What is the relationship between Km (Michaelis constant) and the affinity of an enzyme for its substrate?

## Michaelis Constant (Km) and Substrate Affinity ### Definition of Km **Key Point:** Km is defined as the substrate concentration at which the enzyme operates at half its maximum velocity (Vmax/2). It is expressed mathematically as: $$K_m = \frac{k_{-1} + k_2}{k_1}$$ where k₋₁ is the rate of enzyme-substrate complex dissociation, k₂ is the rate of product formation, and k₁ is the rate of ES complex formation. ### Inverse Relationship with Affinity **High-Yield:** The critical relationship is: - **Lower Km** = enzyme binds substrate **more tightly** = **higher affinity** - **Higher Km** = enzyme binds substrate **more loosely** = **lower affinity** This is because Km reflects the dissociation constant of the ES complex. A lower Km means the enzyme-substrate complex is more stable and dissociates less readily, indicating stronger binding. ### Clinical Interpretation **Clinical Pearl:** When comparing two enzymes acting on the same substrate: - Enzyme A: Km = 0.1 mM → binds substrate more tightly - Enzyme B: Km = 10 mM → binds substrate more loosely Enzyme A has greater affinity for the substrate despite a lower Km value. ### Mnemonic **Mnemonic:** **"Low Km = Loves the substrate"** — A low Km value indicates the enzyme "loves" (has high affinity for) its substrate and reaches half-maximal velocity at a lower substrate concentration.