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Unformatted text preview: BIOC*2580
Lecture
15:
Enzyme
assay,
detection
&
kinetics

 
 1
 
 Synopsis:
Enzymes
catalyze
most
biochemical
reactions,
governing
the
chemical
changes,
which
 we
call
metabolism.
We
can
gain
some
understanding
of
enzyme
behaviour
through
the
study
 of
 rates
 of
 enzyme‐catalyzed
 reactions,
 and
 by
 the
 mathematical
 analysis
 of
 rate,
 enzyme
 kinetics.
Simple
measures
of
enzyme
reactions
include
activity,
specific
activity
(activity
per
unit
 mass)
and
turnover
number
(activity
per
mole
of
enzyme).
Turnover
number
also
represents
the
 actual
number
of
times
an
enzyme
molecule
reacts
per
second.

 
 Reading:
Lehninger
p.
194‐205
(4th
ed
p.
202‐
212).
 
 
 Enzymes
 speed
 up
 the
 rate
 of
 a
 reaction
 by
 a
 definite
 amount,
 proportional
 to
 quantity
 of
 enzyme
present.

 
 Enzyme
assay
is
the
process
or
measuring
enzyme
catalyzed
reaction
rate.

 
 Enzyme
kinetics:
mathematical
analysis
of
how
the
observed
reaction
rate
varies
with
substrate
 concentration;
kinetic
behaviour
can
be
used
to
test
models
of
reaction
mechanism
 (rules
out
 wrong
models).

 
 Measurement
of
enzyme
rate:
 
 The
 enzyme
 is
 placed
 above
 the
 reaction
 arrow
 because
it's
a
catalyst,
not
consumed
in
the
reaction.
 The
complete
reaction
cycle
 restores
the
 enzyme
to
 its
initial
state.

 
 To
 measure
 reaction
 rate,
 some
 property
 difference
 between
 reactant
 and
 product
 must
 be
 identified.
Rate
can
be
measured
as
disappearance
of
reactant
or
accumulation
of
product.
 
 Examples:
 measure
volume
of
O2
gas
produced.

 
 
 measure
pH
increase
as
[H+]
is
consumed.
 
 It’s
more
difficult
when
the
reactants
and
products
 are
 chemically
 similar.
 You
 could
 separate
 the
 products
and
analyze
each
one,
 but
that
would
be
 a
lot
of
work
in
this
case.
 
 Page
1
of
5
 BIOC*2580
Lecture
15:
Enzyme
assay,
detection
&
kinetics

 
 2
 
 One
 approach
 might
 be
 to
 measure
 the
 increase
 in
 total
 reactive
 terminal
 amino
 groups
 by
 reaction
with
the
amino
acid
detection
reagent,
ninhydrin.
 1)
Take
a
sample
from
the
enzyme
reaction
mixture
at
intervals,
 2)
Add
ninhydrin
to
each
sample:
ninhydrin
only
reacts
with
N‐terminal
amino
groups,
not
with
 peptide‐bonded
NH
groups.
The
enzyme
reaction
creates
one
new
N‐terminal
amino
group
per
 peptide
bond
hydrolyzed.
 
 However
this
is
also
a
lot
of
work

 
 A
more
efficient
method
for
trypsin
and
other
hydrolytic
enzymes:
 
 Artificial
substrate:

an
artificial
substrate
is
a
compound
with
a
structure
sufficiently
similar
to
 the
 real
 substrate
 that
 the
 enzyme
 is
 fooled
 and
 binds
 and
 reacts
 with
 the
 artificial
 substrate,
 but
 is
designed
so
that
one
of
the
products
has
a
distinguishing
property.

For
trypsin,
a
short
 peptide
 ends
in
lysine,
however
the
lysine
is
amide‐bonded
to
p‐nitroaniline.

Trypsin
binds
and
 recognises
the
peptide
sequence
ahead
of
the
lysine,
so
the
nitroanilide
bond
is
accepted
as
if
it
 was
a
peptide
bond,
and
is
a
target
for
hydrolysis.
Trypsin
proceeds
to
hydrolyze
the
amide
bond
 between
lysine
carboxylate
and
the
aniline
NH2.
The
free
p‐nitroanilinehas
a
distinctive
 colour,
 which
is
easily
measured.
 
 Rate
 of
 increase
 of
 pink
 colour
 is
 a
 direct
 measure
 of
 rate
 of
 appearance
of
product.
 
 Artificial
substrates
are
often
used
for
enzymes
which
hydrolyze
simple
ester,
amide
or
glycoside
 bonds.


