Velocity decrease with higher temperature: Further elevation of the temperature causes a decrease in reaction velocity as a result of temperature-induced denaturation of the enzyme (see Fig. 5.7).
The optimum temperature for most human enzymes is between 35°C and 40°C. Human enzymes start to denature (see p. 20) at temperatures above 40°C, but thermophilic bacteria found in hot springs have optimum temperatures of 70°C.
C. pH 1.
pH effect on active site ionization: The concentration of protons ([H+]) affects reaction velocity in several ways. First, the catalytic process usually requires that the enzyme and substrate have specific chemical groups in either an ionized or unionized state in order to interact. For example, catalytic activity may require that an amino group of the enzyme be in the protonated form (−NH3+). Because this group is deprotonated at alkaline pH, the rate of the reaction declines.
2.
pH effect on enzyme denaturation: Extremes of pH can also lead to denaturation of the enzyme, because the structure of the catalytically active protein molecule depends on the ionic character of the amino acid side chains.
3.
Variable pH optimum: The pH at which maximal enzyme activity is achieved is different for different enzymes and often reflects the [H+] at which the enzyme functions in the body. For example, pepsin, a digestive enzyme in the stomach, is maximally active at pH 2, whereas other enzymes, designed to work at neutral pH, are denatured by such an acidic environment (Fig. 5.8).
VI. MICHAELIS-MENTEN KINETICS
Leonor Michaelis and Maude Menten proposed a simple model that accounts for most of the features of many enzyme-catalyzed reactions. In this model, the enzyme reversibly combines with its substrate to form an ES complex that subsequently yields product, regenerating the free enzyme. The reaction model, involving one substrate molecule, is represented below: where S is the substrate. E is the enzyme. ES is the enzyme–substrate complex. P is the product. k1, k−1, and k2 (or, kcat) are rate constants.
A. Michaelis-Menten equation
The Michaelis-Menten equation describes how reaction velocity varies with substrate concentration:
The following assumptions are made in deriving the Michaelis-Menten rate equation.
1.
Enzyme and substrate relative concentrations: The substrate concentration ([S]) is much greater than the concentration of enzyme so that the percentage of total substrate bound by the enzyme at any one time is small.
2.
Steady-state assumption: The concentration of the ES complex does not change with time (the steady-state assumption), that is, the rate of formation of ES is equal to that of the breakdown of ES (to E + S and to E + P). In general, an intermediate in a series of reactions is said to be in steady state when its rate of synthesis is equal to its rate of degradation.
3.
Initial velocity: Initial reaction velocities (vo) are used in the analysis of enzyme reactions. This means that the rate of the reaction is measured as soon as enzyme and substrate are mixed. At that time, the concentration of product is very small, and therefore, the rate of the back reaction from product to substrate can be ignored.
B. Important conclusions 1. Km characteristics: Km, the Michaelis constant, is characteristic of an enzyme and its particular substrate and reflects the affinity of the enzyme for that substrate. Km is numerically equal to the substrate concentration at which the reaction velocity is equal to one half Vmax. Km does not vary with enzyme concentration.
a. Small Km: A numerically small (low) Km reflects a high affinity of the enzyme for substrate, because a low concentration of substrate is needed to half-saturate the enzyme—that is, to reach a velocity that is one half Vmax (Fig. 5.9).