ENZYMES
The study of enzyme kinetics through the investigation of
Michaelis-Menten theory
Author: Faaiumalo Aluni (z3333839)
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Abstract
An experiment that determines the rate at which maximum number of marbles is
transferred within 10 seconds was used to analyze and investigate the MichaelisMenten theory on enzyme kinetics was carried out. Data was collected for each
different substrate concentration at constant time. Two separate graphs were plotted
for each enzyme depicting the value of maximum enzyme reaction rate (Vmax) and
constant Km.
It is found that the approximated and calculated values of Vmax and Km were different
by several factors. This is dependent on the individual approximation and
interpretations of the data collected from the experiment.
The data collected displayed signs of variability that affected the calculated and
estimated values of Km and Vmax. This may be due to the lack of control factors and
for the enzyme was slowly adapting to the surrounding conditions. Therefore, I would
recommend a change of surrounding conditions (room temperature) which would be
more suitable for the enzyme to function in and also increase the number of trials in
doing so, outliers can be eliminated from the results and producing more accurate
values.
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Introduction
by lowering the activation energy and
Life depends on a well-orchestrated
stabilizing transition-state immediate.
series of chemical reactions. Many of
An enzyme active site, which is usually
these reactions, however, proceed too
only a small part of the protein,
slowly on their own to sustain life.
comprises two functional parts: a
Enzymes are catalytic proteins that
substrate-binding site and a catalytic
accelerate the rate of cellular reactions
site. The amino acids composing the
active site are not necessarily adjacent
Enzymes are sensitive indicator of
in the amino acid sequence but are
diseases that can be measured or
brought into proximity in the native
detected by the most suitable
conformation.
substrate thus denoting their relevance
In general, an enzyme reaction
and significance in patients’ diagnosis.
involves a series of reactions. The
For instance, glucose sensors rely on
activity of all enzymes are controlled
enzymes to indicate whether if a
by the three dimensional structure or
patient is producing enough insulin in
shape that is has, and many enzymes
the case of determining a rough
have pockets of folds in their shape,
estimate of how much insulin needed
that are known as active sites, where
to be injected in diabetic patients.
the protein is being degraded or
Ethanol sensors for determining blood
modified will fit to enable the chemical
alcohol level are also dependent on
reactions to occur.
enzymatic kinetics. Through a simple
Each enzyme is highly specific and
breath test, results for blood alcohol
only allows a particular substrate to
level and alcohol concentrations are
bind to its active site. They remain
indicated by the simple colour change
unchanged by the reactions thus
of the substrates being used in the
allowing it to be reused again.
sensor design.
However, it can be modulated by
_______________________________
several factors such as acidity,
Materials and method
temperature, competitive inhibitors and
concentration.
This report aims to investigate the
kinetics of an enzyme called “marbler
transferase” as described by
Michaelis-Menten kinetics whereby it
relates the reaction rate (V) to the
substrate concentration [S]. This
theory was examined in an
experimental and analytical manner
producing results that are interpreted
and justified throughout the report.
The method was carried out in two
components: experimental and
analytical components with the
required materials encompassed
within the instructions of the
corresponding component.
Experimental Component:
This component puts marbler
transferase into action using about 50
marbles, two plastic trays or
containers, stopwatch, blindfold and 4
was chosen randomly to prevent the
team members.
marbler transferase from learning that
Seat the marbler transferase in front of
there will be more or less enzymes
the substrate and product containers
than the previous run.
and blindfold marbler transferase. The
Swap roles within your group and
marble deployment officer dispenses a
repeat steps 1-8. Collect data for at
given number of marbles into the
least three marbler transferase and
substrate container without marbler
proceed to the analytical component.
transferase knowledge of the number
of marbles in the substrate container.
Analytical Component
The timekeeper is in control and tells
The kinetics of many enzymes can be
marbler transferase when to start and
described by the Michaelis-Menten
stop the experiment. Marbler
kinetics and most enzyme reactions
transferase is blindfolded and is
can be modeled in the expression
expected to transfer as many marbles
below
as possible in 10 seconds using just
two fingers and transferring marbles
one at a time from the substrate tray to
the product container.
