This work was supported by National Science Foundation Grant NSF DUE-9950288.
A lactate dehydrogenase (LDH) enzyme kinetics laboratory experiment has been developed in which students obtain kinetic data using a microplate spectrophotometer (reader). These instruments have the capability of reading absorbances of many samples in a very short time frame. In this experiment 12 samples are prepared at a time and the absorbances read in less than 1 min. In a 3-hr laboratory period, students collect data at five different substrate concentrations without inhibitor and also in the presence of two different concentrations of inhibitor. Students have enough time to repeat each part if they obtain too much scatter in their data. The enzyme examined, LDH, correlates with the study of metabolism and has particular relevance for students who are interested in medical careers. The LDH assay itself is not new, but the microplate format and the use of urea as a quench reagent are novel features. Students plot Michaelis–Menten and Lineweaver–Burk plots and calculate values for Vmax, apparent Vmax (Vmaxapp), Km, apparent Km (Kmapp), kcat, and KI. Students typically obtain results correctly showing that oxalic acid is a competitive inhibitor and oxamic acid is a noncompetitive inhibitor when lactate is the substrate of the reaction.
Enzyme kinetics is a topic foundational to biochemistry. However, as instructors know, students typically find this topic difficult. Some reasons for this, as well as one possible solution involving computer simulations, have been addressed by Gonzalez-Cruz et al. . Our current biochemistry course for majors has a required laboratory component. Students at our university in a previously offered 6-hr elective biochemistry lab commented that they understood enzyme kinetics much better after carrying out a related lab experiment. For the above reasons, we wished to develop an assay that allowed students to collect enough data, during one 3-hr laboratory period, to fully explore inhibition and obtain accurate values for Km, Vmax, kcat, and KI. The use of a quenched assay together with a microplate photometer, also called a microplate reader, has made this possible, even with 12 pairs of students in the laboratory section.
Use of a microplate reader is gaining popularity in biochemistry labs, as evidenced by recent posters at national conferences. One example, recently published in this journal, involves screening for inhibitors of phosphatases . Protein assays are also easily performed with these instruments . From a pedagogical standpoint, the microplate reader also introduces students to high-throughput techniques common to industrial settings. From a financial standpoint, with this quenched assay experiment, one microplate reader is sufficient for 12 student pairs, circumventing the need for one spectrometer for each pair of students. The reason for this is that multiple samples can be prepared in a single microplate, and the absorbances for an entire 24-well plate can be measured in less than 1 min [http://www.biotek.com/products (accessed July 25, 2006); http://www.biocompare. com (accessed July 25, 2006)].
Many different enzymes are used in undergraduate laboratory kinetics experiments published in standard laboratory texts, but none are written for use with a microplate reader. These enzymes include tyrosine hydroxylase [4, 5], alkaline phosphatase , and lactate dehydrogenase (LDH)1 . We chose LDH since it catalyzes a reaction that is often familiar to students. Many students have heard of the buildup of pyruvate in muscle tissue during extended exercise  and thus have an immediate connection with this system. Students also have the opportunity to see this enzyme again during the discussion of metabolism in lecture. Finally, for those students interested in medical careers, LDH is used as a diagnostic enzyme for heart attacks and a few diseases . At the time of development of our assay, we were aware of a cell-based microplate colorimetric assay (Promega) that measured LDH activity as an indicator of cell death. However, since this was a coupled enzyme assay, we chose to proceed in a different direction so as to keep the assay simpler for ourselves and for the students. The laboratory text that includes LDH assays  does not include a study of inhibition and also differs from ours in other aspects described below.
LDH (EC 188.8.131.52) is a tetrameric oxidoreductase most commonly associated with the production of lactic acid (lactate) in muscle tissue during strenuous exercise. Depending on substrate availability and pH, however, the reaction can proceed in either direction (see review ). For this experiment, we modified the method described by Gutmann and Wahlefeld  in which L-lactate and nicotinamide adenine dinucleotide (NAD+) are the substrate and coenzyme, respectively, and pyruvate and reduced nicotinamide adenine dinucleotide (NADH) are the products. Gutmann and Wahlefeld's method also incorporates a second reaction that converts pyruvate to pyruvate hydrazone in a fast, nonenzymatic reaction (Scheme 1). Since pyruvate hydrazone cannot bind as well as pyruvate to the active site of LDH, the coupled reaction prevents reversibility and also decreases the likelihood of product inhibition. Additionally, the use of a high pH buffer favors the reaction in the direction of pyruvate production. Farrell and Taylor's procedure  does not use the coupled reaction, but carries out the experiment at a higher pH. Gutmann and Wahlefeld's method is more typically used to measure lactate concentration, but the level of enzyme used here allows for determination of kinetic and inhibition constants.
