CHE414 Lecture 16 (Enzyme Kinetics Continued; F24)

Lecture 16: The Michaelis-Menten Equation and Fun Kinetic Parameters

• Introduction to the topic with a light-hearted comment.

Overview of the Michaelis-Menten Theory

• Key Components of Reaction Equilibrium:

  • Enzyme (E) + Substrate (S) ⇌ ES ⇌ E + Product (P)

  • Reaction Constants: k-1, k1, k2.

• Assumptions Made by Michaelis and Menten:

  • Assumption 1: The overall reaction is considered irreversible for measuring initial rates.

  • Assumption 2: The conversion of ES to E + P is the rate-limiting step.

  • Assumption 3: The concentration of ES remains constant during the early course of the reaction (steady state assumption).

Steady State Concept

• A graphical representation shows that [ES] remains steady as substrate is converted to product.

The Michaelis-Menten Equation

• Mathematical Expression: Vmax[S] / (KM + [S]) = v0

  • Where:

    • v0 = Initial velocity, measured at the start of the reaction.

    • [S] = Substrate concentration.

    • KM = Michaelis constant, indicative of enzyme affinity.

    • Vmax = Maximum reaction velocity achieved when all enzyme active sites are saturated.

Enzyme Scorecard

• Key Parameters:

  • KM: Substrate concentration for enzyme saturation.

  • kcat: Catalytic constant or turnover number, represented as Vmax/[E]total.

  • kcat/KM: Catalytic efficiency, combining enzyme substrate affinity and turnover rate.

Understanding KM (Michaelis Constant)

• Interpretation of KM:

  • High KM indicates low enzyme affinity for substrate, requiring more substrate to achieve saturation.

  • Low KM indicates high enzyme affinity for substrate, needing less substrate to achieve saturation.

• Importance of Units for KM.

Kinetics and Reaction Velocity

• The equation is hyperbolic:

  • At half Vmax, KM = [S], suggesting occupancy of half of the active sites.

The Role of kcat in Enzyme Activity

• Definition and significance of kcat:

  • kcat represents the maximum rate of reaction per enzyme molecule at saturation.

• Units of kcat indicating reaction speed.

Catalytic Efficiency: kcat/KM

• Combines KM and kcat to measure enzyme efficiency.

• Importance of balancing substrate binding affinity and product formation speed.

Diffusion-Controlled Limit for Catalysis

• Maximum rate at which two freely diffusing molecules can collide: 10^8 to 10^9 M-1 s-1.

• Catalytic perfection is when enzymes work as efficiently as substrate collisions.

• Example: Triose phosphate isomerase showcases rapid electronic rearrangements.

Experiment Design for Vmax and KM Determination

• Acknowledgment that Vmax is never fully reached in experimental data.

Lineweaver-Burk Plot

• Conversion of the Michaelis-Menten equation:

  • y = (KM/Vmax)(1/[S]) + (1/Vmax)

• Helps linearize data for easier determination of KM and Vmax.

Application of the Lineweaver-Burk Plot

• Insight into determining values from a given graph.

Enzyme Inhibition

• Definition: Substances that interfere with enzyme function.

• Role in therapeutics, food preservation, and cellular regulation.

• Classifications:

  • Irreversible (e.g., 5-fluorouracil covalently modifying enzymes).

  • Reversible (e.g., competitive and noncompetitive).

Types of Reversible Inhibition

• Competitive Inhibition:

  • Inhibitor directly competes for the enzyme's active site.

  • Affects KM but not Vmax—the enzyme's apparent affinity decreases.

• Example: Malonate as a competitive inhibitor of succinate dehydrogenase.

Effects of Competitive Inhibition

• Competitive inhibitors increase KM due to reduced substrate availability but do not affect Vmax; high substrate concentrations can overcome inhibition effects.

Analyzing Inhibitor Efficacy

• Investigating the effects of inhibitors in drug design and therapeutic applications with specific examples.

Competitive Inhibition and Drug Design

• Example: Lipitor's inhibitory capability with given values for KM and KI with respect to HMG-CoA reductase.