Michaelis Menten Equation and Graph


The equation for this curve is:


where v is the reaction rate, vmax is the maximum reaction rate, Km is the concentration at which the reaction is running at half the maximum rate, and [S] is the concentration of the substrate.The graph starts at 1st order with low [S], then becomes 0th order as S approaches infinity.

Lineweaver Burk Equation and Graph


The equation for this curve is:


This equation is simply derived from the equation above. The axes are both reciprocals of the axes on the graph above. This linear equation provides a good way to easily find vmax and Km.

Notes on Inhibition

  • Competitive: The inhibitor binds to and blocks the enzyme’s active site. This does not change the vmax, but it does increase Km.
    • In a Michaelis Menten plot,the max height will stay the same, but the rate will rise less steeply as concentration increases.
    • In a Lineweaver Burk plot, the line grows more steep and the x intercept (which is negative) moves closer to x = 0.
  • Noncompetitive: The inhibitor binds to the enzyme in a place where it just makes the enzyme work less efficiently. This does not change Km, but it decreases vmax.
    • In a Michaelis Menten plot, vmax will decrease, so ½*vmax will decrease as well. Make sure the Km for the new, lower ½*vmax is the same as the old Km for the old, higher ½*vmax.
    • In a Lineweaver Burk plot, the line grows more steep (again), but this time because the y intercept gets bigger.
  • Uncompetitive: The inhibitor can only bind to the complex formed by the enzyme and substrate. This lowers Km and lowers vmax.
    • In a Michaelis Menten plot just check to make sure both Km and vmax are changing.
    • In a Lineweaver Burk plot, the new line will be parallel to the old line, but will have a larger x and y intercept.