Jacob Siegel
Enzyme Kinetics
Performed on April 1, 2013
Introduction:
In the body, there exist millions of different molecules of all different sizes and function
from proteins to fats to neurons and so on. Since there are so many bits to the whole, it is
important to make sure that each bit is in moderation and is not negatively affecting the
rest of the system. This applies to almost any system in nature, man-made systems, and
systems not yet discovered. Knowing how different molecules interact and use up each
other is very important in maintaining this balance in the system. The methods used in this
experiment illustrate finding concentrations of products or reactants, how the two
correlate, and find an optimal concentration for the system to run. How all of these factors
affect the speed of a reaction is collectively called the study of enzyme kinetics.
Enzymes are chemical catalysts, meaning that they can be used to expedite reactions that
may be otherwise too slow to be effective. They speed up these reactions by lowering the
activation energy, allowing the reaction to proceed without having to put in a lot of outside
energy. The enzyme used in this experiment is an alkaline phosphatase. This enzyme is
sometimes used an indicator of cholestasis in dogs (Alkaline Phosphatase). It is used in the
lab to catalyze the cleaving of a phosphate group from p-Nitrophenylphosphate (PNPP) to
make p-Nitrophenol (PNP). This formation of PNP is accompanied by a yellow color, which
is measured by a spectrophotometer at 420nm to find its absorbance and then its
concentration from the use of a standard curve. The kinetics of the enzyme can then be
studied by observing rates of formation and optimal concentrations. PNP is toxic, so it is to
be handled with care.
Alkaline
phosphatase
p-Nitrophenol phosphate + H2O
substrate
COLORLESS

p-Nitrophenol +
product
YELLOW
H3PO4
product
Studies on enzyme kinetics began in the 18th century when catalyst enzymes were first
discovered. In 1897, the scientist Eduard Buchner was the first to really understand
enzymes in his studies regarding fermentation and how different factors affect the speed of
an enzymatic process (Laidler). In 1912, scientists Leonor Michaelis and Maud Leonora
Menten published work that helped graphically represent enzymatic reactions and their
efficacy by plotting different substrate concentrations against rate of product formation
(Leonor Michaelis and Maud Leonora Menten). These graphic representations were
somewhat hard to interpret and use though due to the logarithmic nature, so scientists
Lineweaver and Burk developed a plot of the reciprocals of reaction velocity and substrate
concentration, yielding a linear trend. The trend line has a y-intercept equal to the
reciprocal of the maximum reaction velocity and an x-intercept equal to the negative
reciprocal of the Km value, defined as the substrate concentration at which maximum
velocity is half. In 1940, scientist Arnold Beckman invented the spectrophotometer,
bringing kinetics to life (History of Spectrophotometer). This tool emits light at a constant
wavelength and passes it through a solution undergoing a reaction. The amount of light
that passes through the solution, transmittance, is measured, and the logarithm of its
inverse is the amount of light absorbed by the solution. These two values can tell how
quickly a product of a certain color is being formed or a reactant is being used. The plotting
of these values or concentrations with which they are correlated against time can be very
useful because they aid in finding the maximum velocity of an enzyme (Vmax) and the
substrate concentration at which Vmax is half (Km). Vmax and Km shed light onto which
enzymes work best in certain reactions and how much of an enzyme can be used to have a
desired speed or thoroughness of the reaction. These values can be identified for each
particular enzyme, giving its activity, conventionally one unit of which is one micromole of
product per minute, or the specific activity, which is the activity per milligram of protein.
For these values however, it is important that the enzyme is purified because otherwise the
results will be inaccurate (Begley).
Methods:
This experiment began with the creation of a standard curve from different
concentrations of PNP. All stock solutions in the experiment were kept on ice for the
entirety. Cuvettes containing the different concentrations of PNP were made from the
following table:
Tube No.
