Document 191745

To Teach Principles of Enzyme Kinetics
rypsin and soybean trypsin inhibitor (Kunitz
inhibitor) can be used in a relatively simple and inexpensive student exercise to demonstrate the usefulness
of enzyme kinetics. The study of enzyme kinetics is
essential to biology because enzymes play such a crucial role in the biochemical pathways of all living
organisms. The data from enzyme kinetics experiments not only reveal the mechanisms and limits of
enzyme-catalyzed reactions, but also provide insights
on how to manipulate these reactions. Numerous laboratory exercises exist in which students learn how to
perform enzyme kinetics experiments and calculate
the numerical parameters describing enzyme efficiency. However, in our experience, it is often difficult to
persuade students of the importance and relevance of
their enzyme kinetics data. The purpose of this student
exercise is to convince college students in Introductory
Cell Biology that the ability to understand and calculate the values that describe enzyme activity is worthwhile and has concrete applications. Although
designed for college laboratories, ways to adapt this
experiment to high school classes are included.
Many enzyme-substrate interactions follow
Michaelis-Menten kinetics. In Michaelis-Menten reactions, the reaction can be simplified to three steps. In
the first step, substrate binds at the active site of the
enzyme to form an enzyme-substrate complex. In the
second step, substrate is converted to product, which
remains bound at the active site. Product is released in
the third step.
For enzymes that follow Michaelis-Menten kinetics, Vmax and Km describe key parameters of their func-
DAVID R. HOWARD is Associate Professor of Biology at the
University of Wisconsin-La Crosse, La Crosse, WI 54601;
e-mail: [email protected] JULIE HERR and RHIANNON
HOLLISTER were undergraduate students in the Department of
Biology at Truman State University, Kirksville, MO 63501.
tion. The maximum velocity, Vmax, is defined as the rate
of product formation when enzyme is saturated with
substrate. At Vmax, enzyme-substrate binding is not limiting and does not affect the rate. Hence, Vmax indicates
the combined rates for the catalytic conversion of substrate to product and the product release step. For our
purposes, the combined rate of these two steps will be
referred to as the “rate of catalysis.” The value Km is
called the Michaelis constant and is equal to the substrate concentration at which the reaction proceeds at
one-half the Vmax. At 1/2Vmax, one-half of the enzyme will
be bound to substrate and one-half will be free
enzyme. The substrate concentration at which this balance occurs depends on the affinity between the particular enzyme and substrate. Thus, the Km describes
the enzyme’s affinity for the substrate. Vmax and Km can
most readily be understood and obtained by analyzing
hyperbolic (Michaelis-Menten) and double-reciprocal
(Lineweaver-Burk) plots.
H O W- T O - D O - I T
Using Trypsin & Soybean Trypsin Inhibitor
In the experiment outlined here, students collect
initial reaction velocities over a range of substrate concentrations and plot the rate of product formation versus substrate concentration (Figure 1). For enzymatic
reactions that follow Michaelis-Menten kinetics, the
resulting graph is hyperbolic. This hyperbolic plot
presents the students with a clear visual image of how
Vmax and Km are related.
Students then transform the data from the hyperbolic plot into a Lineweaver-Burk plot to calculate the
values of Vmax and Km. The Lineweaver-Burk plot (Figure
2) is the double reciprocal of the hyperbolic plot (that
is, 1/rate of product formation graphed against 1/[substrate]). The regression of the Lineweaver-Burk plot is a
straight line from which Vmax and Km may be calculated.
Vmax is equal to the inverse of the y-intercept; Km is equal
to the negative inverse of the x-intercept.
While determining the values for Km and Vmax is by
itself useful, we found that it was difficult to capture
Michaelis-Menten Plot
Minus Inhibitor
Plus Inhibitor
Initial Velocity (uMol/min)
Initial Velocity (uMol/min)
[BAPNA] (mM)
BAPNA Concentration (mM)
Figure 1.
A Michaelis-Menten (hyperbolic) plot of student-collected data for trypsin initial reaction
velocities in the presence (triangles) and absence (squares) of Kunitz inhibitor. The figure
was constructed using Excel,which does not accurately calculate and plot a best fit line.The
inset shows a graph produced using Graphpad Prism,which has a kinetics plotting function.
