Enzymes – Catalysis, Kinetics, Inhibition & Regulation (Comprehensive Notes)

Chymotrypsin Catalysis of Peptide‐Bond Hydrolysis

• Active-site architecture (catalytic triad)
  • Ser195 = nucleophile
  • His57 = general acid/base
  • Asp102 = electrostatic anchor that orients/charges His57
  • Collectively increases the nucleophilicity of Ser O-H.
• Substrate-binding elements
  • "Specificity pocket" accommodates the side-chain N-terminal to the scissile bond (explains preference for large hydrophobics).
  • "Oxyanion hole" donates two NH H-bonds to stabilise negative charge that develops on the tetrahedral intermediate.
• Stepwise mechanism
  1. ES complex – substrate docks non-covalently; His57 abstracts Ser-H → Ser-O⁻ attacks carbonyl C.
  2. First tetrahedral (oxyanion) intermediate – $\text{C}=\text{O}$ becomes $\text{C}^{*}-\text{O}^-$; stabilised in the oxyanion hole.
  3. Acyl-enzyme – collapse expels the C-terminal fragment; N-terminal acyl chain is now ester-linked to Ser195.
  4. Water activation – His57 deprotonates incoming H₂O → OH⁻ attacks the acyl carbon.
  5. Second tetrahedral intermediate – again stabilised by the oxyanion hole.
  6. Product release – collapse frees the N-terminal fragment, regenerating Ser195.
• Chemical principles illustrated
  • Covalent catalysis (transient Ser-acyl bond).
  • General acid–base catalysis (His).
  • Transition-state stabilisation via H-bond network (oxyanion hole).
  • Proximity/orientation effects (specificity pocket positions scissile bond).

Coenzymes, Vitamins & Metals

• Definitions
  • Cofactor = non-protein partner required for activity (metal ion or organic).
  • Coenzyme = organic cofactor that is transiently or permanently bound.
  • "Metalloenzyme" = enzyme containing tightly bound metal ion.
• Vitamin origin
  • Many coenzymes are vitamin derivatives; animals cannot synthesise them at needed rates.
  • Example: NAD⁺ comes from niacin (Vit B₃); deficiency → pellagra.
• Functional roles
  • Redox shuttles (NAD⁺/NADH, FAD/FADH₂).
  • Group-transfer carriers (CoA, biotin, THF).
  • Charge stabilisation Lewis acids (Zn²⁺, Mg²⁺).
• Metal-ion catalysis example (carboxypeptidase A)
  • Zn²⁺ is tetrahedrally bound to 3 residues + a water ligand.
  • Aligns water for nucleophilic attack and stabilises tetrahedral transition state negative charge.

Enzyme Kinetics (Michaelis–Menten)

• Basic scheme: $E + S \xrightleftharpoons[k<em>{-1}]{k</em>1} ES \xrightarrow{k_2} E + P$
• Velocity equation: $V<em>0 = \frac{V</em>{\text{max}}[S]}{[S]+K_M}$
• Parameter meanings
  • $V<em>{\text{max}}$ = maximal rate when all active sites full (units M·s⁻¹). • $K</em>M$ = [S] giving $V<em>0 = \tfrac12 V</em>{\text{max}}$; operational affinity measure (10⁻¹–10⁻⁷ M typical).
  • Analogy to $P_{50}$ for O₂ binding in haemoglobin/myoglobin.
• Limiting cases
  i. $[S] \ll K<em>M$ ⇒ $V</em>0 \propto [S]$ (first-order).
  ii. $[S] = K<em>M$ ⇒ $V</em>0 = \tfrac12 V<em>{\text{max}}$. iii. $[S] \gg K</em>M$ ⇒ $V<em>0 \approx V</em>{\text{max}}$ (zero-order in S).
• Physiological illustration: hexokinase vs glucokinase
  • Hexokinase I ($K<em>M \approx 0.04\,\text{mM}$) is saturated at normal intracellular glucose (2–15 mM); provides constant flux. • Liver glucokinase ($K</em>M \approx 7.5\,\text{mM}$) responds proportionally to blood glucose, suiting glucose buffering role.
• Temperature-sensitive kinetics (Siamese cat)
  • Tyrosinase Gly→Arg mutation lowers Tm – active only in cooler extremities → melanin only in tail, ears, face (pointed pattern).
  • Demonstrates link between kinetic parameters and phenotype; environment modulates enzyme activity.

Enzyme Inhibition

• Competitive
  • I resembles S; competes for active site.
  • Raises apparent $K<em>M$ (weaker binding) but $V</em>{\text{max}}$ unchanged.
  • Examples:
  – Nirmatrelvir in Paxlovid blocks SARS-CoV-2 3C protease.
  – Captopril mimics angiotensin I peptide to inhibit ACE (↓BP).
  – Warfarin mimics vitamin K in clotting factor activation cascade.
• Uncompetitive
  • I binds only ES at separate site; no S resemblance.
  • Lowers both $K<em>M$ and $V</em>{\text{max}}$ (parallel Lineweaver-Burk).
  • Typically observed in multi-substrate reactions.
• Mixed / non-competitive (not deeply covered but implied) – alters both parameters unequally.
• Irreversible
  • Covalent modification of active residues; generally toxic or antibiotic.
  • DFP & sarin phosphorylate Ser in acetylcholinesterase → nerve signal failure.
  • Penicillin acylates Ser in bacterial transpeptidase → weak cell wall; selective toxicity.

