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Enzyme Catalysis, Kinetics, Mechanism, and Regulation

Learning Objectives

• Understand the fundamental factors responsible for enzymatic rate enhancements.
• Understand the basis of steady-state kinetics.
• Understand the information gained through inhibition analysis.
• Understand basic mechanisms of enzymatic action.

General Concepts

• Enzymes: Biological catalysts that speed up chemical reactions.
• Substrates: Reactants that enzymes bind to and transform into products.

Why Enzyme Catalysts Over Inorganic Catalysts?

• Specificity: Enzymes are highly specific and evolved for particular jobs.
• Enzyme Example: Nitrogenase, which facilitates nitrogen fixation under specific conditions.
  • Conditions: 37°C, 200 atm, and pH 7.

Naming Enzymes

• Naming conventions usually end with -ase.
• Prefix often indicates the substrate or type of reaction.

Table 6-3: International Classification of Enzymes

1. Oxidoreductases: Transfer of electrons (hydride ions or H atoms).
2. Transferases: Group transfer reactions.
3. Hydrolases: Hydrolysis, transferring functional groups to water.
4. Lyases: Elimination of groups to form double bonds or addition of groups to double bonds.
5. Isomerases: Isomeric transformations within molecules.
6. Ligases: Formation of bonds via condensation reactions requiring ATP.
7. Translocases: Movement or separation of molecules/ions across membranes.

Enzyme-Substrate Complex

• Enzymes bind substrates at the active site, forming an enzyme-substrate (ES) complex.
• This interaction can involve various forces: hydrophobic interactions, van der Waals, weak covalent interactions.

Enzyme Kinetics

Relationship Between Equilibrium Constant and Free Energy Change

• The relationship can be expressed as:
  $ext{At B, L, P, t Q} imes ext{TS} o riangle G^ ext{t} = R T ext{ln} K$
• Free energy change ($ riangle G$) does not change for an enzyme-catalyzed reaction; enzymes primarily lower activation energy ($ riangle E$).

Lowering Activation Energy

• Enzymes effectively lower the activation energy, allowing faster reaction rates.
• General equation representation:
  $riangle G^{ ext{uncat}} o riangle G^{ ext{cat}} o riangle E$

Rate Constants

• Rate constants are determined by activation free energy:
  $K_R = \frac{1}{k} e^{-\frac{ riangle G^{ ext{t}}}{RT}}$
• Boltzmann's Constant: Essential to understanding the temperature dependence of reaction rates.
• A higher rate constant corresponds to lower activation free energy.

Typical Rate Enhancements by Enzymes

• Enzymes can enhance reaction rates significantly, with examples:
  • Cyclophilin: $10^5$
  • Carbonic anhydrase: $10^7$
  • Triose phosphate isomerase: $10^9$
  • Carboxypeptidase A: $10^{11}$
  • … up to Orotidine monophosphate decarboxylase: $10^{17}$

Binding Energy

• Binding energy is crucial for enzyme function, stabilizing the transition state (TS) and facilitating product release.
• Change in enthalpy (ΔH) and entropy (ΔS) can determine the favorability of binding interactions.

Mechanisms of Catalysis

1. Acid-Base Catalysis:
   • Specific: Involves water constituents (e.g., $H_3O^+$ or $OH^-$).
   • General: Other weak acids and bases aid in catalysis.
2. Covalent Catalysis:
   • Transient covalent bond forms between enzyme and substrate.
3. Metal Ion Catalysis:
   • Metal ions enhance substrate binding and redox reactions.

Chymotrypsin as a Case Study

• Chymotrypsin is a serine protease that accelerates hydrolysis of peptide bonds.
  • Catalytic triad: Asp102, His57, and Ser195 form the active site essential for function.

Classes of Proteases

1. Serine: Uses serine for covalent bond formation.
2. Cysteine: Utilizes cysteine for bond formation.
3. Aspartyl: Employs aspartate for water attack on carbonyl.
4. Metalloproteases: Involve metal ions to facilitate reactions.

Inhibition of Enzymes

• Inhibitors: Compounds that decrease enzyme activity; can be irreversible or reversible.
• Competitive Inhibition: Competes for active site, affecting Km but not Vmax.
• Uncompetitive Inhibition: Binds to ES complex, affecting both Vmax and Km.
• Mixed Inhibition: Affects both Km and Vmax through various interactions.

Michaelis-Menten Kinetics

• Classic model relating velocity ($v$) to substrate concentration ([S]):
  E + S
  ightleftharpoons ES
  ightarrow E + P
• Assumes rapid product dissociation and steady-state for ES formation.

Turnover Number (kcat)

• Defines the maximum number of substrate molecules converted to product per enzyme per unit time, expressed as:
  $k<em>{cat} = \frac{V</em>{max}}{[E]_{total}}$

Specificity Constant

• Reflects the overall effectiveness of an enzyme in substrate conversion under specific conditions, calculated as:
  $ext{Specificity Constant} = \frac{k<em>{cat}}{K</em>m}$

Lineweaver-Burk Plot

• A double-reciprocal plot of the Michaelis-Menten equation to analyze kinetic data.
• Useful for visualizing inhibition types and determining kinetic parameters (Vmax and Km).

Additional Considerations for Inhibition Types

• Competitive: Vmax unchanged, Km increased; lines intersect on y-axis.
• Uncompetitive: Both Vmax and Km affected by the same factors; parallel lines in LB plots.
• Mixed: Both Vmax and Km affected differently, necessitating recognition from experimental data.

Problem Solving in Kinetics

• Example: Determining inhibition type based on changes in Vmax and Km values when an inhibitor is present.
• Identify the context and use graphical methods to interpret data effectively.