Michaelis-Menten kinetics

• Core Concept
  • Describes the kinetics of most enzyme-catalyzed reactions. It relates the initial reaction velocity (v) to the substrate concentration ([S]).
  • Equation:

$$V=\frac{V_{\text{max}}[S]}{K_m+[S]}$$

• Key Parameters
  • V​_max (Maximum Velocity):
    • The maximum rate of reaction when the enzyme is fully saturated with substrate.
    • Directly proportional to the enzyme concentration. The only way to increase V_max is to increase the enzyme concentration.
  • K​_m (Michaelis Constant):
    • The substrate concentration ([S]) at which the reaction velocity is half of V​_max (½ V​_max).
    • It is an intrinsic property of the enzyme for its substrate.
    • Inversely related to the affinity of the enzyme for its substrate.
    • Low K​_m = High affinity (less substrate needed to reach ½ V​_max).
    • High K​_m = Low affinity (more substrate needed to reach ½ V​_max).
• Reaction Order
  • At low [S] (when [S] << K​_m):
    • The reaction rate is directly proportional to the substrate concentration.
    • Approximates first-order kinetics.
  • At high [S] (when [S] >> K​_m):
    • The reaction rate is independent of substrate concentration and is at V​_max.
    • Approximates zero-order kinetics (enzyme is saturated).

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Lineweaver-Burk Plot

• Description
  • A double reciprocal plot of Michaelis-Menten kinetics (1/v vs. 1/[S]), which linearizes the hyperbolic curve.
  • Useful for determining V_max and K_m and for analyzing the effects of enzyme inhibitors.
• Interpreting the Plot
  • Y-intercept = 1/V​_max
    • A higher Y-intercept means a lower V​_max.
  • X-intercept = -1/K​_m
    • A point further to the right (closer to zero) on the x-axis indicates a higher K_m (and thus lower affinity).
• Effect of Inhibitors (High-Yield)
  • Competitive Inhibitors:
    • Mechanism: Bind to the active site, competing with the substrate. Can be overcome by increasing [S].
    • Effect: Increases K​_m (affinity decreases). V​_max is unchanged.
    • Lineweaver-Burk: Lines intersect at the y-axis.
  • Noncompetitive Inhibitors:
    • Mechanism: Bind to an allosteric (different) site, changing enzyme conformation. Cannot be overcome by increasing [S].
    • Effect: Decreases V​_max. K​_m is unchanged (affinity for substrate is not affected).
    • Lineweaver-Burk: Lines intersect at the x-axis.