BIOCHEMISTRY - Textbook - Ostapchenko L. I. - 2012

Chapter 7. ENZYMOLOGY

7.5. Fundamentals of enzyme reaction kinetics

7.5.4. Dependence of enzyme reaction rate on substrate concentration

If the Enzyme Concentration is kept constant while only The amount of substrate is varied, the plot of the enzyme reaction rate describes a hyperbola (Fig. 7.19).

As the amount of substrate increases, the initial rate increases. When the enzyme becomes completely saturated with substrate—meaning The formation of the enzyme-substrate complex is maximized for the given enzyme concentration—the highest rate of product formation is observed. A further increase in Substrate Concentration does not lead to an increase in product formation, i.e., the reaction rate does not rise. This state corresponds to the maximum reaction rate, Vmax. Thus, the enzyme concentration is the limiting factor in product formation. This observation formed The basis of enzyme kinetics developed by Leonor Michaelis and Maud Menten in 1913.

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Fig. 7.19. Dependence of reaction rate on substrate concentration (S).

Vmax is the maximum reaction rate at a given enzyme concentration under optimal reaction conditions; Km is the Michaelis constant

The enzymatic process can be expressed by the following equation:

where k₁ is the rate constant for the Formation of the enzyme-substrate complex; k-₁ is the rate constant for the reverse reaction, the dissociation of the enzyme-substrate complex; k₂ is the rate constant for the formation of the reaction product.

The following ratio of rate constants (k-₁+ k₂)/k₁ is called the Michaelis constant and is denoted as Km. The reaction rate is proportional to the concentration of the enzyme-substrate complex ES, and The rate of ES formation depends on the substrate concentration and the free enzyme concentration. The concentration of ES is influenced by the rates of its formation and dissociation. The maximum reaction rate is observed when all enzyme molecules are bound to the substrate in the enzyme-substrate complex ES, meaning [E] = [ES]. The dependence of the enzyme reaction rate on substrate concentration is expressed by the following equation (the mathematical derivation of this formula can be found in textbooks on enzyme kinetics):

This equation is known as the Michaelis-Menten Equation.

If the reaction rate is equal to half of the maximum, K_m = [S] (Fig. 7.19). Thus, the Michaelis constant is numerically equal to the substrate concentration at which half of the maximum velocity is reached. The Michaelis-Menten equation is the fundamental equation of enzyme kinetics, describing how the enzyme reaction rate depends on substrate concentration.

If the substrate concentration is much greater than K_m (S >> K_m), an increase in substrate concentration by the value of K_m has practically no effect on the sum (K_m + S), which can be considered equal to the substrate concentration. Consequently, the reaction rate becomes equal to the maximum rate: V = V_max. Under these conditions, the reaction is of zero order, meaning it is independent of substrate concentration. It can be concluded that Vmax is a constant value for a given enzyme concentration and does not depend on the substrate concentration.

If the substrate concentration is much lower than K_m (S << K_m), the sum (K_m + S) is approximately equal to Km, and accordingly, V = V_max[S]/K_m; that is, in this case, the reaction rate is directly proportional to the substrate concentration (the reaction is of the first order).

V_max and K_m are kinetic parameters that describe the efficiency of enzyme action.

V_max characterizes the catalytic activity of an enzyme and has the dimension of an enzyme reaction rate in mol/L, thus determining the maximum potential for product formation at a given enzyme concentration and under conditions of substrate saturation.

Km characterizes the affinity of a given enzyme for a specific substrate and is a constant value independent of the enzyme concentration. The smaller the Km, the higher the affinity of the enzyme for the substrate and the higher the initial reaction rate; conversely, the larger the Km, the lower the initial reaction rate and the lower the enzyme's affinity for the substrate.

Fig. 7.20 shows the dependence of the rates of two enzymatic reactions (1 and 2) on substrate concentration. The Michaelis constant of the first enzyme is lower than that of the second enzyme (Km₁ < Km₂). Therefore, the affinity of the first enzyme for the substrate is higher than that of the second, and the initial rate of the reaction catalyzed by the first enzyme is higher compared to the second enzyme.

Fig. 7.20. Effect of different substrate concentrations on the rate of Reactions Catalyzed by Enzymes 1 and 2