Michaelis Menten Equation and Graph

The equation for this curve is:

where v is the reaction rate, v_max is the maximum reaction rate, K_m 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 v_max and K_m.

Notes on Inhibition

• Competitive: The inhibitor binds to and blocks the enzyme’s active site. This does not change the v_max, but it does increase K_m.
  • 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 K_m, but it decreases v_max.
  • In a Michaelis Menten plot, v_max will decrease, so ½*v_max will decrease as well. Make sure the K_m for the new, lower ½*v_max is the same as the old K_m for the old, higher ½*v_max.
  • 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 K_m and lowers v_max.
  • In a Michaelis Menten plot just check to make sure both K_m and v_max 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.