## Vmax and Km: Kinetic Parameters Defined ### Vmax (Maximum Velocity) **Key Point:** Vmax is the maximum reaction velocity achieved when all enzyme active sites are saturated with substrate ([S] >> Km). **High-Yield:** Vmax is **directly proportional to total enzyme concentration** [E]₀: $$V_{max} = k_{cat} \cdot [E]_0$$ where k_cat is the turnover number (catalytic constant). ### Km (Michaelis Constant) **Key Point:** Km is the substrate concentration at which V₀ = Vmax/2. It is derived from the rate constants of enzyme-substrate binding and dissociation: $$Km = \frac{k_{-1} + k_2}{k_1}$$ **High-Yield:** Km is **independent of enzyme concentration**. It reflects the intrinsic affinity of the enzyme for its substrate and is a property of the enzyme-substrate pair, not the amount of enzyme present. ## Comparison Table | Parameter | Depends on [E]₀? | Depends on [S]? | Biological Meaning | | --- | --- | --- | --- | | **Vmax** | Yes (directly proportional) | No | Catalytic capacity | | **Km** | No | No | Substrate affinity | | **Kcat** | No | No | Turnover rate per enzyme | ## Clinical Pearl **Clinical Pearl:** In enzyme assays, doubling the enzyme concentration doubles Vmax but leaves Km unchanged. This principle is used to diagnose enzyme deficiencies—reduced Vmax with normal Km indicates reduced enzyme amount; altered Km suggests a mutant enzyme with changed substrate affinity.
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