Biochemistry lab course
BB1100 and BB2060
September 2009
Enzyme kinetics
An investigation of the enzyme glucose-6- phosphate isomerase
Goals
− Training in experimental design
− Understanding of Vmax, kcat, KM, Ki, kcat/KM, ΔG, ΔH and ΔS and how they can be
experimentally determined, energy diagrams, apparent kinetics and graphical
determinations of kcat and KM.
Examination
− Written pre-exam: Molecular structures of the chemicals used, see instructions
on next page.
− A written laboratory report containing recipies used, primary data, all
calculations and the results thereof.
− A 20-30 minutes individual oral exam, covering the above mentioned topics.
Kalle Hult
rev 2005, 2007 Linda Fransson
Department of Biotechnology
KTH, Stockholm
BB1040/BB2060
Enzyme kinetics
Pre-exam
Molecular structures and reactions to know before the lab starts. Structures of
sugars should be given both in open and in ring-closed form. Contact Linda to set a
time for examination; [email protected].
Main reaction
D-fructose-6- phosphate
D-Glucose-6-phosphate
− Molecular structures of participating molecules?
− Name of the enzyme?
− In what metabolic pathway can the reaction be found?
Help reaction
Glucose-6- phosphate + NADP+
6-phosphoglucono-δ-lactone + NADPH + H+
− Molecular structures of participating molecules – including the cofactor?
− Name of the enzyme?
− In what metabolic pathway can the reaction be found?
Inhibitor
Sorbitol-6- phosphate
− Molecular structure?
Buffer
Tris
− Molecular structure?
− How does the buffer work?
Introduction
This laboratory exercise is an investigation of basic enzyme kinetics as well as a
training in planning and execution of your own experiments. To encourage independent thinking, this outline does not contain all of the instructions for the different
procedures and measurements. Instead, you will plan your own work. You will also
need a biochemistry book for further information.
Studied reaction
The kinetics of the enzyme glucose phosphate isomerase will be determined. The
enzyme catalyses the isomerisation reaction:
D-glucose-6-phosphate
⇋
D-fructose-6-phosphate
The kinetic parameters Vmax, kcat and KM will be determined, as well as the inhibition constant for the inhibitor sorbitol-6-phosphate. Further, the reaction free
energy difference and the free activation energy is to be determined. In this laboratory exercise the reaction will be studied in the direction
fructose-6-fosphate → glucose-6-phosphate.
Analytic equipment
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Enzyme kinetics
All experiments will be analysed spectrofotometrically, but neither the reactant nor
the product causes any change in absorbance. Therefore, the quantification of
glucose-6-phosphate will be done using the enzyme glucose-6-phosphate
dehydrogenase which catalyses the reaction
glucose-6-phosphate + NADP+
6-phosphoglucono-δ-lactone + NADPH + H+
20
The difference in the molar extinction
coefficients, ε, for NADP+ and NADPH
allows the reaction to be followed spectrophotometrically. The absorbance spectra for
NADP+ and NADPH is shown in figure 1.
12
16
ε (M-1 cm-1)
ε (mM-1 cm-1)
NADP+
NADPH
260 nm 340 nm
18.0
0
14.8
6.2
8
4
NADPH
Wavelength (nm)
Figure 1. Absorption spectra of NADP+
and NADPH.
Problems
A. Determination of Vmax, KM and KI
Problem 0.5
There are several ways of graphically analyzing kinetic data for determination of Vmax and KM. Four of them are shown in appendix A together with
some experimental data. Calculate Vmax and KM according to the methods.
Also include the true data in each diagram. Conclusion?
Problem 1
Now back to our experimental system. What components are required in a
system for spectrophotometric analysis of the reaction rate for conversion of
fructose-6-phosphate to glucose-6-phosphate catalyzed by glucose phosphate
isomerase? What does actually occur in the cuvette? Which wavelength
should be used? How will the absorbance change as the reaction proceeds?
What should be used as a control for this experiment? The control should
demonstrate that it is actually the glucose phosphate isomerase reaction that
causes the change in absorbance.
Problem 2
Calculate the concentrations of the components in an assay for spectrophotometric determination of Vmax and KM for glucose phosphate isomerase. Begin
by calculating the amount of enzyme that gives a maximal reaction rate of
approximately 0.2 ΔA/min. The molar extinction coefficients for NADP+
and NADPH can be determined using figure 1.The accuracy of your pipetting will be too low for volumes smaller than 50 μl. The substrate concentration [S] should cover the interval 0 ≤ [S] ≤ 2 mM. For guidelines on
choosing substrate concentrations, see Problem 3. A final volume of 2.00 ml
in the cuvettes should be used. All available solutions are listed at the end of
the instructions.
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Enzyme kinetics
Problem 3
Guess a value of KM for glucose phosphate isomerase somewhere between
0.01 and 1 mM. Using the method of direct linear plot in appendix B, choose
three suitable concentrations of fructose-6-phosphate for a first determination of KM. All of the solutions should be temperature adjusted to room temperature before use. Perform the measurements.
Problem 4
Using the information from the previous experiment, assign two new values
of appropriate substrate concentrations to use in a final determination. Use
the five different concentrations (the three previous and two new) of
fructose-6-phosphate for the final determination of Vmax and KM. Don't forget
the control! Check if you need additional data points. Calculate Vmax and KM
from the direct linear plot and from the three linearization methods.
Problem 5
Sorbitol-6-phosphate inhibits glucose-6-phosphate isomerase. Determine the
type of inhibition and the inhibition constant, KI. Use 0.1 mM sorbitol-6phosphate in the reaction mixture. Note that it is an apparent KM ( K Mapp ) and
app
an apparent Vmax ( Vmax
) that are derived from the plots.
