In-Depth Notes on Enzyme Kinetics and Metabolism

Enzyme-Substrate Binding and Enzymatic Reactions

• Enzyme-Substrate (ES) Complex Formation

• Enzymes bind substrates to form the ES complex, also known as the Michaelis complex.

• The reaction can proceed forward, converting substrate to product at a rate denoted as k₂.

• The reaction is reversible; products can revert back to reactants under certain conditions.

• Key Terms

• k₁: Rate of formation of ES complex

• k_{−1}: The rate of breakdown of the ES complex back into free enzyme (E) and substrate (S)

• k₂ (k-cat): Rate of conversion of ES to product (P)

• Michaelis constant (Km): Describes the affinity between enzyme and substrate; higher Km means lower affinity, and vice versa.

Rate Law and Measurement Challenges

• Aim: To determine the rate of an enzymatic reaction at varying substrate concentrations.
• The rate of product formation (dP/dt) can be described by the equation:
• dP/dt = k₂ [ES]
• Challenge: Measuring [ES] concentration is complicated due to the dynamic equilibrium of formation and breakdown.

Assumptions for Rate Determination

1. Initial Rate Assumption:
   • Measure initial rates (V₀) at time close to zero when the reaction is linear; negligible conversion of products back to substrates.
2. Steady State Assumption:
   • Under physiological conditions, substrate concentration is much greater than enzyme concentration (E << S), leading to a steady formation of the ES complex.

Equations Derived from Assumptions

• Formation of ES: Rate = k₁[E][S]
• Breakdown of ES: Rate = k_{−1}[ES] + k₂[ES]
• Using steady-state and initial rate assumptions, have:
• From total enzyme: E_total = [ES] + [E]
• Substituting to derive the final rate equation that expresses velocity as a function of substrate concentration.

Michaelis-Menten Equation

• The derived equation allows calculating reaction rates without directly measuring [ES]. Typically expressed as:
• V₀ = (Vmax [S]) / (Km + [S])
• Where
• Vmax = maximum rate (
• Km = constant reflecting substrate concentration at half Vmax

Lineweaver-Burk Plot

• A double reciprocal plot to linearize the Michaelis-Menten equation helps in determining kinetic parameters easily:
• 1/V₀ = (Km/Vmax)(1/[S]) + 1/Vmax
• Slope = Km/Vmax
• Y-intercept = 1/Vmax
• X-intercept = -1/Km

Competitive and Noncompetitive Inhibitors

• Inhibitors slow down enzymatic reactions.

• Competitive Inhibitors:

• Compete with substrates for binding to the active site.

• Increases Km (decreases affinity) with Vmax remaining the same.

• Seen in Lineweaver-Burk plot as a shift to the right in x-intercept.

• Ratio: alpha = Km_apparent / Km

• Noncompetitive Inhibitors:

• Bind to an allosteric site, not directly competing with the substrate but modifying active site's conformation, reducing Vmax while Km remains unchanged.

• Lineweaver-Burk slope changes as Vmax decreases, but Km remains constant.

Enzyme Activity Regulation

• Metabolism Overview:
• Involves catabolism (energy release) and anabolism (energy consumption for biosynthesis).
• ATP as Energy Currency:
• ATP hydrolysis releases energy and is utilized in cellular functions. The breakdown releases ≈ 30 kJ/mol, indicative of how energetically favorable ATP hydrolysis is.

Thermodynamics in Reactions

• Free Energy (ΔG):

• Key to understanding reaction spontaneity:

• ΔG < 0 → Reaction favors products (spontaneous)

• ΔG > 0 → Reaction favors reactants (non-spontaneous)

• ΔG = 0 → Equilibrium

• Equation:

• ΔG = ΔG°' + R(T) ln([Products]/[Reactants])

• Where ΔG°' = standard free energy change under specific conditions (1 M, 25°C, pH 7).

Importance of Equilibrium and Conditions

• The actual ΔG within cells can vary depending on concentrations and temperature, altering the favorability of reactions, making the study of enzymatic reactions contextually important.

Conclusion

• Understanding the fundamentals of enzyme kinetics, inhibitor dynamics, and thermodynamics lays the groundwork for advanced studies in metabolic pathways and enzyme regulation.