Enzyme Kinetics as an Approach to Understanding Mechanism:- Kinetic Parameters Are Used to Compare Enzyme Activities

It is important to distinguish between the Michaelis-Menten equation and the specific kinetic mechanism on which it was originally based. The equation describes the kinetic behavior of a great many enzymes, and all en zymes that exhibit a hyperbolic dependence of V₀ on [S] are said to follow Michaelis Menten kinetics. The practical rule that Km=[S] when V₀=1/2 Vmax (Eqn 6–23) holds for all en zymes that follow Michaelis-Menten kinetics. (The most important exceptions to Michaelis-Menten kinetics are the regulatory enzymes, discussed in Section 6.5.) How ever, the Michaelis-Menten equation does not depend on the relatively simple two-step reaction mechanism proposed by Michaelis and Menten (Eqn 6–10). Many enzymes that follow Michaelis-Menten kinetics have quite different reaction mechanisms, and enzymes that catalyze reactions with six or eight identifiable steps of ten exhibit the same steady-state kinetic behavior. Even though Equation 6–23 holds true for many enzymes, both the magnitude and the real meaning of Vmax and Km can differ from one enzyme to the next. This is an important limitation of the steady-state approach to en zyme kinetics. The parameters Vmax and Km can be obtained experimentally for any given enzyme, but by themselves they provide little information about the number, rates, or chemical nature of discrete steps in the reaction. Steady-state kinetics nevertheless is the standard language by which biochemists compare and characterize the catalytic efficiencies of enzymes.

Interpreting V_max and K_m Figure 6–12 shows a simple graphical method for obtaining an approximate value for Km. A more convenient procedure, using a double reciprocal plot, is presented in Box 6–1. The Km can vary greatly from enzyme to enzyme, and even for different substrates of the same enzyme (Table 6–6). The term is sometimes used (often inappropriately) as an indicator of the affinity of an enzyme for its substrate. The actual meaning of Km depends on specific aspects of the reaction mechanism such as the number and relative rates of the individual steps. For reactions with two steps,

When k2 is rate-limiting, k₂<<k_-1 (6–24) k 1 and Km reduces to k_-1/k₁, which is defined as the dissociation constant, Kd, of the ES complex. Where these conditions hold, K_m does represent a measure of the affinity of the enzyme

for its substrate in the ES complex. However, this scenario does not apply for most enzymes. Sometimes k2>>k 1, and then Km=k₂/k₁. In other cases, k₂ and k₁ are comparable and Km remains a more complex function of all three rate constants (Eqn 6–24). The Michaelis-Menten equation and the characteristic saturation behavior of the enzyme still apply, but Km cannot be considered a simple measure of substrate affinity. Even more common are cases in which the reaction goes through several steps after formation of ES; K_m can then become a very complex function of many rate constants. The quantity V_max also varies greatly from one en zyme to the next. If an enzyme reacts by the two-step Michaelis-Menten mechanism, V_max=k₂[Et], where k₂ is rate-limiting. However, the number of reaction steps and the identity of the rate-limiting step(s) can vary from enzyme to enzyme. For example, consider the quite common situation where product release, EP→E P, is rate-limiting. Early in the reaction (when [P] is low), the overall reaction can be described by the scheme

In this case, most of the enzyme is in the EP form at saturation, and Vmax k3[Et]. It is useful to define a more general rate constant, k_cat, to describe the limiting rate of any enzyme-catalyzed reaction at saturation. If the reaction has several steps and one is clearly rate limiting, kcat is equivalent to the rate constant for that limiting step. For the simple reaction of Equation 6–10, k_cat=k₂. For the reaction of Equation 6–25, k_cat=k₃. When several steps are partially rate-limiting, kcat can become a complex function of several of the rate constants that define each individual reaction step. In the Michaelis-Menten equation, k_cat V_max/[Et], and Equation 6–9 becomes

The constant k_cat is a first-order rate constant and hence has units of reciprocal time. It is also called the turnover number. It is equivalent to the number of substrate molecules converted to product in a given unit of time on a single enzyme molecule when the enzyme is saturated with substrate. The turnover numbers of several enzymes are given in Table 6–7.

Comparing Catalytic Mechanisms and Efficiencies The kinetic parameters kcat and Km are generally useful for the study and comparison of different enzymes, whether their reaction mechanisms are simple or complex. Each enzyme has values of k_cat and K_m that reflect the cellular environment, the concentration of substrate normally encountered in vivo by the enzyme, and the chemistry of the reaction being catalyzed. The parameters kcat and K_m also allow us to evaluate the kinetic efficiency of enzymes, but either parameter alone is insufficient for this task. Two enzymes catalyzing different reactions may have the same kcat (turnover number), yet the rates of the uncatalyzed reactions may be different and thus the rate enhancements brought about by the enzymes may differ greatly. Experimentally, the Km for an enzyme tends to be similar to the cellular concentration of its substrate. An enzyme that acts on a substrate present at a very low concentration in the cell usually has a lower Km than an enzyme that acts on a substrate that is more abundant. The best way to compare the catalytic efficiencies of different enzymes or the turnover of different substrates by the same enzyme is to compare the ratio k_cat/K_m for the two reactions. This parameter, sometimes called the specificity constant, is the rate constant for the conversion E+S to E +P. When [S]<< K_m, Equation 6–26 reduces to the form

V0 in this case depends on the concentration of two reactants, [Et] and [S]; therefore, this is a second-order rate equation and the constant kcat/Km is a second-order rate constant with units of M^-1s-¹. There is an upper limit to kcat/Km, imposed by the rate at which E and S can diffuse together in an aqueous solution. This diffusion-controlled limit is 10⁸ to 10⁹ M^-1 s^-1, and many enzymes have a kcat/Km near this range (Table 6–8). Such en zymes are said to have achieved catalytic perfection. Note that different values of kcat and Km can produce the maximum ratio.

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مواضيع ذات صلة

Enzyme Kinetics as an Approach to Understanding Mechanism: -The Relationship between Substrate Concentration and Reaction Rate Can Be Expressed Quantitatively

Enzyme Kinetics as an Approach to Understanding Mechanism: -Substrate Concentration Affects the Rate of Enzyme-Catalyzed Reactions

How Enzymes Work:- Specific Catalytic Groups Contribute to Catalysis

How Enzymes Work:- Binding Energy Contributes to Reaction Specificity and Catalysis

How Enzymes Work:- Weak Interactions between Enzyme and Substrate Are Optimized in the Transition State

Protein Interactions Modulated by Chemical Energy: Actin, Myosin, and Molecular Motors: -Additional Proteins Organize the Thin and Thick Filaments into Ordered Structures

Protein Interactions Modulated by Chemical Energy: Actin, Myosin, and Molecular Motors: - The Major Proteins of Muscle Are Myosin and Actin

Reversible Binding of a Protein to a Ligand: Oxygen-Binding Proteins: -The Antibody-Antigen Interaction Is the Basis for a Variety of Important Analytical Procedures

Reversible Binding of a Protein to a Ligand: Oxygen-Binding Proteins: -Antibodies Bind Tightly and Specifically to Antigen

Complementary Interactions between Proteins and Ligands: The Immune System and Immunoglobulins: -Antibodies Have Two Identical Antigen-Binding Sites

Complementary Interactions between Proteins and Ligands: The Immune System and Immunoglobulins: -Self Is Distinguished from Nonself by the Display of Peptides on Cell Surfaces

Complementary Interactions between Proteins and Ligands: The Immune System and Immunoglobulins: -The Immune Response Features a Specialized Array of Cells and Proteins