LABORATORY EXPERIMENT pubs.acs.org/jchemeduc
Kinetic Parameters for the Noncatalyzed and Enzyme-Catalyzed Mutarotation of Glucose Using a Blood Glucometer John R. Hardee,* Bryan Delgado, and Wray Jones Department of Chemistry, Henderson State University, Arkadelphia, Arkansas 71999, United States
bS Supporting Information ABSTRACT: The kinetic parameters for the conversion of R-D-glucose to β-Dglucose were measured using a blood glucometer. The reaction order, rate constant, and Arrhenius activation energy are reported for the noncatalyzed reaction and turnover number and Michaelis constant are reported for the reaction catalyzed by porcine kidney mutarotase. The experiment is relatively simple and inexpensive and can be used in general chemistry and undergraduate biochemistry laboratories. KEYWORDS: Upper-Division Undergraduate, Biochemistry, Laboratory Instruction, Physical Chemistry, Hands-On Learning/Manipulatives, Aqueous Solution Chemistry, Biophysical Chemistry, Catalysis, Enzymes, Kinetics
’ EXPERIMENTAL DETAILS R-D-Glucose (99þ%) was purchased from Acros Organics. The glucometer used was a One Touch Ultra 2 manufactured by LifeScan, Inc., a Johnson and Johnson company. Solutions were prepared in 30 °C deionized water and then placed in a constant temperature bath at 30 °C. A drop of the solution was placed on the test strip and a glucose reading was given in 5 s. Solutions of known glucose concentration were prepared and given 12 h to reach equilibrium. A calibration curve was obtained by plotting glucose concentration versus meter reading. For the noncatalyzed kinetics, solutions were prepared in 30 °C deionized water and rapidly transferred to a 30 °C constant temperature bath. The porcine kidney mutarotase (aldose-1-epimerase) was obtained from Calzyme Laboratories, Inc. It was reported to be 90% protein with an activity of 5000 U/mg protein. An enzyme solution was prepared by dissolving the enzyme in a 5.0 mM sodium EDTA solution. The enzyme concentration was 4.2 104 mg dL1. The enzyme molar mass was taken to be 4.0 104 g mol1.5 Glucose solutions were prepared by dissolving glucose in 30 °C enzyme solutions, which were quickly transferred to a 30 °C constant temperature bath.
B
lood glucometers have been described for laboratory use several times in this Journal.13 The most recent article showed that, at least in principle, a blood glucometer could be used to study the kinetics of the mutarotation of glucose. Because R- and β-D-glucose are optical isomers, a direct technique for monitoring the kinetic process of mutarotation in solution has been polarimetry, which requires a relatively expensive instrument. While studying the mutarotation of R-D-glucose, Perles and Volpe3 found an excellent correlation between polarimeter readings and blood glucometer readings. However, the authors did not directly use a blood glucometer to obtain the kinetic parameters such as reaction order, reaction rate constant, and the Arrhenius activation energy. The chemistry of the blood glucometer has been discussed in detail elsewhere.4,5 Blood-glucose test strips contain a working electrode, a counter or reference electrode, an enzyme such as glucose oxidase, and a redox mediator such as ferricyanide.4 After glucose oxidase reacts with glucose, it is reoxided by the mediator. The mediator is in turn reoxidized at the electrode and a current is produced. The quantity of current produced is proportional to the amount of glucose in the sample. Older blood glucometers took at least 30 s to give a result, which made initial rate kinetics difficult to obtain. Newer glucometers overcome this problem by giving readings in as little as 5 s. The decrease in analysis time is in part a result of improving the solubility and rate of dissolution of the redox mediator.4 The purpose of this research is to describe in detail the use of a simple, inexpensive, commercial blood-glucose meter and the initial rate data to obtain these kinetic parameters and to obtain MichaelisMenten kinetic parameters for the enzyme-catalyzed mutarotation of glucose. This work provides an experimental procedure that could be used in advanced general chemistry laboratory, physical chemistry laboratory, and in undergraduate biochemistry laboratory. Copyright r 2011 American Chemical Society and Division of Chemical Education, Inc.
’ HAZARDS Porcine kidney mutarotase may cause irritation to skin, eyes, and respiratory tract and may induce a cough and cause allergic reactions in sensitive individuals. Sodium EDTA may cause irritation to skin, eyes, and respiratory tract and may be harmful if swallowed or inhaled.
Published: April 08, 2011 798
dx.doi.org/10.1021/ed101079k | J. Chem. Educ. 2011, 88, 798–800
Journal of Chemical Education
LABORATORY EXPERIMENT
Figure 3. The natural logarithm of the initial rate versus the natural logarithm of the initial R-D-glucose concentration. Figure 1. β-D-glucose concentration in milligram per deciliter (mg dL1) versus the meter reading.
Figure 4. Initial rate data at three temperatures.
Figure 2. Initial rate data for the mutarotation of R-D-glucose at 30 °C for different initial R-D-glucose concentrations.