Because of its biological significance and
its affordability, trypsin was chosen as the
enzyme for this experiment. Trypsin is a specific serine proteinase that cleaves peptide
bonds after lysine or arginine amino acids
(Ferdinand, 1976). Trypsin’s main function is to catalyze the hydrolysis of ingested proteins into small
fragments, enabling them to pass through the epithelial lining of the small intestine (Zeffren & Hall,
1973). In mammals, trypsin is synthesized in the
pancreas as an inactive zymogen, trypsinogen. Upon
secretion into the small intestine, trypsinogen is proteolytically converted to the active form, trypsin
(Zeffren & Hall, 1973). Regulating trypsin is imperative because if trypsin molecules were produced in
an active form, they would hydrolyze proteins and
enzymes in their cell of origin, including other
trypsin molecules (Zeffren & Hall, 1973).
To monitor the activity of trypsin in these experiments, the chromogenic substrate N-benzoyl-DLarginine-p-nitroanilide (BAPNA) is used. In the presence of trypsin, BAPNA is converted into p-nitroaniline, a yellow product. The accumulation of this colored product is easily measured using a spectrophotometer. The reaction is as follows:
Trypsin + BAPNA (colorless) <=> arginine +
p-nitroaniline (yellow) + benzoic acid + trypsin
Soybean trypsin inhibitor or Kunitz inhibitor
[Type I-S, Soybean TI, MW = 20 kD] (Birk, 1985) is
the inhibitor used in this experiment. One physiological function of soybean trypsin inhibitor may be
as a defense mechanism to protect legume seeds against
insect predation. Many seed-eating insects have trypsinlike enzymes present in their digestive tracts. Consuming
legume seeds that contain trypsin inhibitor slows digestion
in insects and reduces their survival (Birk, 1985).
Lineweaver-Burk (Double Reciprocal Plot)
1/initial Velocity (1/umol/min)
student interest with an experiment that
merely determined these values. However,
comparing the Km and Vmax in the presence
and absence of enzyme inhibitors more
vividly demonstrates the utility of enzyme
kinetics to students. Inhibitors are biological
or synthetic chemical compounds that
reduce the activity of enzymes, thereby altering the values of Vmax and/or Km. Students
can illustrate these inhibitor-induced
changes by graphing data sets of enzyme
activity with and without an inhibitor together on the same Lineweaver-Burk plot.
Moreover, this plot can be compared to
accepted models of inhibition to determine
the inhibitor’s mode of inhibition (Figure 3).
Through this guided-inquiry experiment,
students see the kinetic parameters for an
enzyme change, and consequently they
develop a better understanding of how kinetics can be applied to relevant questions like
the mechanisms of drug action.
Minus Inhibitor
Plus Inhibitor
1/BAPNA Concentration (1/mM)
Figure 2.
A Lineweaver-Burk (double-reciprocal) plot of the student collected data shown
in Figure 1.In the presence of inhibitor (dotted line), the Km (x-intercept) clearly
increases,while the Vmax (y-intercept) slightly decreases.The lines are based on a
linear regression by the least squares method (Excel). Minus Inhibitor: r2 =
0.993. Plus Inhibitor: r2 = 0.987.
In addition to the biological relevance of trypsin,
there are other reasons why the combination of trypsin
and Kunitz inhibitor was chosen as the enzyme system
for this experiment. First of all, there are conflicting
reports in the literature concerning the effects of Kunitz
Materials & Methods
Chemicals & Supplies
• Tris-[hydroxymethyl]-aminomethane (Tris)
• Trypsin, from porcine pancreas, Type II crude
• Trypsin inhibitor, Type I-S from soybean
• N-benzoyl-DL-arginine-p-nitroanilide (BAPNA)
• CaCl2-2H2O
• Hydrochloric Acid
• Dimethyl sulfoxide (DSMO)
• p-nitroaniline (1 mM)
• Cuvettes
Mixed Noncompetitive
Figure 3.
