Michaelis-Menten Equation Overview

Michaelis-Menten Equation

• The Michaelis-Menten equation describes the rate equation for a one-substrate enzyme-catalyzed reaction.
• It's expressed as: V₀ = (Vmax [S]) / (Km + [S])
• V₀ represents the initial velocity.
• Vmax represents the maximum velocity.
• [S] represents the initial substrate concentration.
• Km represents the Michaelis constant.
• V₀, Vmax, [S], and Km can be measured experimentally.

Enzyme Action (Michaelis-Menten)

• Enzyme and substrate combine to form a complex (ES) in a fast, reversible step.
  • This is described by the reaction E + S ⇌ ES
• The ES complex then breaks down to yield the free enzyme and the reaction product (E + P) in a slower step.
  • This is represented by the reaction ES ⇌ E + P
• The second step limits the overall reaction rate.
• The overall reaction rate is proportional to [ES].

Lineweaver-Burk Equation

• Simplifying the Michaelis-Menten equation leads to the Lineweaver-Burk equation.
• The Lineweaver-Burk equation is useful for graphically determining the kinetic parameters for an enzyme.
• The equation is expressed as 1/V₀ = (Km/Vmax) (1/[S]) + 1/Vmax.

Interpreting Km

• Km can vary for different substrates of the same enzyme.
• Km values for different enzymes and substrates are in a table.

Interpreting Vmax

• The number of reaction steps and the rate-limiting step(s) differ among enzymes.
• For a two-step Michaelis-Menten mechanism:
  • If the rate-limiting step is ES → EP, then Vmax = k₂[Et].
  • If the rate-limiting step is EP → E + P, then Vmax = k₃[Et].

kcat (Turnover Number)

• kcat is the turnover number.
• It's the number of substrate molecules converted to product per enzyme molecule per unit of time when the enzyme is saturated.
• kcat values for different enzymes and substrates are in a table.

Comparing Catalytic Mechanisms and Efficiencies

• Comparing the ratio kcat/Km for two reactions is important to compare catalytic efficiencies or turnover.
• The specificity constant is the rate constant for the conversion of E + S to E + P.

kcat/Km

• kcat/Km has units of M⁻¹s⁻¹.
• The upper limit for kcat/Km is 10⁸ to 10⁹ M⁻¹s⁻¹.
• A table lists enzymes with kcat/Km close to the diffusion-controlled limit (10⁸ to 10⁹ M⁻¹s⁻¹).

Reactions with Multiple Substrates

• Enzymes catalyzing reactions involving two or more substrates account for nearly 2/3 of all enzymatic reactions.
  • Often they have two substrates and two products.
• Examples
  • Group transfer reactions
  • Oxidation-reduction reactions

Ternary Complex

• Substrates can bind in a random sequence or in a specific order.
• Some reactions involve a ternary complex (enzyme-substrate-substrate).
  • These reactions have a different reaction mechanism compared to simpler reactions
• Some enzyme reactions do not form a ternary complex.
  • Ping-Pong, or double-displacement reactions