Chapter 6

Chapter 6: The Behavior of Proteins: Enzymes

Enzymes

• Definition: Biological catalysts, typically globular proteins, which facilitate biochemical reactions.

• Exceptions: Self-splicing RNA serves as a non-protein enzyme.

• Functionality: Enzymes significantly increase the reaction rate, achieving enhancements up to a factor of $10^{20}$ compared to uncatalyzed reactions.

• Specificity: Highly specific; can differentiate between stereoisomers of a compound.

• Regulation: Enzyme activity is modulated by various regulatory mechanisms.

Thermodynamic Principles - Enzyme Catalysis

• Standard Free Energy Change (ΔG°):
    - Represents the difference in energy between reactants and products under standard conditions.

• Equilibrium Constant: Enzymes influence reaction rates but do not modify the equilibrium constant or free energy change.

• Reaction Rate: Derived from the activation energy $ext{ΔG°‡}$ (energy needed to initiate a reaction).
    - Comparison of Activation Energies: $ext{ΔG°‡}$ is higher in uncatalyzed reactions than in catalyzed reactions.

The Transition State

• Definition: The transition state represents a temporary configuration during the reaction where existing bonds are in the process of breaking and new bonds are forming.

• Energy Profile: In energy plots of spontaneous reactions, the transition state is situated at the peak between reactants and products.

• Activation Free Energy: The free energy required to transition from reactants to the transition state can be quantified as $ext{ΔG°‡}$.

Effect of Catalysts on Activation Energy

• Catalytic Action: An example involving the reaction:
    $2H_2O_2 <br>ightarrow 2H_2O + O_2$
    - $ext{ΔG°‡}$ is reduced when the reaction is facilitated by platinum surfaces, and further reduced in the presence of the enzyme catalase.

Enzyme Catalysis

• Free Energy Change Expression: For a reaction at constant temperature and pressure, the change in free energy is expressed as:
    $ext{ΔG°} = ext{ΔH°} - T ext{ΔS°}$
    - Here, $ext{ΔG°}$ denotes the energy difference from the initial to final states, while $K_{eq}$ relates the change in free energy to the equilibrium constant by:
    $ext{ΔG°} = -RT ext{ln}K_{eq}$

Temperature Dependence of Catalysis

• Temperature Effect: Rising temperature increases kinetic energy of reactants, thereby accelerating approach to transition states.
    - Limitations: Prolonged temperature increases can lead to enzyme denaturation, thereby impairing function.

Enzyme–Substrate Binding

• Binding Dynamics:
    - The substrate (S) must bind to the active site of the enzyme where the reaction occurs, utilizing noncovalent interactions (hydrogen bonds, electrostatic interactions, van der Waals forces).

• Binding Models:
    - Lock-and-key model: The geometry of the substrate and active site are complementary.
    - Induced-fit model: The binding of the substrate causes a conformational shift in the enzyme to accommodate the substrate.

Enzyme–Substrate Complex Formation

• ES Complex Formation: Binding of enzyme (E) and substrate (S) forms the enzyme-substrate complex (ES), lowering its energy relative to the separate components (E + S).
    - The energy diagram shows ES complex needing to achieve transition state formation (EX‡) for reaction progression.

• Enhancement Factors: Proximity and orientation of the substrate molecules aid in speeding up the reaction chemistry.

Michaelis–Menten Approach to Enzyme Kinetics

• Basic Equation: The enzymatic reaction follows:
    $E + S <br>ightleftharpoons ES <br>ightarrow E + P$
    - Where
      - $k_1$ = Rate constant for the formation of ES
      - $k_{-1}$ = Rate constant for dissociation of ES
      - $k_2$ = Rate constant for conversion of ES to P.

Rate (Velocity) of an Enzymatic Reaction

• Initial Rate (Vinit or V0): The initial rate is dependent on substrate concentration $[S]$ while holding enzyme concentration constant.

