CHAPTER 6: Exam 2

Chapter 6: Enzymes

Physiological Significance of Enzymes

• Enzymes are crucial biological catalysts responsible for accelerating chemical reactions in biological systems.

Origin of Catalytic Power of Enzymes

• The catalytic ability of enzymes arises from their specific structures that facilitate substrate binding and transform chemical processes efficiently.

Chemical Mechanisms of Catalysis

Mechanisms of Chymotrypsin and Lysozyme

• Chymotrypsin and lysozyme showcase specific catalytic mechanisms that highlight the diverse roles of enzymes in biochemical processes.

Description of Enzyme Kinetics and Inhibition

• Enzyme kinetics is the study of the rates at which enzymatic reactions occur, detailing how various factors affect enzyme activity and reaction rates.

Key Topics about Enzyme Function

What are Enzymes?

• Enzymes are biological catalysts that:

  • Catalyze reactions and increase reaction rates without being consumed.

  • Most enzymes are globular proteins, but some RNA molecules (ribozymes, such as ribosomal RNA) also exhibit catalytic properties.

Why Biocatalysis Over Inorganic Catalysts?

• Advantages of enzymes include:

  • Greater reaction specificity: Enzymes ensure that side products are minimized by selectively binding specific substrates.

  • Milder reaction conditions: Enzymes operate effectively under physiological conditions (ambient temperature, physiological pH).

  • Higher reaction rates: Enzymes provide a means to achieve reaction rates that are biologically useful in a timely manner.

  • Capacity for regulation: Enzymes can be regulated to control biological pathways, allowing cells to respond dynamically to changing conditions.

  • Metabolite pathways: Enzymes bias the outcome of reactions to favor specific metabolic pathways.

Enzyme-Substrate Complex

• Enzymes function by binding to substrates through noncovalent interactions, forming the Michaelis complex.

  • This complex serves as the foundational element for understanding enzyme kinetics and behavior in reaction mechanisms. (rate of the catalyzed enzyme reaction depends on the concentration of the substrate.

Enzymatic Catalysis

• Enzymes influence the rate of reaction without altering the equilibrium state of the reaction.

• Notably, enzymes lower the activation energy (ΔG‡) required for reactions to occur:

  • Enzymes enhance reaction rates (k) by reducing ΔG‡, which is critical for reactions facing significant activation barriers.

How to Lower ΔG‡

• Enzymes pay the entropy cost through their binding energy:

  • Uncatalyzed bimolecular reactions transition from two free reactants into a restricted transition state, which is entropically unfavorable.

  • Uncatalyzed unimolecular reactions transition from flexible reactants into a rigid transition state, which is also entropically unfavorable.

  • Enzymatic catalysis organizes substrates to form a stable enzyme-substrate (ES) complex that effectively reduces the entropy penalty during the transition to the transition state.

Support for the Proximity Model

• The proximity of reacting molecules increases their likelihood of reaction.

  • Reactants need to collide effectively; thus, enhancing their concentration and proper orientation is crucial for reaction rate enhancement.

Enzymes Bind Transition States Best

• Proposed by Linus Pauling in 1946, this model claims:

  • Enzyme active sites are complementary to the transition state, allowing for better binding and stabilization than to the substrate or product.

  • Stronger interactions with the transition state lower the activation energy (ΔG‡).

Catalytic Mechanisms

1. Acid-Base Catalysis: Involves donation and acceptance of protons.

2. Covalent Catalysis: Changes the reaction pathway through transient covalent bonding.

3. Metal Ion Catalysis: Utilizes metal ions for oxidation-reduction reactions and pKa shifts.

4. Electrostatic Catalysis: Involves preferential interactions with the transition state.

Covalent Catalysis

• This involves a temporary covalent bond between enzyme and substrate, modifying the reaction pathway.

  • Requires a nucleophile on the enzyme such as serine, thiolate, amine, or carboxylate.

Metal Ion Catalysis

• Metal ions associated with enzymes facilitate substrate binding and stabilization of negative charges, participating in oxidation reactions.

  • Note: Mechanisms involving metal ions will be analyzed in depth in BCHM 164 (Bioinorganic Chemistry).

Chymotrypsin as Zymogen

• Chymotrypsin originates from chymotrypsinogen (inactive form), which is converted into its active form through digestive processes.

