Enzymes as Catalysts II – Comprehensive Study Notes

Page 1: Introduction & Context

• Lecture: “Enzymes as Catalysts II” by Amy M. Hicks, PhD, MPH (Biochemistry Course Director, VCOM-Carolinas).

• Reading assignment: Lieberman & Peet, Chapter 9.

• Continuation of foundational enzyme principles; bridges prior lecture (Enzymes I: catalytic mechanism/transition-state stabilization) with regulation and clinical relevance.

Page 2: Full List of Lecture Objectives

1. Single-substrate reaction terminology
   • Recognize symbols $E,\;S,\;E\cdot S,\;P$ and rate constants $k<em>1,k</em>2,k<em>3,k</em>4$.

2. Multi-substrate reaction terminology (A & B ➝ C & D; intermediate $EAB$).

3. Define rate-limiting step (RLS) and identify it (usually product formation).

4. Recall catalytic rate constant $k_{cat}$ and its meaning at saturation.

5. Recall & dissect the Michaelis–Menten (MM) equation.

6. Interpret MM hyperbolic plot of $v$ vs $[S]$.

7. Predict velocity when $[S]\gg K<em>M$, $[S]=K</em>M$, $[S]\ll K_M$.

8. When $K<em>M\approx K</em>D$, use it as an affinity metric.

9. Compare hexokinase vs glucokinase (affinity vs tissue glucose availability).

10. Use Lineweaver–Burk to extract $K<em>M$ & $V</em>{max}$.

11. Contrast reversible vs irreversible inhibition.

12. Detail competitive vs non-competitive inhibition (effects on $K<em>M$ & $V</em>{max}$).

13. Distinguish mechanism-based (suicide) vs non-covalent irreversible inhibition.

Page 3: Why Medical Students Must Master Kinetics

• Kinetics links enzyme structure/function to regulation.

• Underpins homeostasis during:
  • Varied energy demand/ATP status.
  • Environmental/physiologic changes.

• Essential for understanding disease mechanisms & pharmacology (drug-enzyme interactions).

Page 4: Single-Substrate Reaction Scheme & Principles

$E + S \;\overset{k<em>1}{\underset{k</em>2}{\rightleftharpoons}}\;E\cdot S\;\overset{k<em>3}{\underset{k</em>4}{\rightleftharpoons}}\;E + P$
Key points

• Cellular [E] ≪ [S] ⇒ when substrate abundant, rate dictated by enzyme concentration.

• E·S is a reversible, non-covalent complex.

• Product release (step $k_3$ ➝ $E+P$) is commonly RLS.

Page 5: Practical Velocity Facts & $k_{cat}$

Assuming low intracellular $[P]$ → back reaction (rate $k_4$) negligible.

• Instantaneous velocity: $v = k_3[E\cdot S]$.

• Under saturation (all E bound): $k<em>3 = k</em>{cat}$ (turnover number).

• Relationship: $V<em>{max} = k</em>{cat}[E]_{total}$.

Page 6: Derivation & Meaning of Michaelis–Menten Equation

Classical form
$v = \frac{V<em>{max}[S]}{K</em>M + [S]}$
with
$V<em>{max} = k</em>3[E]<em>{total}$ $K</em>M = \frac{k<em>2 + k</em>3}{k_1}$
Interpretations

• $V_{max}$: theoretical max rate (100 % active sites occupied).

• $K<em>M$: composite constant. If $k</em>3$ small relative to $k<em>2$, then $K</em>M\approx\frac{k<em>2}{k</em>1}=K_D$ (true dissociation constant) ⇒ inverse affinity metric.

Page 7: Hyperbolic MM Plot

• Shape: rectangular hyperbola (substrate saturation curve).
  • $v→V<em>{max}$ as $[S]→∞$. • $K</em>M=[S]$ at which $v=\tfrac12 V_{max}$.
  Clinical/experimental utility: reveals affinity & catalytic capacity visually.

