Chapter 9/10 - Enzymatic Catalysis and Kinetics Review Flashcards

General Properties of Enzymes

• Biological Catalysts: Virtually all biochemical reactions in living systems are mediated by proteins known as enzymes. Enzymology, the study of enzymes, evolved from 19th-century investigations into fermentation and digestion.

• Historical Context:

  • Louis Pasteur initially assumed a "vital force" was required for biochemical reactions.

  • Justus von Liebig argued reactions were caused by chemical substances called "ferments."

  • Wilhelm Kühne coined the name "enzyme" (Greek: en, in + zyme, yeast) in 1878 to represent the catalytic substance in yeast.

  • Eduard Buchner (1897) demonstrated that cell-free yeast extract could convert glucose to ethanol (alcoholic fermentation): $C_6H_{12}O_6 \rightarrow 2CH_3CH_2OH + 2CO_2$.

  • James Sumner (1926) crystallized jack bean urease, proving enzymes are proteins.

• Ribozymes: Notable exceptions to the protein rule; certain RNA molecules, such as ribosomal RNA, catalyze peptide bond formation. These are considered vestiges of a pre-cellular "RNA world."

• Enzymes vs. Chemical Catalysts:

  1. Higher Reaction Rates: Rates are typically $10^6$ to $10^{12}$ times greater than uncatalyzed reactions and orders of magnitude higher than chemical catalysts.

  2. Milder Reaction Conditions: They operate at temperatures below $100\,^∘C$, atmospheric pressure, and near-neutral pH.

  3. Greater Specificity: Enzymes rarely produce side products and have high selectivity for substrates (reactants) and products.

  4. Capacity for Regulation: Activities vary in response to substances other than substrates via allosteric control, covalent modification, or variation in enzyme synthesis.

Enzyme Classification and Nomenclature

• Naming Conventions: Often use the suffix "-ase" appended to the substrate (e.g., urease) or the catalytic action (e.g., alcohol dehydrogenase).

• IUBMB Systematic Classification: Each enzyme is assigned a four-part classification number (EC number) and a systematic name.

  1. Oxidoreductases: Catalyze oxidation–reduction reactions.

  2. Transferases: Transfer functional groups.

  3. Hydrolases: Catalyze hydrolysis reactions.

  4. Lyases: Group elimination to form double bonds.

  5. Isomerases: Catalyze isomerization.

  6. Ligases: Catalyze bond formation coupled with ATP hydrolysis.

  7. Translocases: Catalyze movement of molecules across/within membranes.

• EC Number Example: Aconitase (EC 4.2.1.3). The first digit (4) is the class (Lyase); (2) is the subclass (carbon-oxygen lyase); (1) is sub-subclass (hydrolase); (3) is specific for the substrate aconitate.

Substrate Specificity and stereospecificity

• The Active Site: A pocket or cleft on the enzyme surface where catalysis occurs. Binding involves noncovalent forces: van der Waals, electrostatic, hydrogen bonding, and hydrophobic interactions.

• Complementarity:

  • Geometric Complementarity: The shape of the active site matches the substrate.

  • Electronic Complementarity: Amino acid residues are arranged to attract the substrate.

• Induced Fit: Binding sites are largely preformed but undergo conformational change upon substrate binding to position catalytic groups properly.

• Stereospecificity: Enzymes are absolutely stereospecific due to the asymmetric nature of the active site.

  • Example: Aconitase distinguishes between the two prochiral carboxymethyl groups of citrate through a "three-point attachment."

• Geometric Specificity: Varies among enzymes.

  • Alcohol dehydrogenase can oxidize ethanol, methanol, and isopropanol (though at different rates).

  • Chymotrypsin is permissive, hydrolyzing various peptide and ester bonds.

Transition State Theory and Activation Energy

• Theory Origin: Developed in the 1930s by Henry Eyring.

• Reaction Coordinate: A plot of free energy ($G$) vs. reaction progress.

  • Transition State ($X^‡$): The point of highest free energy where bonds are in the process of breaking and forming.

  • Free Energy of Activation ($\Delta G^‡$): The energy barrier between reactants and the transition state.

