Enzyme Catalysis, Inhibition & Carbohydrate Chemistry – Core Vocabulary

Course & Lecture Road-Map

• Mon (current class): finish first half of Chapter 8 (catalysis); begin covalent catalysis.
• Wed: finish protease portion of Ch 8 → start Ch 9 (monosaccharides). • Watch Ch 9 video in advance; in-class will be free-hand, hint-filled, not slide-driven.
• After Ch 9 (structures/memorisation) the course loops back to the kinetics half of Ch 8.
• Target: reach kinetics section before next Wednesday.

Enzyme Catalysis – Core Concepts

• Enzymes = biological catalysts; speed reactions without altering overall ΔG.
• Five canonical catalytic strategies (textbook list):
  1. Proximity, orientation & entropy reduction.
  2. Acid–base catalysis.
  3. Covalent catalysis.
  4. Transition-state stabilisation.
  5. Metal-ion catalysis.
• Serine proteases provide one textbook example that showcases 4 / 5 (all but metal ion).

Acid–Base Catalysis Review

• Amino-acid side-chains act as proton donors/acceptors altering nucleophilicity & leaving-group ability.
• pK_a values inside proteins differ (“PK values are BS in the absolute” – micro-environment dictates activity).

Covalent Catalysis (focus of current lecture)

• Enzyme forms a transient covalent bond with substrate ⇒ alters reaction pathway: more steps, but each lower E_a.
• General scheme (example: lysine ε-amine + substrate carbonyl):
  • Deprotonated Lys acts as nucleophile → tetrahedral intermediate(s) → water elimination → Schiff base (imine).
  • Electronics: C=O ↔ C=N^+ shift makes carbon more electrophilic; stabilises subsequent transition-states vs enolate path.
  • Process must be reversible: water ultimately hydrolyses imine, regenerating enzyme.
• Amino-acid nucleophiles used: deprotonated Ser/Thr/Tyr (alkoxides), Cys (thiolate), Lys (amine), His (imidazolate).

Transition-State Stabilisation Example

• Comparison of uncatalysed enolate transition-state vs imine intermediate: neutral vs anionic; proximity to positive N^+ lowers energy.
• “Many small steps < one large leap” metaphor.

Metal-Ion Catalysis Essentials

• Metal ions participate in binding, redox, charge stabilisation, or water activation.
• Classic triad of metal roles:
  1. Bind substrates/TS (electrostatic attraction).
  2. Undergo redox (Fe, Cu, Mn etc.).
  3. Polarise/ionise water → hydroxide generation.

Carbonic Anhydrase Detailed Mechanism

• Active-site Zn^{2+} coordinated by 3 His + water.
• Zn lowers water pK_a ≈ 7 → OH^– formed.
• Proton removed via “proton wire” (H-bonded water chain) to bulk solvent via His 64 flip.
• OH^– attacks CO₂ giving bicarbonate; product release resets system; rate ≈ 10^6 s^{–1}.

Serine Proteases

Why Important?

• Thousands of papers; every residue mutated & studied.
• Digestive (trypsin, chymotrypsin, elastase), blood clotting, antibodies etc.
• Demonstrate proximity/orientation, TS stabilisation, acid–base & covalent catalysis in one enzyme.

Biological Problem

• Peptide (amide) bonds extremely stable; need cleavage at 37\,^{\circ}\mathrm{C}, pH ≈ 7, and in a selective fashion.
• Proteins must be digested to ≤ tripeptides for absorption.

Specificity Pockets

• Binding in pocket positions exactly one scissile bond adjacent to catalytic triad ⇒ proximity/orientation contribution.

Catalytic Triad (Asp–His–Ser)

• Spatial (not sequence) triad: Asp 102, His 57, Ser 195 (ChT numbering).
• Asp–His share a “strong H-bond” → His partially negative → raised basicity.
• His abstracts Ser OH → Ser O^{–} (alkoxide) nucleophile.
• Convergent evolution: same triad appears in unrelated folds (subtilisin, carboxypeptidase II, etc.).

