Enzyme Kinetics

Lock-and-Key Model (older, simplified): • Enzyme active site is rigid and pre-shaped • Substrate fits perfectly like a key in a lock • No conformational change occurs

Induced Fit Model (current, more accurate): • Active site is flexible and changes shape • Substrate binding INDUCES conformational change • This change:

• Optimally positions catalytic residues
• Strains substrate bonds (lowers activation energy)
• May exclude water from active site
• Increases specificity

Key difference: The induced fit model explains how enzymes actively participate in lowering activation energy through conformational changes, not just providing a rigid binding site.

Example: Hexokinase closes around glucose like a clam shell when glucose binds.

Use Michaelis-Menten equation: V = (Vmax × [S]) / (Km + [S])

(a) [S] = 2 mM = Km V = (100 × 2) / (2 + 2) V = 200 / 4 = 50 μmol/min

When [S] = Km, velocity is exactly half of Vmax!

(b) [S] = 10 mM (5 × Km) V = (100 × 10) / (2 + 10) V = 1000 / 12 = 83.3 μmol/min

At high [S], approaching Vmax (83% of maximum)

(c) [S] = 0.5 mM (0.25 × Km) V = (100 × 0.5) / (2 + 0.5) V = 50 / 2.5 = 20 μmol/min

At low [S], velocity is much lower (20% of maximum)

Pattern: As [S] increases, V approaches but never exceeds Vmax.

COMPETITIVE INHIBITION: Mechanism: • Inhibitor binds to active site • Competes directly with substrate • Can be overcome by increasing [S]

Effect on kinetics: • Km increases (appears to have lower affinity) • Vmax unchanged (can still reach max with enough substrate)

Lineweaver-Burk: • Lines intersect on y-axis (same 1/Vmax) • Different slopes and x-intercepts

Example: Malonate inhibits succinate dehydrogenase

NONCOMPETITIVE INHIBITION: Mechanism: • Inhibitor binds to allosteric site (not active site) • Changes enzyme shape, reducing activity • Cannot be overcome by increasing [S]

Effect on kinetics: • Km unchanged (affinity not affected) • Vmax decreases (fewer functional enzymes)

Lineweaver-Burk: • Lines intersect on x-axis (same -1/Km) • Different slopes and y-intercepts

Example: Heavy metals binding to distant cysteine residues

Key distinction: Competitive can be "outcompeted" by substrate; noncompetitive cannot.

Km (Michaelis constant): • Substrate concentration at which V = ½Vmax • Measure of enzyme-substrate affinity • Units: concentration (M, mM, μM, etc.)

What Km tells us: • LOWER Km = HIGHER affinity (enzyme binds substrate tightly) • HIGHER Km = LOWER affinity (enzyme binds substrate weakly) • Reflects the dissociation constant for ES complex

Comparison: Enzyme A: Km = 0.1 mM → reaches ½Vmax at low [S] Enzyme B: Km = 10 mM → needs high [S] to reach ½Vmax

Enzyme A has HIGHER affinity (100× higher!)

Biological significance: • Enzymes with low Km are efficient at low substrate concentrations • High-affinity enzymes (low Km) are often used when substrate is scarce • Glucose transporters in brain (low Km) vs. liver (high Km)

Analogy: Low Km is like a strong magnet (grabs substrate easily), high Km is like a weak magnet (needs lots of substrate around).

Allosteric Regulation: Mechanism: • Regulatory molecules bind to site OTHER than active site • Binding causes conformational change • Change affects active site shape and activity • Can be positive (activation) or negative (inhibition)

Phosphofructokinase (PFK) Example: PFK catalyzes: Fructose-6-phosphate → Fructose-1,6-bisphosphate (committed step of glycolysis)

NEGATIVE Regulators (inhibitors):

1. ATP (high energy state) • When ATP is abundant, glycolysis slows down • "We have enough energy, stop making more" • Feedback inhibition

2. Citrate (TCA cycle intermediate) • Indicates sufficient biosynthetic precursors • No need for more glycolysis

POSITIVE Regulators (activators):

1. AMP (low energy state) • When ATP is depleted, AMP rises • "We need energy, speed up glycolysis!" • Feedforward activation

2. ADP (also signals low energy) • Similar to AMP effect

Physiological significance: • PFK is the rate-limiting enzyme of glycolysis • Allosteric regulation allows rapid response to energy needs • No transcription/translation required • Energy status directly controls metabolic flux

This is an example of feedback regulation maintaining metabolic homeostasis!