Models depicting how different types of enzyme inhibitors affect the
look of a Lineweaver-Burk plot. In each graph, 1/velocity is plotted on
the y-axis, and 1/[substrate] on the x-axis.The solid line represents the
enzyme activity in the absence of inhibitor, and the dotted line in the
presence of inhibitor. a: effects of a competitive inhibitor. b: effects of an
uncompetitive inhibitor.c:effects of a noncompetitive inhibitor.d:effects
of a mixed noncompetitive inhibitor.
inhibitor on Km and Vmax (see Data Interpretation Section
for further explanation). In our experience, introductorylevel students can collect useful kinetics data, yet still not
achieve the precise changes in Km or Vmax predicted by an
inhibitor’s mechanism of action. Therefore, with trypsin
and Kunitz inhibitor, insignificant student errors can be
validly explained by the literature. Another advantage is
that both trypsin and soybean trypsin inhibitor are relatively inexpensive.
The purpose of this experiment is for students to calculate the Vmax and Km values of the protease trypsin in the
presence and absence of inhibitor. The observed changes
in Km and Vmax are used to determine the mode of inhibition
of soybean trypsin inhibitor. Student learning objectives
from this experiment are:
1. how to graphically analyze data
2. how to use standard curve data
3. how to calculate Vmax and Km from hyperbolic plots
and Lineweaver-Burk graphs
4. how to use Vmax and Km to describe enzyme/substrate interactions
5. how to use enzyme kinetics data to determine the
mode of inhibition of an enzyme inhibitor
6. to appreciate enzymes as biological catalysts.
• 10 ml pipets
• Test tubes (>10 ml)
• Micropipets
• Beckman DU-70, Spectronic 20, or other spectrophotometer
All chemicals were purchased from the Sigma
Chemical Company.
Tris buffer: Add 6.06 g Tris base and 0.147 g CaCl22H2O to 950 ml of de-ionized water and pH to 8.2
with HCl. Add dH2O to 1 L.
Stock Trypsin: Add 20 mg trypsin to 10 ml of 0.001 N
HCl. At acidic pH, the activity of trypsin is inhibited, thus preventing the proteolysis of the trypsin
Stock substrate (2.5 mM BAPNA): Add 0.1087 g
BAPNA in 2 ml of DSMO and vortex to dissolve
(warming to 37°C may be necessary to dissolve
BAPNA substrate working solution: Add 2 ml of
BAPNA stock to 100 ml of Tris buffer at 60˚C.
Because BAPNA is poorly soluble in water, slowly
(0.5 ml at a time) release the BAPNA stock under
the surface of the Tris buffer. After each addition
swirl the solution well. Place the substrate solution
at room temperature. If a yellow precipitate forms,
the solution will not work. If a white/clear crystalline precipitate forms, the solution will still give
meaningful results.
The experiment reported here was performed with
all solutions at room temperature (20-24˚C).
However, if precipitation becomes a problem, maintain the stock substrate solution at 30˚C.
Trypsin inhibitor stock: Add 0.1 mg of trypsin
inhibitor per ml of Tris buffer.
Note that the inhibitor and BAPNA stocks may be
made at least a week ahead of time and frozen at
-20°C. However, trypsin should be prepared daily.
Data Collection
This exercise consists of three sections: measuring a
standard curve, kinetics measurements of trypsin alone,
and kinetics measurements of trypsin plus inhibitor.
Standard Curve
Using a pure solution of the product p-nitroaniline (1
mM), students prepare standard curve solutions as shown
in Table 1. Vortex the final solutions. Measure the
absorbance at 410 nm of each solution. At concentrations
above 30 µM, the absorbance of light by p-nitroaniline
becomes nonlinear.
Kinetics of Trypsin Activity
is added to the substrate and buffer prior to enzyme addition. The length of time that the inhibitor and substrate
preincubate prior to enzyme addition does not significantly affect enzyme activity. However, if the enzyme and
inhibitor are preincubated prior to substrate addition,
enzyme activity varies as a function of preincubation time
(Liu & Markakis, 1989). Therefore, although certain
enzymes are sometimes pretreated with inhibitor to maximize inhibitor effect, this strategy produces inconsistent
student data for trypsin and trypsin inhibitor.
