LABORATORY EXPERIMENT pubs.acs.org/jchemeduc
A Comprehensive Enzyme Kinetic Exercise for Biochemistry Janice S. Barton* Department of Chemistry, Washburn University, Topeka, Kansas 66621-1100 United States
bS Supporting Information ABSTRACT: This article describes a comprehensive treatment of experimental enzyme kinetics strongly coupled to electronic data acquisition and use of spreadsheets to organize data and perform linear and nonlinear least-squares analyses, all in a manner that promotes development of important reasoning skills. Kinetic parameters are obtained for the stable enzyme bovine alkaline phosphatase by fitting the dependence of velocity on substrate and inhibitor concentration using regression algorithms of Excel. KEYWORDS: Upper-Division Undergraduate, Biochemistry, Laboratory Instruction, Collaborative/Cooperative Learning, Computer-Based Learning, Problem Solving/Decision Making, Enzymes, Kinetics, Laboratory Computing/Interfacing reactions in the visible wavelength range,10 the effect of alcohols on trypsin amidase activity,11 and specific activities of glucose oxidaseperoxidase coupled reactions.12
T
his article describes a comprehensive treatment of experimental enzyme kinetics strongly coupled to electronic data acquisition and use of Excel to organize data and perform linear and nonlinear least-squares analyses, all in a manner that promotes development of important reasoning skills. The Supporting Information includes guidance for data acquisition with a cost-effective Vernier software program, for data uploading to Excel, and for fitting the collected kinetic data to the Michaelis Menten substrate-saturation curve using the Excel Solver algorithm. From this experience students learn the process for obtaining kinetic data, become familiar with statistical analysis through the use of Excel algorithms, and achieve a deeper understanding of enzyme kinetic concepts through graphical and mathematical data analyses. The results reported here were gathered over a period of ten years by students enrolled in an upper-level biochemistry laboratory course. Typical results obtained by student pairs and ten-year averages of key parameters are presented. Since the early 1950s a wealth of articles have appeared in this Journal covering various aspects of enzyme kinetics. Theoretical articles addressed new ways of considering the kinetic equations of enzymology where Ault introduced fractional representation of kinetic equations,1 Alberty2 considered rapid equilibrium forms for two substrate enzymes, Northrop3 considered the meaning of Km and V/Km from the MichaelisMenten equation, Hofstee4 recommended equal distribution of data points about the Km value and against use of the double reciprocal plot, Chong5 demonstrated errors inherent in least-squares treatment of linearized equation forms, Martin6 addressed the preferred equation forms to extract accurate characteristic parameters, and Bruist7 focused on enzyme kinetic simulation using spreadsheets. A wide range of experimental articles covered the many aspects of enzymology including innovative visual demonstration of enzymatic activity,8 colorimeters interfaced to computers,9 coupled Copyright r 2011 American Chemical Society and Division of Chemical Education, Inc.
