5.2 Michaelis-Menten kinetics and inhibition

Enzyme kinetics and inhibition are crucial concepts in understanding how enzymes work. Michaelis-Menten kinetics describe how enzyme reaction rates change with substrate concentration, using key parameters like Vmax and Km to characterize enzyme behavior.

Inhibitors can alter enzyme activity in different ways. Competitive inhibitors fight for the active site, noncompetitive inhibitors bind elsewhere, and uncompetitive inhibitors only attach to enzyme-substrate complexes. These mechanisms affect Vmax and Km differently, helping scientists develop targeted drugs.

Michaelis-Menten Kinetics

Key Parameters

• The Michaelis-Menten equation describes the relationship between the rate of an enzyme-catalyzed reaction and the substrate concentration
• Vmax represents the maximum velocity of the reaction achieved when the enzyme is saturated with substrate
• Km, the Michaelis constant, is the substrate concentration at which the reaction rate is half of Vmax
  • Km measures the enzyme's affinity for the substrate (lower Km indicates higher affinity)
• kcat, the turnover number, represents the maximum number of substrate molecules converted to product per enzyme molecule per unit time
• The catalytic efficiency of an enzyme is determined by the ratio kcat/Km
  • kcat/Km indicates the enzyme's specificity and efficiency (higher ratio implies greater efficiency)

Interpreting Kinetic Data

• The Michaelis-Menten equation: $v = \frac{V_{max}[S]}{K_m + [S]}$
  • v is the reaction velocity, [S] is the substrate concentration
• Plotting reaction velocity (v) against substrate concentration [S] generates a hyperbolic curve
  • The curve approaches Vmax asymptotically at high substrate concentrations
• The Michaelis-Menten equation allows determination of Km and Vmax from experimental data
  • Km is the [S] at which v = 1/2 Vmax
  • Vmax is the maximum velocity reached at saturating substrate concentrations
• The Michaelis-Menten model assumes steady-state conditions and a single substrate binding site per enzyme molecule

Lineweaver-Burk Plots

Linearizing Michaelis-Menten Kinetics

• Lineweaver-Burk plots, also known as double-reciprocal plots, are graphical representations of enzyme kinetics that linearize the Michaelis-Menten equation
• The Lineweaver-Burk equation: $\frac{1}{v} = \frac{K_m}{V_{max}}\frac{1}{[S]} + \frac{1}{V_{max}}$
• Plotting 1/v against 1/[S] generates a straight line with a y-intercept of 1/Vmax and an x-intercept of -1/Km
• The slope of the Lineweaver-Burk plot is equal to Km/Vmax

Applications and Limitations

• Lineweaver-Burk plots can be used to determine the type of inhibition affecting an enzyme by comparing the plots in the presence and absence of an inhibitor
  • Changes in the slope, x-intercept, and y-intercept provide information about the inhibition mechanism
• Lineweaver-Burk plots are useful for analyzing enzyme kinetics data
  • They allow easy determination of Km and Vmax from the intercepts
• However, Lineweaver-Burk plots are sensitive to experimental errors, especially at low substrate concentrations
  • Small errors in v at low [S] can significantly impact the plot due to the double-reciprocal nature

Enzyme Inhibition Types

Competitive Inhibition

• Competitive inhibition occurs when the inhibitor binds to the active site of the enzyme, competing with the substrate
• The inhibitor increases the apparent Km without affecting Vmax
  • Higher [S] is required to reach 1/2 Vmax due to competition between substrate and inhibitor
• In Lineweaver-Burk plots, competitive inhibition shows increased slope and unchanged y-intercept
  • The lines intersect on the y-axis at 1/Vmax
• Examples of competitive inhibitors: succinate dehydrogenase inhibited by malonate, dihydrofolate reductase inhibited by methotrexate

Noncompetitive Inhibition

• Noncompetitive inhibition occurs when the inhibitor binds to an allosteric site on the enzyme, distinct from the active site
• The inhibitor decreases Vmax without changing Km
  • The inhibitor reduces the enzyme's catalytic efficiency without affecting substrate binding
• In Lineweaver-Burk plots, noncompetitive inhibition shows increased slope and decreased y-intercept
  • The lines are parallel, indicating unchanged Km
• Examples of noncompetitive inhibitors: phosphofructokinase inhibited by ATP, acetylcholinesterase inhibited by snake venom fasciculins

Uncompetitive Inhibition

• Uncompetitive inhibition occurs when the inhibitor binds only to the enzyme-substrate complex, not to the free enzyme
• The inhibitor decreases both Vmax and Km
  • Binding of the inhibitor stabilizes the enzyme-substrate complex, reducing catalytic efficiency and apparent Km
• In Lineweaver-Burk plots, uncompetitive inhibition shows decreased slope and decreased y-intercept
  • The lines are parallel to the uninhibited plot but with a lower y-intercept
• Examples of uncompetitive inhibitors: pepsin inhibited by pentapeptides, xanthine oxidase inhibited by allopurinol

Inhibitor Effects on Kinetics

Quantifying Inhibition

• Inhibitors modulate enzyme activity by binding to the enzyme and altering its kinetic properties
• The presence of an inhibitor can change the apparent values of Km and Vmax, depending on the type of inhibition
• The dissociation constant for the enzyme-inhibitor complex (Ki) is a measure of the inhibitor's affinity for the enzyme
  • A lower Ki value indicates a stronger binding affinity and more potent inhibition
• The effects of inhibitors on enzyme kinetics can be quantified by comparing the kinetic parameters (Km, Vmax, and kcat) in the presence and absence of the inhibitor
  • Competitive inhibitors increase apparent Km, noncompetitive inhibitors decrease Vmax, and uncompetitive inhibitors decrease both Km and Vmax

Determining Inhibition Mechanisms

• The mode of inhibition (competitive, noncompetitive, or uncompetitive) can be determined by analyzing the changes in kinetic parameters and the patterns observed in Lineweaver-Burk plots
• Competitive inhibition: increased Km, unchanged Vmax, lines intersect on y-axis in Lineweaver-Burk plot
• Noncompetitive inhibition: unchanged Km, decreased Vmax, parallel lines in Lineweaver-Burk plot
• Uncompetitive inhibition: decreased Km and Vmax, parallel lines with lower y-intercept in Lineweaver-Burk plot
• Understanding the effects of inhibitors on enzyme kinetics is crucial for drug discovery
  • Many pharmaceuticals act as enzyme inhibitors to modulate biological processes (statins as HMG-CoA reductase inhibitors, ACE inhibitors for hypertension treatment)