Page 8: Using the MM Equation Under Three [S] Regimes

1. $[S]\gg K<em>M$ → $v\approx V</em>{max}$ (enzyme saturated; independent of [S]).

2. $[S]=K<em>M$ → $v=\tfrac12 V</em>{max}$.

3. $[S]\ll K<em>M$ → $v=\frac{V</em>{max}[S]}{K_M}$ (first-order; velocity proportional to [S]).
   Cells exploit these regimes to fine-tune metabolic flux.

Page 9: Interpreting $K_M$ as Affinity

• Most enzymes: rapid binding (large $k<em>1$), slow chemistry (small $k</em>3$), moderate dissociation (small $k<em>2$) ⇒ $k</em>3$ negligible.
  Thus $K<em>M≈K</em>D$; lower $K_M$ ⇒ higher substrate affinity.

• Diagrammatic recap:
  $E+S\overset{k<em>1}{→}E\cdot S\overset{k</em>2}{→}E+S$ (dissociation)
  $K<em>D=\tfrac{k</em>2}{k_1}$.

Page 10: Physiologic Example—Hexokinase vs Glucokinase

Reaction: $\text{Glucose}+\text{ATP} \rightleftharpoons \text{Glucose-6-P}+\text{ADP}$.

• Hexokinase (brain, most tissues)
  • $K_M≈0.1\,\text{mM}$ → high affinity.
  • Ensures phosphorylation even at low circulating glucose; brain priority.

• Glucokinase (liver, β-cells)
  • $K_M≈10\,\text{mM}$ → low affinity.
  • Acts as glucose sensor; only active when portal glucose high, avoiding futile trapping when supply limited.
  Implication: Tissue-specific isozyme differences align with nutrient availability & physiologic role.

Page 11: Lineweaver–Burk (Double-Reciprocal) Transformation

Equation: $\frac{1}{v}=\frac{K<em>M}{V</em>{max}}\cdot\frac{1}{[S]}+\frac{1}{V<em>{max}}$ • Straight-line form $y=mx+b$ with: – Slope $m=\tfrac{K</em>M}{V<em>{max}}$. – $y$-intercept $b=\tfrac{1}{V</em>{max}}$.
– $x$-intercept $=-\tfrac{1}{K_M}$.
Applications

• Experimentally derive $K<em>M$, $V</em>{max}$ with minimal data.

• Diagnose inhibition mechanisms by pattern shifts (see Pages 16-17).

Page 12: Multi-Substrate (Bi-Bi) Reactions Framework

General scheme: $E+A+B \rightleftharpoons EAB \rightarrow ECD \rightleftharpoons E+C+D$.
Example: Hexo/glucokinase with glucose & ATP.
Kinetic insights

• Both substrates required → absence of either blocks flux.

• At constant high [A], velocity increases with [B] (and vice-versa).
  • Hyperbolic dependence on each substrate when the other is saturating.

Page 13: Lineweaver–Burk with Multiple Substrates

• Because binding sites overlap, reciprocal plots taken at varying [A] with fixed [B] (or vice versa) reveal intersecting lines; patterns help deduce ordered-vs-random binding & sequential-vs-ping-pong mechanisms.

Page 14: Enzyme Cofactors

Categories

1. Coenzymes (small organic; e.g., NAD⁺, FAD, CoA).

2. Essential ions / metal cofactors (Mg²⁺, Zn²⁺, Fe²⁺/³⁺).
   Binding modes

• Prosthetic groups: permanent/tightly bound.

• Cosubstrates: transient; enter & leave active site each catalytic cycle.
  Role: broaden enzyme chemistry (electron transfer, group transfer, stabilization).

Page 15: Overview of Enzyme Inhibition Classes

• Prerequisite for catalysis: formation & conversion of $E\cdot S$.
  Reversible (non-permanent):

1. Competitive: binds active site; mutually exclusive with substrate.

2. Non-competitive: binds allosteric (near or overlapping active site) & impairs catalysis.
   Irreversible (permanent):

3. Mechanism-based (suicide): covalent bond forms during normal catalytic cycle.

4. Non-covalent high-affinity: binds like transition state; dissociation negligible.

Page 16: Reversible Inhibition—Kinetic Consequences

• Competitive
  • Apparent $K<em>M\uparrow$ (↓ affinity) because more [S] needed to reach ½$V</em>{max}$.
  • $V_{max}$ unchanged (can outcompete with excess substrate).

