Michaelis-Menten Kinetics: The Enzyme-Catalyzed
Hydrolysis of Sucrose1
Background
Of the numerous chemical reactions whose kinetics have been studied, some of the most interesting and complex are those which take place in living organisms. These reactions, when studied under non-biological conditions (lack of organisms and their various biomolecules), are often exceptionally slow: often hours or days, and sometimes even years are required before equilibrium is reached. Yet life requires seconds or even fractions of seconds to produce the same results, and it does this through the use of biological catalysts called enzymes. Enzymes are proteins with special clefts or pockets in their structures in which the reactions occur: the tremendous advantage that enzymes have is that these pockets, by nature of their shape and chemical environment, force the reactants to form transition states much lower in energy than the transitions states the reactants would form under other circumstances, say in solution. Thus, life can subsist at a reasonable pace and it does not take us a week to walk across a room or digest an apple.
Of the many kinetic models for enzymes currently used, the first (and simplest) developed is the Michaelis-Menten Model, developed in 1913 by Leonor Michaelis and
Maud Menten, which is still quite useful today. One of its early triumphs was the successful explanation of the kinetics of sucrase, or β-fructofuranidase, an enzyme found in yeast which cleaves sucrose (common table sugar) into glucose and fructose, and it is this process that will be the focus of our lab.
Theory
The overall reaction catalyzed by sucrase is:
(1)
where S is sucrose, E is the enzyme, and G and F are glucose and fructose, respectively.
The overall rate law for the rate of reaction, r, predicted by the Michaelis-Menten Model is: (2) where [S] is the