Enzyme Kinetics, Inhibition, and Substrate Recognition: Study Notes

Enzymes and Enzyme Kinetics

Enzyme Structure and Function

Enzymes are biological catalysts that accelerate chemical reactions by lowering the activation energy required for the reaction to proceed. They are highly specific for their substrates and often require additional components, such as cofactors, for activity.

• Active Site: The region on the enzyme where substrate molecules bind and undergo a chemical reaction. It contains specific amino acid residues that interact with the substrate.

• Cofactor: A non-protein chemical compound that is required for the enzyme's activity. Cofactors can be metal ions or organic molecules (coenzymes).

• Activation Energy (Ea): The minimum amount of energy required to convert reactants into products. Enzymes lower Ea by stabilizing the transition state.

• Substrate Specificity: Enzymes are selective for their substrates due to the precise arrangement of amino acids in the active site.

Michaelis-Menten Kinetics

The Michaelis-Menten model describes the rate of enzymatic reactions by relating reaction velocity to substrate concentration.

• Key Parameters:

  • Vmax: The maximum velocity of the reaction when the enzyme is saturated with substrate.

  • Km: The Michaelis constant; the substrate concentration at which the reaction velocity is half of Vmax.

  • kcat: The turnover number; the number of substrate molecules converted to product per enzyme molecule per unit time.

  • Enzyme Efficiency: Given by $\frac{k_{cat}}{K_m}$, representing catalytic efficiency.

• Michaelis-Menten Equation:

$V_0 = \frac{V_{max}[S]}{K_m + [S]}$

• Initial Velocity (V0): The rate of reaction measured at the very beginning, before significant substrate depletion or product accumulation.

Graphical Analysis

• Velocity vs. [S] Plot: Shows a hyperbolic relationship between initial velocity and substrate concentration for Michaelis-Menten enzymes.

• Lineweaver-Burk Plot (Double-Reciprocal Plot): Linearizes the Michaelis-Menten equation for easier determination of Vmax and Km:

$\frac{1}{V_0} = \frac{K_m}{V_{max}} \cdot \frac{1}{[S]} + \frac{1}{V_{max}}$

• Activation Energy and Rate Constants: The rate-limiting step in a multi-step reaction is the step with the highest activation energy (slowest rate constant).

Enzyme Inhibition and Regulation

Types of Inhibition

• Competitive Inhibition: Inhibitor resembles the substrate and binds to the active site, preventing substrate binding. Increases apparent Km, Vmax unchanged.

• Noncompetitive Inhibition: Inhibitor binds to a site other than the active site, reducing Vmax without affecting Km.

• Uncompetitive Inhibition: Inhibitor binds only to the enzyme-substrate complex, decreasing both Vmax and Km.

Example: Sulfapyridine is a competitive inhibitor of the enzyme that uses p-aminobenzoic acid as a substrate, as it structurally mimics the substrate and competes for the active site.

Effects of Inhibitors on Kinetic Parameters

• Competitive Inhibitor: Increases Km (decreases affinity), Vmax remains the same.

• Double-Reciprocal Plot: In the presence of a competitive inhibitor, the slope increases, but the y-intercept (1/Vmax) remains unchanged.

Protein Function: Substrate Recognition and Binding

Active Site and Substrate Interactions

The enzyme active site is often lined with specific amino acid residues that interact with the substrate through non-covalent interactions such as hydrogen bonds, hydrophobic interactions, and ionic bonds.

• Hydrophobic Residues: Amino acids like alanine (Ala), valine (Val), leucine (Leu), and isoleucine (Ile) provide a nonpolar environment for hydrophobic substrates.

• Hydrophilic Substitutions: Introducing hydrophilic groups (e.g., -COOH) to a hydrophobic substrate can decrease binding affinity due to unfavorable interactions with a hydrophobic active site.

• Substrate Shape: The geometric complementarity between the substrate and the active site is crucial for binding and catalysis.

Example: If a hexagonal substrate is heavily substituted with hydrophilic groups, its binding to a hydrophobic active site will be reduced, lowering enzyme activity.

Substrate and Inhibitor Recognition

• Penicillin and D-Ala-D-Ala: Penicillin mimics the D-Ala-D-Ala moiety of bacterial cell wall precursors, allowing it to bind to and inhibit DD-transpeptidase, an enzyme involved in cell wall synthesis.

• Recognition Sites: The enzyme recognizes specific functional groups and stereochemistry in the substrate/inhibitor.

• Residue Interactions: Acidic residues (e.g., Asp) are more likely to interact with basic or polar groups, while nonpolar residues (e.g., Ala) interact with hydrophobic regions.

Calculations in Enzyme Kinetics

Key Equations

• Turnover Number (kcat): $k_{cat} = \frac{V_{max}}{[E]_{total}}$

• Enzyme Efficiency: $\frac{k_{cat}}{K_m}$

Example Calculation: If Vmax = 13.0 μM s-1 and [E]total = 2 nM:

$k_{cat} = \frac{13.0 \times 10^{-6} \text{mol/L/s}}{2 \times 10^{-9} \text{mol/L}} = 6.5 \times 10^{3} \text{s}^{-1}$

Enzyme efficiency can then be calculated if Km is known.

Summary Table: Effects of Inhibitors on Enzyme Kinetics

Type of Inhibitor	Effect on Vmax	Effect on Km	Binding Site
Competitive	Unchanged	Increases	Active site
Noncompetitive	Decreases	Unchanged	Allosteric site
Uncompetitive	Decreases	Decreases	Enzyme-substrate complex

Additional info:

• Activation energy diagrams and velocity vs. [S] plots are commonly used to visualize enzyme kinetics and the effects of inhibitors.

• Penicillin acts as a suicide inhibitor, covalently modifying the active site of DD-transpeptidase.