The reaction rate is determined based on the NADH concentration at the 4-min time point as measured by its absorbance. The reduced coenzyme (NADH) absorbs in the 320–350 nm region, while NAD+ does not. Ideally, one obtains kinetic constants by monitoring the rate continually over time so that a true value for initial rate can be obtained. However, to facilitate completion of this lab in a 3-hr time block with 24 students, use of a quenched assay was required. Urea was chosen to stop the reaction since we found that typical quench reagents such as strong acids or NaOH either did not stop the reaction completely or interfered with NADH quantitation. High concentrations of urea denature the enzyme, resulting in a complete quench. The 4-min time point was chosen since evaluation of absorbance vs. time plots for all concentrations of substrates and inhibitors showed linearity (R2 = 0.99) for 4 min or longer.
Students should be proficient in the use of microliter-scale pipettors (e.g. Eppendorf type) and familiar with spectroscopy and the Beer–Lambert law. In our laboratory, students complete protein assays using the microplate reader 1 or 2 wk prior to the LDH experiment. Also, it is recommended that students have already studied the theory of enzyme kinetics and analyzed graphical data in lecture. In preparation for the lab, students read a handout containing background information like that in the previous section of this paper and answer the following questions:
What is the full name and abbreviation of the enzyme used in the experiment?
What is the name of the substrate? Product?
What are the full name and abbreviation of the coenzyme and the abbreviation of its product?
Which of the compounds gives the absorbance that is measured in the assay?
In addition, students are instructed to write out the enzymatic and nonenzymatic reactions using structures and to draw the structures of the two inhibitors that will be used in the experiment. They must do a bit of searching on their own to find these structures; however, these could be provided for the students if the instructor desires. In addition to a basic enzyme kinetics discussion during the pre-lab lecture, the instructor could also discuss limiting reagents, coupled reactions, reversibility of enzyme reactions, error, and reproducibility.
The experiment requires one microplate reader with a 340-nm filter for a class of 24 students. We employed the Packard SpectraCount instrument initially, and more recently, the BioTek PowerWave XS. Each pair of students will need two 24-well microplates, timer, microliter-scale pipettors, and tips for 1,000- and 100-μL volumes. Chemicals were purchased from Sigma or Fisher. Hydrazine was purchased as the hydrate, β-NAD+ was purchased in 50 mg vials (one vial per student pair), and rabbit muscle LDH (∼915 U/mg) was used.
Stock solutions include: Buffer (0.50 M Glycine and 2.5 mM EDTA, pH 9.5) and the following solutions prepared in the buffer, 0.30 M Lactate, 14.3 mM β-NAD+, 0.52 M Hydrazine, 16–19 U/mL LDH, 9.0 M Urea, and either 0.20 M Oxalic Acid or 0.40 M Oxamic Acid as an inhibitor. The β-NAD+ should be made fresh. The enzyme should be kept on ice, and a small aliquot allowed to equilibrate to room temperature just before addition to the assay. All other reagents can be kept at room temperature during the experiment and stored in the refrigerator for several weeks. One should be cautious when preparing hydrazine as it can cause skin and eye burns and is considered a poison. It should be measured out under the hood since it fumes slightly when the bottle is opened. Disposal of chemicals is the same as for other organic flammables and corrosives.
Volumes of buffer, and hydrazine, lactate, and NAD+ stock solutions are pipetted into duplicate rows of a 24-well plate according to Table I. Samples are mixed by swirling the plate on the benchtop. The reaction is started by adding 40 μL of the LDH stock solution and again swirling the plate. The reaction is allowed to proceed for exactly 4 min, then 500 μL of 9.0 M urea is added to stop the reaction. Absorbances are read at 340 nm using the microplate reader. Our students used single-channel pipettors. However, multichannel pipettors could be used to dispense all solutions except the lactate and buffer.
Table I. Volumes of solution for LDH assay without inhibitor
Since this experiment requires some coordination of pipetting and timing, students are given a timing grid (Table II) to follow. Thus, to start the reaction, they pipet the LDH in well A1 at time 0:00, in well B1 at 0:10, in well A2 at 0:30, and in well B2 at 0:40, etc. The addition of the stop solution follows the same order and timing sequence, so that each reaction proceeds for exactly 4.0 min.
Table II. Time grid for two rows of 24-well microplate
Students then prepare the first set of reactions with inhibitor using the empty rows of the same 24-well plate and 60 μL of inhibitor stock solution (oxalic or oxamic acid). The volume of buffer is adjusted so that the total reaction volume per well (1,200 μL) is the same as in the previous set of reactions. A second concentration of the same inhibitor is examined on a second microplate using 180 μL of inhibitor stock solution. Again, buffer volumes are adjusted so that the total reaction volume per well remains constant for all assays.
