Enzyme Catalysis and Kinetics: Structured Study Notes Ch 6

Enzymes as Effective Biological Catalysts

Definition and Properties of Enzymes

Enzymes are biological catalysts, primarily proteins, that accelerate chemical reactions in living organisms. They are highly specific and efficient, often increasing reaction rates by factors up to $10^{20}$ compared to uncatalyzed reactions.

• Enzyme: A protein (rarely RNA) that catalyzes biochemical reactions.

• Catalysis: The process of increasing the rate of a chemical reaction by lowering the activation energy.

• Specificity: Enzymes typically act on specific substrates, producing specific products and minimizing undesired side reactions.

Example: The hydrolysis of ATP to ADP and inorganic phosphate ($ATP + H_2O \rightarrow ADP + P_i$) is catalyzed by ATPase, with a standard free energy change of $\Delta G^\circ = -30.5$ kJ mol-1.

Kinetics vs. Thermodynamics

Distinction Between Kinetics and Thermodynamics

Kinetics describes the rate at which a reaction proceeds, while thermodynamics determines the direction and extent of the reaction.

• Activation Energy ($E_a$): The energy barrier that must be overcome for a reaction to occur.

• Enzymes: Lower the activation energy, providing an alternative pathway for the reaction.

• Thermodynamics: Determines whether a reaction is spontaneous based on $\Delta G$ (Gibbs free energy).

Example: The decomposition of hydrogen peroxide ($H_2O_2 \rightarrow H_2O + O_2$) is thermodynamically favorable but kinetically slow without a catalyst.

Enzyme Kinetic Equations

Basic Rate Laws and Reaction Orders

Enzyme kinetics quantifies the rate of enzyme-catalyzed reactions and how it depends on substrate concentration.

• Rate Law: $\text{Rate} = k[A]^m[B]^n$ where $k$ is the rate constant, and $m$, $n$ are reaction orders.

• Zero Order: Rate is independent of substrate concentration (enzyme saturated).

• First Order: Rate is proportional to substrate concentration.

• Second Order: Rate depends on the product of two reactant concentrations.

Example: For a reaction $A + B \rightarrow P$, $\text{Rate} = k[A][B]$ (second order overall).

Enzyme-Substrate Binding

Active Site and Binding Interactions

Enzymes possess an active site where substrate binding and catalysis occur. The specificity arises from the precise arrangement of amino acids in the active site.

• Active Site: The region on the enzyme where the substrate binds via noncovalent interactions (hydrogen bonds, electrostatic forces, van der Waals attractions).

• Substrate: The reactant molecule acted upon by the enzyme.

• Enzyme-Substrate Complex (ES): The intermediate formed when substrate binds to the enzyme.

Example: Lysozyme binds its substrate in a cleft formed by the protein fold, demonstrating the importance of enzyme structure for specificity.

Models of Enzyme-Substrate Complex Formation

Lock-and-Key vs. Induced Fit Models

Two primary models explain how enzymes recognize and bind substrates:

• Lock-and-Key Model: The substrate fits into the enzyme's active site with a complementary shape, like a key into a lock.

• Induced Fit Model: Substrate binding induces a conformational change in the enzyme, resulting in a complementary fit.

Example: Hexokinase undergoes a significant conformational change upon glucose binding, supporting the induced fit model.

Michaelis-Menten Approach to Enzyme Kinetics

Michaelis-Menten Equation and Its Implications

The Michaelis-Menten equation describes the relationship between reaction rate and substrate concentration for many enzymes.

• Equation: $v = \frac{V_{max}[S]}{K_m + [S]}$

• $V_{max}$: Maximum reaction rate (enzyme saturated with substrate).

• $K_m$: Michaelis constant; substrate concentration at which the reaction rate is half of $V_{max}$.

• First Order: When $[S] \ll K_m$, $v \approx \frac{V_{max}}{K_m}[S]$ (rate depends on $[S]$).

• Zero Order: When $[S] \gg K_m$, $v \approx V_{max}$ (rate independent of $[S]$).

Example: Urease catalyzes the hydrolysis of urea, and its kinetics can be analyzed using the Michaelis-Menten equation.

Lineweaver-Burk Plot

Double Reciprocal Transformation

The Lineweaver-Burk plot linearizes the Michaelis-Menten equation for easier determination of kinetic parameters.

• Equation: $\frac{1}{v} = \frac{K_m}{V_{max}} \cdot \frac{1}{[S]} + \frac{1}{V_{max}}$

• Slope: $K_m/V_{max}$

• Y-intercept: $1/V_{max}$

Application: Used to determine $K_m$ and $V_{max}$ from experimental data.

Examples of Enzyme-Catalyzed Reactions

Biological and Laboratory Examples

Enzymes catalyze a wide variety of reactions essential for life.

• ATP Hydrolysis: $ATP + H_2O \rightarrow ADP + P_i$

• Hydrogen Peroxide Decomposition: $2H_2O_2 \rightarrow 2H_2O + O_2$ (catalyzed by catalase)

• Urea Hydrolysis: $\text{Urea} + 2H_2O \rightarrow 2NH_4^+ + HCO_3^-$ (catalyzed by urease)

Condition	Activation Free Energy (kJ mol-1)	Activation Free Energy (kcal mol-1)	Relative Rate
Uncatalyzed	75.2	18.0	1
Surface Catalyzed	48.9	11.7	2.7
Enzyme Catalyzed	23.0	5.5	6.5

Enzyme Inhibition

Types and Mechanisms of Inhibition

Enzyme inhibitors are compounds that decrease the rate of enzyme-catalyzed reactions. They are important in regulation and as drugs.

• Reversible Inhibitors: Bind non-covalently and can dissociate from the enzyme.

• Competitive Inhibition: Inhibitor binds to the active site, competing with the substrate. Increases apparent $K_m$, $V_{max}$ unchanged.

• Non-Competitive Inhibition: Inhibitor binds to a site other than the active site, affecting enzyme function. $K_m$ unchanged, $V_{max}$ decreases.

• Uncompetitive Inhibition: Inhibitor binds only to the enzyme-substrate complex, decreasing both $K_m$ and $V_{max}$.

• Irreversible Inhibitors: Covalently modify the enzyme, permanently inactivating it.

Example: Penicillin acts as an irreversible inhibitor of bacterial transpeptidase.

Type of Inhibition	Binding Site	Effect on $K_m$	Effect on $V_{max}$
Competitive	Active site	Increases	No change
Non-Competitive	Allosteric site	No change	Decreases
Uncompetitive	ES complex	Decreases	Decreases
Irreversible	Covalent modification	Varies	Decreases

Additional info:

• Enzyme catalysis is a central topic in biochemistry, underlying metabolism, drug action, and biotechnology.

• Understanding enzyme kinetics is essential for interpreting experimental data and designing inhibitors.