Transcript Lecture PPT

Enzyme Kinetics II
Nov. 11, 2008
Robert Nakamoto
2-0279
380 Snyder
[email protected]

Studying the photograph of a
racehorse cannot tell you how fast it
can run.

Jeremy Knowles
Eadweard Muybridge, 1878
Why bother with kinetics?
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The rates at which a reaction occurs,
compared to other reactions in a pathway,
will determine the rate limiting and
controlling reaction
A→B→C→D→E
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if the reaction C→D is the slowest then
regulating the enzyme carrying out this
reaction will control the amount of E made
[C] will accumulate
A→B→C→D→E
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If only the production of E is followed then
one cannot tell which enzyme is
controlling the overall rate
Or if only the disappearance of A were
followed, then one cannot tell how fast E is
made
Lots of information in a reaction time course

If only one time point is taken, then many important
aspects may be missed.
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A non-linear rate
A lag before the steady state
Running out of substrate
A competing activity or build up of product inhibition
[product]
time
Enzyme velocity at steady stateMichaelis-Menton considerations
E+S
V =
Ks
ES
kcat
E+P
[E]o [S] kcat
Ks + [S]
Where kcat[E]o = Vmax, then
Valid when binding is
much faster than kcat
V =
The [S] at which v=1/2 Vmax is the Km
[S] Vmax
Km + [S]
v = Vmax = kcat [E]o
Vmax/2
Km
[S]
Linear vs Log activity plots
Vmax is estimated from asymptote of
maximal measured binding
v/Vmax
1.0
0.5
Km at ½ saturating
Km at ½ saturating
[S]
-1 0 +1
log [S]
Linear plot is hyperbolic.
In log plot, it takes two orders
of magnitude in [S] to go from
10-90% saturation.
Note: you use the same mathematical considerations for ligand binding to a receptor
What does the Km mean?
E+S
E+S
Km =
Ks
k+1
k-1
ES
ES
k+2 + k-1
k+1
kcat
k+2
E+P
Valid when if k+2 << k-1
E+P
More general form
Ks approximates Km if k+2 << k-1
Elementary rate constants depend on the
energy and entropy of activation
Transition state theory: temperature and the
activation energy
activated
complex
enthalpy
EA forward
reaction
transition state
E’A reverse
reaction
reactants
DH of reaction
products
Reaction coordinate
EA is the activation energy for the forward reaction.
E’A is the activation energy for the reverse reaction.
EA- E’A = DH, enthalpy change for the reaction.
Temperature and activation energy:
the Arrhenius relationship
d lnK
dT
d lnk
dT
P
DH°
=
RT2
EA
=
P
RT2
Van’t Hoff equation shows the change
with temperature of an equilibrium constant.
A similar relationship holds for a reaction
rate constant.
This equation is rearranged to give: d lnk =
And integrated to give: lnk = lnA -
EA
EA
dT
R
T2
and finally k = A e
RT
A = integration factor
-EA
RT
What does the Arrhenius eq. mean?
-EA
k = A e RT
A is the frequency of collisions with the proper orientation to
produce a chemical reaction.
Can be as fast as 1013sec-1, which is about the frequency of
collision in liquids.
Thus, Arrhenius theory says that the rate constant is determined by
i) the ratio of EA to T and
ii) by the frequency of collisions
The Arrhenius plot
slope =
log v
-
EA
R
DH‡ = EA - RT
1/T
DS‡=Rln(ANh/RT)-R
DG‡ = DH‡ + T(DS‡)
Note that a lower slope means a lower activation energy EA
and that the reaction goes faster.
The “better enzyme” will reduce EA to a greater extent.
Example: amino acid substitutions can affect
EA, better or worse catalyst.
The Assay
If you want to understand the kinetics of a reaction,
like the binding of a ligand to a receptor, or
an enzymatic reaction, like a phosphorylation or
dephosphorylation of a signaling protein, or
transport of an ion across a membrane, or
transcriptional activation of a gene,
You need an assay with the proper “time constant”
Time domains of various techniques
Laser scatter
Dielectric relaxation and electric dichroism
Fl polarization
Pressure jump
EPR and NMR
Ultrasound absorption and electric field jump
Spectroscopic methods
10-10
Stopped flow and continuous flow
Flash and T jump
10-5
seconds
Hand mixing
100
102
Specificity of the reaction
Is the reaction you are measuring carried out by only one enzyme?
Temperature? Co-factors? Competing activities?
Are there “non-enzymatic” pathways to the products?
Controls, controls, controls.
Example of kinetic analysis of a
chemical reaction: ATP hydrolysis
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Detection of ATP hydrolysis
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Pi production: How?
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“Coupled” assays
Colorimetric or Chromogenic assay
Radioactivity
What are the variables?
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Sensitivity
Time domain
Background
Chromogenic reactions for Pi
production
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Acid Molybdate
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Taussky and Shorr (Fe2+ at acid pH)
Fiske and SubbaRow (1-amino-2-naphthol-4sulfonic acid with sulfite buffer
Lin and Morales (Vanadate at alkaline pH)
Malachite Green
These assays stop the reaction, one time
point per sample.
Luciferase assay
hn
ATP + luciferin  ADP +
luciferase
Enzyme coupled assay
YFE
ATP  ADP + Pi
Pyruvate kinase
ADP + Phosphoenol pyruvate  Pyruvate + ATP
Lactate dehydrogenase
Pyruvate + NADH  Lactate + NAD+
Follow absorbance change at 340 nm in the spectrophotometer.
Radioactivity detection of ATP
hydrolysis
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Labels: [g-32P]ATP
OR a or b labels or 14C (3H) labels on adenine
Separation of labeled Pi from labeled ATP
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Acid molybdate
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Organic extraction
Selective precipitation
Extraction of ATP by charcoal Norit
TLC to separate ATP, ADP and Pi
For fast reactions, rapid mixing and quench of
the reaction is needed
Assay for production of
radioactive Pi from [g-32P]ATP
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Reactions are prepared by having an enzyme solution
and a substrate solution.
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[g-32P]ATP is isotopically diluted with non-radioactive ATP.
Reactions are carried out. The reaction stopped with
acid. One or more samples for each time point.
An acid molybdate solution is added to precipitate the Pi
Samples are centrifuged to sediment precipitate,
supernatants are removed
The pelleted precipitates are dissolved in alkali solution
Radioactivity each sample is determined by scintillation
counting

