Enzyme Kinetics
Enzyme kinetics studies the rate of enzyme-catalyzed reactions and how reaction rate is affected by substrate concentration, inhibitors, pH, and temperature.
Michaelis-Menten Equation
For E + S ⇌ ES → E + P:
v = Vmax × [S] / (Km + [S])
- Vmax: Maximum velocity (when all enzyme molecules are saturated with substrate). Proportional to total enzyme concentration.
- Km (Michaelis constant): [S] at which v = Vmax/2. Approximates substrate affinity. Low Km = High affinity. Numerically = (k₋₁ + k₂) / k₁.
- When [S] << Km: reaction is first-order in [S]. When [S] >> Km: reaction is zero-order (rate ≈ Vmax).
Lineweaver-Burk Plot (Double Reciprocal)
1/v = (Km/Vmax) × (1/[S]) + 1/Vmax. Straight line: slope = Km/Vmax, y-intercept = 1/Vmax, x-intercept = -1/Km. Used to determine type of inhibition.
Enzyme Inhibition
- Competitive Inhibition: Inhibitor structurally similar to substrate; competes for active site. Effect: Km ↑ (apparent), Vmax unchanged. Can be overcome by increasing [S]. Example: Methotrexate (inhibits dihydrofolate reductase competitively). On LB plot: lines intersect on y-axis.
- Non-competitive Inhibition: Inhibitor binds to a site other than active site (can bind E or ES). Effect: Vmax ↓, Km unchanged. Cannot be overcome by ↑[S]. On LB plot: lines intersect on x-axis.
- Uncompetitive Inhibition: Inhibitor binds only to ES complex. Effect: Both Vmax and Km decrease by same factor. On LB plot: parallel lines.
- Irreversible Inhibition: Inhibitor forms covalent bond with enzyme. Examples: Aspirin acetylates COX permanently; Organophosphates inhibit acetylcholinesterase (nerve agents).
Feedback Inhibition
End product of a metabolic pathway inhibits the first committed step (allosteric). Example: CTP inhibits ATCase (first step of pyrimidine synthesis). This is the most common regulatory mechanism in anabolic pathways.
Factors Affecting Enzyme Activity
- Temperature: Rate increases with temperature (Q10 effect) until denaturation occurs. Optimal T ~ body temperature (37°C). High temp denatures enzyme.
- pH: Optimal pH varies by enzyme (pepsin pH 2, trypsin pH 8, most intracellular enzymes pH 7.4). pH affects ionization of active site residues and substrate.
- Substrate concentration: Follows Michaelis-Menten kinetics for most enzymes.
- Allosteric enzymes: Show sigmoidal kinetics (cooperativity) instead of hyperbolic. Hill coefficient (n) > 1 indicates positive cooperativity.
Kcat (Turnover Number)
Number of substrate molecules converted to product per enzyme molecule per second when fully saturated. Catalytic efficiency = kcat/Km. The most efficient enzymes approach the diffusion limit (~10⁸–10⁹ M⁻¹s⁻¹).