Graphical Analysis of Enzyme Kinetics Enzyme Kinetics Go back
Mathematical Analysis
Michaelis-Menten (MM) Kinetics Extended MM equation for interacting sites Rectangular hyperbolic plot Double-reciprocal plot
Assumptions and givens:

  • -- steady-state approximation

  • [P] = 0 -- at time zero

  •  

  • [Etotal] = [E] + [ES]

  • Vmax = k3 [Etotal]

  •  
    at V = (1/2) Vmax
=  MM equation
Assumptions and givens:

  •  -- steady-state approximation

  • [P] = 0 -- at time zero

  • [Etotal] = [E] + [ESn]

  • Vmax = n k3 [Etotal]


  • at V = (1/2) Vmax

where h = Hill coefficient

where h = 1 for a MM enzyme

where h = 1 for a MM enzyme
Hill plot
 Scatchard plot

where
 h = 1 for a MM enzyme and
r/[S] =
([S]h-1/Kmh)*(n-r)
where h = 1 for a MM enzyme
Direct linear plot (n = 1)
where
"y" = Vmax "x" = Km b = V a = V/[S]
Empirical Definitions
Km = [S] at 50% Vmax = [S]50%;  h = Hill coefficient; k3 = kcat = Vmax/[E]total = "turnover number"
where turnover number = number of product molecules/enzyme molecule/unit time.
© Duane W. Sears
Revised: October 07, 2010