74 For this exercise, graph the Michaelis–Menten relation giving v as a function of s for two different values of V and of Km.
a. On the basis of your graphs, what is the horizontal asymptote of v?
b. On the basis of your graphs, what value of s makes v(s) = V /2? How is that value related to Km?
c. In practice you don’t know the values of V or Km. Instead, you take measurements and find the graph of v as a function s. Then you use the graph to determine V and Km. If you have the graph, how will that enable you to determine V ? How will that enable you to determine Km?