All of the following statements regarding Michaelis-Menten enzyme kinetics are correct EXCEPT:

Explanation

## Analysis of Michaelis-Menten Kinetics Statements ### Correct Statements **Statement 1: Km is independent of enzyme concentration** - Km (Michaelis constant) = (k₋₁ + k₂) / k₁ - This is a ratio of rate constants and does NOT depend on [E] - Km represents the substrate concentration at which v₀ = Vmax/2 - This is a TRUE statement **Statement 2: Vmax is proportional to enzyme concentration** - Vmax = kcat × [E]total - When substrate is saturating (all enzyme active sites occupied), velocity increases linearly with enzyme concentration - This is a TRUE statement **Statement 4: Lineweaver-Burk plot linearizes the equation** - The reciprocal form: 1/v₀ = (Km/Vmax) × (1/[S]) + 1/Vmax - This is a straight line with slope = Km/Vmax and y-intercept = 1/Vmax - This is a TRUE statement ### The INCORRECT Statement **Statement 3: At [S] << Km, reaction follows zero-order kinetics** $$v_0 = \frac{V_{max} \cdot [S]}{K_m + [S]}$$ When [S] << Km: $$v_0 \approx \frac{V_{max} \cdot [S]}{K_m} = \frac{V_{max}}{K_m} \cdot [S]$$ This is **first-order kinetics** (velocity is directly proportional to [S]), NOT zero-order. **Key Point:** At [S] << Km, the reaction is **first-order with respect to substrate**. At [S] >> Km, the reaction becomes zero-order (velocity independent of [S]). **High-Yield:** Remember the kinetic order inversely: - Low [S] relative to Km → first-order (v depends on [S]) - High [S] relative to Km → zero-order (v independent of [S]) ### Summary Table | Condition | Kinetic Order | Velocity Equation | |-----------|---------------|-------------------| | [S] << Km | First-order | v ≈ (Vmax/Km) × [S] | | [S] = Km | Mixed | v = Vmax/2 | | [S] >> Km | Zero-order | v ≈ Vmax | [cite:Lehninger Principles of Biochemistry Ch 6]