Enzyme-Catalyzed Reactions and the Michaelis-Menten Kinetics

Most of the metabolic reactions in living organisms would not proceed at a physiologically reasonable rate if specific enzymes which act as catalysts were not present. Enzymes are special protein molecules, i.e., biopolymers with amino acids as monomeric units of a polypeptide chain and with a molecular weight of the order up to 10. Since there are 20 different amino acids, a tremendous number of different proteins could be formed among which, however, only a very small fraction is stable and biologically meaningful. For the purpose of this book, we need not go into the details of protein chemistry which may be found in any textbook of biochemistry. 

The next step in the development of our simple model is an ansatz for the reaction rates J2 in terms of the concentrations of the chemical species involved in these reactions  

Let us now study the steady state properties of our reaction system. To this purpose, we consider the concentrations of substrate S and product P as kept fixed by some appropriate transport process. The steady state is then defined as a state where all time derivatives vanish. We expect that such a state will be achieved for t — 00 provided that all parameters are kept constant. From (2.2) we see that the steady state in our system implies = 3 2, the bar indicating the steady state condition. Inserting the ansatz (2.4) we obtain 

For an application of (2.6) to enzyme experiments, one usually assumes P 0, which means an elimination of P from the reaction by a very fast transport process, or k2 0, which means that the binding site of the enzyme has a high attractivity only to the substrate S but not to the product P. With this assumption, the plot of T versus S has the form given in Fig. 1 (Michaelis-Menten kinetics) 

For high values of S, the reaction rate T shows saturation. A comparison of the experimental plot of 1 versus S allows a determination of the rate constants. 

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Enzyme-Catalyzed Reactions and the Michaelis-Menten Kinetics... 

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