Laboratory Experiment pubs.acs.org/jchemeduc
Exploring the Hydrolysis of Sucrose by Invertase Using Nuclear Magnetic Resonance Spectroscopy: A Flexible Package of Kinetic Experiments Joanne D. Kehlbeck,*,† Clancy C. Slack,† Marilyn T. Turnbull,‡ and Susan J. Kohler† †
Department of Chemistry, Union College, Schenectady, New York 12308, United States Department of Chemistry, Wellesley College, Wellesley, Massachusetts 02481, United States
‡
S Supporting Information *
ABSTRACT: Nuclear magnetic resonance spectroscopy (NMR) is a viable alternative to current methods to introduce enzymatic reactions and monitor kinetics in the undergraduate curriculum. Using NMR to observe the invertase-catalyzed conversion of sucrose to fructose and glucose, one can gather information about the order of the reaction, as well as the maximum rate (vmax) and the Michaelis constant (KM). Kinetic parameters determined in this NMR study are comparable to the results obtained through polarimetry, the method often used to study this reaction at the undergraduate level. The breadth of information that NMR provides can give students a better understanding of the changes in reactant and product concentration over time, giving a visual connection to the rate law they derive. KEYWORDS: Second-Year Undergraduate, Upper-Division Undergraduate, Analytical Chemistry, Laboratory Instruction, Physical Chemistry, Hands-On Learning/Manipulatives, Kinetics, NMR Spectroscopy, Enzymes
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elsewhere.14 More recently, a method employing the use of a blood glucometer to measure the kinetic parameters of sucrose and lactose hydrolysis has been described.15 In contrast to those experiments, NMR provides a clear platform for students to visualize the appearance of products and disappearance of reactants to demonstrate reaction monitoring and kinetics measurements. In addition, NMR can be used to account for the mutarotation of α- to β-glucose, as signals for both anomers are sufficiently resolved.16−19
uclear magnetic resonance spectroscopy (NMR) is a powerful and versatile analytical tool. Though most frequently used to study structure, binding, and dynamics of enzymes and proteins, the use of NMR in the undergraduate curriculum is often limited to structural confirmation and elucidation in introductory courses or a discussion of technical aspects of NMR instrumentation in upper-level courses. A few examples of undergraduate experiments using NMR to study kinetics have been reported,1−5 and only one of these4 involved Michaelis−Menten kinetics. Consequently, a laboratory experiment to include enzyme kinetics was designed to expand on the classical experiments routinely implemented in the undergraduate curriculum. This flexible and robust package of exercises employs 1H NMR spectroscopy to measure the kinetics of the enzymatic hydrolysis of sucrose to its initial products (Scheme 1), the reaction used to generate the liquid center of cordial creams in the confectionary industry. This reaction, commonly known as the inversion of sucrose, is catalyzed by β-fructofuranosidase (invertase, sucrase), producing initially α-glucose and β-fructose. The reaction has been studied extensively6−11 since Michaelis and Menten completed their historic work in the early 20th century.12,13 While the experimental system described can appear deceptively simple, several important aspects of experimental design and data analysis arise that provide an opportunity for students to think more deeply about these issues. Experiments employing polarimetry to explore the kinetics of invertase-catalyzed hydrolysis of sucrose have been described © 2014 American Chemical Society and Division of Chemical Education, Inc.
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LEARNING OUTCOMES These exercises are designed to provide students with an enhanced appreciation and understanding of NMR, and its potential application to quantitative problems. Independent thinking and problem solving by students are promoted and the full power of NMR techniques across a broad spectrum of chemical fields are illustrated with laboratory experiments that are feasible in a typical undergraduate laboratory setting. The pseudo-zero-order case (experiment 1), in which a single reaction is followed over time in the presence of a high sucrose concentration, is used as a demonstration in a general education course. It is also used as a student experiment lasting less than 2 h in introductory organic courses to illustrate basic concepts of NMR. In addition to receiving an introduction to kinetics, students observe that mixtures can be studied using NMR and Published: April 3, 2014 734
dx.doi.org/10.1021/ed300889s | J. Chem. Educ. 2014, 91, 734−738
Journal of Chemical Education
Laboratory Experiment
Scheme 1. The Enzymatic Hydrolysis of Sucrose
eyewear and can use protective gloves to prepare solutions. Students are instructed to collect used solutions in properly labeled containers so they can be collected by environmental health and safety at your institution.
that peak area is proportional to concentration. These are challenging concepts to convey to students who use NMR exclusively for standard organic product analysis. In its fundamental form, the initial rates exercise (experiment 2) is routinely completed in one 3−4 h laboratory session. Students monitor the initial rates of a series of reactions and learn the standard methods for analysis of enzyme-mediated reactions. They consider how to measure initial rates and explore the limitations of the method. As an extension of the basic experiment, additional mathematical modeling experiments are completed after the laboratory exercise. Students explore the limitations of the Michaelis−Menten assumptions. Comparisons of the linear and nonlinear methods of data analysis can also be included.