The amount (moles) of Pi is determined by comparison to
standards.
Fluorescence assay for Pi
production
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Phosphate binding protein modified with
coumarin
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Fluorescence increase upon binding of Pi
Detects release of Pi from enzyme
Fluorescence change can be followed
continuously in stopped flow
Mechanical mixing-spectroscopic observation
Usual deadtime ~ 1 ms; time resolution is less than 1 ms
Stopped-flow
spectrometers
Pre-steady state
measurements
ATP hydrolysis: production of 32Pi from
[g-32P]ATP (rapid acid quench)
•Syringe A
•1 mM F1
•25 mM TES-KOH
•0.244 mM MgCl2,
•0.20 mM EDTA
Syringe B
25 mM TES-KOH
0.46 mM MgCl2
0.20 mM EDTA
0.50 mM [g32P]ATP
Final
49 mM Mg2+free
107 mM Mg·ATP
0.5 mM F1
pH 7.5
25 °C
Quench
0.3 N PCA
1 mM Pi
Pi release: fluorescence signal from
MDCC-labeled PBP (stopped flow)
•Syringe A
•1 mM F1
•25 mM TES-KOH
•0.244 mM MgCl2,
•0.20 mM EDTA
•10 mM MDCC-PBP
•“Pi mop”
Syringe B
25 mM TES-KOH
0.46 mM MgCl2
0.20 mM EDTA
0.50 mM ATP
10 mM MDCC-PBP
“Pi mop”
Final
49 mM Mg2+free
107 mM Mg·ATP
0.5 mM F1
pH 7.5
25 °C
PMT
hn
Pi mop: purine nucleoside phosphorylase (PNPase), phosphodeoxiribomutase
(PDRM), 100 mM 7-methylguanosine, 0.1 mM a-D-glucose 1,6-bis-phosphate
Pre-steady state: addition of 107 mM ATP·Mg to F1 ATPase
E+ATP↔E·ATP↔E·ADP·Pi→E·ADP+Pi
1. ATP hydrolysis by production of 32Pi
from [g-32P]ATP (rapid quench)
2. Pi release by coumarin labeled Pi
binding protein (stopped flow)

Fit requires a slow step after
hydrolysis and before Pi release
E+ATP↔E·ATP↔E·ADP·Pi
↓ krotation
E’·ADP·Pi→E”·ADP+Pi