Calculations and Data Analysis
Absorbances from the duplicates are averaged and the average blank absorbance (no substrate) is subtracted from the average absorbance for each substrate concentration. To convert absorbance to concentration, Beer's law is used. Students are provided with the literature molar extinction coefficient for NADH (6,220 M−1 cm−1) and the path length (0.90 cm) for the assay. Since these data are collected after the addition of urea, however, the resulting concentrations are more dilute than during the assay. To correct for this, students multiply by the final volume divided by the initial volume. Finally, to obtain the rate, the molar concentration is divided by the time span of the assay (4 min).
Students submit sample calculations and tables of data including lactate volume, lactate concentration (mM), ΔA, ΔA min−1, M min−1, 1/[S], and 1/[v]. Students use Microsoft Excel to prepare Michaelis–Menten and Lineweaver–Burk plots. Data without and with both concentrations of inhibitor are included on each graph. For the Lineweaver–Burk plots, students are instructed to draw straight lines that all intersect on either the x-axis or y-axis. For the Michaelis–Menten plots, they draw a best-fit smooth curve by hand. Students calculate values for Vmax, Vmaxapp, Km, Kmapp separately for each plot and kcat and KI using values obtained from the Lineweaver–Burk plot.
RESULTS AND DISCUSSION
Kinetic values obtained in the absence of inhibitor for Vmax ranged from 15 to 44 μM/min with an average of 33.3 μM/min (n = 6 pairs) during one semester and from 18 to 46 μM/min another semester with an average of 29.4 μM/min (n = 11). (Data were only considered from student pairs with an R2 ≥ 0.99 on the Lineweaver–Burk plot.) Values determined for Km ranged from 13 to 45 mM, with an average of 26 mM (n = 6) during one semester and from 23 to 60 mM with an average of 37.1 mM (n = 11) another semester. This data was similar to that obtained by the instructor on two separate occasions (Vmax = 27.9 and 21.1 μM/min, Km = 16.7 and 12.6 mM). Student kinetic values are also similar to that obtained by the instructor (not shown) using rates obtained one by one with a traditional spectrometer and quartz cuvette from a nonquenched reaction performed in duplicate: Vmax = 37.5 μM/min, Km = 26.5 mM. Representative student and instructor microplate data are shown in Figs. 1 and 2. The vvs. [S] plots shown here were created in Sigma Plot, which easily calculates error bars; however, as noted earlier, students simply use Excel and draw the best-fit smooth curve through their data points. When making kinetic comparisons between labs or when using different batches of enzyme, the enzyme concentration or activity may not be the same. Thus, it is better to compare kcat rather than Vmax. Our average Vmax values from the two semesters would give a kcat of 6,660 or 5,880 min−1.
For the report, students determine the type of inhibition observed for their inhibitor and support their conclusion with the Lineweaver–Burk plot results and with their numerical values of Vmax, Vmaxapp, Km, and Kmapp. They discuss whether or not their conclusion is reasonable based on comparison of the structures of inhibitor and substrate. The structure of oxalic acid is more similar to lactate than oxamic acid and would be expected to fit into the lactate binding site, exhibiting competitive kinetics. Student data almost always allow the correct determination that oxalic acid is competitive and oxamic acid is noncompetitive in this assay. We routinely use duplicate samples and two inhibitor concentrations, which makes it easier to draw conclusions than when we used only one inhibitor concentration. We recommend having the instructor or teaching assistant check the raw data before the student leaves the lab. If precision is low or if the expected trend is not observed, students should repeat the experiment. Since the lowest substrate volume typically has the most error, and since the Lineweaver–Burk plot exaggerates the error for larger 1/[S] values, it may be helpful to have students consider the intersection of lines without this data point if no clear pattern is observed. Student data have been collected during two different semesters. With the first group of students, the average KI for oxalic acid was 14.3 mM (standard deviation (Sx) = 4.7; n = 4) and for oxamic acid, 23.8 mM (Sx = 9.3; n = 4). This agrees with data from Nisselbaum et al.  which shows that oxamic acid has a higher KI than oxalic acid under similar conditions. The following semester, the average student KI was 11. 4 mM (Sx = 11.3; n = 8) for oxalic acid and 15. 3 mM (Sx = 1.5; n = 7) for oxamic acid. It is unclear why student KI varied so much for the oxalic acid inhibitor with the second group of data. Application of the Q test (90% confidence level) allows one value to be discarded and results in an average KI of 7.9 mM (Sx = 5.4). Thus, this data also agrees with that of Nisselbaum et al. .
Students also compare the Vmax and Km values obtained from the Michaelis–Menten plot with those obtained from the Lineweaver–Burk plot. This allows them to see the limitations of the graphs. At the highest concentration of lactate used in this experiment, Vmax is not reached. Thus, the Vmax which students estimate from the vvs. [S] graph will be lower than that obtained from the Lineweaver–Burk plot.