  • Enzymatic autolysis leads to the active (α-chymotrypsin) via the action of trypsin on its precursor.

Chymotrypsin Mechanism

Step-by-Step Process

1. Substrate Binding:

   • The substrate binds active site, positioning peptide bond for attack.

   • Key residues: Asp102, His57, Ser195.

2. Nucleophilic Attack:

   • Ser195 forms an alkoxide ion to attack peptide's carbonyl, creating an acyl-enzyme intermediate, stabilized in the oxyanion hole.

3. Substrate Cleavage:

   • Collapse of intermediate causes peptide bond breakage; His57 facilitates protonation of the leaving group.

4. Water Comes In:

   • Water molecule deprotonated to generate a strong hydroxide ion, attacking the acyl-enzyme linkage.

5. Water Attacks:

   • Collapse forms second product and displaces Ser195.

6. Break-off from the Enzyme:

   • Second product released, regenerating free enzyme.

7. Product Dissociates:

   • Enzyme is now free to catalyze additional reactions.

Peptidoglycan and Lysozyme

• Peptidoglycan is a critical component of many bacterial cell walls that contributes to structural integrity.

• Lysozyme cleaves peptidoglycan, resulting in bacteriolysis, and is a significant antibacterial enzyme.

Cleavage of Peptidoglycan by Lysozyme

• Involves two successive SN2 reaction steps:

  1. Asp52 acts as a nucleophile; Glu35 acts as a general acid, protonating the leaving group.

  2. Water hydrolyzes the covalent glycosyl-enzyme intermediate; Glu35 deprotonates water to facilitate the second step.

What is Enzyme Kinetics?

• Enzyme kinetics focuses on the rate of enzymatic reactions and the influencing factors:

  • Type of enzyme (wild-type versus mutant)

  • Nature of substrate

  • Presence of effectors (activators & inhibitors)

  • Environmental conditions (temperature, pH)

  • Age of enzyme (shelf-life).

The Goal of Enzyme Kinetics

• Key objectives include:

  • Comparing catalytic abilities of different enzyme variants.

  • Understanding enzyme preferences for substrates.

  • Elucidating enzyme mechanisms (sequential vs. ping-pong).

  • Assessing inhibitor effects (reversible vs. irreversible; competitive vs. noncompetitive).

Quantifying Enzyme Catalysis

Specific Activity

• Specific activity is commonly expressed as $ext{mmol/min/mg}$; assesses enzyme activity in one set of conditions.

Michaelis-Menten Constants

• Key parameters include $k<em>{cat}$ (turnover number) and $K</em>m$ (Michaelis constant), providing insight on enzyme-substrate interactions under varying conditions.

How to Collect Kinetic Data

• Various modalities can be used to collect kinetic data, such as:

  • Colorimetric methods (spectroscopy).

  • Radiometric and direct/indirect detection methodologies.

  • Continuous vs. discontinuous approaches to monitor enzymatic activities.

Michaelis-Menten Equation

$[E] + [S] = [ES] = [EP] = [E] + [P]$

• Assumptions in this model include the steady-state assumption and saturation conditions.

Kinetic Constants

• $K_m$ defines the concentration at which the reaction rate is half of its maximum ( ext{Vmax}).

• $k_{cat}$ represents how fast the enzyme can work under saturating substrate conditions.

Kinetic Parameters and Curve-Fitting

• Data can be used for fitting parameters through Lineweaver-Burk plot, facilitating the determination of kinetics.

Bisubstrate Reactions

• Different binding orders lead to distinct kinetic patterns, employed to classify mechanisms based on their substrate interactions.

Enzyme Inhibition

Types of Inhibitors

1. Irreversible Inhibitors: Permanently disable enzymes by binding covalently.

2. Reversible Inhibitors: Can dissociate from the enzyme, affecting its activity based on binding positions:

   • Competitive: Competes with substrate.

   • Uncompetitive: Binds only ES complex.

   • Mixed (Noncompetitive): Can bind E or ES, affecting both aspects of enzyme action.

Competitive Inhibition Effects

• Increases KM app with unchanged Vmax; lines intersect on the 1/v axis.

Uncompetitive Inhibition Effects

• Lowers both Vmax and KM app; no effect on KM/Vmax.

