To Teach Principles of Enzyme Kinetics D AV I D R. H O WA R D T 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. JULIE HERR RHIANNON HOLLISTER 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 PRINCIPLES OF ENZYME KINETICS 99 Michaelis-Menten Plot 0.1 Minus Inhibitor Plus Inhibitor 0.08 0.06 0.1 0.04 Initial Velocity (uMol/min) Initial Velocity (uMol/min) 0.02 0 0.5 1 1.5 [BAPNA] (mM) 2.0 0 0 0.5 1 1.5 2 2.5 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). 100 THE AMERICAN BIOLOGY TEACHER, VOLUME 68, NO. 2, FEBRUARY 2006 Lineweaver-Burk (Double Reciprocal Plot) 30 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 25 20 15 10 5 0 -1.5 -1 -0.5 0 0.5 1 1.5 2 2.5 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 a Materials & Methods b Chemicals & Supplies • Tris-[hydroxymethyl]-aminomethane (Tris) • Trypsin, from porcine pancreas, Type II crude • Trypsin inhibitor, Type I-S from soybean Competitive Uncompetitive • N-benzoyl-DL-arginine-p-nitroanilide (BAPNA) • CaCl2-2H2O c d • Hydrochloric Acid • Dimethyl sulfoxide (DSMO) • p-nitroaniline (1 mM) • Cuvettes Noncompetitive 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. Solutions 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 itself. 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). 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. PRINCIPLES OF ENZYME KINETICS 101 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 Tube p-nitroaniline (µl) Tris Buffer (mL) Final [p-nitroaniline] (µM) cuvettes prior to enzyme addition. Use the blank 0 10.000 0 blank to set the baseline on the spectropho#1 25 9.975 2.5 tometer prior to adding enzyme to the other cuvettes. Because initial velocities provide the #2 50 9.95 5.0 most accurate kinetics data, trypsin should #3 100 9.90 10.0 not be added to Tubes 1 through 6 until imme#4 200 9.80 20.0 diately before the students place the cuvettes #6 300 9.70 30.0 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, Tube Tris Buffer 2.5 mM BAPNA Trypsin Final Substrate which automatically measures the (mL) (Substrate) (mL) (Enzyme) (mL) Concentration (mM) six samples every 20 seconds. If a blank 2.90 0.00 0.10 0.00 manual spectrophotometer is used, #1 2.30 0.60 0.10 0.50 absorbance can be read every 30 seconds for 4 minutes. Reaction vol#2 2.00 0.90 0.10 0.75 umes can be scaled up or down to #3 1.70 1.20 0.10 1.00 match cuvette size. #4 1.40 1.50 0.10 1.25 Kinetics of Tryspin in the #5 1.10 1.80 0.10 1.50 Presence of #6 0.80 2.10 0.10 1.75 Trypsin Inhibitor Table 3. Solution volumes for measuring initial velocities of trypsin with inhibitor. This portion of the exercise is performed as described above for trypsin alone except for the addition of trypsin inhibitor (see Table 3). An important aspect of this protocol is that the inhibitor Tube Tris Buffer (mL) 2.5 mM BAPNA (Substrate) (mL) Kunitz inhibitor (mL) Trypsin (Enzyme) (mL) Final Substrate Concentration (mM) blank #1 #2 #3 #4 #5 #6 2.90 2.30 2.00 1.70 1.40 1.10 0.80 0.00 0.60 0.90 1.20 1.50 1.80 2.10 0.08 0.08 0.08 0.08 0.08 0.08 0.08 0.10 0.10 0.10 0.10 0.10 0.10 0.10 0.00 0.50 0.75 1.00 1.25 1.50 1.75 102 THE AMERICAN BIOLOGY TEACHER, VOLUME 68, NO. 2, FEBRUARY 2006 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 PRINCIPLES OF ENZYME KINETICS 103 (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. Acknowledgments 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. References 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 convert)? 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- 104 THE AMERICAN BIOLOGY TEACHER, VOLUME 68, NO. 2, FEBRUARY 2006 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.
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