Mechanism:

1. Induced fit model:

   • Enzyme changes shape when substrate binds
   • Active site molds around substrate
   • Forms enzyme-substrate complex
   • Products released, enzyme returns to original shape

2. Enzyme + Substrate ⇌ ES complex → Enzyme + Product

Factors Affecting Enzyme Activity

1. Temperature

• Optimal temperature maximizes activity
• Too low: slow molecular movement
• Too high: denaturation (lose shape)
• Most human enzymes optimal at 37°C

2. pH

• Each enzyme has optimal pH
• Extreme pH denatures enzyme
• Examples:
  • Pepsin (stomach): pH 2
  • Trypsin (intestine): pH 8

3. Substrate Concentration

• Low [S]: activity increases with more substrate
• High [S]: enzyme saturation (plateau)
• Maximum velocity (Vmax) reached

4. Enzyme Concentration

• More enzyme = more activity
• Linear relationship (if substrate abundant)

Enzyme Regulation

Competitive Inhibition

• Inhibitor competes with substrate for active site
• Similar shape to substrate
• Can be overcome by adding more substrate

Noncompetitive Inhibition

• Inhibitor binds to allosteric site (not active site)
• Changes enzyme shape → active site altered
• Cannot be overcome by adding substrate

Allosteric Regulation

• Regulatory molecule binds to allosteric site
• Can be activator or inhibitor
• Changes enzyme shape and activity

Feedback Inhibition

• End product inhibits earlier enzyme in pathway
• Prevents overproduction
• Example: ATP inhibits glycolysis enzymes

Cofactors and Coenzymes

• Cofactors: inorganic helpers (metal ions like Zn²⁺, Fe²⁺)
• Coenzymes: organic helpers (vitamins like NAD⁺, FAD)
• Required for enzyme function

Key Concepts

1. Enzymes lower activation energy but don't change ΔG
2. Active site binds substrate with high specificity
3. Induced fit: enzyme changes shape upon binding
4. Temperature and pH affect enzyme shape and activity
5. Competitive inhibitors block active site
6. Noncompetitive inhibitors change enzyme shape
7. Feedback inhibition regulates metabolic pathways

At high [S]:

• All active sites saturated
• Maximum rate achieved
• Further ↑[S] has no effect
• Zero-order kinetics (rate independent of [S])

Michaelis-Menten Curve:

Velocity (v)
    ^
Vmax|_ _ _ _ _ _ _ _ _ ___________
    |                  /
    |                 /
Vmax|_ _ _ _ _ _ _   /
 2  |             \ /
    |              X  ← Km
    |            / |
    |          /   |
    |        /     |
    |      /       |
    |____/____|____|_____________> [S]
              Km

(b) Definitions:

Vmax (Maximum velocity):

• Rate when enzyme is saturated with substrate
• All active sites occupied
• Cannot go faster (limited by enzyme concentration)
• Units: μmol/min, mM/s, etc.

Km (Michaelis constant):

• Substrate concentration at half-maximal velocity (Vmax/2)
• Measure of affinity:
  • Low Km = high affinity (reaches Vmax quickly)
  • High Km = low affinity (needs more substrate)
• Units: mM, μM, nM

Michaelis-Menten equation:

$v = \frac{V_{max}[S]}{K_m + [S]}$

At [S] = Km: $v = \frac{V_{max} \cdot K_m}{K_m + K_m} = \frac{V_{max}}{2}$

(c) Interpretation of Km values:

Low Km (e.g., 0.01 mM):

• ✓ High affinity for substrate
• Enzyme binds substrate tightly
• Reaches Vmax at low [S]
• Efficient at low substrate concentrations
• Example: Hexokinase for glucose (Km ~ 0.1 mM)
  • Works well even when blood glucose is normal (5 mM)

High Km (e.g., 10 mM):

• ✗ Low affinity for substrate
• Enzyme binds substrate weakly
• Needs high [S] to reach Vmax
• Only efficient when substrate abundant
• Example: Glucokinase in liver (Km ~ 10 mM)
  • Only active when blood glucose is high (after meal)
  • Acts as "glucose sensor"

Comparison:

Physiological significance:

• Hexokinase: active even at low glucose → ensures cells get energy
• Glucokinase: only active at high glucose → liver stores excess as glycogen

$\boxed{\text{Low } K_m = \text{ high affinity; High } K_m = \text{ low affinity}}$

Lineweaver-Burk plot (double reciprocal):

$\frac{1}{v} = \frac{K_m}{V_{max}} \cdot \frac{1}{[S]} + \frac{1}{V_{max}}$

Linearizes data:

• y-intercept = 1/Vmax
• x-intercept = -1/Km
• slope = Km/Vmax