Lecture17-linearplots

Lecture17-linearplots -...

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: BIOC*2580
Lecture
17:

Experimental
Enzyme
Kinetics
 Linear
Plots
 1 Synopsis:
 The
 kinetic
 behaviour
 of
 enzymes
 is
 described
 by
 the
 Michaelis‐
 Menten
 equation,
 and
the
two
characteristic
constants
associated
with
this
equation,
 Vmax
and
KM.
Every
enzyme
 has
 specific
 values
 for
 these
 constants,
 which
 must
 be
 measured
 experimentally.
 Linear
 plots
 like
 the
 Lineweaver‐Burk
 plot
 provide
 the
 simplest
 means
 of
 fitting
 potentially
 error
 prone
 experimental
values
to
the
Michaelis‐Menten
equation.
 
 Reading:
Lehninger
p.
194‐205
(4th
ed
p.202‐212).
 
 
 Experimental
measurement
of
enzyme
kinetic
properties
 
 The
 kinetic
 properties
 of
 enzymes
 may
 be
 characterized
 by
 measuring
 reaction
 rates
 for
 a
 series
of
different
substrate
concentrations.
Each
rate
measured
should
be
an
 initial
velocity,
 either
by
taking
the
slope
of
a
progress
curve
 ([S]
or
[P]
plotted
versus
time)
at
zero
time,
or
by
 allowing
 the
 reaction
 to
 proceed
 for
 a
 very
 brief
 time
 and
 measuring
 extent
 of
 reaction.
 The
 reaction
should
be
demonstrated
to
be
linear
over
the
short
time
interval.


 
 A
 different
 progress
 curve
 is
 obtained
 for
 each
 initial
 substrate
 concentration,
 which
 is
 indicated
 by
 where
 the
curve
starts
on
the
[S]
axis.

A
slope
is
measured
for
 each
curve
at
t
=
0.

These
slopes
are
the
initial
rates,
vo
 used
 in
 the
 Michaelis‐Menten
 plot.
 The
 Michaelis
 Menten
Hyperbolic
plot.
 
 Initial
 rates
 taken
 from
 the
 progress
 curves
 are
 then
 plotted
 as
 a
 function
 of
 [S].
 
 The
 graph
 follows
 a
 characteristic
 hyperbolic
 shape
 that
 matches
 the
 Michaelis‐Menten
equation.
 
 
 
 Vmax
 is
 the
 limiting
 maximum
 rate
 as
 [S]
 tends
 to
 infinity.
 
 Once
Vmax
has
been
determined
we
find
the
 point
 on
the
curve
where
vo
=
½
Vmax;
 the
 concentration
 [S]
at
this
point
gives
the
value
of
KM.
 
 Page
1
of
3
 BIOC*2580
Lecture
17:

Experimental
Enzyme
Kinetics
 Linear
Plots
 2 KM
and
Vmax
tell
you
about
the
enzyme’s
properties
as
a
catalyst.
 
 Vmax
 indicates
catalytic
 rate
when
 100%
of
enzyme
is
occupied
by
substrate
higher
Vmax
 means
 faster
reaction,
better
catalysis.
 Vmax
 is
not
a
true
constant
 ‐
it
is
only
constant
if
the
same
amount
of
enzyme
is
used
for
each
 rate
measurement.

Vmax
is
proportional
to
the
concentration
of
enzyme
present:
 
 Vmax
=
k2
[E]total
 
 From
 Vmax,
we
can
calculate
the
true
constant
 k2,
the
rate
constant
for
the
catalytic
step
of
the
 two
step
enzyme
reaction.

k2
(sometimes
written
as

kcat)
is
the
turnover
number
of
the
enzyme.
 
 binding catalysis 
 k2
 
 E



+




S













ES





 





E


+


P
 KM
indicates
the
affinity
of
the
substrate
for
the
enzyme.

 Low
KM
means
high
affinity,
the
enzyme
binds
this
substrate
strongly;
 High
KM
means
low
affinity,
the
enzyme
binds
this
substrate
more
weakly.
 
 An
enzyme
that
recognizes
different
substrates
will
have
a
different
KM
for
each
substrate.

To
 measure
KM
 of
substrate
B,
 keep
[A]
high
and
constant,
 measure
rate
as
a
function
of
 varying
 [B].
 
 Measuring
Vmax
and
KM
can
be
tricky
 
 Unfortunately
 it's
 not
 as
 easy
 as
 it
 seems
 to
 estimate
 Vmax
 by
 inspection
 of
 the
 hyperbolic
 plot,
since
the
curve
keeps
creeping
up
even
at
 very
high
[S].
Most
people
underestimate
Vmax
 by
 10‐20%
 when
 using
 this
 method.
 If
 the
 estimate
of
 Vmax
is
bad,
the
estimate
of
 ½
Vmax
 and
KM
is
also
affected.

 
 Real
 experimental
 data
 also
 tends
 to
 scatter
 off
 the
theoretical
curve
due
to
measurement
 errors,
making
graphing
the
correct
curve
even
 more
difficult.
 Page
2
of
3
 BIOC*2580
Lecture
17:

Experimental
Enzyme
Kinetics
 Linear
Plots
 3 Linear
Plots
 
 Instead,
 the
 Michaelis‐Menten
 equation
 may
 be
 rewritten
 to
 plot
 as
 a
 straight
 line,
 which
 is
 much
easier
for
graphing
experimental
data.
This
is
known
as
a
linear
transform.


 
 Lineweaver‐Burk
or
Double
Reciprocal
Plot
 
 Take
 reciprocals
 of
 both
 sides
 of
 the
 Michaelis‐Menten
 equation
and
then
cancel.
 
 If
we
substitute
y
for
1
/
vo
and
x
for
1
/
[S],
this
is
now
the
 standard
equation
for
a
straight
line,
with
slope
=
KM
/
Vmax,
 and
y
intercept
=
1
/
Vmax.

 
 A
 straight‐line
 plot
 is
 much
 preferred
 over
 a
 curve,
 particularly
when
the
data
is
slightly
 scattered
 due
to
experimental
error.
Slopes
and
intercepts
 are
relatively
easily
obtained
from
a
straight‐line
graph.

The
result
is
known
as
the
Lineweaver‐ Burk
plot,
or
Double
Reciprocal
plot.
 
 Y‐axis
 1
/
vo

 X‐axis
 1
/
[S]
 Slope
 KM
/
Vmax
 Y‐intercept
 1
/
Vmax
 X‐intercept
 KM
/
Vmax
 
 The
Lineweaver‐Burk
plot
is
usually
extrapolated
to
the
negative
x‐axis.
Although
there's
no
data
 with
negative
x
values,
the
negative
x‐intercept
can
be
used
to
obtain
KM.
 X‐intercept
=
–
Y‐intercept
/
slope.

 
 A
hint
for
correlating
axis
labels
and
intercepts:

The
 y‐axis
is
 1
/
vo,
so
its
intercept
is
 1
/
Vmax
 The
x
axis
is
1
/
[S]
so
its
intercept
is
–
1
/
KM.
(the
negative
sign
corrects
for
the
intercept
having
 a
negative
value).

Remember
that
KM
 is
a
concentration,
the
concentration
[S]
that
 happens
to
 give
50%
of
maximum
rate
or
0.5
×
Vmax.
 
 Page
3
of
3
 ...
View Full Document

This note was uploaded on 09/21/2011 for the course BIOOC 2580 taught by Professor Douger during the Fall '10 term at University of Guelph.

Ask a homework question - tutors are online