After the data are collected, a standard curve is plotted
using the first set of data. The standard curve is used to
convert the rates of trypsin activity from absorbance per
minute (OD/min) to µM of product formed per minute
(µM p-nitroaniline/min). The reaction volume (3 mL) is
The recipes to determine the activity of
trypsin as a function of varying substrate conTable 1. Solution volumes for the standard curve.
centrations are provided in Table 2. Buffer and
substrate should be added directly to the
p-nitroaniline (µl)
Tris Buffer (mL)
Final [p-nitroaniline] (µM)
cuvettes prior to enzyme addition. Use the
blank to set the baseline on the spectropho#1
tometer prior to adding enzyme to the other
cuvettes. Because initial velocities provide the
most accurate kinetics data, trypsin should
not be added to Tubes 1 through 6 until imme#4
diately before the students place the cuvettes
into the spectrophotometer. Immediately after
mixing the cuvettes, the absorbance
at 410 nm should be recorded every
Table 2. Solution volumes for measuring the initial velocities of trypsin at
20 seconds for 4 minutes. Our procedure is designed to take advantage
varying substrate concentrations in the absence of inhibitor.
of the time drive function and sixplace cuvette holder in a DU-70,
Tris Buffer
2.5 mM BAPNA
Final Substrate
which automatically measures the
(Substrate) (mL)
(Enzyme) (mL)
Concentration (mM)
six samples every 20 seconds. If a
manual spectrophotometer is used,
absorbance can be read every 30 seconds for 4 minutes. Reaction vol#2
umes can be scaled up or down to
match cuvette size.
Kinetics of Tryspin in the
Presence of
Table 3. Solution volumes for measuring initial velocities of trypsin with inhibitor.
This portion
of the exercise is
described above
for trypsin alone
except for the
trypsin inhibitor
(see Table 3). An
important aspect
of this protocol is
that the inhibitor
Tris Buffer
2.5 mM BAPNA
(Substrate) (mL)
inhibitor (mL)
(Enzyme) (mL)
Final Substrate
Concentration (mM)
then used to convert from µM p-nitroaniline/min to µmol
p-nitroaniline/min. The converted data are then plotted
with the rate of product formed per minute on the y-axis
and the final BAPNA concentration on the x-axis (Figure
1). After the construction of this hyperbolic plot, the
inverse of the data is calculated and plotted to produce a
Lineweaver-Burk plot (Figure 2). Using the LineweaverBurk plot, students calculate the Vmax and Km of trypsin and
determine trypsin inhibitor’s mechanism of inhibition.
Data Interpretation & Results
Following the protocol outlined here, students in a
typical experiment found the Km of trypsin for BAPNA to
be 1.05 mM without inhibitor and 1.22 mM with inhibitor
(Figures 1 & 2). The ranges of student findings for Km are
typically 1.0-1.1 mM without inhibitor and 1.2-1.4 mM
with inhibitor. The published Km value for bovine trypsin
with BAPNA substrate is 0.94 mM (Walsh, 1970). So student data agrees closely with that reported in the literature.
That students typically find slightly higher values for Km
than those reported in the literature is probably attributable to the use of porcine rather than bovine trypsin and
that the experiment is run at room temperature, rather
than 37˚C. However, even at ambient temperatures students achieve data close to published values.
With the trypsin concentration used here, students
found the Vmax to be 0.131 µmol/min without inhibitor and
0.126 µmol/min plus inhibitor. We have not found a published value for the Vmax of trypsin with BAPNA. Because
Vmax varies as a function of the enzyme concentration used,
students would not gain information by comparing their
Vmax values to published Vmax values derived using a different amount of trypsin.
The fifth student learning objective from this experiment is to determine the mode of inhibition of the Kunitz
inhibitor. As mentioned previously, the binding of an
inhibitor to an enzyme alters either the rate of catalysis
(Vmax), the enzyme’s affinity for the substrate (Km), or both.
Therefore, by using a Lineweaver-Burk plot to examine the
changes in Vmax and Km that occur upon inhibitor addition,
students can infer the mode of inhibition. There are four
basic mechanisms of inhibition.
A competitive inhibitor blocks the active site of a free
enzyme, inhibiting the formation of enzyme-substrate complexes. However, when enzyme-substrate complexes are
formed, the inhibitor does not affect enzyme activity. As a
result, these inhibitors do not affect the Vmax of the enzyme,
but raise the Km (Figure 3a).
An uncompetitive inhibitor binds only to the
enzyme-substrate complex at a site other than the active
site (an allosteric site). This binding stabilizes the complex,
but reduces the activity of the enzyme. Therefore, uncompetitive inhibitors proportionally lower both the Vmax and
Km so that the slope of the line plus inhibitor is equal to the
slope of the control (Figure 3b).