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RESULTS
NMR Spectra 1
H NMR spectra of sucrose, glucose, fructose, and a mixture of the three sugars were obtained at field strengths of 4.7 T (200 MHz) (Figure 1) and 9.4 T (400 MHz) (Figure 2). These
EXPERIMENT
Overview
Stock solutions of sucrose in D2O, α-glucose in D2O, β-fructose in D2O, acetate buffer (pH 4.9), and invertase in acetate buffer were prepared for students. Typically, student groups require 2 h in laboratory to complete experiment 1 and 2 h for experiment 2. Because we have one spectrometer, student groups reserve time to complete the exercise outside of the normally scheduled laboratory period. Experiment 1 (Excess Sucrose/Pseudo-Zero-Order)
Each student group prepares three standard NMR solutions of sucrose in acetate buffer, α-glucose in acetate buffer, and βfructose in acetate buffer. The NMR spectrum for each solution is acquired and used to identify unique NMR signals for each sugar. Each student group prepares a fourth NMR solution of sucrose, acetate buffer, and invertase. Over a period of 90 min, a series of spectra are acquired as one data set for kinetic analysis. Each spectrum is analyzed by integrating appropriate signals and calculating the change in sucrose and glucose concentration over time.
Figure 1. 1H NMR spectra of sucrose and its component sugars. The spectra were acquired on a 200 MHz spectrometer. Resonances at 5.4 ppm (sucrose) and 5.2 + 4.6 ppm (combined anomers for glucose) were used to monitor reaction progress. The signal at 4.6 ppm can be used to account for the anomerization of glucose.
Experiment 2 (Initial Rates Experiment)
Each student group prepares nine NMR samples of varying sucrose concentration. NMR spectra of each sample are acquired approximately every 20 s in the initial 3−5 min of the reaction. Students are asked to record the time measured from adding the enzyme until data collection has finished. The combined peak areas of glucose and sucrose are used to represent the peak area that would correspond to the initial sucrose concentration. Initial rates are calculated from the rate of disappearance of the sucrose.
spectra were given to the students and they identified unique signals for sucrose and glucose that could be used to monitor the progress of the hydrolysis of sucrose. Typically, they identified the doublet at 5.4 ppm to track the disappearance of sucrose and the doublet at 5.2 ppm to observe the appearance of the product glucose. The doublet at 4.6 ppm was pointed out to arise from mutarotation of glucose and must also be included in longer experiments where anomerization is a factor. These resonances were clearly resolved at both the low and high field strengths and were sufficiently removed from the water signal (approximately 4.8 ppm). At the higher field strength, there were other resonances that could be used as well, such as the sucrose doublet at 4.2 ppm and the glucose multiplet at 3.25 ppm. 1H NMR signals for sucrose and glucose are sufficiently resolved to monitor this reaction at field strengths as low as 60 MHz (see Supporting Information).
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HAZARDS All materials used in this experiment are level 1 health hazards. Precautions to prevent skin contact, inhalation, and ingestion should be taken. Sodium acetate is an irritant and is slightly hazardous in case of skin or eye contact. Deuterium oxide is hazardous in case of ingestion. Students should wear protective 735
dx.doi.org/10.1021/ed300889s | J. Chem. Educ. 2014, 91, 734−738
Journal of Chemical Education
Laboratory Experiment
Over the course of a 10-h experiment, the total area varied less than 0.2%. On modern instruments, such as a 400 MHz spectrometer, methods to obtain relative peak areas from multiple spectra are available and reliable, so this method was not required. The Excess Sucrose/Pseudo-Zero-Order Experiment (Experiment 1)
The pseudo-zero-order experiment was used to monitor the course of the sucrose inversion reaction under conditions of high substrate concentration (S0 ≫ KM). Under these conditions, the Michaelis−Menten kinetics model predicts that the reaction rate will depend linearly on enzyme concentration and will not depend on sucrose concentration. The reaction rate should be constant with a rate of vmax, and a plot of either substrate (sucrose) concentration versus time or product (glucose) concentration versus time should be linear with a slope equal to the reaction rate. Student results from three separate experiments performed under these conditions, in which both sucrose disappearance and glucose appearance were monitored, are shown in Figure 3. The average rate calculated from the slopes of these plots was 6.9 × 10−6 M s−1 and k2 was calculated to be 350 s−1.
