In the Laboratory
Analysis of Iron in Ferritin, the Iron-Storage Protein A General Chemistry Experiment Maureen J. Donlin, Regina F. Frey, Christopher Putnam, Jody K. Proctor, and James K. Bashkin* Department of Chemistry, Washington University, St. Louis, MO 63130
In a traditional chemistry curriculum, problems with increasing complexity are introduced in a sequential fashion so that beginning students are not exposed to the interesting chemical problems that motivate professional chemists to conduct research. In the general chemistry experiment described here, we have attempted to break with that tradition by introducing a complex biochemical problem that examines both the ironrelease process and the structure of the iron-storage compounds in living cells. Students examine the chemical properties of ferritin, the major iron-storage protein in living organisms. They determine the total amount of iron in a ferritin sample and then measure the amount of iron released from the protein by reduction of the mineral core. The importance of iron storage and the controlled release of iron from ferritin is demonstrated using concepts from general chemistry, such as redox reactions, metal chelation, and absorption spectroscopy. In addition, basic concepts of threedimensional protein structure and of chemical bonding are presented, using a computer graphics tutorial. The experiment was developed to teach fundamental chemical principles in the context of a biological system, to show the importance of chemistry in interdisciplinary areas, and to integrate the use of computer modeling and visualization with experimental techniques. At Washington University,1 the experiment is a secondsemester general-chemistry experiment and the students have had some prior experience with absorption spectroscopy and Beer’s law. The experiment is performed over a two-week period with 4 hours of laboratory and 1 hour of lecture per week. In the first week, students are reacquainted with absorption spectroscopy by determining the λ max and ε for the iron complex. They receive an exercise based on the computer tutorial, which introduces them to the threedimensional protein structure and helps to clarify the ironrelease process. In the second week, students determine the total iron content of ferritin and then determine the amount of iron released within a given time period.
release iron in a controlled fashion is essential (2). Cells have solved this problem of iron storage by developing ferritins, a family of iron-storage proteins that sequester iron inside a protein coat as a hydrous ferric oxide–phosphate mineral similar in structure to the mineral ferrihydrite (3). As shown in Figure 1, the protein is a spherical shell comprising 24 subunits with a combined molecular weight of 474,000 g/mol. The walls of the ferritin shell are approximately 10 Å thick and surround a spherical space approximately 80 Å in diameter (4). This spherical space can contain a maximum of 4500 iron atoms, which is equivalent to an iron concentration of ~0.25 M, or about 1016-fold more concentrated than Fe(III) ions in aqueous solution. Several good reviews of ferritin by Harrison (5, 6) and Theil (4) are available. The crystal structures of two ferritin proteins have been solved (7, 8); they provided the crystallographic data used in our graphics tutorial. The tutorial is designed to introduce three-dimensional protein structure and to provide background on the transport of iron out of ferritin. Among the important structural features of ferritin are the two types of channels that form at the protein-subunit interfaces. Iron is probably transported through the 3-fold channels, which are lined with hydrophilic side chains of the amino acid residues
Biochemistry of Ferritin Iron, an essential element in living organisms, is commonly used in the Fe(II) oxidation state, but in our oxidizing atmosphere Fe(III) is the more prevalent oxidation state. At the physiological pH of 7, the Fe(III) ion concentration in aqueous solution is minimal. However, most organisms maintain an intracellular concentration of Fe(III) several orders of magnitude higher than simple aqueous solutions permit. This discrepancy in concentrations demonstrates the striking ability of biochemical systems to concentrate and store iron (1). Conversely, iron can be very toxic, so the ability to store and *Corresponding author.
Figure 1. Molecular model of ferritin with subunits displayed in the CPK representation. All 24 subunits are identical, but they have been color coded to help illustrate the structure. The blue subunits are the nearest subunits, the green are farthest away, and red subunits are in between. Coordinates for the model were determined from Xray crystallography data (13, 14). The four blue subunits form the walls of a 4-fold channel. The 3-fold channels occur at the intersection of the green, red, and blue subunits. The locations of 3-fold channels are indicated, but the channels themselves are obscured from this viewing angle.
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Figure 2. Molecular model of the 3-fold channel with the three intersecting subunits represented as ribbons. To clarify the position of the 3-fold channel within the ferritin shell, the three intersecting subunits have the same color code as the corresponding subunits in Fig. 1. The amino acid residues lining the channel (aspartate and glutamate) are shown as CPK models. The hydrogens are omitted from the CPK representations for visual clarity.