B = Blank
Alkaline Buffer
(mL)
Stock PNP (mL)
1
2
3
4
5
6
7
8
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
nmol PNP/4 mL
(nmol)
[PNP] (μM)
4
3.9
3.8
3.7
3.6
3.5
3.4
3.3
3.2
0
0.02
0.04
0.06
0.08
0.1
0.12
0.14
0.18
0
0.08
0.16
0.24
0.32
0.4
0.48
0.56
0.64
The calculated concentrations of PNP and nmol of PNP in each cuvette are also in the table.
The Stock PNP had a concentration of 0.8 μM. While the cuvettes were being prepared, on
the spectrophotometer (Thermo Spectronic GENESYS 10 UV), ‘Utility’ was selected,
followed by ‘Stored Tests Directory’, then ‘Kin ‘05’. When the test was ready to begin, ‘Run’
was changed to ‘Tabular’, then the blank was inserted and ‘Measure Blank’ was selected.
Once the blank was set, each tube was put one by one into the spectrophotometer and
‘Measure Sample’ was selected to obtain the absorbance, which was recorded. A plot of
absorbance vs nmol of product was created to make the standard curve.
The second part of the experiment was the optimization of the assay by varying the
enzyme concentration. Three vials of different enzyme concentrations were made:
undiluted, 1:4, and 1:8. The alkaline buffer was used to perform a serial dilution to make 1
mL volumes of each dilution. It is important to perform the dilution with the buffer because
the enzyme runs at optimal performance in the buffer conditions, rather than if it were to
be diluted with water. These volumes were kept on ice. The spectrophotometer was
blanked before each assay to ensure consistency. Three reaction tubes were prepared with
1.5 mL of the 30.0 mM PNPP substrate and 2.4 mL of the alkaline buffer. When ready, 0.1
mL of the enzyme dilution was quickly added to the tube, mixed, and put in the
spectrophotometer. It is of ultimate importance that the enzyme is added last because
otherwise the reaction would run before being measured, ruining the experiment by
prematurely generating product. The absorbance was taken immediately and that
absorbance was used for time t=5 seconds. The absorbance was recorded every 10 seconds
for the first 2 minutes and every 20 seconds for 3 more minutes. This was done for each of
the three dilutions. The absorbances were then plotted against time, with all three dilutions
on the same graph. The enzyme with the most data points between 0.1 and 1.0 in the first
two minutes was used for the remainder of the experiment.
The third part of the experiment was the actual kinetics experiment where the substrate
concentration was varied. The PNPP substrate was prepared in 5 different concentrations
by doing a serial dilution from the undiluted 30 mM concentration to 15 mM, 7.5 mM, 3.75
mM, and 1.88 mM. The alkaline buffer was used to dilute the solution and 1.5 mL of each
concentration were made except the last dilution that had 3 mL due to the dilution. Each
reaction tube was prepared with 1.5 mL of a different dilution of PNPP substrate and 2.4
mL of alkaline buffer. The spectrophotometer was blanked with the same alkaline buffer
blank before each reaction for consistency. When ready, 0.1 mL of the optimal enzyme
dilution was quickly added to the tube, mixed, and put in the spectrophotometer. The
absorbance was taken immediately and that absorbance was used for time t=5 seconds.
The absorbance was recorded every 10 seconds for the first 2 minutes and every 20
seconds for 3 more minutes. This was done for each of the five substrate dilutions. The
absorbances were then plotted against time, with all five dilutions on the same graph. All
waste was disposed of in the proper waste bins, not down the sink, and aseptic technique
was employed throughout the experiment.
Results:
nanomoles
of product Absorbance
0
0
0.08
0.031
0.16
0.137
0.24
0.339
0.32
0.4
0.4
0.533
0.48
0.587
0.56
0.675
0.64
0.837
Table 1: Standard Curve Data- This table shows the absorbance at 420 nm of each of the
standard solutions next to the quantity of PNP in nanomoles that each contained. These
data were used to generate the standard curve for PNP formation.
