Enzyme Kinetics
High-Yield Summary
- Rate rises with [S] until every active site is occupied (saturation) — rate then plateaus at Vmax, the enzyme's maximum velocity.
- Michaelis-Menten equation: v = (Vmax × [S]) / (Km + [S]) — hyperbolic saturation curve.
- Km = [S] at half-maximal velocity. Low Km → high substrate affinity; high Km → low affinity.
- kcat (turnover number) = substrate molecules converted per enzyme per second at saturation; Vmax = [E] × kcat. kcat/Km = catalytic efficiency, used to compare enzymes.
- Lineweaver-Burk plot (1/v vs. 1/[S]) linearizes the curve: y-intercept = 1/Vmax, x-intercept = −1/Km, slope = Km/Vmax.
- Cooperative enzymes deviate from Michaelis-Menten; Hill coefficient >1 = positive cooperativity, <1 = negative, =1 = none.
Key Terms
- Saturation
- State where every enzyme active site is occupied; rate maxes out.
- Vmax
- Maximum reaction rate, achieved at saturation.
- Km (Michaelis constant)
- Substrate concentration at half-maximal velocity; inverse proxy for affinity.
- kcat (turnover number)
- Substrate molecules converted to product per enzyme molecule per second, at saturation.
- Catalytic efficiency (kcat/Km)
- Combines turnover speed and affinity into one number for comparing enzymes.
- T and R states
- Tense (low-affinity) and Relaxed (high-affinity) conformations in cooperative enzymes.
Michaelis-Menten Equation
v = (Vmax × [S]) / (Km + [S])
- v = Reaction rate
- [S] = Substrate concentration
- Vmax = Maximum rate at saturation
- Km = Substrate concentration at v = Vmax/2
- Setting v = Vmax/2 and solving gives [S] = Km — the defining relationship.
- Low [S] → rate rises sharply with [S]; high [S] → rate plateaus toward Vmax.
kcat, Vmax, and Catalytic Efficiency
Vmax = [E] × kcat → v = (kcat × [E] × [S]) / (Km + [S])
- [E] = Enzyme concentration
- kcat = Turnover number (substrate converted per enzyme per second)
- kcat/Km = Catalytic efficiency
- When Km ≫ [S] (substrate limiting), simplifies to v = (kcat × [E] × [S]) / Km.
- Larger kcat or smaller Km both raise catalytic efficiency. Catalase approaches the diffusion-limited theoretical maximum.
Lineweaver-Burk Plot (Double Reciprocal)
1/v = (Km/Vmax)(1/[S]) + 1/Vmax
- y-intercept = 1/Vmax
- x-intercept = −1/Km
- slope = Km/Vmax
- Linearizes the hyperbolic Michaelis-Menten curve for precise Km/Vmax extraction.
Hill Coefficient Interpretation
| Value | Meaning |
|---|---|
| > 1 | Positive cooperativity — binding one substrate eases further binding |
| < 1 | Negative cooperativity — binding one substrate hinders further binding |
| = 1 | No cooperativity — standard Michaelis-Menten kinetics |
Common MCAT Trap
- Low Km means HIGH affinity (less substrate needed to reach half-max rate) — easy to invert under pressure.
- kcat/Km compares enzymes to each other; Km or kcat alone describes only one enzyme's behavior — don't use one number to imply the whole comparison.
- On Lineweaver-Burk, the x-intercept is −1/Km (negative), not 1/Km.
Quick Recall
What does a low Km indicate about enzyme-substrate affinity?
How is Vmax related to kcat?
What does the y-intercept of a Lineweaver-Burk plot equal?
A Hill coefficient of 2.5 indicates what kind of binding?