Mixed Inhibition Effects

• Reduces Vmax with possible alterations in KM app, demonstrating mixed effects on substrate binding and catalysis.

🔹 Theory of Enzyme Catalysis

• Enzymes speed up reactions by lowering activation energy (Ea).

• They stabilize the transition state → makes it easier for substrates to become products.

• Don’t change ΔG or equilibrium, only the rate.

🔹 Michaelis–Menten Equation

Equation:

v=Vmax[S]Km+[S]v = \frac{V_{max}[S]}{K_m + [S]}v=Km​+[S]Vmax​[S]​

• Low [S]: v≈VmaxKm[S]v ≈ \frac{V_{max}}{K_m}[S]v≈Km​Vmax​​[S] → 1st order (rate depends on [S]).

• High [S]: v≈Vmaxv ≈ V_{max}v≈Vmax​ → zero order (enzyme saturated).

• [S] = Km: v=12Vmaxv = \frac{1}{2}V_{max}v=21​Vmax​.

🔹 Interpreting Enzyme Kinetics (v vs [S])

• Plot v vs [S] → hyperbolic curve (levels off at Vmax).

• Slope at low [S] shows how sensitive the enzyme is.

• Use Lineweaver–Burk plot (1/v vs 1/[S]) for straight line.

🔹 Kcat and Km

• Kcat (“turnover number”): # of substrate molecules converted to product per enzyme per second.

  Kcat=Vmax[E]tK_{cat} = \frac{V_{max}}{[E]_t}Kcat​=[E]t​Vmax​​

• Km: [S] at ½ Vmax. Measure of affinity (low Km = high affinity).

🔹 Catalytic Efficiency (kcat/Km)

• Combines speed (kcat) + affinity (Km).

• High kcat, low Km → high efficiency.

• Perfect enzyme: diffusion-limited ~10⁸–10⁹ M⁻¹s⁻¹.

🔹 Enzyme Inhibition

1. Irreversible: covalent binding (enzyme permanently dead).

2. Reversible:

   • Competitive: ↑Km, Vmax same.

   • Uncompetitive: ↓Km, ↓Vmax.

   • Noncompetitive (mixed): Vmax ↓, Km can ↑, ↓, or same.

🔹 Alpha & Ki

• α (alpha): factor by which Km (or slope) is changed by inhibitor.

• Ki (inhibition constant):

  Ki=[I]α−1K_i = \frac{[I]}{α - 1}Ki​=α−1[I]​

(lower Ki = stronger inhibitor).

🔹 pH-Rate Profiles

• Activity vs. pH looks like a bell curve.

• Shows which groups must be protonated/deprotonated for activity.

• Reveals mechanism (acid-base catalysis).

🔹 Plot Interpretation

• v vs [S]: hyperbolic (MM), sigmoidal (allosteric).

• 1/v vs 1/[S] (Lineweaver–Burk):

  • Competitive → lines cross at y-axis.

  • Uncompetitive → parallel lines.

  • Noncompetitive → lines cross left of y-axis.

🔹 Bisubstrate Mechanisms

• Sequential (ternary complex): both substrates bind before reaction (ordered or random).

• Ping-Pong: one substrate binds → product leaves → enzyme modified → second substrate binds.

🔹 Chymotrypsin Mechanism

• Key residues: Ser195 (nucleophile), His57 (base/acid), Asp102 (stabilizes His).

• Steps:

  1. Ser attacks → tetrahedral intermediate.

  2. Collapse → peptide bond broken.

  3. Water attacks → second tetrahedral intermediate.

  4. Product released.

• Burst kinetics: fast acylation step, slower deacylation.

• DIFP: irreversible inhibitor of Ser195.

• pH-rate profile: activity peaks when His and Ser are in proper protonation states.

🔹 Lysozyme Mechanism

• Residues: Glu35 (acid/base), Asp52 (stabilizes carbocation).

• Mechanisms:

  1. SN1-like: carbocation intermediate stabilized by Asp.

  2. SN2-like: direct displacement.

• Evidence supports SN2 with covalent intermediate.

🔹 Allosteric Enzymes

• Exist in R (active) vs T (tense/inactive) states.

• Activators stabilize R, inhibitors stabilize T.

• Show sigmoidal v vs [S] curves (cooperative binding, like hemoglobin).

• Positive cooperativity: binding of one substrate ↑ affinity of others.