Introduction to Enzyme Kinetics

Introduction to Enzyme Kinetics
Key concepts, definitions, and equations for understanding how enzymes catalyze reactions and how their rates are measured.

1. Basic Terminology

2. The Michaelis‑Menten Model

2.1 Reaction scheme

[ E + S ;\underset{k_{-1}}{\overset{k_{1}}{\rightleftharpoons}}; ES ;\xrightarrow{k_{2}}; E + P ]

• E – free enzyme
• ES – enzyme–substrate complex
• k₁, k₋₁ – association/dissociation rate constants
• k₂ – catalytic rate constant (often called k_cat)

2.2 Derivation assumptions

1. Steady‑state approximation – concentration of ES remains constant after an initial transient.
2. Initial‑rate conditions – product concentration is negligible, so reverse reaction (P → S) can be ignored.
3. Single substrate – only one substrate binds to the enzyme.

2.3 Michaelis‑Menten equation

[ v = \frac{V_{\max},[S]}{K_{M} + [S]} ]

• When ([S] \ll K_M): (v \approx \frac{V_{\max}}{K_M}[S]) (first‑order with respect to S).
• When ([S] \gg K_M): (v \approx V_{\max}) (zero‑order; enzyme saturated).

2.4 Relationship to kinetic constants

[ V_{\max} = k_{cat}[E]_{T} ]

[ K_{M} = \frac{k_{-1}+k_{2}}{k_{1}} ]

• Low (K_M) → high affinity (enzyme reaches half‑V_max at low [S]).
• High (k_{cat}) → fast turnover.

3. Experimental Determination of Kinetic Parameters

3.1 Initial‑rate method

1. Prepare a series of substrate concentrations (typically 5–10 points spanning <0.1 K_M to >10 K_M).

2. Measure initial reaction rates (v₀) under identical enzyme concentration, pH, temperature, and ionic strength.

3. Plot data:

   • Michaelis‑Menten plot (v vs. [S]) – visual fit.
   • Linear transformations for parameter extraction:

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