 
 Some
natural
substrates
show
absorbance
change
on
conversion
to
product:
 
 Lactate
 dehydrogenase
 oxidizes
 the
 secondary
 alcohol
 in
 lactate
 to
 a
 carbonyl
 in
 pyruvate.
 Lactate
dehydrogenase
removes
2
H
atoms
(not
H+)
from
the
substrate,
hence
the
enzyme
name
 dehydrogenase.
 The
 2
 H
 atoms
 are
 donated
 to
 a
 common
 biological
 oxidizing
 agent,
 NAD+,
 nicotinamide
adenine
dinucleotide,
which
is
reduced
to
NADH
+
H+.
 
 +
 NAD does
not
absorb
 ultraviolet
at
340
nm
 
 NAD
strongly
absorbs
 ultraviolet
at
340
nm
 Page
2
of
5
 Many
 metabolic
 enzymes
 follow
 this
 naming
 pattern:
 name
 of
 substrate
 +
 type
 of
 process.
 The
 reaction
 progress
 can
 be
 monitored
 by
 measuring
 the
 ultraviolet
absorbance
increase
 at
 340
 nm
 due
 to
 the
 formation
of
NADH.
 BIOC*2580
Lecture
15:
Enzyme
assay,
detection
&
kinetics

 
 3
 
 Coloured
or
Ultraviolet
absorbing
molecules
possess
chromophores.
 A
 chromophore
 is
 a
 part
 of
 a
 molecule
 that
 contains
 conjugated
 double
 bonds,
 a
 series
 of
 at
 least
 two
 double
 bonds
 that
 alternate
 with
 single
 bonds,
 e.g.
 N–C=C–C=O.
 
 The
 chromophore
 absorbs
 visible
 (400‐700
 nm
 wavelength)
 or
 ultraviolet
 light
 (200‐400
 nm).
 
 Compounds
 that
 absorb
 visible
 light
 appear
 with
 a
 colour
 opposite
 to
 what’s
 absorbed,
 so
 a
 compound
 that
 absorbs
blue
 appears
yellow
(white
minus
blue
=
yellow).
Relatively
few
biochemical
substances
 absorb
visible
light,
so
they
are
mostly
colourless,
but
several
key
compounds
absorb
ultraviolet.
 
 Larger
chromophores
with
many
conjugated
double
bonds
tend
to
absorb
at
longer
wavelengths
 for
example,
heme,
the
red
pigment
in
blood
(Lehninger
Fig.5‐1,
p.154,
4th
ed.
p.159)
 
 Absorbance
measurement
for
ultraviolet
or
visible
light.
 NADH
has
a
relatively
 small
 chromophore,
 so
 absorbs
 ultraviolet
 at
 340
 nm.
 The
 alternative
 resonance
form
 extends
 the
 chromophore
 through
 the
 N
 atom
 to
 the
 third
double
bond.
 
 Absorbance
is
measured
in
a
spectrophotometer,
which
provides
a
light
source
with
selectable
 wavelength
 in
 the
 range
 200‐700
 nm
 (ultraviolet
 and
 visible
 light).
 Sample
 is
 contained
 in
 a
 square
chamber
or
cuvet
of
exactly
1.00
cm
thickness.
The
light
passing
through
the
sample
is
 then
measured
and
recorded
by
a
detector.

 If
light
is
absorbed
by
the
sample,
the
measured
intensity
 I
 passing
through
the
sample
is
less
 than
the
original
intensity
of
the
beam
Io.
 
 I Absorbance
A
of
the
sample
is
defined
as
A
=
log10
(
 o/
I
),
so
if
90%
is
absorbed,
I
=
0.1
Io
and
A
 =
log10
(10)
=
1.000.

Most
spectrophotometers
read
out
directly
in
absorbance
units
in
the
range
 0
‐
3.000,
so
the
user
never
has
to
deal
directly
with
intensity
ratios.
 
 Page
3
of
5
 BIOC*2580
Lecture
15:
Enzyme
assay,
detection
&
kinetics

 
 4
 
 The
absorbance
of
a
sample
is
directly
proportional
to
concentration
(Beer's
Law)
and
to
sample
 thickness
 (Lambert's
 Law).
 When
 these
 two
 relationships
 are
 combined,
 we
 get
 the
 Beer‐ Lambert
equation:

 
 Absorbance
A
=
ε 
.
c
.
l
 
 where
 ε 
=
extinction
coefficient,
a
characteristic
constant
for
a
given
absorbing
substance.
For
 NADH
at
340
nm,
ε
=
6200
L
mol‐1
cm‐1.
 c
=
concentration
of
NADH
in
mol
/
L,
 l
=
thickness
of
the
sample
in
cm
(usually
1.00
cm
for
standard
sample
cuvettes).