• Non-competitive
  • $V<em>{max}\downarrow$ (some E effectively removed). • $K</em>M$ unchanged (substrate binding unaffected).

Page 17: Visualizing Inhibitor Effects (Lineweaver–Burk)

Competitive:
• $x$-intercept shifts toward 0 (−1/$K<em>M$ less negative). • $y$-intercept constant (1/$V</em>{max}$ unchanged).
Non-competitive:
• $y$-intercept rises (1/$V_{max}$ increases).
• $x$-intercept unchanged.

Page 18: Mechanism-Based (Covalent / Suicide) Inhibitors

• Mimic substrate; enter normal catalytic pathway.

• Active site residue (Ser, Cys, Lys, etc.) forms irreversible covalent adduct.

• Result: enzyme destroyed; turnover number becomes 0.
  Key phrase: The enzyme commits suicide on the inhibitor.

Page 19: Aspirin (Acetyl-salicylic Acid) & Cyclooxygenase (COX)

Reaction synopsis

• COX generates prostaglandin H → pain & inflammation signaling.

• Aspirin transfers its acetyl group to an active-site Ser → covalent inactivation (irreversible, mechanism-based).
  Comparators

• Ibuprofen & acetaminophen: lack acetyl; act as reversible competitive inhibitors (no covalent bond).
  Clinical relevance: Explains prolonged platelet COX-1 inhibition vs shorter NSAID effects.

Page 20: Organophosphate Nerve Agents & Acetylcholinesterase (AChE)

• AChE terminates synaptic signal by hydrolyzing acetylcholine.

• Organophosphates (sarin, malathion): phosphorylate active-site Ser in AChE ⇒ irreversible; leads to cholinergic crisis.
  Therapeutic note: Pralidoxime can reactivate AChE before “aging” occurs.

Page 21: Non-Covalent Irreversible Inhibition (Transition-State Analogues)

• Inhibitor structurally mimics transition state ⇒ maximal complementary binding.

• Affinity so high (sub-pM $K_D$) that dissociation probability ≈ 0 within physiologic time frame; effectively permanent though non-covalent.

Page 22: HIV Protease Inhibitors

• HIV protease: Aspartyl protease essential for processing gag-pol polyprotein.

• Drugs (e.g., ritonavir, indinavir): resemble tetrahedral transition state; bind active site with very high affinity (irreversible competitive in practice).
  Outcome: Blocks viral maturation, reduces infectivity.

Page 23 & 24: Clinical Application Question—Ethanol vs Ethylene Glycol

Scenario recap

• Ethylene glycol metabolized by alcohol dehydrogenase (ADH) → toxic organic acids (metabolic acidosis).

• Administer ethanol to compete for ADH active site.
  Data: Lineweaver-Burk shows ↑$K<em>M$, unchanged $V</em>{max}$.
  Conclusion: Competitive inhibition.
  Therapeutic rationale: Saturating ADH with ethanol slows oxalate production; kidneys can excrete unmetabolized glycol.

Page 25 & 26: Concept Check—Penicillin / HIV-Protease Inhibitors

• Student debate highlights definitions:
  • Irreversible competitive: binds active site non-covalently but permanently (very high affinity or covalent?).
  • Suicide inhibition: covalent bond formed during catalysis.

• Correct resolution:
  – Penicillin: forms covalent adduct with transpeptidase ⇒ suicide inhibitor (and competitive because binds active site).
  – HIV protease inhibitors: irreversible competitive (non-covalent, transition-state analogues).

Page 27: Institutional Footer

Edward Via College of Osteopathic Medicine (VCOM) – Carolinas Campus
Course: Cell Biology & Physiology – Enzymes as Catalysts II