Therapeutic Enzymes & Drug Examples

• Enzyme inhibitors as medicines (selected)
  • Amrubicin (topoisomerase II) – anticancer.
  • Celebrex (COX-2) – anti-inflammatory arthritis.
  • Lipitor (HMG-CoA reductase) – cholesterol lowering.
  • Viagra (PDE5) – vasodilation for ED/PAH.
• Enzyme activation for therapy
  • Tissue plasminogen activator (tPA) converts plasminogen → plasmin to dissolve clots.
• Metabolic deprivation strategy
  • Asparaginase (Elspar/Oncaspar) deaminates circulating Asn → Asp; ALL tumour cells starve (cannot synthesize enough Asn) while normal cells compensate.

Cooperative & Allosteric Regulation

• T ⇌ R model analogous to haemoglobin.
  • T = low-affinity, R = high-affinity.
  • Binding of S shifts equilibrium to R (positive cooperativity) producing sigmoidal $v\,vs\,[S]$ curve.
• Quantitative effect
  • At physiological $[S]_c$, velocity is most sensitive to small changes – ideal for metabolic control.
  • Allosteric activators stabilise R → left shift (higher rate).
  • Allosteric inhibitors stabilise T → right shift (lower rate).
• Phosphofructokinase-1 (PFK-1) classic allosteric enzyme controlled by ATP (inhibitor) & AMP/F-2,6-BP (activators).

Cellular Regulation of Enzyme Activity

• 1 Substrate/Product-level control
  • Rate dictated by [substrate]; product inhibition (e.g., glucose-6-P inhibiting hexokinase) self-limits flux.
• 2 Feedback inhibition in pathways
  • End product E inhibits first committed step (enzyme 1) to prevent wasteful accumulation of B, C, D.
  • Provides metabolic cross-talk and homeostasis.
• 3 Gene expression (transcriptional)
  • Metabolite sensors modulate transcription → adjust [enzyme] over minutes-hours.
  • Example: lac operon induction by lactose/IPTG.
• 4 Post-translational covalent modification
  • 4A Reversible phosphorylation: kinase adds $\text{PO}_4^{3-}$ (ATP-driven), phosphatase removes – switches activity on/off (e.g., glycogen phosphorylase).
  • 4B Proteolytic activation of zymogens (irreversible):
  – Digestive enzymes: trypsin, chymotrypsin, elastase synthesised inactive in pancreas → activated in intestine; shielded by pancreatic secretory trypsin inhibitor.
  – Activation cascade (trypsin auto-activation then activates others) amplifies response.
  – Blood-clotting cascade: sequential protease activations; tightly controlled; warfarin inhibits vitamin K cofactor regeneration.

Metabolic Pathway Context & Systems View

• Enzymes function in interconnected networks (Roche metabolic map) covering carbohydrate, lipid, amino acid, nucleotide, steroid, and bacterial pathways.
• Branch points, reversible segments, and shared intermediates necessitate multilayered regulation (substrate, allosteric, covalent, transcriptional).

Ethical, Medical & Practical Implications

• Toxins vs drugs: chemical principles of irreversible inhibition underlie both antibiotics (penicillin) and WMDs (sarin). Regulatory oversight essential.
• Precision medicine: understanding $K_M$ allows tissue-selective drug design (e.g., exploiting glucokinase in liver).
• Nutritional policy: vitamin deficiencies directly impair coenzyme-dependent enzymes — public health interventions (fortification) mitigate.

Key Equations & Numerical Facts (LaTeX syntax)

• Michaelis–Menten: $V<em>0 = \frac{V</em>{\text{max}}[S]}{[S] + K_M}$
• Half-max velocity condition: $[S] = K<em>M \; \Rightarrow \; V</em>0 = \tfrac12 V_{\text{max}}$
• Competitive inhibition apparent constant: $K<em>M^{\text{app}} = K</em>M \left(1 + \frac{[I]}{K_I}\right)$ (not shown in slides but conceptually implied).
• Cooperative Hill equation (qualitative): $v = V<em>{\text{max}} \frac{[S]^n}{K</em>{0.5}^n + [S]^n}$ for n > 1 sigmoidal behaviour.

Summary Checklist

• Catalytic strategies: covalent, acid-base, metal-ion, transition-state stabilisation, proximity/orientation.
• Enzyme kinetics parameters and their physiological/numerical ranges.
• All reversible vs irreversible inhibitor categories plus exemplar drugs/toxins.
• Four major endogenous regulation layers: substrate, feedback/allosteric, gene expression, covalent/proteolytic.
• Clinical/biotechnological applications: drugs, enzyme therapies, phenotype explanations.