Biochemical Engineering Fundamentals, Part 1 - Bailey J., Ollis D. 1989

Kinetics of Enzyme-Catalyzed Reactions
Other Factors Affecting Enzymatic Activity
Effect of pH on the Kinetics of Enzymatic Reactions in Solutions

Figure 2.15 shows the structural formulas of various Amino Acids that make up all Proteins. Since amino acids possess basic, neutral, and acidic groups, an intact enzyme at any given pH can contain both positively and negatively charged groups. Charged groups are often part of the active sites of Enzymes, as many Mechanisms of Enzymatic Catalysis are based on acid- or base-type catalysis. A prerequisite for acid or base catalysis may be the presence of a specific charge on the ionizable groups of the Active Site. It follows that the catalytically active form of the enzyme exists in only one strictly defined ionization state, and depending on the pH, a larger or smaller fraction of the total enzyme present in the mixture can be converted into this form. Figure 3.23 illustrates The Effect of pH on The activity of certain enzymes; it is easy to see that as the pH increases, the catalytic activity of the enzyme reaches a maximum (at the optimum pH) and then declines.

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FIG. 3.23. Dependence of enzyme activity on pH and the range of maximum enzyme activity depending on its nature. (Reproduced with permission from: Fruton J. S., Simmonds S., General Biochemistry, p. 260, John Wiley and Sons, Inc., New York, 1953.)

A useful mathematical expression relating enzyme activity to pH can be derived using the following simple model of active site ionization:

In these acid-base reactions, E^- represents the active form of the enzyme, while E and E^2- represent the inactive forms resulting from the protonation and deprotonation of the active site E^-, respectively. The equilibrium constants for these reactions are designated as K₁ and K₂. We will not consider other ionization states of the enzyme here, as it is assumed that deprotonation of E^- already completely inactivates the enzyme.

By writing the equilibrium conditions for the two ionization steps as

where h⁺ = [Н⁺], we can determine the relative amount of enzyme in the active form. If we denote the total Enzyme Concentration as е₀, so that

е₀ = е + е- + е^2-      (3.62)

then the active fraction of the enzyme у^- is equal to е^-/е₀ and is defined by the equation

Equation (3.63) represents one of Michaelis's pH Functions. The other two, у and у^2-, determine the relative amounts of the enzyme in the acidic and basic forms, respectively.

The dependence of the function у^- on pH is represented by a curve of the same type as those shown in Fig. 3.23 for the experimentally determined pH-Dependence of enzymatic activity. The function у^- has a single maximum at the following pH:

where pK_i =-1 gK_i. The function у^- decreases uniformly and symmetrically as the pH moves away from its optimal value.

Protonation and deprotonation reactions are extremely rapid processes compared to the rates of most other Reactions in Solution. Therefore, the fraction of the enzyme in the active state can be assumed to be equal to у^- even when the enzyme is functioning as a catalyst. It follows that the expression for the maximum reaction rate can be obtained by replacing the total enzyme concentration е₀ with the total concentration of its active form е₀у^-:

Using data on enzymatic activity at various pH values, the parameters K₁ and K₂ can be determined from the latter equation. Indeed, the pH of maximum enzyme activity is related to K₁ and K₂ by equation (3.64). The experimentally determined dependence of enzymatic activity on pH establishes an independent relationship between K₁ and K₂, thus allowing both parameters to be determined.

According to an extended interpretation of the Michaelis–Menten Equation for the simplest enzyme-catalyzed reaction sequence [Equation (3.4)], pH can also affect the Michaelis constant, K_m. However, if the substrate cannot exist in multiple ionized states with different affinities for the enzyme, and if The formation of enzyme-substrate complexes with each enzyme form does not affect K₁ and K₂, then it can be shown that K_m is independent of pH. Experimental data indicate that, as a rule, K_m is very weakly dependent on pH; therefore, in practice, only Equation (3.65) is most commonly used to express the pH dependence of enzyme-catalyzed reaction rates.

It should always be kept in mind that all the above reasoning may fail at pH values significantly far from the optimum. In such situations, the disruption of Forces Stabilizing the conformation of the native protein can lead to its Denaturation, and then, even after restoring the optimal (or near-optimal) pH, rapid reactivation of the enzyme becomes unlikely or even impossible.