Mechanistic Cycle (8 steps = 4 × 2 repeat)

1. Substrate binds (selectivity pocket).
2. His acts as base; Ser O^{–} attacks carbonyl → tetrahedral TS.
   • Oxyanion hole (backbone NHs) donates 2 H-bonds → ΔG^{‡}↓.
3. Collapse: His protonates leaving-group N → peptide bond cleaved; C-terminal fragment leaves.
4. Acyl-enzyme (Ser–CO) remains.
5. Water enters; His deprotonates → OH^{–}.
6. OH^{–} attacks acyl carbon → second tetrahedral TS (same oxyanion hole).
7. Collapse: His reprotonates Ser O^{–} → ester bond broken; N-terminal fragment released.
8. Enzyme regenerated; kinetic steps mirror 1–4.

Key Features

• Oxyanion hole = backbone NH of Ser 195 + Gly 193 (ChT) hydrogen-bond exclusively with TS.
• Rate acceleration factors: covalent path, TS-stabilisation, orientation, general acid/base.

Evolutionary Notes

• Triad order varies in sequence (evidence for convergent evolution vs divergent).
• Other serine-hydrolases (β-lactamase, transpeptidase) use same chemistry for different outcomes.

Carbohydrate Chemistry Crash-Course

Linear (Fischer) Forms – Memorisation Tips

• D-Glucose = reference; pattern (C2 R, C3 L, C4 R, C5 R).
• Epimers:
  • D-Mannose = C2 epimer of glucose.
  • D-Galactose = C4 epimer.
• Fructose: identical to glucose from C3 → C6; differs at C1/C2 (ketose).
• Ribose: all OH right (D-form).
• D vs L: look at furthest chiral centre (C5 in hexoses). Mirror image inverts all chiral centres.

Ring (Haworth) Formation

• Intramolecular hemi-acetal/ketal: C5 OH attacks C1 (aldoses) → 6-membered pyranose; C5 OH→C2 (ketoses) → 5-membered furanose.
• Anomeric carbon = new chiral centre (C1 for aldoses, C2 for ketoses).
• Rule of thumb (D-sugars, Haworth):
  • Groups right in Fischer → down in Haworth.
  • Left → up.
• C6 (CH₂OH) points up in all D-pyranoses.

Alpha vs Beta Anomers

• Compare anomeric OH to CH₂OH:
  • Opposite sides = α.
  • Same side = β.
• Mutarotation: interconversion via open-chain form; equilibrium for glucose ≈ 64 % β-D-glucopyranose, 36 % α.

Reducing vs Non-Reducing Sugars

• Reducing sugar: free anomeric OH → can re-open to carbonyl → acts as reducing agent. (E.g.
  all monosaccharides, maltose.)
• Non-reducing sugar: anomeric OH involved in glycosidic bond (O-, N-, S-, or C- type) → locked α/β, no mutarotation.

Glycosidic Bonds & Directionality

• Formed by condensation (loss of H₂O). Name: (α|β)-(donor C #)→(acceptor C #). E.g. maltose = α-1,4.
• Chains written from non-reducing → reducing end.

Disaccharide Examples

• Enzymatic specificity: most human glycosidases hydrolyse α linkages; β-linkages (cellulose) pass through as fibre.

Enzyme Kinetics & Reversible Inhibition

Michaelis–Menten Refresher

v0 = \frac{V{\max}[S]}{K_m + [S]}

• Lineweaver–Burk: \frac1{v0}=\frac{Km}{V{\max}}\,\frac1{[S]}+\frac1{V{\max}}

Competitive Inhibition (I binds free E)

• Scheme: E+I \rightleftharpoons EI \; (K_i)
• Apparent values:
  Km^{app}=\alpha Km \quad ; \quad V{\max}^{app}=V{\max}
  \alpha =1+\frac{[I]}{K_i}
• L–B plot: same y-intercept; x-intercept moves right; steeper slope.
• Examples: malonate vs succinate dehydrogenase; transition-state analogs; bisubstrate analogs occupy two binding sites simultaneously ⇒ potent competitors.

Uncompetitive Inhibition (I binds ES only)

• Scheme: ES+I \rightleftharpoons ESI \; (K_{i}' )
• Apparent: Km^{app}=\frac{Km}{\alpha'} \; ;\; V{\max}^{app}=\frac{V{\max}}{\alpha'}
• Parallel Lineweaver–Burk lines (↑y-int, ↓x-int, same slope).