’ MATERIALS AND METHODS The exercise described here has been performed by numerous upper-level biochemistry students for at least a decade with pleasingly similar outcomes. Students performed the exercise in pairs to gather shared data. For the pH profile study, students worked in groups, each student pair preparing a solution of designated pH for the group, but they reverted to pairs for data collection. The exercise featured the enzymatic alkaline phosphatase (APase, EC 3.1.3.1) reaction with p-nitrophenyl phosphate as substrate. The relatively inexpensive bovine (Sigma P7640) enzyme with g10 units/mg at 37 °C in diethanolamine at pH 9.8 was used. This enzyme with extinction coefficient 13 14 E1% 278 = 7.2 and monomer size of 64 kDa is a metallohydrolase homodimer containing two zinc ions that catalytically chelate the phosphate group and one stabilizing magnesium binding site. The reaction (Scheme 1) was monitored at 410 nm for production of the p-nitrophenolate ion from the Sigma substrate P4744; product concentration was determined based on an absorptivity of 16.2 μmol1 cm1 mL13 in a 1.0 M Tris pH 10.0 buffer. Detailed directions are given in the Supporting Information, as are representative graphs. The basic reaction mixture called for 3 mL of substrate and a combination of enzyme and buffer totaling 100 μL. A variety of Eppendorf pipettors, appropriate to the volume range, were employed to create the reaction mixtures. Data were collected every second for two minutes with Genesys 20 spectrometers interfaced to computers with the Vernier Spectro Pro program. Published: June 15, 2011 1336
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Scheme 1. The Alkaline Phosphatase Reaction
Product accumulation as measured by absorbance increase was linear for the two minute interval for all collected data. Analysis of saved exported data was accomplished in Excel. Working in pairs students spent two weeks gathering data in duplicate. Depending on scheduling needs, either a third week of class was allowed to complete analysis or the report was due two to three weeks after completion of data collection. The necessary enzyme kinetic concepts were covered in lecture class and reviewed in the laboratory lecture. Materials supplied students included protocol instructions, alkaline phosphatase dissolved in water at a nominal 0.10 mg/mL, a 4.0 mg/ mL solution of the disodium form of substrate dissolved in 1.0 M Tris, pH 10 buffer, and 0.050 M inhibitors (disodium hydrogen phosphate and tetrasodium EDTA) dissolved in water. Working with these reagents, students created many different reaction samples making appropriate dilutions with the Tris buffer. Discussion of the principles of dilution and other calculations were included during the laboratory class as needed, and students were responsible for checking their calculations with the instructor prior to proceeding.
’ DATA COLLECTION As steady-state initial velocity conditions for the Michaelis Menten model were desired, students began by demonstrating the linear dependence of velocity on enzyme concentration for a 1.0 mg/mL substrate concentration, used throughout the exercise except when varying the substrate concentration. As expected, the majority of students found a linear relationship with a zero intercept over a range of 1.3 to 5.3 μg of enzyme in 3.1 mL of reaction mixture. The remaining data collection used 3.3 μg of alkaline phosphatase per reaction mixture as that value lay midway in the linear range of tested enzyme concentrations. Velocity dependence on substrate concentration was measured over the range of 0.12 mg/mL to 4.0 mg/mL for six data points in duplicate. Subsequently, the effect of inhibition was determined for the same set of substrate concentrations using 75 μL of a 0.050 disodium phosphate solution in lieu of buffer to complete the 100 μL of the 3.1 mL of the reaction mixture. Additionally, students compared the percent inhibition of enzyme caused by EDTA and disodium phosphate, investigated heat inactivation of enzyme activity, and conducted a five data point examination of velocity and pH relationship; see Figures S1S3 in the Supporting Information. All duplicate measurements were made at ambient temperature, unless specified otherwise. ’ HAZARDS For each of the following chemicals, with the CAS number in parentheses, the material data safety sheet (MSDS) description lists similar potential health hazards, which may cause irritation to skin, eyes, and lungs: Tris base (77-861), tetratsodium EDTA (6381-92-6), bovine alkaline phosphatase (9001-78-9),
Figure 1. Alkaline phosphatase time course of reaction with 1.1 μg/mL enzyme and 1.0 mg/mL substrate in 1.0 M Tris, pH 10.0.
disodium phosphate (7558-79-4), and sodium p-nitrophenyl phosphate (4264-83-9).