Figure 3. Molecular model of the 4-fold channel with the four intersecting subunits represented as ribbons and the residues lining the channel (leucine) represented as CPK models. The subunits have the same color code as the corresponding subunits in Fig. 1. The hydrogens are omitted from the CPK representations for visual clarity.
aspartate and glutamate, as shown in Figure 2 (9). A second channel, the 4-fold channel, is formed where 4 subunits meet. It is lined with hydrophobic side chains of the amino acid leucine (Fig. 3). Molecular oxygen, reducing agents, and other small molecules may enter the ferritin cavity through these hydrophobic channels (10). The growth of the mineral core and the release of iron from the core in ferritins are redox-switched processes that depend on the different thermodynamic stability (solubility) and kinetic lability of aqueous Fe(II) and Fe(III). The in vivo biomineralization and iron-release mechanisms are not completely established, but substantial features have been demonstrated in vitro (11). It is known that the reactions occur in aqueous solution and that they depend on the pKa’s of the Fe(H 2O)6n+ ions. At the physiological pH of 7, Fe(II) is soluble whereas Fe(III) is not; therefore, iron is transported into and out of the protein in the Fe(II) oxidation state (12). Exactly how iron is released from ferritin in vivo has not been established. However numerous studies on the in vitro release of iron from ferritin have demonstrated that a variety of reducing agents and chelators can be used to trigger iron release (6, 10, 13, 14). In the lab, we present to our students a very simplified mechanism for the release of iron consisting of the following steps: (i) transport of electrons across the channels into the interior cavity; (ii) reduction of Fe(III) to Fe(II) and disruption of oxo-bridges between the iron atoms; and (iii) transfer of Fe(II) ions through the 3-fold channels and chelation with the chromophoric indicator. Since it is beyond the scope of a general chemistry experiment to discuss such a mechanism in detail, our emphasis when discussing the iron release from ferritin is that the iron is released at a controlled rate at which it can be used for biosynthetic processes. This concept of controlled release is reinforced in the kinetics section of the lab experiment.
Materials and Methods
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Experimental Material Type I ferritin from horse spleen was obtained from Sigma and used without further purification. It was stored at 4 °C and kept on ice during the laboratory period. A stock solution of 0.5 mg/mL was prepared in 0.15 M NaCl. A 12.5 mM stock solution of the Fe(II) chelating/indicator ferrozine, 3-(2-pyridyl)-5,6-bis(4-phenyl-sulfonic acid)-1,2,4-triazine (Sigma), shown in structure 1, was prepared in distilled water. Its final concentration in the experiment was 1 mM. A standard Fe(II) solution approximately 4–5 × 10 ᎑4 M was prepared from Fe(NH4) 2(SO4)2ⴢ6H2O in 0.02 M H2SO4. The reducing agent was dihydroxyfumaric acid (DHF, Sigma), shown in structure 2 in its dianionic form. Fresh 5 mM stock solutions were prepared daily in distilled water. 4– N Fe(II) N
N N
OH
-O
O3S
SO3
O
C
C
C
C
O
OH
O
-
3
1
2
There is significant iron contamination in the most recently obtained manufacturer’s lot of DHF. This contamination was removed by treating the solution of DHF with Amberlite 120-IR Plus cation exchange resin (Sigma). For 500 mL of 5 mM DHF, 10 g of washed resin was added after all the DHF had gone into solution and the resin was stirred with the DHF solution for 30 min at room tempera-
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In the Laboratory
ture. The DHF solution was then filtered to remove the resin. It is stored at 4 °C and kept on ice during the laboratory period. The cation exchange resin was washed with methanol and acetone, followed by distilled water before use.2
Computer Tutorial Methods CPK models, stick representations, and ribbon representations were displayed using the Insight II molecular modeling system from MSI3 on a Silicon Graphics workstation. The ferritin protein (and its channels) and the synthetic model of the iron core were generated from X-ray crystal coordinates (7, 8). The peptides (protein subunits) and the residues were generated from templates within Insight II and were not optimized. The three-dimensional structures of the reducing agent (DHF), the ligand indicator (ferrozine), and the ligand–metal complex [Fe(ferrozine)3]4᎑ were generated and optimized with the Discover program using the ESFF forcefield (15) from MSI. Two-dimensional representations of the smaller molecules were drawn using ChemDraw (Cambridge Scientific). All graphics files are in GIF format and the tutorial is written in HTML. The tutorial is accessible on the World Wide Web under the Washington University Department of Chemistry home page.4 Procedure In the first week, students determine λmax and the molar absorptivity coefficient for the [Fe(ferrozine)3]4᎑ complex. In the second week, they determine the total iron content of ferritin and the amount of iron released within a given time period using the reducing agent DHF. The reagents DHF and ferrozine were chosen primarily to optimize the kinetic measurements. They provide a high rate of iron release and a high absorptivity coefficient for the iron–indicator complex while requiring relatively small amounts of protein. To reduce cost, the kinetics portion may be omitted or less costly reagents (e.g., reductants hydroquinone or hydroxylamine hydrochloride and the chelator/indicator 1,10-phenanthroline) may be used.