Problem 6
Calculate the catalytic constant, kcat, from the value of Vmax. The catalytic
constant is the maximal number of substrate molecules reacted per active site
per second. The molecular weight of glucose phosphate isomerase is
145 000 Da and there is one active site per molecule. Also calculate the
-1
specificity constant, kcat/KM, in s-1 M .
B. Determination of the equilibrium constant
If the equilibrium constant, Keq, for a reaction is known, ΔG can be calculated.
Additionally, ΔH and ΔS can be calculated from the temperature dependence of the
equilibrium constant.
Problem 7
Propose components to be included in a system for determination of the
equilibrium constant for the reaction catalyzed by glucose phosphate
isomerase. How should the concentrations of glucose-6-phosphate and
fructose-6-phosphate be determined at equilibrium? What control should be
used in this experiment?
Problem 8
Determine the equilibrium constants for the reaction fructose-6-phosphate to
glucose-6-phospate at three temperatures: Cold water, room temperature and
37°C. (Check and note temperature). How does the amount of enzyme effect
the equilibrium constant? Determine ΔG, ΔH and ΔS for the reaction at
25°C.
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Enzyme kinetics
C. Determination of the activation energy
The (Gibbs) activation energy, ΔG‡, can be calculated from the temperature dependence of a rate constant. Therefore the reaction rate must be determined at different
temperatures. For practical reasons we will not control the temperature of the
cuvette chamber in the spectrophotometer, instead the reaction mixture will be
incubated in water baths of different temperatures.
Problem 9
Suggest components which should be included in a reaction mixture for
determination of ΔG‡.
Problem 10
Estimate the amount of enzyme needed to afford a change in absorbance of
approximately 0.5 absorbance units over a period of 5 minutes at 25°C with
2 mM fructose-6-phosphate. What is an appropriate control for this experiment if the substrate fructose-6-phosphate is contaminated with some
glucose-6-phosphate?
Problem 11
Perform the experiment at three different temperatures: Cold water, room
temperature and 37°C. (Check and note the actual temperature). Calculate
the activation energy. Make an energy profile diagram for the reaction below
catalyzed by glucose-6-phosphate isomerase.
Solutions
150 ml
3 ml
4 ml
1 ml
4 ml
2.5 ml
1 ml
2 ml
Tris-HCl buffer, pH 8.0, 50 mM
fructose-6-phosphate in Tris buffer, pH 8.0, 40 mM
NADP+ in Tris buffer, pH 8.0, 10 mM
sorbitol-6-phosphate in Tris buffer, pH 8.0, 4.0 mM
glucose-6-phosphate dehydrogenase, 20 U/ml
glucose-6-phosphate isomerase, ~20 U/ml, 46 µg/ml
HCl, 1.0 M
NaOH, 1.0 M
The solutions except the buffer are to be kept cold on ice and adjusted to the
desired temperature before use. All dilutions of any reagents must be done with the
Tris-HCl buffer.
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Enzyme kinetics
Appendix A
Analysis of Michaelis-Menten kinetics.
a) Through a Michaelis-Menten curve.
b) Through linearisations
− Lineweaver-Burk plot
invert the Michaelis-Menten equation, plot 1/v versus 1/[S]
−
Eadie-Hofstee plot
multiply the Michaelis-Menten equation with (KM +[S]), plot v versus v/[S]
−
Hanes-Wolff plot
invert the Michaelis-Menten equation, multiply with [S], plot [S]/v versus [S].
True values
KM
Vmax
12 μM
100 μM/s
Experimental data
[S] (μM)
0.98
1.95
3.91
7.81
15.63
31.25
62.50
125.00
250.00
v (μM product formed *s-1)
10
12
28
40
55
75
85
90
97
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Enzyme kinetics
Appendix B
Eisenthal och Cornish-Bowden har beskrivit en helt annorlunda metod att
analysera enzymkinetiska resultat, som kallas “direct linear plot”. Metoden
har flera fördelar. Den är snabb och lämpar sig därför för uppföljning under
experimentens gång och avslöjar lätt felaktiga resultat. Den kräver inga
beräkningar och ger en
statistiskt bra uppskat12
tning av Vmax och KM.
KM
10
Uppmätta
8
Rita ett diagram med
hastigheter
Använda
KM och Vmax som x6
substratkonrespektive y-axel. För
centrationer
4
varje försök markeras
den använda substrat2
Vmax
koncentrationen på den
0
negativa x-axeln och -20
-15
-10
-5
0
5
10
-2
den uppmätta hastigheten på y-axeln. Drag
sedan en rät linje emellan dem. Om flera linjer drages på detta sätt för flera
observationer av v och [S], kommer dessa linjer skära varandra i en punkt
vars koordinater ger värden på Vmax och KM. I ett verkligt experiment erhålls
naturligtvis inte en enda skärningspunkt utan flera. Den bästa uppskattningen av Vmax och KM ges då av den mellersta skärningspunkten för Vmax
respektive KM.
”Direct linear plot” är också ett bra verktyg för planering av kinetiska
försök: Antag värden på Vmax och KM och markera motsvarande punkt i ett
Vmax-KM-diagram. Genom denna punkt drages nu linjer som skär Vmax-axeln
så att en jämn fördelning erhålles. Dessa linjer skär KM-axeln i punkter –[S]
som anger de substratkoncentrationer som är lämpliga att användas vid
försöket.
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