• Kinetic Expression: The rate constant $k$ is related to activation energy by $k = e^{-\Delta G^‡/RT}$.

• Rate-Determining Step: In multistep reactions ($A \rightarrow I \rightarrow P$), the step with the highest activation energy acts as the bottleneck.

• Catalyst Function: Reduces $\Delta G^‡$ without changing the overall $\Delta G$ of the reaction ($\Delta G_{reaction}$). It accelerates the approach to equilibrium but does not alter the equilibrium itself.

• Efficiency Calculation: A 10-fold rate enhancement at $25\,^∘C$ requires a reduction in activation energy ($\Delta\Delta G_{cat}^‡$) of only $5.71\,kJ \cdot mol^{-1}$.

Catalytic Mechanisms of Enzymes

• Binding Energy: Free energy released from noncovalent interactions between enzyme and substrate, used to lower $\Delta G^‡$.

• Transition State Binding: Linus Pauling (1946) proposed enzymes bind the transition state more tightly than the substrate. This mechanical strain or stabilization promotes the reaction.

• Cofactors: Small molecules required for activity, acting as "chemical teeth."

  • Coenzymes: Organic molecules; include cosubstrates (transiently associated, e.g., $NAD^+$/$NADH$) and prosthetic groups (permanently bound, e.g., heme).

  • Holoenzyme: Active enzyme-cofactor complex.

  • Apoenzyme: Inactive protein after cofactor removal.

• Specific Catalytic Strategies:

  1. Acid–Base Catalysis: Proton transfer lowers transition state energy.

     • Residues: Asp, Glu, His, Cys, Tyr, Lys.

     • Example: Bovine pancreatic RNase A uses His12 (base) and His119 (acid) in a concerted mechanism to hydrolyze RNA via a $2',3'-cyclic$ nucleotide intermediate.

  2. Covalent Catalysis: Transient formation of an enzyme-substrate covalent bond (nucleophilic catalysis).

     • Example: Decarboxylation of acetoacetate involving a Schiff base (imine) intermediate with a Lys amine group.

  3. Metal Ion Catalysis: Metalloenzymes use transition metals ($Fe^{2+}$, $Cu^{2+}$, $Zn^{2+}$).

     • Mechanism: Orient substrates, shield charge, or polarize water to facilitate nucleophilic attack (e.g., $Zn^{2+}$ in carbonic anhydrase).

  4. Proximity and Orientation Effects: Enzymes bring substrates together in the correct spatial relationship and freeze translational/rotational motion. Orientation alone can increase rates by $∼ 100$-fold; total freezing can provide enhancement up to $10^7$.

Lysozyme Mechanism

• Function: Cleaves $\beta(1 \rightarrow 4)$ glycosidic linkages between NAM and NAG in bacterial cell walls.

• Structure: Determined by David Phillips (1965). Contains an active site cleft accommodating six sugar residues (A–F).

• The D-Ring Distortion: Subsite D forces the NAM residue into a strained "half-chair" conformation to avoid steric clash with the enzyme. This mimics the transition state oxonium ion.

• Catalytic Residues:

  • Glu35: Located in a nonpolar pocket, remain protonated ($pK ∼ 6.2$) to act as a general acid.

  • Asp52: Negatively charged, stabilizes the oxonium ion and forms a covalent glycosyl-enzyme intermediate.

• Experimental Support: Stephen Withers demonstrated the covalent intermediate using $2-deoxy-2-fluoro$ substrate analogs and mass spectrometry ($ESI-MS$) on an E35Q mutant enzyme.

Serine Proteases

• Examples: Chymotrypsin (bulky hydrophobic residues), Trypsin (positive residues), Elastase (small neutral residues).

• Identification of Residues:

  • Ser195: Labeled by diisopropylphosphofluoridate (DIPF).

  • His57: Identified by affinity labeling with TPCK.

• The Catalytic Triad: Consists of Ser195, His57, and Asp102.

