Previous Class
•Michaelis – Menten equation
•Steady state vs pre-steady state
Today
Review derivation and interpretation
¾Graphical representation
¾Michaelis – Menten equations and parameters
The Michaelis – Menten Equation
v = Vmax [S]
Km + [S]
Km = Michaelis constant: Concentration of Substrate
needed to reach half maximum velocity – measure of
substrate affinity
Vmax = maximum velocity – directly proportional to
enzyme concentration
The Michaelis – Menten Equation
Km
Ef + S
k1
k-1
ES
k2
Ef + P
[E][S] = k-1 + k2 = Km
[ES]
k
Eqn 1
1
Km is an apparent dissociation constant (Ks)
and represents the [S] when v = ½ Vmax
Therefore, a lower Km value indicates a higher affinity for
the substrate
The Michaelis – Menten Equation
The Michaelis – Menten Equation
Interpretation
Obtain kinetic behaviour of an enzyme
E+S
k2 = kcat
kcat = Vmax/[ET]
k1
k-1
ES
k2
E+ P
Catalytic constant of the reaction (first
order) when k2 is fast (saturating kinetics)
(When EP → E + P is fast)
kcat is also known as the turnover number of the enzyme –
defining the maximum number of substrate molecules
converted to product per unit of time
Units
v0 = initial velocity of Product formation = moles Product
formation (moles substrate loss)/litre x time
= mM s-1
Vmax = represents the maximum rate the enzyme reaction can
achieve. Vmax occurs when all of the enzyme is in the ES
complex.
Km = [S] at Vmax/2 = µM
kcat = first order rate constant = s-1
# of catalytic cycles active site undergoes per unit of time
The Michaelis – Menten Equation
kcat/Km
At any [S] including:
At very low [S] ([S]→0) : pre-steady state conditions
v0 = Vmax [S]
Km + [S]
becomes
v0 = Vmax[S] = kcat[E][S]
Km
Km
The second order rate constant kcat/Km indicates the catalytic efficiency
of the enzyme:
A direct measure of the efficiency of the enzyme in transforming Subst.
kcat/Km combines: the effectiveness of transformation of bound product
the effectiveness of productive substrate binding
Units
v0 = initial velocity of Product formation = moles Product
formation (moles substrate loss)/litre x time
= mM s-1
Vmax = represents the maximum rate the enzyme reaction can
achieve. Vmax occurs when all of the enzyme is in the ES
complex.
Km = [S] at Vmax/2 = µM
kcat = first order rate constant = s-1
# of catalytic cycles active site undergoes per unit of time
kcat/Km = second order rate reaction of E and S = M-1 s-1
The Michaelis – Menten Equation
Lineweaver-Burke transformation of the
Michaelis-Menton equation.
•Velocity vs substrate plots are useful for visually
estimating kinetic parameters
•Hyperbolic curves cannot properly determine the upper
limit of the curve (Vmax)
•Transforming the data to a form that can be plotted as a
line.
Lineweaver-Burke transformation of the
Michaelis-Menton equation.
v = Vmax [S]
Km + [S]
Reciprocal of the equation is:
1
Km + [S]
=
v Vmax [S]
Express reciprocal in the familiar form y = mx + b
Lineweaver-Burke transformation of the
Michaelis-Menton equation.
y = mx + b
1
V
=
Km
Vmax [S]
+
1
Vmax
1
V
Km
Vmax [S]
=
+
1
Vmax
Lineweaver-Burke equation represents a straight line with
slope = Km/Vmax, y intercept = 1/Vmax, and
x intercept = -1/Km
A
0.6
B
0.5
1/v (mM/min)
0.4
0.3
0.2
0.1
0.3
0.25 0.20 0.15 0.10
0.1
1/[S] (mM)
0.15 0.2 0.25
0.30 0.35
Lineweaver-Burke transformation of the
Michaelis-Menton equation.
•Most commonly used
•Magnitude of errors can become distorted
•Furthest point to the right (lowest [S]) influences where
line is drawn
•e.g. small error in v = large error in 1/v
•Good for observing enzyme inhibition
Eadie-Hofstee Plot
•Multiply both sides of L.B. by Vmax
•Multiply both sides by v
•Rearrange for v
v0
v
K
m
0
Vmax
=
[S]
Plot
v0
vs
v0
[S]
Eadie-Hofstee Plot
Vmax
v0
-Km = slope
Vmax
Km
v0/[S]
Eadie-Hofstee Plot
•Best for controlling slight deviations from linearity
•One disadvantage is that the least precise parameter (v0)
is expressed in both sides of the equation and plot
Plotting kinetic data
Michaelis-Menten kinetics (steady state kinetics)
Measure Initial rates (v0) at different substrate concentrations by
detecting the absorbance difference over time and obtaining the
slope of the line
Obtain various initial rates at different substrate concentrations and
plot
Use Lineweaver-Burke plots to obtain kcat, Km, kcat/Km
Plotting kinetic data
Measuring initial rates:
•The initial velocity is the amount of product produced per minute
•Assay involves adding all of the components including substrate
first
•Abs vs time can be plotted
•Determine slope of tangent
Absor.
•Once enzyme is added the absorbance is continually monitored and
recorded with respect to time
Enzyme
added
time
Plotting kinetic data
Measuring initial rates:
•The slope of tangent = ∆Abs/unit of time (min)
•Recall A = εcl, therefore ∆A = ε∆cl
(change in conc of Product)
•When ∆c occurs in a known time period then ∆c min-1 = v0
•v0 = ∆A min-1/ εl = ∆c min-1
•Has M/min after multiplying by vol. of enzyme assay solution the
units change to mol/min.
Plotting kinetic data
Determine v0 at different substrate concentrations and plot