Standard Curve of PNP
0.9
0.8
y = 1.258x
0.7
Absorbance
0.6
0.5
Standard Curve of PNP
0.4
Linear (Standard Curve of
PNP)
0.3
0.2
0.1
0
0
0.1
0.2
0.3
0.4
0.5
Quantity of Product (nmol)
0.6
0.7
Figure 1: Standard Curve- This figure shows the graph of the standard curve of PNP as
generated from Table 1. The equation generated from the line of best fit was later used to
calculate different concentrations from absorbance values. The line was set to have a yintercept through 0 because there is no product at the beginning of the reactions and PNPP
has an absorbance of 0.
Time (min)
Undiluted 1 to 4
1 to 8
0
0
0
0
0.083333333
0.049
-0.047
0.021
0.166666667
0.333333333
0.5
0.666666667
0.833333333
1
1.166666667
1.333333333
1.5
1.666666667
1.833333333
2
2.333333333
2.666666667
3
3.333333333
3.666666667
4
4.333333333
4.666666667
5
0.171
0.341
0.466
0.574
0.63
0.672
0.859
1.054
1.259
1.495
1.713
1.986
2.324
2.298
2.524
2.568
2.92
0.024
0.036
0.24
0.099
0.254
0.388
0.444
0.379
0.288
0.281
0.403
0.597
0.602
0.489
0.739
0.94
1.231
1.157
1.223
1.426
1.482
0.036
0.041
0.057
0.068
0.077
0.098
0.129
0.132
0.137
0.173
0.224
0.307
0.435
0.481
0.53
0.567
0.51
0.507
0.501
0.651
0.536
Table 2: Assay Optimization Data- This table contains the data collected from the assay
optimization with absorbances at 420 nm of dilutions of the alkaline phosphatase
(undiluted, 1:4, 1:8) against time in minutes. Any blank boxes indicate that the absorbance
value of the sample was greater than could be read by the spectrophotometer. The values
that are most accurate are those between 0.1 and 1.0 due to the manufacturing of the
spectrophotometer.
Assay Optimization Curves
3.5
3
Absorbance
2.5
2
Undiluted
1.5
1 to 4
1
1 to 8
0.5
0
-0.5
0
1
2
3
4
5
6
Time (min)
Figure 2: Assay Optimization Graph- This figure show the absorbances of the reactions of
the assay optimization plotted against time using data drawn from Table 2. Some of the
absorbance values at the beginning read below zero possibly because of the presence of
something on the blank tube causing the zero value to be higher than it should have been.
The 1:4 dilution was determined to be the optimal dilution because it had the most
readable points (between 0.1 and 1.0) in the first two minutes.
Time (min)
0
0.083333333
0.166666667
0.333333333
0.5
0.666666667
0.833333333
1
1.166666667
1.333333333
1.5
1.666666667
30 mM
0
0.006
0.049
0.074
0.097
0.119
0.137
0.157
0.17
0.188
0.24
0.328
15 mM
0
0.023
0.043
0.066
0.085
0.104
0.126
0.153
0.185
0.22
0.247
0.266
7.5 mM
0
0.015
0.03
0.024
0.051
0.066
0.085
0.097
0.111
0.123
0.131
0.147
3.75 mM 1.88 mM
0
0
0.006
0.003
0.012
0.008
0.018
0.014
0.019
0.02
0.02
0.023
0.022
0.028
0.033
0.033
0.04
0.039
0.045
0.042
0.049
0.042
0.053
0.046
1.833333333
2
2.333333333
2.666666667
3
3.333333333
3.666666667
4
4.333333333
4.666666667
5
0.37
0.409
0.522
0.563
0.599
0.677
0.795
0.902
0.957
1.066
1.211
0.282
0.299
0.385
0.442
0.466
0.548
0.633
0.686
0.727
0.784
0.88
0.163
0.176
0.197
0.242
0.256
0.294
0.323
0.369
0.397
0.417
0.437
0.059
0.068
0.069
0.093
0.112
0.124
0.137
0.162
0.167
0.197
0.189
0.05
0.053
0.062
0.068
0.075
0.085
0.097
0.095
0.095
0.103
0.113
Table 3: Kinetics Data- This table shows the absorbance values at 420 nm of each of the
five different concentrations of the PNPP substrate for each of the time points taken. Each
column begins at zero because there is no product at the very beginning of the reaction and
the first value recorded by the spectrophotometer was used as a t=5 seconds time point
due to the time between the addition of the enzyme and the start of the recording of the
spectrophotometer.
