Enzyme Kinetics: Understanding Michaelis-Menten Theory

Enzyme kinetics is the study of the rates of enzyme-catalyzed reactions. The Michaelis-Menten model is the foundation for understanding how enzymes work.

The Michaelis-Menten Equation

The basic model assumes a rapid equilibrium between enzyme (E), substrate (S), and the enzyme-substrate complex (ES):

E + S ⇌ ES → E + P

The Michaelis-Menten equation: v₀ = Vmax[S] / (Km + [S])

Where: - v₀ = initial velocity - Vmax = maximum velocity (when all enzyme is saturated) - [S] = substrate concentration - Km = Michaelis constant (substrate concentration at half Vmax)

Key Parameters

Km (Michaelis Constant) - Lower Km = higher affinity for substrate - Km = [S] when v₀ = Vmax/2 - Independent of enzyme concentration

Vmax - Maximum rate when all enzyme active sites are saturated - Vmax = kcat × [E]total - Depends on enzyme concentration

kcat (Turnover Number) - Number of substrate molecules converted per enzyme per second - Typical range: 1 to 10⁶ s⁻¹

Catalytic Efficiency (kcat/Km) - Combines binding and catalytic steps - Upper limit: diffusion limit (~10⁸-10⁹ M⁻¹s⁻¹) - Enzymes approaching this limit are "catalytically perfect"

Linearization Methods

Lineweaver-Burk Plot (Double Reciprocal) 1/v₀ = (Km/Vmax)(1/[S]) + 1/Vmax

• y-intercept = 1/Vmax
• x-intercept = -1/Km
• slope = Km/Vmax

Enzyme Inhibition

Competitive Inhibition - Inhibitor competes with substrate for active site - Km increases, Vmax unchanged - Overcome by increasing [S]

Non-competitive Inhibition - Inhibitor binds at a different site - Vmax decreases, Km unchanged

Uncompetitive Inhibition - Inhibitor binds only to ES complex - Both Vmax and Km decrease