 
 Sample
calculation:
 A
 lactate
 dehydrogenase
 reaction
 gave
 an
 increase
 in
 absorbance
 of
 0.357
 units
 due
 to
 the
 NADH
formed.
 
 absorbance
increase 0.357 
 Increase
in
[NADH]
 = 
 
=
 
 = 
5.76
x
10‐5 
mol/L 
 ε .l 6200 

 
 € Quantitative
description
of
enzyme
catalysis
 
 Rate
of
reaction

 =
concentration
of
substrate
disappearing
per
unit
time
(mol
L–1
sec–1)
 
 Or

 
 
 
 
 Enzyme
activity

 
 =

concentration
of
product
produced
per
unit
time
(mol
L–1
sec–1)
 =
moles
converted
per
unit
time

=
rate
x
reaction
volume
 Enzyme
activity
is
a
measure
of
quantity
of
enzyme
present.

The
SI
unit
is
the
katal,
1
katal
=
1
 mol
s‐1,
but
this
is
an
excessively
large
unit.
A
more
practical
value
is
1
enzyme
unit
(EU)
=
1
µmol
 min‐1
(µ
=
micro,

10‐6).
 
 Specific
activity

 =
moles
converted
per
unit
time
per
unit
mass
of
enzyme
 =
enzyme
activity
/
actual
mass
of
enzyme
present

 
 SI
units:
katal
kg‐1;


 Practical
units:
µmol
mg‐1
min‐1
or
µmol
µg‐1min‐1.

 
 Specific
activity
is
a
measure
of
enzyme
efficiency,
usually
constant
for
a
pure
enzyme.
 
 If
the
specific
activity
of
100%
pure
enzyme
is
known,
then
an
impure
sample
will
have
a
lower
 specific
activity,
allowing
purity
to
be
calculated.
 
 specific
activity
of
enzyme
sample %
purity
 = 
100%
x
 
 specific
activity
of
pure
enzyme 

 
 The
impure
sample
has
lower
specific
activity
because
some
of
the
mass
is
not
actually
enzyme.

 
 € Page
4
of
5
 BIOC*2580
Lecture
15:
Enzyme
assay,
detection
&
kinetics

 
 5
 
 Turnover
number
 = 
 

 moles
of
substrate
converted
per
unit
time 
 (usually
per
second)
 
 moles
of
enzyme 
 € 






=


specific
activity
x
molar
mass
of
enzyme

 (with
necessary
unit
conversions!)

 
 Multiplying
mass
by
molar
mass
converts
specific
activity
(per
unit
mass)
into
activity
per
mole.
 
 If
 n
moles
of
substrate
are
catalyzed
by
one
mole
of
enzyme
per
second,
then
 n
molecules
of
 substrate
are
catalysed
by
each
molecule
of
enzyme
per
second.

 
 Hence
 turnover
 number
 represents
 the
 number
 of
 times
 per
 second
 that
 the
 enzyme
 completes
a
reaction
cycle.
 
 Sample
calculations:
 A
solution
contains
initially
25.0
×
10–‐4
mol
L–1
of
peptide
substrate
and
1.50
µg
chymotrypsin,
in
 2.5
mL
volume.

After
10
minutes,
18.6
×
10–‐4
mol
L–1
of
peptide
substrate
remains.
Molar
mass
 of
chymotrypsin
is
25,000
g
mol–1.
 
 peptide
substrate
consumed

 =
6.4
x
10–4
mol
L–1
in
10
minutes
 Rate
of
reaction
 =
6.4
x
10–5
mol
L–1
min–1
 
 
 Enzyme
activity
 =
6.4
x
10–5
mol
L–1
min–1
x
2.5
x
10–3
L
 (rate
x
volume)
 =
1.6
x
10–7
mol
min–1
 
 
 Specific
activity
 =
1.6
x
10–7
mol
min–1
/
1.50
µg
 (activity
/
mass)
 =
1.1
x
10–7
mol
µg–1
min–1
 
 
 Turnover
number
 =
1.1
x
10–7
mol
µg–1
min–1
x
25,000
g
mol–1
x
106
µg
g–1
 (sp.
act.

molar
mass)
 =
2.7
x
103
min–1
=

45
s–1
 
 
 If
 the
 specific
 activity
 calculated
 above
 refers
 to
 pure
 chymotrypsin,
 and
 another
 sample
 of
 chymotrypsin
is
found
to
have
specific
activity
2.0
x
10–8
mol
µg–1
min–1,
what
is
the
purity
of
the
 second
sample?


 
 2.0
x
10‐8 Purity
 = 
100%
x
 
 = 
18% 
 1.1
x
10‐7 

 
 
 1.0
µg
of
sample
is
actually
only
0.18
µg
active
chymotrypsin
and
0.82
µg
other
impurities.
 € 
 Page
5
of
5
 ...
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