Figure 2. 1H NMR spectra of sucrose and its component sugars. The spectra were acquired on a 400 MHz spectrometer. In addition to the individual resonances at 5.4 ppm (sucrose) and 5.2 + 4.6 ppm (combined anomers for glucose), resonances at 4.2 ppm (sucrose) and 3.25 ppm (glucose) may also be used to monitor reaction progress. The resonance at 4.6 ppm is significantly larger than that in Figure 1 due to greater anomerization of the glucose in this sample.
Initial Rates Experiment (Experiment 2) Relationship between Peak Area and Concentration
To determine initial rates for experiment 2, students monitored peak areas as a function of time over the first 5 min of the reaction. The slope of a plot of peak area versus time provided the information to calculate the initial rate. However, at lower sucrose concentrations (0.03 and 0.06 M), at least 50% of the reaction was completed within the first 5 min. Therefore, in these cases, the slope was not appropriate to determine the initial rate and students determined the initial rate (v0) from the difference in area of the sucrose peak at an initial time point (approximately 60 s, AS 60) and combined peak areas of the glucose and sucrose peak (AS + AG) representing the initial sucrose concentration (eq 1):
These experiments were dependent on the assumption that the area of an NMR peak was proportional to constituent concentration. There are several methods that may be used to determine quantitatively this relationship using either external or internal standards, and the method of choice may depend on the capabilities of the instrumentation available. On an aging 200 MHz spectrometer, peak areas from multiple spectra could not be measured on the same scale. In this case, students used a sum of sucrose and glucose peaks as an internal standard. Since the sum of sucrose and glucose concentrations remained constant and equal to the initial sucrose concentration, students were led to the assumption that the sum of the peak areas of the 5.4 and the combined 5.2 + 4.6 ppm resonances would be constant, and thus, the ratio of the sucrose peak area to the sum would represent the fraction of sucrose remaining at a given time. Students validated this assumption by monitoring the combined peak areas during experiment 1.
v0 =
[(AS + A G) − AS60] [S0] d[S] = × dt t (A S + A G )
(1)
Experiment 2 was a typical Michaelis−Menten experiment in which the initial reaction rate was monitored as a function of
Figure 3. (A) Sugar concentration versus time. Results from three typical student experiments show the decrease in sucrose concentration (black circles) and the increase in glucose concentration (red circles) for the enzyme-limited case with an initial sucrose concentration of 0.5 M and invertase concentration of 2 × 10−8 M. (B) 1H NMR spectra showing reaction progress. The spectra were acquired on a 200 MHz spectrometer. Signals at 5.4 ppm (sucrose) and 5.2 + 4.6 ppm (combined, glucose) were integrated to monitor concentration. 736
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Laboratory Experiment
Figure 4. (A) Michaelis−Menten analysis. The data from three typical student experiments are plotted along with the accompanying nonlinear leastsquares fit. (KM = 0.11 M and vmax = 0.027 M min−1). (B) Lineweaver−Burke analysis. The data from three typical student experiments are plotted along with the accompanying linear least-squares fit. (KM = 0.064 M and vmax = 0.022 M min−1). (C) Eadie-Hofstee analysis. The data from three typical student experiments are plotted along with the accompanying linear least-squares fit. (KM = 0.076 M and vmax = 0.024 M min−1). (D) HanesWoolf analysis. The data from three typical student experiments are plotted along with the accompanying linear least-squares fit. (KM = 0.11 M and vmax = 0.027 M min−1).
Modeling the Limiting Case of Excess Sucrose
initial sucrose concentration. The initial rate was calculated from the rate of disappearance of sucrose as monitored by the disappearance of the 5.4 ppm doublet. The data were plotted according to the traditional Michaelis−Menten method (Figure 4A), as well as the linearized Lineweaver−Burke (Figure 4B), Eadie-Hofstee (Figure 4C), and Hanes-Woolf (Figure 4D) methods. Excel was used for linear regression analysis and results were used as initial estimates in a Mathematica program used for nonlinear regression analysis of the Michaelis−Menten plot. From these analyses, values for the maximum rate (vmax), the Michaelis constant (KM) and the turnover number (k2, also known in the literature as kcat), were obtained (Table 1).
One of the limiting cases of Michaelis−Menten kinetics occurred when [S0] was significantly greater than KM and the rate of the reaction reached its limiting value of vmax (=k2E0). Values for KM were on the order of 0.1 M and achieving sucrose concentrations in large excess of this value were difficult experimentally due to solubility constraints. Students answered the question “How much sucrose is enough?” by using a spreadsheet program, such as Excel, to model experiments with given K M , k 2 , and E o values, and varying initial S o concentrations. Under initial rate conditions (
