The Michaelis-Menten mechanism for the catalysis of biological chemical reactions is one of the most important chemical reaction mechanisms in biochemistry. (Maud Menten graduated from the University of Toronto, but she was unable to obtain a university position in Canada because of the exclusion of women from Canadian universities at that time. As a consequence she did her work the United States.)

The Michaelis-Menten mechanism for enzyme kinetics is:

. (1)E is the enzyme, S is the "substrate" (the molecule on which the enzyme does its work), and ES is an enzyme-substrate complex. (It is presumed that the substrate must somehow bind to the enzyme before the enzyme can do its work.)

We analyze this mechanism as usual. First, we define the reaction rate as the rate of formation of product and write the kinetic equation implied by this mechanism,

. (2)The enzyme-substrate complex, ES, is a transient species so we set up an equation for its rate of change and apply the steady state approximation,

. (3)Solve for [ES],

, (4)and substitute it into the equation for the rate,

. (5)We might think that we are finished, but there is a complication and some new notation to introduce. First we introduce the Michaelis-Menten constant,

, (6)so that the rate becomes,

. (7)Now we must deal with the difficulty that [E] is the concentration of free (uncomplexed) enzyme and this is usually not known. What is known is the total enzyme concentration, [E]

(8)from which we obtain,

. (9)The rate becomes, then,

(10).

Define the reaction velocity as *v* = Rate. So,

. (11)Note that the reaction velocity,

, (12)then

. (13)Note that the kinetics of the reaction are characterized by two parameters,

In order to deal with experimental data we write,

(14)In an experiment one measures

. (15)

**Enzyme With Inhibitor**

Recall the basic Michaelis-Menten mechanism,

. (1)There are several possibilities for an inhibitor, I, to interfere with this reaction:

. (16)In words, the inhibitor binds with the enzyme to the exclusion of the substrate.

. (17)In words, the inhibitor binds to the enzyme-substrate complex and alters the action of the enzyme on the substrate. You can have 1) or 2) or both. We will only work out the first case. The procedure is the same as for the uninhibited Michaelis-Menten mechanism except for an additional term in the expression for the total enzyme concentration and a new transient, EI. The rate is still

, (18)and we apply the steady state approximation to ES, which leads to

, (19)and the same rate expression

. (20)Use the same definition of

, (21)which leads to,

. (22)But the enzyme-inhibitor complex is also a transient,

. (23)giving

. (24)Now the total enzyme concentration has an extra term

(25a, b)leading to

(26)and the rate is

. (27)

(28)so the reaction velocity becomes

(29)and then

. (30)We still plot 1/

, (31)and

. (32)We must do several different experiments at different [I] to get

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