# 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" = Km b = V a = V/[S]

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

Graphical Analysis of Enzyme Kinetics