After 10 seconds, the timekeeper
The initial binding of substrate (S) to
informs and instructs the marbler
enzymes (E) results in the formation of
transferase to stop. The marbler
an enzyme-substrate complex (ES)
deployment officer and quality
which then undergoes one or more
assurance officer count the number of
reactions to catalyzed by the catalytic
marbles transferred into the product
groups in the active site until the
container. The scribe notes this value
products (P) are formed and diffuse
in their laboratory notebook.
away from the enzyme. From plots of
This measurement is repeated three
reaction rate versus substrate
times before the marble deployment
concentration, two characteristic
officer changes the number of marbles
parameters of an enzyme can be
in the substrate container.
determined: the MIchaelis constant Km
Repeat steps 1-7 varying the number
a rough measure of enzyme’s affinity
of marbles in the substrate container
for converting substrate into product,
between 5-50. However, this number
and the maximal velocity Vmax a
concentration [S] and how the values
measure of its catalytic power.
of Vmax, Km come about.
Note: k1, k2, k3 are constants.
Plotting 1/V vs. 1/[S] graph for all three
Through careful derivation of
enzymes is an alternative in finding the
Michaelis-Menten from [1] Vmax and
value for Km by using the
Km are defined below
approximated Vmax (value from V vs.
[S] graph) using the relationship
Vmax=k2 [E]o
between the gradient and the Vmax as
seen below
Therefore,
V=Vmax[S]
Km+[S]
The results data from the experimental
component is tabulated and displayed
in graphs that portray the relationship
between reaction rate (V), substrate
Average number of marbles transferred (V)
Results
14
13
12
11
10
9
8
7
6
5
4
3
2
1
0
-10
0
10
20
30
Substrate concentration [S]
40
50
60
Figure1: Reaction rate of enzyme 1 (V) vs. substrate concentration [S]
Average number of marbles transferred (V)
13
12
11
10
9
8
7
6
5
4
3
2
1
0
-10
0
10
20
30
Substrate concentration [S]
40
Figure 2: Reaction rate of enzyme 2 (V) vs. substrate concentration [S]
50
60
Average number of marbles transferred in 10s
(V)
-10
14
13
12
11
10
9
8
7
6
5
4
3
2
1
0
-1 0
-2
10
20
30
40
50
60
Substrate concentration [S]
Figure 3: Reaction rate of enzyme 3 (V) vs. substrate concentration [S]
0.28
0.27
0.26
0.25
0.24
0.23
0.22
0.21
0.2
0.19
0.18
0.17
0.16
0.15
0.14
0.13
0.12
0.11
0.1
0.09
0.08
0.07
0.06
0.05
0.04
0.03
0.02
0.01
0
y = 1.0145x + 0.0543
y = 0.8477x + 0.0485
1
y = 0.7785x + 0.052
2
3
Linear (1)
Linear (2)
Linear (3)
0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1 0.11 0.12 0.13 0.14 0.15 0.16 0.17 0.18 0.19 0.2
Figure 4: Lineweaver –Burk Plot for all three enzymes.
Enzyme reaction rate vs. Substrate
From Lineweaver-Burk
concentration
Marbler
Plot Graph
Vmax
Vmax/2
Km
Vmax
Km
1
11.5
5.75
10
18.4
18.7
2
12.5
6.25
8
20.6
17.5
3
12.6
9.5
18
19.2
14.5
Transferase
The highest approximated value of the
react.
trendline is taken as the value of Vmax
For instance, at particular substrate
and is used for calculating Km using
concentrations, all three enzymes
the Michaelis-Menten theory of
have different overall reactions and
enzymatic kinetics. Using the gradient
respond (as recorded and displayed in
relationship described in analytical
the Figure 1, Figure and Figure 3).For
method, values of Km and Vmax are
example at higher substrate
calculated and estimated from the
concentrations [S] of 30-50, enzyme 1
Lineweaver-Burk plot graph (Figure 4).
displayed an increasing progress
(upright parabolic shape) whilst
Figures 1-3 displays the trendlines
from the average reaction rate values
from the action of enzymes 1-3
individually. The values of Vmax is
estimated from these graphs and are
used to determine the corresponding
values of Km as well.
