BIOCHEMISTRY: A TEXTBOOK FOR HIGHER EDUCATION - E. S. Severin - 2004

SECTION 2. ENZYMOLOGY

V. Fundamentals of Enzyme Reaction Kinetics

Enzyme reaction kinetics is a branch of enzymology that investigates how The rate of enzyme-catalyzed Chemical Reactions depends on the Chemical Nature of the reactants and various environmental factors.

To measure the catalytic activity of Enzymes, parameters such as reaction rate or enzyme activity are used. The rate of an enzymatic reaction is determined by The change in the number of substrate or product molecules per unit of time. The reaction rate serves as a measure of the enzyme's catalytic activity and is formally referred to as enzyme activity.

Mathematically, the rate of an enzymatic reaction is expressed as the change in Substrate Concentration (decrease) or product concentration (increase) per unit time:

V = D[S]/t = D[Р]/t.

At the initial stage [0 — t₀], the reaction rate is directly proportional to time, exhibiting a linear relationship. Graphically, the change in the rate of an enzymatic reaction is determined by the slope (tangent of the angle) of the tangent line to the reaction profile curve. The steeper the slope, the greater the change in the reaction rate (Fig. 2-15).

Class="center">Fig. 2-15. Dependence of product accumulation (A) and substrate depletion (B) on the time (duration) of the reaction. The rate of an enzymatic reaction is determined by the change in product or substrate concentration per unit time. In Reactions Catalyzed by enzymes 1 and 2, the initial rate of the reaction catalyzed by enzyme 1 is lower than that catalyzed by enzyme 2. This is because the slope of the tangent to the reaction profile curve drawn from the origin («0») is steeper for the second enzyme, both for product accumulation (A) and substrate depletion (B). The reaction rate at any given time t is determined by the slope of the tangent to the reaction profile at time t. The time interval [t₀ - t₁] of the enzymatic reaction is characterized by a linear accumulation of product (or depletion of substrate) relative to reaction time. The interval [t₁ - t_x] is characterized by non-linear product accumulation (or substrate depletion) over time.

Over time, under experimental conditions, the rate of an enzymatic reaction decreases, as indicated by the reduction in the slope of the tangent line at time point 1. This decline in reaction rate can be caused by several factors: a decrease in substrate concentration, an accumulation of product that may exert an inhibitory effect, changes in solution pH, or Enzyme inactivation, among others.

During the stage [t₁- t_x], the reaction rate changes non-linearly with time. Therefore, to determine the rate of an enzymatic reaction, researchers typically examine the rate change at the initial stage [t₀ - t₁], where a linear change in product (or substrate) concentration is observed.

The rate of an enzymatic reaction depends on numerous factors, including the amount and activity of enzymes, substrate concentration, Temperature, solution pH, and the presence of regulatory molecules (activators and inhibitors). Let us examine METABOLISM/18.html">The Influence of these factors on enzymatic reaction rates.

A. Dependence of enzymatic reaction rate on The amount of enzyme

When an enzymatic reaction is carried out under conditions of substrate excess, the reaction rate depends directly on the Enzyme Concentration. This graphical relationship yields a straight line (Fig. 2-16). However, the absolute amount of an enzyme is often impossible to determine directly; therefore, in practice, conventional units characterizing enzyme activity are used: one International Unit (IU) of activity corresponds to the amount of enzyme that catalyzes The conversion of 1 µmol of substrate per 1 min under optimal reaction conditions. Optimal conditions are specific to each enzyme and depend on the ambient temperature and solution pH in the absence of activators and inhibitors.

Fig. 2-16. Dependence of the enzymatic reaction rate (V) on enzyme concentration.

The number of activity units nIU is calculated using the formula:

In 1973, a new unit of enzyme activity was adopted: 1 katal (kat), which corresponds to the amount of catalyst that converts 1 mol of substrate per 1 s. The number of katals is determined using the formula:

The International Unit of enzymatic activity (IU) is related to the katal by the following equations:

1 kat = 1 mol S/s = 60 mol S/min = 60 х 10⁶ µmol/min = 6 х 10⁷ IU,

1 IU = 1 µmol/min = 1/60 µmol/s = 1/60 µkat = 16.67 nkat.

In medical and pharmaceutical practice, international units (IU) are frequently used to express enzyme activity. To estimate the amount of an enzyme relative to other Proteins within a specific tissue, its specific activity is determined. Specific activity is defined numerically as the number of enzyme activity units (IU) per sample divided by the total protein mass (mg) in that tissue:

Specific activity serves as an indicator of Enzyme Purification: the lower the amount of extraneous proteins, the higher the specific activity.

B. Effect of temperature on the Rate of an Enzymatic Reaction

Raising the temperature up to a certain limit increases the rate of an enzymatic reaction, much like its effect on any chemical reaction. Higher temperatures accelerate molecular motion, thereby increasing the likelihood of productive collisions between reacting molecules. Furthermore, temperature can increase the kinetic energy of the reactants, further accelerating the reaction. However, enzyme-catalyzed reactions possess a distinct temperature optimum. Exceeding this optimum leads to a decline in enzymatic activity due to the thermal Denaturation of the protein molecule (Fig. 2-17).