’ RESULTS AND DATA ANALYSIS For all data sets, absorbance was linear with time during the two minutes of data collection. The typical raw data result of Figure 1 was obtained with 1.0 mg/mL of substrate and 3.3 μg of enzyme; the velocity of reaction is given by the slope of the displayed fitted linear line. Because absorbance was used in data collection, it was necessary for students to convert that part of the velocity term to μmole per milliliter units using the product absorptivity to obtain the value of Vm in the proper units. Additionally, calculation of Km values required conversion of substrate concentrations to a molarity basis. Rather than having students calculate the molecular mass of substrate from the above structure, they were encouraged to consult the reagent bottle for the molecular formula and formula mass. This provided students the opportunity to recognize the contribution of counterions and hydration to the formula mass. Students were expected to use the Excel Trendline algorithm to extract velocities from the raw data for each reaction mixture; the raw data were plotted to ensure a linear dependence of product accumulation on time. Using Excel, students generated the graphs of Figure 2 containing the MichaelisMenten saturation graph, the LineweaverBurk double reciprocal plot, and the EadieHofstee graph. For the linear plots of LineweaverBurk and EadieHofstee, Km and Vm values were obtained using Excel linear least-squares algorithms of Trendline or Linest. Students also obtained these kinetic parameters from the nonlinear substrate saturation data using the Excel Solver algorithm following a provided protocol and example, patterned from the work of Harris.15 Students were instructed to present the Km and Vm values determined by calculation from each of the kinetic plots in a table with statistical analysis that included the 95% confidence interval. A typical student result is presented in Table 1. Now students were prepared to discover the type of inhibition exhibited by phosphate and to calculate Ki, the inhibition dissociation constant. Kinetic plots of substrate only and substrate with inhibitor were presented on the same graph. The inhibitor phosphate, also a main product, is competitive with substrate; however, that fact was not shared with the students. As happens in reality, the linear plots did not perfectly coincide at the ordinate intercept and students were challenged to consider 1337
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LABORATORY EXPERIMENT
Figure 2. Velocity dependence on substrate concentration with 1.1 μg/mL enzyme, 010.0 mM substrate (diamond), plus 1.2 mM phosphate inhibitor (square), in 1.0 M Tris, pH 10.0. Plots are (A) MichaelisMenten, (B) LineweaverBurk, and (C) EadieHofstee. Solid lines are calculated.
Table 1. Typical Student Kinetic Results Km/(mmol method
L1)
Vm/ (μmol
Ki/ (mmol kcat/
min1mL1) L1) min1
LineweaverBurk
1.1
0.0101
0.85
EadieHofstee
1.1
0.0104
0.77
MichaelisMenten
1.4
0.0111
0.64
average
1.2
0.0105
0.75
std error % error
0.085 7.1
0.00030 2.9
0.062 8.2
1650
SA/(μ mol min1 mg1)
13
the calculated Linest intercept error for the substrate only and substrate with inhibitor data. Some students were able to execute the statistical analysis, find, and justify competitive inhibition; other students were not able to execute the statistical analysis, finding mixed inhibition instead. Students then calculated the Ki values from the slope values for competitive inhibition (Table 1) or they determined Ki and Ki0 from the slope and intercept values, respectively, for mixed inhibition. Additionally, for a 1.0 mg/mL substrate solution students measured the inhibition of enzyme and calculated the percent inhibition caused separately by 75 μL of 0.050 M disodium phosphate and tetrasodium EDTA. As indicated in Table 1, students also reported the specific activity (SA) and kcat. Determination of these parameter values required calculation of the enzyme concentration. These particular activities required some sophistication of thought to recognize the necessity for calculating the enzyme concentration in the reaction mixture and to use that value in obtaining the specific activity and kcat. Students were given the absorbance at 278 nm and the E1% value for the stock enzyme solution. As the E1% concept arose earlier in the semester, students were familiar with its meaning and use. A class discussion centered on dilution and the concentration of enzyme, substrate, and inhibitor in the reaction mixture; although hints were given about the calculation, a specific protocol for the process was not supplied. Most students calculated these three parameters, but not all successfully included the dilution effect. The kcat and SA values presented in Table 1 were calculated from the average value of Vm.
