The dependence of enzymic activity on pH is well known and the simplest reaction schemes that encapsulate this dependence are elaborations of the Michaelis-Menten one. In general, changes come about in Fmax and Km because of changes in one or a combination of the following: (1) ionization of groups in the substrate; (2) ionization of groups involved in binding the substrate; (3) groups involved in catalysis; and (4) ionization of other groups on the enzyme such as effector binding sites.

Because the topic is well described in many books on enzyme kinetics,(4-7) only one illustrative example of a pH effect on a simple enzyme will be given here. This is the simplest of all enzymic-reaction schemes.

If we assume that there are no relevant ionizable groups on E or EA, then the scheme that describes just ionization of the substrate is h k2 A + E EA — E + P.

This is analogous to pure competitive inhibition (Section 2.2.2) and hence the rate equation is

where Ka denotes the acid (hence the subscript a) dissociation constant of the HA+ complex and it is given by

Note that at the start of the reaction

It is also evident that the apparent Michaelis constant, Km, depends on pH, with the protons acting like a competitive inhibitor.

Thus, if the pH is decreased the apparent Michaelis constant will increase because there is a decrease in the concentration of the 'true' substrate, HA+.

Another model of substrate ionization entails the enzyme binding the protonated form of the substrate, then the rate equation is the same as Eqn [3.31] except that

There are seemingly countless possible models of the pH-dependence of MichaelisMenten and more complex enzymic reactions. The book by Roberts'7' is especially good on this topic.

Q: Draw a series of Michaelis-Menten plots for a single-substrate enzyme that has an ionizable substrate with a single pKa of 7.0. Suppose that the forward catalytic breakdown rate constant (see Section 3.2.3) of the enzyme is 1000 s-1, [E]0 = 10-6 M, and Km = 1.0 mM.

A: A consistent enzyme reaction scheme is that given in Eqn [3.30]; and the mathematical function is given by Eqn [3.31].

10-pH

The following parameters are given:

From these we can determine the Fmax and Ka values, K. = 10-pKa ;

and a plot of Eqn [3.31] as a function of substrate concentration from pH 4 - 6.

plotTable = Table[v0 [s] /. pH -> 3.5 + i * 0.5, {i, 5}]; Plot[Evaluate[plotTable], {s, 0, 100 Km}, AxesLabel 0 {" [s] (M) ", "v0 [s] (Ms-1)"}];

Figure 3.5. The effects of pH on the kinetics of a particular enzyme. Note that in moving from the upper to the lower curve the rates are at pH 6, 5.5, 5, 4.5, and 4.

Figure 3.5. The effects of pH on the kinetics of a particular enzyme. Note that in moving from the upper to the lower curve the rates are at pH 6, 5.5, 5, 4.5, and 4.

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