Kinetics of an Enzyme at Different Substrate
Concentrations
1.4
1.2
Absorbance
1
30 mM
0.8
15 mM
0.6
7.5 mM
3.75 mM
0.4
1.88 mM
0.2
0
0
1
2
3
Time (min)
4
5
6
Figure 3a: Kinetics Graph- This figure shows the absorbance values at 420 nm of each of
the reaction tubes of each of the five different concentrations of the PNPP substrate plotted
against time for each of the time points taken. The higher the absorbance indicates the
greater presence of product PNP.
Kinetics Initial Velocities (Before 2 min)
0.45
0.4
0.35
Absorbance
0.3
30 mM
0.25
15 mM
0.2
7.5 mM
0.15
3.75 mM
0.1
1.88 mM
0.05
0
-0.05
0
0.5
1
1.5
Time (min)
2
2.5
Figure 3b: Initial Velocities Graph- This figure shows the absorbance values at 420 nm of
each of the reaction tubes of each of the five different concentrations of the PNPP substrate
plotted against time for each of the time points taken in the first two minutes of the
reactions. Trend lines were added to each set of data to show the general trend of each of
the reactions. The first two minutes were shown separately because the values in this
particular timeframe illustrate the initial velocities of the different PNPP substrate
concentrations rather than the overall trends. This gives a more accurate portrayal of how
the substrate concentration affects the rate of reaction. The steeper the trend line indicates
a greater reaction velocity.
[PNPP] (mM)
30
15
7.5
3.75
1.88
[PNPP] as diluted in
assay (mM)
Slope (ΔA/min)
nmol PNP/min
11.25
0.1874
0.148966614
5.625
0.1503
0.119475358
2.8125
0.0854
0.067885533
1.40625
0.0309
0.024562798
0.703125
0.026
0.020667727
Table 4: Michaelis-Menten Data- This table shows the values useful in the generation of a
Michaelis-Menten plot. The concentration of PNPP from the serial dilutions is shown in the
far left column and the second column is the PNPP concentration resulting from the
preparation of the reaction tubes. The slope values were drawn from the equations of the
trend lines in Figure 3b, also known as the initial velocities. The nmol PNP/min values
were generated through the use of the standard curve to calculate the concentration of
product PNP correlated with the absorbances values taken.
Michaelis-Menten Plot
0.16
Rate (nmol PNP/min)
0.14
0.12
0.1
0.08
nmol PNP/min
0.06
Log. (nmol PNP/min)
0.04
0.02
0
0
2
4
6
8
10
Concentration of PNPP (mM)
12
Figure 4: Michaelis-Menten Plot- This figure shows illustrates the Michaelis-Menten plot
of concentration of substrate PNPP against the rate of product PNP formed as drawn from
Table 4. There is a trend line with a logarithmic fit, typical of the Michaelis-Menten plot.
The maximum velocity is equal to the greatest rate shown on the plot and Km is equal to
the concentration of PNPP at which maximum velocity is half.
[PNPP] =
[S] (mM)
11.25
5.625
2.8125
1.40625
0.703125
V
(nmol/min)
0.148966614
0.119475358
0.067885533
0.024562798
0.020667727
1/[S]
(1/mM)
0.088888889
0.177777778
0.355555556
0.711111111
1.422222222
1/V
(min/nmol)
6.712913554
8.369926813
14.73067916
40.71197411
48.38461538
Table 5: Lineweaver-Burk Data- This table shows the sets of data useful in generating a
Lineweaver-Burk plot. The concentration of PNPP is that as once diluted in the reaction
tubes. The second column is the initial velocity for each of the dilutions and the fourth
column is the reciprocal of each. The third column is the reciprocal of the first column.