’ DISCUSSION Electronic data acquisition, although very convenient, is not required to implement this exercise in the biochemistry laboratory
class. Rates of reaction can be calculated from the slope of strip charts, absorbance values printed from a spectrometer or integrator, even from hand-gathered data. Initially, the classes used Spectronic 20 instruments, stopwatches, and lower concentrations of enzyme to slow down the rate of reaction. Although not done in duplicate, usable data were collected. About ten years ago, e-acquisition with a Vernier single-cell four-wavelength colorimeter interfaced to a computer was introduced and evolved to the Genesys 20 connected directly to computers using Spectro Pro software. Logger Pro, the sequel to our Spectro Pro, is available from Vernier for a nominal cost, allowing the computer to gather data via cable from several brands of low cost spectrometers. Thermal stability14,16 is a distinct advantage of using alkaline phosphatase for a student kinetic exercise. Although students are told to maintain the stock enzyme solution on ice, much less damage is done by failure to follow instructions in this case. Each student pair received a fresh solution of enzyme, which was stored frozen for use the second week of the project. The relative molecular mass of 128,00014 was used in calculating kcat rather than the approximate 160 kDa listed by Sigma. Several assay conditions exist for hydrolysis of p-nitrophenyl phosphate including the buffer, wavelength of observation, and absorptivity. Early on, we chose the conveniently available Tris buffer, the wavelength of 410 nm and absorptivity of 16.2 μmol1 cm1 mL.13 The effect of disodium phosphate as product or inhibitor on buffer pH is less than 0.4%. As in Figure 1, the displayed slope was taken for the velocity, and in most cases there was good linear correlation. Assay preparation, mixing by inversion and placement in the spectrometer with opening and closing the cell compartment lid took between 1 and 2 s. The turbulence in that period due to opening, sample insertion, and closing the spectrometer was eliminated for velocity calculations. Though the substrate showed a tinge of color, buffer was the convenient blank choice for the desired slope parameter. The kinetic parameter values obtained by students over a tenyear period are shown in Table 2. These data were average values collected from individual student reports. The magnitude of percent standard error is good considering the variation from year to year in the enzyme concentration, which affects several parameters, as measured spectrophotometrically throughout the decade. The error was less than 10% except for Km and Ki. Variation in Km may reflect the formula mass values for the substrate used by students who may not have accounted for all counterions or waters of hydration; additionally differences could 1338
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Table 2. Ten-Year Average Kinetic Results [Eo]/ Km/(mmol Vm/(μmol nmol statistic L1) min1 mL1) L1
SA/(μmol Ki/(mmol kcat/ L1) min1
min1 mg1)
average
2.9
0.0149
7.7
1.2
1870
std error
0.44
0.000839
3.7
0.26
124
15 0.66
%
15
5.61
4.8
22
6.63
4.4
have arisen in stock solution dilution and reaction mixture preparation. Lack of including the dilution factor for inhibitor concentration in the reaction mixture is one possible contributor to the error in Ki values. Additionally, there are a number of ways to extract the Ki value from the kinetic data with each procedure having the potential to introduce variation. One could obtain alpha values from the ratio of slopes of LineweaverBurk and EadieHofstee plots, from Km and the apparent value of Km derived from fitting the saturation curves, from substituting values of Km and Vm into the LineweaverBurk or EadieHofstee slope term for inhibited data, from the x-axis intercept, or even from the least desirable visual estimation of MichaelisMenten plots. The product phosphate, hydrolyzed from the substrate, should show competitive inhibition; however, that was not found by all students. For the majority of linear plots prepared by students, the intercepts did not coincide graphically, nor were the calculated values identical. Students who obtained the Linest values and statistics for their data were able to conclude that phosphate was a competitive inhibitor as the 95% confidence intervals overlapped. In examining some individual student data, I found using the linear equations introduced deviation in the Vm value of inhibited data from that for the substrate only. The deviation was greater for the LineweaverBurk than for Eadie Hofstee approach. Vm values for inhibited data extracted with Solver treatment of the nonlinear saturation form were in better agreement with the Vm for data collected with substrate only. These findings are consistent with the analysis of Martin,6 who demonstrated the effect of biased weighting of the linear plots. The weighting error varied with the fourth power of inverse velocity for double reciprocal and the second power for the single reciprocal equations. Several aspects of this exercise provided students analytical thinking and reasoning opportunities. The concentrations of reactants, enzyme, and inhibitor needed in most calculations were not those of the supplied stock solutions. Thus the students must realize the necessity to include a dilution factor into the concentration problem, determine the correct dilution factor value, and apply it correctly to achieve the reaction mixture concentration. In assigning the category of phosphate reversible inhibition students had to recognize that lack of intersection of the calculated lines for the LineweaverBurk and EadieHofstee plots with substrate only and substrate plus inhibitor did not automatically rule out competitive inhibition and that the failure to coincide might be caused by experimental error, which could be assessed by the calculated error in the y intercept. Qualitatively, it seems most students handled these issues appropriately, suggesting improved thinking and reasoning abilities.