Mixed / Non-Competitive Inhibition

• Mixed: I binds E and ES (two constants Ki, Ki'). Effects depend on relative values.
• Non-competitive: special case where Ki = Ki'.
  • Result: Km^{app}=Km unchanged, V{\max}^{app}=\frac{V{\max}}{\alpha} decreases.
  • L–B: lines intersect on x-axis (same x-int, ↑y-int).

Irreversible Inhibition & Drug Design

General Principles

• Covalent modification of essential residue → permanent loss of activity.
• Must be highly selective to avoid off-target toxicity.
• Generic electrophiles (e.g. iodoacetamide for Cys) too indiscriminate.

Targeting Catalytic Serines

• Activated serines (within catalytic triad) react with organophosphorus “suicide inhibitors” (e.g. DIFP) → stable phospho-Ser adduct, bulky, cannot be hydrolysed.

TPCK – Chymotrypsin-Specific Irreversible Inhibitor

• TPCK mimics Phe side-chain → enters chymotrypsin pocket.
• Electrophilic chloromethyl-ketone positioned beside His 57. His attacks → covalent alkyl-His adduct; triad disabled.

Penicillin: β-Lactam Suicide Substrate

• Bacterial cell-wall cross-links formed by transpeptidase (Ser-His-Asp triad) between D-Ala–D-Ala & Gly₅.
• Penicillin resembles D-Ala–D-Ala; enzyme performs first half-reaction: Ser attacks β-lactam → acyl-enzyme, ring opens.
• Acyl adduct cannot be resolved (no room for Gly₅ nucleophile) → enzyme trapped, cell-wall synthesis stops.
• Human cells unaffected (no peptidoglycan, extracellular target).

Resistance via β-Lactamase

• Some bacteria encode β-lactamase (also triad enzyme). Mechanism:
  1. Binds β-lactam; Ser attacks and opens ring.
  2. Water (small) accesses active site, hydrolyses acyl-enzyme.
  3. Enzyme regenerated; penicillin destroyed.
• Medical counter-strategy: co-administer β-lactamase inhibitors (clavulanic acid, etc.).

Key Equations & Constants

• Michaelis–Menten: v0 = \frac{V{\max}[S]}{K_m + [S]}
• Lineweaver–Burk: \frac1{v0}=\frac{Km}{V{\max}}\,\frac1{[S]}+\frac1{V{\max}}
• Competitive: v0 = \frac{V{\max}[S]}{\alpha K_m + [S]}
• Uncompetitive: v0 = \frac{V{\max}[S]}{K_m+ [S]}\, \frac1{\alpha'}
• Non-competitive (special mixed): v0 = \frac{V{\max}}{\alpha} \frac{[S]}{K_m + [S]}
• Alpha terms: \alpha = 1+\frac{[I]}{Ki}\; ;\; \alpha' = 1+\frac{[I]}{Ki'}

Practical/Exam-Oriented Reminders

• Be able to draw D-glucose (linear & α/β-pyranose), D-fructose (furanose), ribose, mannose, galactose; identify epimers.
• Recognise reducing vs non-reducing sugars and predict mutarotation.
• For serine protease mechanism you need conceptual narrative, not full arrow-pushing.
• Kinetics plots: know qualitative shifts for each inhibitor class.
• Directionality rules: peptides N→C, nucleic acids 5′→3′, carbohydrates non-reducing→reducing.
• Definitions:
  • Oxyanion hole, catalytic triad, Schiff base, glycosidase, bisubstrate analog, transition-state analog.
• Math: manipulate V{\max} & Km algebraically, recognise slopes/intercepts.

Ethical & Practical Implications

• Drug specificity critical to avoid collateral host damage (irreversible inhibitors).
• Antibiotic resistance (β-lactamase) exemplifies evolutionary pressure; underscores prudent antibiotic use & need for inhibitor combinations.
• Convergent evolution of catalytic motifs illustrates “nature cheats off itself” ⇒ understanding motifs aids bioengineering & drug discovery.