Fig. 2-17. Dependence of the enzymatic reaction rate (V) on temperature.

For most human enzymes, the optimal temperature ranges from 37 to 38 °C. However, thermostable enzymes do exist in nature. For example, Taq polymerase, isolated from microorganisms living in hot springs, does not lose activity even when heated up to 95 °C. This enzyme is widely used in biomedical research and Molecular Diagnostics employing the Polymerase Chain Reaction (PCR).

C. Effect of Medium pH on the Rate of an Enzymatic Reaction

Enzyme activity depends heavily on the pH of the solution in which the reaction takes place. Every enzyme has a specific pH value at which its activity reaches a maximum; any deviation from this optimal pH results in decreased activity.

The Effect of pH on enzyme activity is primarily related to the ionization state of the functional groups within amino acid residues that maintain the optimal conformation of the Active Site. Altering the pH away from the optimum changes The ionization of these protein functional groups. For instance, acidification leads to the protonation of free amino groups (NH₃⁺), whereas alkalinization causes the dissociation of protons from carboxyl groups (СОО^-). This alters the conformation of both the enzyme molecule and its active site, thereby disrupting the binding of substrates, Cofactors, and Coenzymes. Additionally, medium pH can affect the ionization state or spatial arrangement of the substrate itself, which further influences its affinity for the active site. Extreme deviations from the optimal pH can cause complete denaturation of the protein molecule and total loss of enzymatic activity.

The pH optimum varies significantly among different enzymes (Fig. 2-18). Enzymes operating in acidic environments (such as Pepsin in The Stomach or lysosomal enzymes) have evolutionarily acquired Conformations that ensure high activity at low pH. Nonetheless, the majority of human enzymes function best at a pH close to neutrality, matching physiological pH (Table 2-1).

Table 2-1. Optimal pH values for selected enzymes

Fig. 2-18. Dependence of the enzymatic reaction rate (V) on medium pH.

D. Dependence of the Enzymatic Reaction Rate on Substrate Concentration

If the enzyme concentration is kept constant while the amount of substrate is varied, the resulting rate curve of the enzymatic reaction follows a hyperbola (Fig. 2-19).

Fig. 2-19. Dependence of the reaction rate (V) on substrate concentration S. V_mах — maximum reaction rate at a given enzyme concentration under optimal reaction conditions. K_m — Michaelis constant.

As the substrate concentration increases, the initial reaction rate rises. Once the enzyme becomes fully saturated with the substrate—meaning the maximum possible amount of enzyme-substrate complexes is formed for that enzyme concentration—the rate of product formation reaches its peak. Further increases in substrate concentration do not result in higher product formation, meaning the reaction rate plateaus. This state corresponds to the maximum velocity, V_mах.

Thus, enzyme concentration acts as a rate-limiting factor in product formation. This observation formed the foundation of enzyme kinetics, developed by Leonor Michaelis and Maud Menten in 1913.

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 (dissociation of the enzyme-substrate complex); and 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 K_m.

The reaction rate is proportional to the concentration of the enzyme-substrate complex ES, while the rate of ES formation depends on the concentrations of both the substrate and the free enzyme. The concentration of ES is determined by its rates of formation and breakdown.

The maximum reaction rate is observed when all enzyme molecules are bound to the substrate—that is, entirely in the enzyme-substrate complex ES, meaning [E] = [ES].

The dependence of the enzymatic 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.

When the reaction rate is equal to half of the maximum velocity, K_m = [S] (Fig. 2-19). Thus, the Michaelis constant is numerically equal to the substrate concentration at which half of the maximum velocity is achieved.

The Michaelis-Menten equation is the fundamental equation of enzyme kinetics, describing how the rate of an enzymatic reaction depends on substrate concentration.

If the substrate concentration is significantly greater than K_m ([S] » K_m), an increase in substrate concentration by K_m has virtually no effect on the sum (K_m + S), which can then be considered approximately equal to the substrate concentration. Consequently, the reaction rate approaches the maximum velocity: V = Vm_ах. Under these conditions, the reaction is zero-order, meaning it is independent of substrate concentration. It follows that Vm_ах is a constant for a given enzyme concentration and does not depend on substrate concentration.

If the substrate concentration is much lower than K_m ([S] « K_m), the sum (K_m + S) is roughly equal to K_m; therefore, V = V_mах[S]/K_m, which means that in this case the reaction rate is directly proportional to the substrate concentration (first-order reaction).

V_mах and K_m are kinetic parameters that measure enzyme efficiency. V_mах reflects the catalytic activity of the enzyme and has the dimensions of an enzymatic reaction rate (mol/L), thereby defining the maximum potential for product formation at a given enzyme concentration under conditions of substrate saturation.

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

Fig. 2-20 illustrates the dependence of the rate of two enzymatic reactions (1 and 2) on substrate concentration. The Michaelis constant of the first enzyme is smaller than that of the second enzyme (K_m1 < K_m2). Consequently, 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 exceeds that of the second.

Fig. 2-20. Effect of varying substrate concentrations on the rate of reactions catalyzed by enzymes 1 and 2.