and previous chemistry classes. Students learn how to extract characteristic parameter values from data employing graphs, equations, various statistical concepts, and Excel computer algorithms. This exercise promotes pair and group cooperation, and importantly, it brings reality to enzyme kinetic concepts so abstract for many students.
’ ASSOCIATED CONTENT
bS
Supporting Information Detailed directions to carry out the exercise and representative graphs; guidance for data acquisition with a cost-effective Vernier software program, for data uploading to Excel, and for fitting the collected kinetic data to the MichaelisMenten substrate-saturation curve using the Excel Solver algorithm. This material is available via the Internet at http://pubs.acs.org.
’ AUTHOR INFORMATION Corresponding Author
*E-mail:
[email protected].
’ ACKNOWLEDGMENT I wish to thank all of the students who performed this exercise and in particular Carole Jontra and Renee Solko, Class of 2008, whose data appear in the figures. ’ REFERENCES (1) Ault, A. J. Chem. Educ. 2008, 85, 1432–1434. (2) Alberty, R. A. J. Chem. Educ. 2008, 85, 1136–1141. (3) Northrop, D. B. J. Chem. Educ. 1998, 75, 1153–1157. (4) Hofstee, B. H. J. Nature 1959, 184, 1296–1298. (5) Chong, D. P. J. Chem. Educ. 1994, 71, 489–490. (6) Martin, R. B. J. Chem. Educ. 1997, 74, 1238–1240. (7) Bruist, M. F. J. Chem. Educ. 1998, 75, 372–375. (8) Johnson, K. A. J. Chem. Educ. 2000, 77, 1451–1452. (9) Hamilton, T. M.; Dobie-Galuska, A. A.; Wietstock, S. M. J. Chem. Educ. 1999, 76, 642–644. (10) Bendinskas, K.; DiJiacomo, C.; Krill, A.; Vitz, E. J. Chem. Educ. 2005, 82, 1068–1070. (11) Correia, L. C.; Bocewicz, A. C.; Esteves, S. A.; Pontes, M. G.; Versieux, L. M.; Teixeira, S. M. R.; Santoro, M. M.; Bemquerer, M. P. J. Chem. Educ. 2001, 78, 1535–1537. (12) Bateman, R. C., Jr.; Evans, J. A. J. Chem. Educ. 1995, 72, A240– A241. (13) Roberts., C. H.; Chlebowski, J. F. J. Biol. Chem. 1985, 260 (12), 7557–7561. (14) Zhang, L; Buchelt, R; Azzar, G. Biochem. J. 2005, 392, 407–415. (15) Harris, D. C. J. Chem. Educ. 1998, 75, 119–121. (16) Manes, T.; Hoylaerts, M. F; Muller, R.; Lottspeich, F.; Holke, W.; Millan, J. L. J. Biol. Chem. 1998, 273 (36), 23353–23360.
’ SUMMARY This exercise promotes analytical thinking and reasoning and comprehensively incorporates application of concepts from this 1339
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