A pure noncompetitive inhibitor binds allosterically
and alters the enzyme’s conformation. A pure noncompet-
itive inhibitor has an equal affinity for free enzymes and
enzyme-substrate complexes. Km remains constant because
the conformational change does not alter the enzyme’s
affinity for the substrate. However, Vmax is lowered as the
rate of catalysis is lowered (Figure 3c).
A mixed noncompetitive inhibitor binds to free
enzymes and enzyme-substrate complexes with different
affinities. As a result, mixed noncompetitive inhibitors
decrease the rate of catalysis, resulting in a lowered Vmax
value, but can increase or decrease the enzyme’s affinity for
the substrate, resulting in a lower or higher Km value,
respectively (Figure 3d).
Data from X-ray crystallography and numerous assays
show that the Kunitz-type soybean trypsin inhibitor binds
to the active site of trypsin as a competitive inhibitor would
(Laskowski, Jr. & Kato, 1980). Furthermore, numerous
activity assays indicate that protein protease inhibitors,
including Kunitz inhibitor, are competitive inhibitors
(Laskowski, Jr. & Sealock, 1971). However, many reports
based on Lineweaver-Burk data alone suggested that the
mechanism of Kunitz inhibitors was either as mixed noncompetitive (pseudononcompetitive) (Kassell, 1970a),
noncompetitive (Laskowski, Jr. & Sealock, 1971), or uncertain (Kassell, 1970b). Student data consistently show an
increase in Km upon addition of inhibitor (Figure 2), supporting the competitive mechanism of Kunitz inhibitors.
However, students usually find a slight inhibitor-induced
decrease in Vmax as well, which fits the early reports of
mixed-noncompetitive inhibition (Figure 2).
Because an increase in Km is the most consistent and
striking student finding, competitive inhibition can be
emphasized in class discussions. Although variations in Vmax
conflict with a competitive mechanism, they correlate with
early controversies in the literature. Observed variations
from competitive inhibition can be used as teaching
moments to illustrate the necessity for multiple approaches
to biological questions. For student reports, the important
issue is whether they interpret their results accurately. Based
on their data, students should address whether the inhibitor
binds at the active site and whether the inhibitor binds to
both free enzyme and enzyme-substrate complexes.
Because virtually all biological processes are ultimately controlled by the inhibition/activation of enzymes, the
relevance of enzyme kinetics can be discussed in terms of
understanding the regulation of virtually any pathway discussed in lecture. In addition, numerous therapeutic drugs
work by targeting specific enzymes and inhibiting their
activity. Enzyme kinetics experiments can reveal the details
of drug action, including whether the drug binds to free
enzyme or to enzyme-substrate complexes and whether an
excess of substrate could overcome the actions of the drug.
By relating the conclusions of their experiment to issues of
human health, the practical application of kinetics can be
demonstrated to students.
The first and second student learning objectives
involve graphing data for analysis. One of the most fundamental steps in data analysis is using the standard curve to
convert absorbance readings into meaningful units
(product concentration). Plotting by hand and graphing on
computer both provide benefits to the students. If the students graph the standard curve by hand and manually convert the raw data, they are more likely to understand the
function of the standard curve. However, computer-aided
graphing provides quick, accurate data conversions for the
students if time is limited. In addition, data analysis by
computer simulates processes used in real-life research situations. Microsoft Excel is adequate for transforming data
and graphing standard curves and Lineweaver-Burk plots
(Figure 2). However, we have not found a way to graph an
accurate hyperbolic line in Excel. When a logarithmic or
exponential trendline is selected in Excel, the program does
not correctly plot the line, partly because there is no way to
force the Y-intercept through zero (Figure 1). More sophisticated statistics and graphing programs (e.g., PRISM,
GraphPad Software, Inc., San Diego, CA) are available to
graph Michaelis-Menten plots more accurately (Figure 1,
inset). The inadequacy of Excel can be used as a teaching
moment to illustrate the power of a Lineweaver-Burk plot.
Suggested Questions for Students
Below are a list of suggested prompts for class assignments and discussions concerning this experiment. In
addition to these questions, assigning students the task of
finding published values of Km and Vmax for trypsin is a challenging exercise in library research.
1. What are your calculated values of Vmax and Km
plus and minus inhibitor? What mode of inhibition does the trypsin inhibitor exhibit?
