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The Vmax and Km values of a certain enzyme
can be measured by the double reciprocal
plot.
The plot provides a useful graphical method
for analysis of the Michaelis–Menten equation.
Taking the reciprocal gives
The double
reciprocal plot:
1/V0 vs 1/[S]
Apply this to equation for a straight line
When we plot
versus
Hanes–Woolf plot:
 A graphical representation of enzyme kinetics in which the
ratio of the initial substrate concentration [S] to the reaction
velocity v is plotted against [S].
Inversting and multiply by [S]:
A perfect data will yield a straight line of slope 1/Vmax, a yintercept of Km/Vmax and an x-intercept of −Km.
Hanes–Woolf plot
Eadie–Hofstee Plot Model
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Is a graphical representation of enzyme
kinetics in which reaction velocity is plotted as
a function of the velocity vs. substrate
concentration ratio:
A plot of v vs v/[S] will yield Vmax as the yintercept, Vmax/Km as the x-intercept, and Km as
the slope.
Like other techniques that linearize the
Michaelis–Menten equation, the Eadie-Hofstee
plot was used historically for rapid
identification of important kinetic terms like Km
and Vmax,
:
invert and multiply with Vmax
Eadie–Hofstee Plot Model
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The "kinetic activator constant"
Km is a constant
Km is a constant derived from rate constants
Km is, under true Michaelis-Menten
conditions, an estimate of the dissociation
constant of E from S
Small Km means tight binding; high Km
means weak binding
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The theoretical maximal velocity
Vmax is a constant
Vmax is the theoretical maximal rate of the
reaction - but it is NEVER achieved in reality
To reach Vmax would require that ALL enzyme
molecules are tightly bound with substrate
Vmax is asymptotically approached as
substrate is increased
Combination of 0-order and 1st-order kinetics
 When S is low, the equation for rate is 1st
order in S
 When S is high, the equation for rate is 0order in S
 The Michaelis-Menten equation describes
a rectangular hyperbolic dependence of v
on S!
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A measure of catalytic activity
kcat, the turnover number, is the number of
substrate molecules converted to product per
enzyme molecule per unit of time, when E is
saturated with substrate.
If the M-M model fits, k2 = kcat
Values of kcat range from less than 1/sec to
many millions per sec
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Name for kcat/Km
An estimate of "how perfect" the enzyme
is
kcat/Km is an apparent second-order rate
constant
It measures how the enzyme performs
when S is low
The upper limit for kcat/Km is the
diffusion limit - the rate at which E and S
diffuse together
Catalytic perfection (rate of reaction being
diffusion-controlled) can be achieved by a
combination of different values of kcat and Km.