• The Mechanism:

  1. Ser195 nucleophilically attacks the scissile peptide carbonyl (facilitated by His57 acting as a base).

  2. Formation of a Tetrahedral Intermediate stabilized by the Oxyanion Hole (hydrogen bonds from Gly193 and Ser195).

  3. Decomposition to an Acyl–Enzyme Intermediate as His57 acts as an acid to protonate the leaving amine group.

  4. Water enters, His57 acts as a base to produce $OH^-$, which attacks the acyl group.

  5. Reformation of the carbonyl group releases the carboxyl product.

• Zymogens: Inactive precursors (e.g., trypsinogen, chymotrypsinogen). Trypsinogen is activated autocatalytically or by enteropeptidase via cleavage of the Lys15–Ile16 bond.

Enzyme Kinetics: First and Second Order

• Velocity ($\nu$): Rate of appearance of product or disappearance of reactant.

• First-Order Reaction ($A \rightarrow P$):

  • $\nu = k[A]$.

  • Integrated form: $ln[A] = -kt + ln[A]_0$.

  • Half-life ($t_{1/2}$): $\frac{0.693}{k}$.

• Second-Order Reaction ($2A \rightarrow P$ or $A + B \rightarrow P$):

  • $\nu = k[A]^2$ or $\nu = k[A][B]$.

  • Integrated form (for 2A): $\frac{1}{[A]} = kt + \frac{1}{[A]_0}$.

Michaelis–Menten Kinetics

• Model: $E + S \rightleftharpoons ES \rightarrow E + P$.

• Assumptions:

  1. Steady State Assumption (Briggs and Haldane, 1925): Rate of ES formation equals rate of breakdown; $[ES]$ is constant.

  2. Initial Velocity ($\nu_0$): Measures rate before significant product accumulation or back-reaction.

• Michaelis–Menten Equation: $\nu_o = \frac{V_{max}[S]}{K_M + [S]}$.

• Michaelis Constant ($K_M$): Substrate concentration at which $\nu_0 = \frac{1}{2}V_{max}$. Definition: $K_M = \frac{k_{-1} + k_2}{k_1}$.

• Catalytic Constant ($k_{cat}$): Turnover number; $k_{cat} = \frac{V_{max}}{[E]_T}$.

• Catalytic Efficiency: Ratio $k_{cat}/K_M$. Theoretically limited by diffusion to $10^8$ to $10^9\,M^{-1} \cdot s^{-1}$ (catalytic perfection).

• Lineweaver–Burk Plot: Linear double-reciprocal plot: $\frac{1}{\nu_o} = \left(\frac{K_M}{V_{max}}\right) \frac{1}{[S]} + \frac{1}{V_{max}}$.

  • Slope = $K_M/V_{max}$.

  • y-intercept = $1/V_{max}$.

  • x-intercept = $-1/K_M$.

Enzyme Inhibition

• Irreversible Inhibitors: Permanently inactivate the enzyme (e.g., DIPF for Ser proteases).

• Reversible Inhibitors:

  1. Competitive: Binds to the active site. Increases apparent $K_M$ ($K_{M,app} = \alpha K_M$); $V_{max}$ remains unchanged.

     • $\alpha = 1 + \frac{[I]}{K_I}$.

  2. Uncompetitive: Binds only to the ES complex. Both $V_{max}$ and $K_M$ decrease proportionally.

     • $V_{max,app} = \frac{V_{max}}{\alpha'}$, $K_{M,app} = \frac{K_M}{\alpha'}$.

  3. Mixed (Noncompetitive): Binds to both E and ES. $V_{max,app}$ decreases; $K_{M,app}$ may increase or decrease.

     • If $K_I = K'_I$, it is strictly noncompetitive ($K_M$ is unchanged).

Control of Enzyme Activity

• Control of Enzyme Availability: Managing synthesis and degradation rates.

• Control of Enzyme Activity:

  1. Allosteric Control: Binding of allosteric effectors at sites other than the active site. These effectors induce conformational changes that alter subunit interactions.

  2. Covalent Modification: Usually phosphorylation/dephosphorylation on Ser, Thr, or Tyr residues mediated by protein kinases and phosphatases.

• Therapeutic Applications: Drugs like oseltamivir (Tamiflu) for influenza and protease inhibitors (ritonavir, darunavir) for HIV target specific enzyme mechanisms through competitive inhibition or transition state mimicry.