Lineweaver-Burk Plot
60
y = 32.446x + 6.411
1/V (min/nmol)
50
40
30
1/V (min/nmol)
Linear (1/V (min/nmol))
20
10
0
-0.2
0.3
0.8
1/[S] (1/mM)
1.3
1.8
Figure 5: Lineweaver-Burk Plot- This figure shows the Lineweaver-Burk plot as
generated from the data in Table 5. This plot gives a linear representation of the reciprocal
of reaction velocity against the reciprocal of substrate concentration. The plot has a yintercept of 6.411 that is equal to the reciprocal of maximum velocity. The plot has an xintercept equal to -0.198 that is equal to the negative reciprocal of Km.
Calculations:
From the Michaelis-Menten plot (Figure 4):
Vmax = 0.150 nmol PNP formed/min
Km= 2.740 mM
This value is the greatest rate value on the graph.
This value was calculated using the equation of the trend line of the
plot and solving for the substrate concentration when rate was equal to 0.150/2.
Km= e^(((0.150/2)-0.239)/0.0507) was the equation used to solve.
From the Lineweaver-Burk plot (Figure 5):
Vmax = 0.156 nmol PNP formed/min
This value is the reciprocal of the y-intercept of
the Lineweaver-Burk plot. The y-intercept is the value at which x=0.
y = 32.446 (0) +6.411 = 6.411 and then 1/6.411 = 0.156
Km = 5.06 mM
This value is the negative reciprocal of the x-intercept of the
Lineweaver-Burk plot. The x-intercept is the value at which y=0.
0 = 32.446 x + 6.411 then -6.411 = 32.446 x then x = -0.1976 then Km = -1/x = 5.06
Discrepancies between the Km values from the two different plots is unclear but could be
the result of outlying data points that lay differently on each of the plots, causing a
difference.
Specific Activity:
This value is Vmax per milligram of enzyme. The milligrams of enzyme is equal to the
volume of enzyme used divided by the dilution factor and then multiplied by the
concentration of the original stock which was 5 mg/mL.
Mg of enzyme = (0.1/4) 5 = 1.25 mg.
-From Michaelis-Menten plot:
Specific Activity = 0.150/1.25 = 0.12 μmol PNP formed/min x mg enzyme
-From Lineweaver-Burk plot:
Specific Activity = 0.156/1.25 = 0.1248 μmol PNP formed/min x mg enzyme
Discussion:
In this experiment, the kinetics of enzymatic reactions were observed by performing
several analyses including one to generate a standard curve that can be seen in Table 1 and
Figure 1, one to find an optimal enzyme dilution seen in Table 2 and Figure 2, and one to
measure the kinetics of a reaction seen in Table 3 and Figures 3a and 3b. The data from
Table 3 and Figures 3a and 3b were then further processed to generate data usable for a
Michaelis-Menten plot (Table 4 and Figure 4) and a Lineweaver-Burk plot (Table 5 and
Figure 5). The reaction that occurred began with PNPP being mixed with alkaline
phosphatase, cleaving the phosphate group, resulting in PNP.
The first section of the lab involved creating a standard curve. Table 1 and Figure 1 show
the concentrations of PNP, the product of the enzymatic reaction at hand, and the
absorbance value correlated with each concentration. This standard curve was used as a
reference to find concentrations from absorbance values, which helped make the data from
the other sections of the experiment usable since concentrations of PNP product were the
main focus and not their absorbance values.
