Van 5 - enzyme kinetics

Enzyme Kinetics Overview

• Study of reaction rates and how they change with different conditions.

• Applications include:

• Measuring enzyme concentration in mixtures

• Investigating enzyme purity

• Establishing enzyme efficiency for different substrates

• Comparing different enzyme forms across tissues/organisms

• Evaluating inhibitor effects.

Initial Velocities

• Initial velocity (V0) is the slope of the progress curve at the start of a reaction, commonly measured in the first 60 seconds.

• Progress curve: [P] (product concentration) over time.

• V0 can be affected by:

• Substrate depletion

• Reverse reaction (P → S) as product accumulates

• Product inhibition of the enzyme

• Enzyme instability.

Hyperbolic Relationships

• Initial velocities plotted against initial substrate concentration ([S0]) show a hyperbolic curve.

• First-order region:

• At low [S0], V0 is approximately linear to [S0].

• Zero-order region:

• At high [S0], V0 becomes independent of [S0] (approaching Vmax).

Kinetics Orders

• First-order kinetics:

• Rate depends on substrate concentration:
  $-d[A]/dt = k[A]$

• Zero-order kinetics:

• Rate is constant, independent of substrate concentration:
  $-d[A]/dt = k$

Key Symbols

• E = Enzyme

• P = Product

• [S] = Substrate concentration

• [E0] = Initial enzyme concentration

• V0 = Initial velocity

• Vmax = Maximum velocity:
  $Vmax = k2[E0]$

• Km = Michaelis constant:
  $Km = \frac{k<em>{-1} + k</em>{2}}{k_1}$

• kcat = Turnover number:
  $kcat = \frac{Vmax}{[E0]}$

Steady State and Pre-Steady State

• Pre-steady state:

• Rapid accumulation of enzyme-substrate complex (ES), measured with specialized equipment.

• Steady state:

• Concentration of ES remains constant; determined from initial velocity.

Derivation of the Michaelis-Menten Equation

• Assumptions:

1. Almost no product accumulates initially.

2. Steady-state assumption (ES concentration is constant).

3. Fast binding (E + S ↔ ES) versus slower catalytic reaction (ES → E + P).

4. [E0] << [S0], substrate concentration approximately constant: [S] ≈ [S0].

5. Total enzyme concentration:
   $[E0] = [E] + [ES]$

Understanding the Michaelis-Menten Equation

• At low [S0], V0 is linearly proportional to [S0]

• At high [S0], V0 approaches Vmax (zero-order conditions).

• Km is the substrate concentration at which V0 = Vmax / 2.

Physical Meaning of Km, Vmax, kcat

• Km: Concentration yielding half-maximal velocity; relates to binding affinity.

• Vmax: Maximum rate when enzyme is saturated with substrate.

• kcat: Number of substrate conversions per enzyme molecule per second at saturation.

Lineweaver-Burk Plot

• Transforming Michaelis-Menten equation gives a linear equation:
  $\frac{1}{V0} = \frac{Km}{Vmax} \cdot \frac{1}{[S0]} + \frac{1}{Vmax}$

• Straight line with Y-intercept = 1/Vmax, slope = Km/Vmax.

• Use caution: high substrate concentration points cluster near origin and error magnification.

Specificity Constant and Rate Enhancement

• The ratio of Kcat to Km, or turnover to binding affinity. Important as indication of enzyme performance.

• High specificity constant implies high efficiency of enzyme turning substrate into products relative to how many bound-enzyme. High specificity constant = high turnover and high affinity.

• Specificity constant:
  ${Specificity Constant}=\frac{kcat}{Km}$

• In comparison with Kcat which only measures how fast the enzyme turns ES to P, this metric takes into account of the specific substrate.

• Rate enhancement measures how much the enzyme reduces activation energy compared to uncatalyzed conditions.

  • Kcat/Kuncat=exp(delta G uncat - delta Gcat)/RT

Specific Activity

• Total activity divided by enzyme concentration, measured in units/mg.

• Important for enzyme purity.

Exam Preparation

• Review applications of enzymes and kinetics.

• Practice exam-style questions on concepts covered in this lesson.