Discussion
With close observation of Figures 1, 2
and 3, the approximated values of Vmax
are slightly different. This can be due
to some of many reasons ranging from
enzyme 2 performs at an increasing
linear manner. However, enzyme 3
portrays an inverse parabolic effect at
an increasing rate. All these
observations are closely related to the
displayed error range (capped lines at
particular points displayed in all
figures) i.e. at particular points where
the curves increase or decrease, a
large error range is involved which
also influences the shape of all the
three curves.
human error to technical error,
Another logical reason to why these
imposing the effect the environment
figures differ from each other is due to
and the surrounding has on the
the difference enzymes’ physicality
enzymes which affected its ability to
and ability to performance at its best at
its most preferable conditions. The
higher substrate concentrations with a
surrounding can be overbearing or too
Vmax value however, the graph is
claustrophobic for an enzyme to
tending to zero value.
behave at its best thus this can affect
With close analysis of Figure 4, it is
its performance and practice. This is
seen from observation that the
depicted in the fluctuations in all three
performances of all enzymes differ
figures throughout different substrate
(comparison of the trend line equations
concentration intervals.
and gradients). Because the gradients
As to elaborate more on this point, pH
different and approximated values of
and temperature are some of the
Vmax from Figure 1,2 and 3, it is also
factors which can modulate and affect
expected that the Km value for all three
the enzyme kinetics and
enzymes will be different.
performances. Since different
enzymes function best at particular
conditions, a slight change in the pH
value can either terminate or slow
down the enzyme’s ability to react and
respond to the substrate. In such
cases, the V vs [S] will not be
asymptotic at a particular Vmax value
but rather slowly decreasing towards
zero. This will have a great impact on
the Km value and the Michaelis-Menten
kinetics theory will not be applicable in
such circumstances.
Changing the temperature will pose an
effect of either increasing or slowing
down the reaction rate of the marbler
transferase. This is due to the
temperature sensitive nature of
enzymes and the conditions they find
most appropriate and suitable to
function efficiently. The curves for the
enzymes will be slowly decreasing at
Since the enzymes’ response to
particular substrates is dependent on
the active site, restricting this can
cause an adverse effect on the
reaction rate as the substrate
concentration increases. An example
is using a rubber band around the
fingers (of the team member playing
the enzyme marbler transferase role).
This will inhibit the fingers from
interacting and handling of the marbles
(substrate) hence with increasing
substrate concentration, it will quite
difficult and time consuming to transfer
the marbles from the substrate
container to the product tray. This will
cause the reaction rate to decrease at
high concentrations therefore the
curve will not asymptotic for this case
scenario thus making it impossible to
calculate the Vmax and Km values.
Possible human errors involved in
Figures 1, 2 and 3 against the
counting the marbles transferred can
calculated value using Figure 4. This is
be contributor to the indifferences. For
may not disprove the Michaelis-
example, the error of rounding values
Menten theory but rather the lack of
and figures during calculations is a
control in this experiment and also
possibility. Technical errors such as
time allocated in completing it.
finding difficulty in reading values off
By analyzing the data collected in
graphs due to a small scale used by
graphs, the relationship between
excel or other graphing programs are
reaction rate and the substrate
also some of the simple faults that add
concentration was obvious which was
to the diverse results.
helpful in later on calculations for the
value of Km.
Conclusion
However, I would recommend that
It is calculated that the value of Km
carrying out the experiment in different
differ amongst the different enzymes
conditions can also display the effect
and also by comparison of the two
of changing pH values along with
values using approximations from
modulating temperatures as well.
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References
[1] Principles of biochemistry, 1993, Englewood Cliffs, NJ : N. Patterson Publishers,
Englewood Cliffs, NJ.
[2] Campbell, M.K. & Campbell, M.K. 2003, Biochemistry, South Melbourne, Vic. :
Thomson/Brooks/Cole, South Melbourne, Vic.
[3] Lehninger, A.L. & Lehninger, A.L. 1982, Principles of biochemistry, New York :
Worth, New York.
[4] Mayne, P.D. & Mayne, P.D. 1994, Clinical chemistry in diagnosis and treatment,
London : Edward Arnold, London.