Enzyme Kinetics and Inhibition: Key Concepts and Mechanisms

Enzyme Kinetics and Inhibition

Significance of KM and kcat

Understanding the parameters KM (Michaelis constant) and kcat (turnover number) is fundamental to enzyme kinetics. These values describe how efficiently an enzyme binds its substrate and converts it to product.

• KM is defined as: $K_M = \frac{k_{-1} + k_2}{k_1}$ where k1 is the rate constant for ES formation, k-1 for ES dissociation, and k2 for product formation.

• KM reflects the affinity of the enzyme for its substrate:

  • Low KM: High affinity (substrate binds tightly), Vmax reached at low [S]

  • High KM: Low affinity (substrate binds weakly), Vmax reached at high [S]

• kcat is the turnover number, representing the number of substrate molecules converted to product per enzyme molecule per unit time when the enzyme is saturated with substrate.

Catalytic Efficiency

The efficiency of an enzyme is often described by the ratio kcat/KM, which combines substrate binding and catalytic turnover.

• Catalytic efficiency: $\text{catalytic efficiency} = \frac{k_{cat}}{K_M}$

• A higher kcat or lower KM indicates a more efficient enzyme.

Enzyme	kcat/KM (M-1s-1)
Acetylcholinesterase	1.6 × 108
Carbonic anhydrase	1.5 × 108
Catalase	4.0 × 107
Superoxide dismutase	1.0 × 109

Additional info: These values approach the diffusion-controlled limit, meaning the enzyme is as efficient as physically possible.

Catalytically Perfect Enzymes

Some enzymes achieve catalytic efficiencies so high that the rate of product formation is limited only by the rate at which substrate encounters the enzyme (diffusion limit).

• If kcat ≫ k-1, then the rate of ES formation determines overall efficiency.

• The maximum possible rate is set by the rate of diffusion (108–109 M-1s-1).

• Further increases in rate can only be achieved by mechanisms such as substrate channeling or multienzyme complexes.

Michaelis-Menten Kinetics and Double-Reciprocal Transformation

The Michaelis-Menten equation describes the relationship between substrate concentration and reaction velocity for many enzymes:

• $V_0 = \frac{V_{max}[S]}{K_M + [S]}$

• Vmax: Maximum velocity at saturating substrate concentration

• KM: Substrate concentration at which velocity is half-maximal

To linearize the data, the double-reciprocal (Lineweaver-Burk) plot is used:

• Take the reciprocal of both sides: $\frac{1}{V_0} = \frac{K_M}{V_{max}[S]} + \frac{1}{V_{max}}$

• Plotting 1/V0 vs. 1/[S] yields a straight line:

  • Slope = KM/Vmax

  • Y-intercept = 1/Vmax

  • X-intercept = -1/KM

Allosteric Enzymes

Allosteric enzymes regulate activity through conformational changes induced by effector molecules. They do not follow Michaelis-Menten kinetics and typically display sigmoidal (S-shaped) velocity vs. substrate concentration curves.

• Allosteric regulation allows for fine control of metabolic pathways.

• Cooperativity among subunits leads to the sigmoidal response.

Enzyme Inhibition

Enzyme inhibitors are molecules that decrease enzyme activity. Reversible inhibitors can be classified as competitive, noncompetitive, or uncompetitive, each affecting kinetic parameters differently.

Types of Reversible Inhibition

Type	KM	Vmax	Mechanism
Competitive	Increases	Unchanged	Inhibitor binds active site, blocks substrate
Noncompetitive	Unchanged	Decreases	Inhibitor binds elsewhere, affects catalysis
Uncompetitive	Decreases	Decreases	Inhibitor binds only ES complex

• Competitive inhibition: Increases KM (decreases affinity), Vmax unchanged. Example: Methotrexate inhibits dihydrofolate reductase by mimicking dihydrofolate.

• Noncompetitive inhibition: Lowers Vmax, KM unchanged. Inhibitor binds to enzyme or ES complex at a site other than the active site.

• Uncompetitive inhibition: Both Vmax and KM decrease by similar amounts. Inhibitor binds only to the ES complex.

Lineweaver-Burk plots are useful for distinguishing inhibition types by their effects on slope and intercepts.