• Maximum Velocity (Vmax): When substrate concentration approaches infinity, the enyzme reaction reaches its maximum velocity.

Michaelis–Menten Equation

• Michaelis Constant (KM): Defined as:
    - A measure of enzyme affinity for the substrate; lower values signify higher affinity.
    - The equation is written as:
    $V_{init} = rac{V_{max}[S]}{K_M + [S]}$

Graphical Determination of Vmax and KM

• Saturation Effect: At saturation, the reaction plateaus at Vmax.

• When [S] = KM: The relationship can be expressed as:
    $V_{max} = 2V_{init}$

Linearizing the Michaelis–Menten Equation

• Reciprocal Transformation: The complex hyperbolic equation can be linearized by taking reciprocals resulting in:
    $rac{1}{V_{max}} + rac{K_M}{V_{max}[S]} = rac{1}{[S]}$

• Straight Line Form: This yields parameters for the double-reciprocal Lineweaver-Burk plot:
    $y = mx + b$

Lineweaver–Burk Plot

• Graphical Interpretation: The slope of the Lineweaver-Burk plot equals $rac{K_M}{V_{max}}$, and the y-intercept equals $rac{1}{V_{max}}$.

Example - Enzyme-Catalyzed Reaction

• Data Analysis: Utilize provided data for 1/[S] vs. 1/V to determine values of $K_M$ and $V_{max}$ using Lineweaver-Burk method.

• Results:
    - Y-intercept = 12
    - X-intercept = -0.155
    - $V_{max} = 0.083 ext{ mM s}^{-1}$
    - $K_M = 6.45 ext{ mM}$

Significance of KM and Vmax

• Half-Max Velocity: At $V = rac{V_{max}}{2}$, $K_M = [S]$.

• Turnover Number (kcat): Defined as the number of substrate moles converted per mole of enzyme per second:
    $k_{cat} = rac{V_{max}}{[E]}$

Turnover Numbers and KM for Typical Enzymes

• Table of Enzyme Activities:
    - Catalase: $k_{cat} = 25, K_M = 4 imes 10^7 ext{ mM}$
    - Carbonic Anhydrase: $k_{cat} = 1 imes 10^6, K_M = 12 ext{ mM}$
    - Acetylcholinesterase: $k_{cat} = 1.4 imes 10^4, K_M = 9.5 imes 10^{-2}$

Inhibitors

• Definition: Substances that reduce the rate of enzymatic reactions.

• Types:
    - Reversible Inhibitors: Can bind and unbind from enzymes (includes competitive, noncompetitive, and uncompetitive inhibitors).
    - Irreversible Inhibitors: Covalently bind to enzymes, leading to permanent enzyme inactivation.

Competitive Inhibition

• Mechanism: Inhibitor resembles substrate and competes for binding to the active site, impacting reaction velocity.

• Equilibrium Expression: $E + S <br>ightleftharpoons ES$ or $E + I <br>ightleftharpoons EI$.

• Kinetic Parameters: Jumps in slope, constant y-intercepts meaning $V_{max}$ remains unchanged but $K_M$ (Michaelis constant) increases.

Noncompetitive Inhibition

• Mechanism: Inhibitor binds to the enzyme distinct from the active site, resulting in distortion and blockage of catalytic activity.
    - Kinetic Effect: $V_{max}$ decreases while $K_M$ remains constant, independent of substrate concentration effects.

Uncompetitive Inhibition

• Mechanism: Inhibitor binds specifically to the ES complex hindering reversion to products.

• Lineweaver-Burk Plot: Exhibits parallel lines indicating simultaneous decrease of both $V_{max}$ and $K_M$.

Irreversible Inhibition

• Definition: Permanent inactivation of enzymes through covalent binding of inhibitors.
    - Suicide Substrates: Molecules that irreversibly bind to and inactivate an enzyme, represented by drug structures such as penicillin.