Enzyme Kinetics

Michaelis-Menton (MM) KineticsExtended MM equation for interacting sites
[E] + [S]
k1

k2
[ES]
k3
 
[E] + [P]
Assumptions and givens:
  • d[ES]/dt = 0 -- steady-state approximation
  • [P] = 0 -- at time zero
  • V = d[P]/dt = k3 [ES]
  • [Etotal] = [E] + [ES]
  • Vmax = k3 [Etotal]
  • Km = (k2+ k3)/k1= [S]1/2
    where V = (1/2) Vmax
V / Vmax = [S] / ([S] + Km ) -- MM equation
[E] + n [S]
k1

k2
[ESn]
k3
 
[E] + n[P]
Assumptions and givens:
  • d[ESn]/dt = 0 -- steady-state approximation
  • [P] = 0 -- at time zero
  • V = d[P]/dt = n k3 [ESn]
  • [Etotal] = [E] + [ESn]
  • Vmax = n k3 [Etotal]
  • Km = (k2+ k3)/k1= ([S]1/2)n
    where V = (1/2) Vmax
V / Vmax = [S]n / ([S]n + Km )
where n = Hill coefficient

 

Graphical Methods
Rectangular hyperbolic plot
(n = Hill coefficient)		Double-reciprocal plot
"Ya" = V / Vmax = [S]n / ([S]n + Km )
where n = 1 for a MM enzyme		Vmax / V = 1 + Km / [S]n
where n = 1 for a MM enzyme
Hill plotScatchard plot
V/( Vmax - V ) = "Ya"/"Yd" = [S]n / Km
where n = 1 for a MM enzyme and
"Yd" = (Vmax - V ) / Vmax = Km / ( [S]n + Km )		(V / Vmax) / [S]n = ( 1 / Km ) * (1 - V / Vmax)
where n = 1 for a MM enzyme
Direct linear plot (n = 1)
Vmax = V + ( V / [S] ) * Km = "Y" = b + a"X" where
"Y" = Vmax"X" = Kmb = Va = V/[S]

Continue the kinetic analysis of enzymes by opening the following Excel spreadsheet

Graphical Analysis of Enzyme Kinetics

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© Duane W. Sears
Revised: July 27, 1998