In an effort to have students think about the meaning of KI, a problem is included describing a “new inhibitor” that has “just been discovered” for LDH with a KI of 3.5 nM. They compare this KI to that of their inhibitor and explain which binds best to the enzyme.
On occasion we have asked students to predict the shape of the absorbance vs. time plot if the reaction were allowed to proceed indefinitely. We also sometimes instruct them to analyze a velocity vs. [E] plot and explain the relationship observed.
If there is enough time, students can collect data for their own velocity vs. enzyme concentration graph. A high concentration of substrate (e.g. 320 μL lactate) should be used. Other components are as before except that buffer volumes are adjusted so that varying enzyme volumes (0–75 μL) are accommodated. If enzyme is added at last, students must remember to change the pipette settings appropriately between samples. Alternately, one could use the lactate to start the reaction. The reaction is quenched and absorbances read as before. If students perform the velocity vs. [E] variation, they are asked to graph velocity vs. microgram of LDH and show sample calculations for this.
For the velocity vs. [E] study, a linear relationship is found when using 0.5–1.5 U of rabbit muscle LDH and performing the assay with 1.3 mM NAD+ and 80 mM lactate. A representative graph from this year's student data is shown (Fig. 3). Student pipetting skills are important in generating a good linear relationship. One-third of the student pairs who submitted their data had an R2 value of 0.992 or higher for this plot. Seventy-two percent of the student pairs had an R2 of 0.980 or higher.
ADDITIONAL ITEMS REGARDING THIS ASSAY
When using the microplate reader, be sure the lid is off before reading the absorbance. All other precautions of spectroscopy still apply. A difference is that the pathlength for a plate reader is the depth of the liquid in the well. Thus, if volumes are adjusted, a new pathlength should be calculated.
Although the 24-well plates used do have a slight absorbance at 340 nm (∼0.2), this becomes part of the blank absorbance. The blank rate (no substrate) is typically negligible if NAD+ is made fresh and EDTA is included in the buffer. However, the A340 of the blank at time zero does increase over time. If the hydrazine concentration is too high, we and others  have seen erratic blanks; however, the concentration reported here has resulted in consistent blank absorbances in our hands.
After the addition of urea, the A340 of all samples except for those with 30 mM oxalic acid are stable for at least 30 min; those with 30 mM oxalic acid are stable for at least 10 min. The addition of EDTA to the buffer has been used by Engel and Jones  in order to suppress drifting endpoints in assays using the glycine–hydrazine buffer.
It will most likely be necessary to adjust the stock concentration of enzyme if LDH of significantly different U/mg is purchased. Variations to the LDH stock concentration or to the other experimental conditions may affect the linearity with respect to time, so this should be checked by the instructor prior to the lab period. Linearity should be checked using a continuous shaking method available on the plate reader. Use of a lower concentration of NAD+ will result in a higher observed Km. Student data using 0.6 mM NAD+ resulted in an average Km of 67 mM (n = 6; Sx = 10).
OTHER VARIATIONS OF THIS LAB
Obvious variations of this experiment include analysis of LDH activity vs. temperature or pH and determination of a Km for NAD+ . Students could also determine whether the concentration of lactate affects the Km of NAD+. For other simple variations of this lab, students could prepare their own NADH standard curve and use this curve to determine NADH concentrations rather than calculating from the Beer–Lambert law. Possible product inhibition could be examined by comparing results with and without the hydrazine.
A more involved variation would be to introduce students to isozymes, which is possible because mammalian LDH exists as five isozymes. It has previously been reported that these isozymes have distinct kinetics constants [11, 13] as well as pH and temperature responses [14, 15]. This lab could be used to compare Km, kcat, and oxamate or oxalate KI values for different isozymes . In doing isozyme studies, however, one should first be sure the concentration of urea listed quenches the LDH reaction since differences in susceptibility to urea denaturation have been reported . Reagent concentrations may also require optimization to obtain linear conditions.
This lab is also easily adaptable for multi-week studies. The LDH enzyme kinetics and inhibition lab could be linked with labs in which this enzyme is first isolated . A recent publication in this journal  uses an LDH assay as part of a comparative study of muscle physiology and energy metabolism. Also, a study of isozyme kinetics could be linked with a native gel separation of LDH isozymes .
The authors thank students in various sections of Biochemistry I laboratory for trying modified versions of this lab throughout the years. We also thank Drs. Carol Chrestensen and Jonathan McMurry (Kennesaw State University) for allowing their lab sections to perform this experiment and share student results for use in this paper. Finally, thanks also to Dr. Chrestensen for help with preparation of figures.
The Abbreviations used are: LDH, lactate dehydrogenase; NAD+, nicotinamide adenine dinucleotide; NADH, reduced nicotinamide adenine dinucleotide.