’ RESULTS The glucometer must be calibrated for use with aqueous solution. Because the blood matrix is different from an aqueous solution, the direct glucometer reading in aqueous solution is not accurate. This may be due to higher diffusion coefficients in less viscous aqueous samples. Also, the glucometer reading may include a correction for other oxidizable substances such as ascorbic and uric acid contained in blood samples at concentration comparable to glucose.1 To conduct this experiment, it is necessary to determine the β anomer concentration from the glucometer reading. Because at equilibrium the ratio of the R anomer concentration to the β anomer concentration is 36 to 64,6 the concentrations of the equilibrated solutions of known glucose concentrations were multiplied by 0.64 to give the β anomer concentrations. This was plotted against the glucometer readings to yield the calibration curve of β anomer concentration versus meter reading (Figure 1). The initial rate data for the mutarotation of R-D-glucose at 30 °C are shown in Figure 2. The slope of each line is equal to the initial reaction rate. To determine the reaction order, δ, and the observed reaction rate constant, k, the natural logarithm of the initial rate was plotted against the natural logarithm of the initial R-D-glucose concentration: Initial rate ¼ k½R-D-glucoseδ
ð1Þ
ln½initial rate ¼ ln k þ δ ln½R-D-glucose
ð2Þ
Figure 5. Arrhenius plot for the mutarotation of R-D-glucose.
The result, shown in Figure 3, yielded a slope of 0.87 and an intercept of 7.5. This result is roughly in agreement with the reported pseudo-first-order kinetics using polarimetry.7 The calculated rate constant from these data is 5.5 104 s1, also in agreement with that reported by others.8 To determine the Arrhenius energy of activation, the initial rate was measured at an initial concentration of 100 mg dL1 of R-D-glucose at 26, 30, and 33 °C. The initial rate data are shown in Figure 4 and the Arrhenius plot is shown in Figure 5. The energy of activation of 91 kJ/mol is reasonably close to the published range of values from 67.2 to 75 kJ/mol.911 To study the enzyme-catalyzed reaction, initial rate data were obtained in 5.0 mM sodium EDTA solution at 30 °C. R-D-Glucose samples were dissolved in the enzyme solution consisting of porcine mutarotase and 5.0 mM sodium EDTA solution. Initial rate data were obtained for the mutarotation of R-D-glucose in EDTA solution. This initial rate from the nonenzyme-catalyzed reaction was subtracted from initial rate data of the enzyme-catalyzed reaction to yield the initial rate data shown in Figure 6. The LineweaverBurk plot for these initial rate data are shown in Figure 7. The slope of the LineweaverBurk plot is 799
dx.doi.org/10.1021/ed101079k |J. Chem. Educ. 2011, 88, 798–800
Journal of Chemical Education
LABORATORY EXPERIMENT
’ AUTHOR INFORMATION Corresponding Author
*E-mail:
[email protected].
’ REFERENCES (1) Wang, J.; Macca, C. J. Chem. Educ. 1996, 73, 797–800. (2) Hardee, J. R.; Montgomery, T.; Jones, W. J. Chem. Educ. 2000, 77 (4), 498. (3) Perles, C. F.; Volpe, P. L. O. J. Chem. Educ. 2008, 85 (5), 686. (4) Heller, A.; Feldman, B. Chem. Rev. 2008, 108, 2482–2505. (5) Gatz, C.; Altschmid, J.; Hillen, W. J. Bacteriol. 1986, 168 (1), 31–9. (6) Carbohydrates page, Department of Chemistry, University of Calgary. http://www.chem.ucalgary.ca/courses/351/Carey5th/Ch25/ ch25-3-3.html (accessed Mar 2011). (7) Pigman, W.; Isbell, H. Adv. Carbohydr. Chem. 1968, 23, 11–57. (8) LeBarc’H, N.; Grossel, J. M.; Looten, P.; Mathlouthi, M. Food Chem. 2001, 74 (1), 119–124. (9) Isbell, H. S.; Pigman, W. W. J. Res. Natl. Bur. Stand. 1937, 18, 141. (10) Perles, C. E.; Volpe, P. L. O. Acta Chim. Slov. 2009, 56, 209–14. (11) Panov, M. Y.; Sokolova, O. B. Russ. J. Gen. Chem. 2004, 74 (9), 1451–1453. (12) Mulhern, S. A.; Fishman, P. H.; Kusiak, J. W.; Bailey, J. M. J. Biol. Chem. 1973, 218 (12), 4163–4173. (13) Li, L.-K.; Chase, L. L.; Lapedes, A. M. J. Cell. Comp. Physiol. 1964, 64, 283–292.
Figure 6. Initial rate data for porcine mutarotase-catalyzed mutarotation of R-D-glucose for different initial R-D-glucose concentrations.
Figure 7. LineweaverBurk plot for porcine mutarotase catalyzed mutarotation of R-D-glucose (the reciprocal of the intital rate versus the reciprocal of the initial glucose concentration).
equal to (KM/k2[E]0) and the intercept is equal to 1/k2[E]0, where KM is the Michaelis constant, k2 is the turnover number, and [E]0 is the initial enzyme concentration. The turnover number obtained from Figure 7 is 1.8 105 min1 and the Michaelis constant is 3.6 mM. The turnover number is in good agreement with literature results for porcine kidney mutarotase and other mutarotases, which range from 1.4 105 to 1.0 106 min1, whereas the Michaelis constant is slightly lower than the published Michaelis constants of 519 mM.12,13
’ CONCLUSION The work reported here shows that a simple blood glucometer could be used instead of polarimetry to study the kinetics of the mutarotation of R-D-glucose. The procedure given here could be used for the measurement of the reaction order, observed reaction rate constant, and the Arrhenius activation energy in an advanced general chemistry lab or a physical chemistry lab. The procedure for the measurement of a turnover number and a Michaelis constant would be appropriate for an undergraduate biochemistry lab. ’ ASSOCIATED CONTENT
bS
Supporting Information Student handout for physical chemistry and biochemistry and instructor notes for physical chemistry and biochemistry. This material is available via the Internet at http://pubs. acs.org. 800
dx.doi.org/10.1021/ed101079k |J. Chem. Educ. 2011, 88, 798–800