2. What would happen if you added an excess of
substrate in the presence of inhibitor?
3. Is it necessary to add the solutions to the
cuvettes in a particular order? Why or why not?
4. How would the data be altered if the laboratory was
particularly warm on the day of the experiment?
ted (0.9 ml Tris Buffer and 2.1 ml BAPNA). After mixing
each tube, incubate 5-10 minutes at room temperature.
Results can be evaluated by eye or by spectrophotometer.
The tube containing both BAPNA (substrate) and trypsin
(enzyme) will be yellow. The other two tubes, each of which
lack one component, should remain clear.
When interpreting results, emphasize that without
enzyme the conversion of substrate to product is too slow
to be detected. In contrast, the tube with both substrate
and enzyme contains yellow product, demonstrating that
enzymes work as catalysts to speed up the rate of reactions. The blank tube containing trypsin without BAPNA
now serves as a control to show that the enzyme does not
produce color by itself.
For the inhibitor treatments, increase the amount of
Kunitz inhibitor used from 0.08 ml to 0.2 ml, and decrease
the volume of Tris buffer used by 0.12 ml (Table 3). As
above, use only the blank, the highest substrate concentration, and an additional tube containing trypsin, trypsin
inhibitor, but no substrate. For these endpoint assays, add
trypsin and Kunitz inhibitor together first, followed by substrate. This change will maximize the effect of the inhibitor.
The presence of Kunitz inhibitor should reduce the intensity of the yellow color. The inhibitor experiments can be
used to demonstrate how chemicals like toxic pollutants or
therapeutic drugs often have their effect on organisms by
inhibiting specific enzymes.
The authors wish to thank Dr. Gary Sells for contributing a trypsin kinetics lab from which this lab was
adapted. This work was supported in part by a Truman
State University Faculty Research Grant.
Birk, Y. (1985). The Bowman-Birk inhibitor. International Journal of
Peptide Protein Resources, 25, 113-131.
5. What advantages does a Lineweaver-Burk plot
have over a hyperbolic plot?
Ferdinand, W. (1976). The Enzyme Molecule. Great Britain: J.W.
Arrowsmith Limited.
6. What is the purpose of a standard curve? What
particular values does it allow us to calculate (or
Kassell, B. (1970a). Bovine trypsin-kallikrein inhibitor (Kunitz
inhibitor, basic pancreatic trypsin inhibitor, polyvalent inhibitor
from bovine organs). In G.E. Perlmann & L. Lorand (Eds.),
Methods in Enzymology, V. 19 (pp. 844-852). NY: Academic Press.
Finally, if time permits this exercise can be used as
starting point for investigative labs. For example, students
can test the effects of altering enzyme concentration.
Alternatively, they can test crude plant extracts or chemicals found in the home for their ability to inhibit trypsin.
Adaptations for High School Courses
The procedures presented here can be adapted to teach
basic enzyme principles instead of enzyme kinetics.
Simplify the procedure by performing endpoint assays with
fewer samples. Do not make the standard curve if product
concentration will not be calculated. Use the blank and
highest substrate concentration (blank and Tube #6,
respectively, Table 2 ). Add one tube where trypsin is omit-
Kassell, B. (1970b). Trypsin and chymotrypsin inhibitors from soybeans. In G.E. Perlmann & L. Lorand (Eds.), Methods in
Enzymology, V. 19 (pp. 853-862). NY: Academic Press.
Laskowski, Jr., M. & Kato, I. (1980). Protein inhibitors of proteinases.
Annual Review of Biochemistry, 49, 591-626.
Laskowski, Jr., M. & Sealock, R.W. (1971). Protein proteinase
inhibitors — molecular aspects. In P.D. Boyer (Ed.), The Enzymes,
V. 3 (pp. 375-473). NY: Academic Press.
Liu, K. & Markakis, P. (1989). Trypsin inhibition assay as related to
limited hydrolysis of inhibitors. Analytical Biochemistry, 178, 159165.
Walsh, K.A. (1970). Trypsinogens and trypsins of various species. In
G.E. Perlmann & L. Lorand (Eds.), Methods in Enzymology, V. 19
(pp. 41-63). NY: Academic Press.
Zeffren, E. & Hall, P.L. (1973). The Study of Enzyme Mechanisms. NY:
Wiley-Interscience Publications.