The second section of the lab was performed to find an enzyme concentration that would
make the reaction occur at a rate that could be read for duration of 5 minutes, allowing the
kinetics of the reaction to be observed for the greatest amount of time. The undiluted
enzyme maxed out the spectrophotometer before the time had finished, so this
concentration was unusable to test again with different substrate concentrations because
the reaction occurred too quickly to be carefully observed. The 1:4 and 1:8 dilutions did not
max out the spectrophotometer and was within the readable bounds of the machine for the
entirety of the time. Regarding the whole 5-minute period, the 1:8 dilution had the most
data points within the 0.1 to 1.0 absorbance range, the optimal and most accurate range of
the spectrophotometer, but the 1:4 dilution had the most data points within that range in
the first 2 minutes of the reaction. It was for this reason that the 1:4 dilution was used for
the kinetics experiment instead of the 1:8 dilution. The first 2 minutes of the reaction were
of particular importance because they best represent the initial velocities of each of the
reactions, which are the velocities of importance.
The third section of the lab was the actual kinetics experiment. This was where the
substrate concentration was varied, showing how effectively the enzyme can work. Since
the enzyme is the rate-limiting factor, changing the amount of substrate shows how much
substrate a certain quantity of enzyme can handle. Varying substrate concentrations were
used to generate a rate of reaction for each concentration. These different rates were used
to generate a curve in a Michaelis-Menten plot that can be effectively used as a spectrum
showing the range of rate of the generation of product in a continuum of substrate
concentrations. From this plot, the maximum velocity of the enzyme, Vmax, was
determined to be 0.150 nmol PNP formed/min. This means that when the enzyme is
working at maximum efficiency, it will generate 0.150 nmol PNP in one minute. From the
plot, the substrate concentration at which Vmax is half, Km, was determined to be 2.740
mM. This means that at the concentration of 2.740 mM of PNPP, the enzyme will operate at
half of the maximum velocity. The specific activity of the enzyme, the rate of the enzyme
per milligram of enzyme was determined to be 0.12 μmol PNP formed/min x mg enzyme,
meaning that each milligram of enzyme will generate 0.12 μmol of PNP in one minute.
However, since the Michaelis-Menten plot generates a logarithmic pattern, the data were
manipulated and put into a Lineweaver-Burk plot. This plots the reciprocals of the
Michaelis-Menten plot, so 1/rate and 1/substrate concentration. From the LineweaverBurk plot, the maximum velocity of the enzyme, Vmax, was determined to be 0.156 nmol
PNP formed/min. This means that when the enzyme is working at maximum efficiency, it
will generate 0.156 nmol PNP in one minute. From the plot, the substrate concentration at
which Vmax is half, Km, was determined to be 5.06 mM. This means that at the
concentration of 5.06 mM of PNPP, the enzyme will operate at half of the maximum
velocity. The specific activity of the enzyme, the rate of the enzyme per milligram of
enzyme was determined to be 0.1248 μmol PNP formed/min x mg enzyme, meaning that
each milligram of enzyme will generate 0.1248 μmol of PNP in one minute. All of these
values found from the plots are specific to the alkaline phosphatase used in this lab in the
reaction with PNPP performed. These values can be determined for most any enzyme that
can be purified and are very useful in determining quantities of drug to administer or
concentrations of chemicals to be used in materials so as to not perform a reaction too
quickly or too slowly to be valid in a system.
Literature Cited
1. "Alkaline Phosphatase." Alkaline Phosphatase. Cornell University, n.d. Web. 30 Mar. 2013.
2. 1. Begley, Gail S. Biochemistry: A Laboratory Manual Spring 2013. N.p.: n.p., 2013. Print.
3. "History of Spectrophotometer." Labsynergy. N.p., n.d. Web. 30 Mar. 2013.
4. Laidler, Keith J. "A Brief History of Enzyme Kinetics." N.p., n.d. Web. 30 Mar. 2013.
5. "Leonor Michaelis and Maud Leonora Menten." Homepage of the Chemical Heritage
Foundation. N.p., n.d. Web. 30 Mar. 2013.