Determination of λmax and Molar Absorptivity Coefficient for [Fe(ferrozine)3] 4᎑ Complex Ferrozine binds to Fe(II) between pH 4 and 9 and forms a bright magenta complex that has an absorptivity coefficient of 27,900 L mol᎑1 cm ᎑1 at 562 nm (16). Whenever an acid treatment was used in the experiment (e.g., to denature ferritin), sodium acetate was used to raise the pH to approximately 6 before the addition of ferrozine. The standard curve was prepared by adding 1–3 mL of the standard Fe(II) solu-
tion to five 25-mL volumetric flasks. To the Fe(II) solutions were added 2 mL of the 5 mM DHF stock solution, 2 mL of 2.5 M sodium acetate, and 2 mL of 12.5 mM ferrozine. The reducing agent ensures that all of the iron remains in the Fe(II) state. We employed scanning spectrophotometers (Genesys 5, Spectronic Instruments) to determine the λmax for one solution. The absorbance at that λmax was then read for the remaining solutions and the molar absorptivity coefficient was determined using linear regression. We encouraged the use of a spreadsheet program, such as Excel, to find the molar absorptivity coefficient by linear-least squares.
Determination of Total Iron Content in Ferritin Students determined the amount of iron in the ferritin by removing the protein shell from the core with acid and quantifying the total amount of iron present. Ferritin has a variable molecular weight, since the amount of iron mineral in the cavity (the iron-mineral core) can vary. The molecular formula of the iron-mineral core is [FeO(OH)]8[FeO(H2PO4)], which has a molecular weight of 879.9 g/mol (i.e., for every mole of Fe(III) present, the molecular weight of the mineral core is 97.7 g). The reaction was done in a 25-mL volumetric flask. In this example, 0.5 mg of ferritin was incubated with 2 mL of 2 M H2SO4 and 2 mL of 5 mM DHF for 30 min to strip off the protein shell and reduce the Fe(III) in the mineral core to Fe(II) ions. Sodium acetate (4 mL of 2.5 M) was added to raise the pH to between 6 and 7. Ferrozine was added (2 mL of 12.5 mM) to complex the Fe(II). The resulting solution was diluted to 25 mL and its concentration was determined spectrophotometrically. (The absorbance of the solution in this example was 0.620 at 562 nm.) The molecular weight of ferritin with no iron in the cavity (apoferritin) is 474,000 g/mol and the molar absorptivity coefficient for the [Fe(ferrozine)3]4- complex is 27,900 L mol᎑1 cm᎑1 at 562 nm. The calculations to determine the total iron per molecule of ferritin were done as shown in the Box below.
Kinetics of Iron Released by Ferritin upon Treatment with Dihydroxyfumarate Incubation of ferritin with an appropriate reducing agent reduces the Fe(III) in the mineral core to Fe(II) ions, which are then released from the protein through the hydrophilic channels in the protein shell (Fig. 2). In our experiment, the Fe(II) ions were complexed by ferrozine, which trapped the iron outside the protein, and the concentration of Fe(II) was determined spectrophotometrically at various time intervals.
Molar concentration Fe(II) × 0.025 L = moles Fe(II) = moles Fe(III) in ferritin iron-mineral core [2.22 × 10᎑5 Fe(II)] × 0.025 L = 5.55 × 10᎑7 moles Fe(II) = 5.55 × 10᎑7 moles Fe(III) Moles Fe(III) in core × 97.7 g iron-mineral core/mol Fe(III) in core = g iron-mineral core (5.55 × 10᎑7 moles Fe(III)) × 97.7 g iron-mineral core/ mole Fe(III) = 5.43 × 10᎑5 g iron-mineral core g ferritin – g iron-mineral core = g apoferritin 5 × 10᎑4 g ferritin – [5.43 × 10᎑5 g iron-mineral core] = 4.45 × 10᎑4 g apoferritin Moles apoferritin = g apoferritin/(474,000 g mol᎑1 apoferritin) (4.45 × 10᎑4 g apoferritin)/(474,000 g mol᎑1 apoferritin) = 9.39 × 10᎑10 moles apoferritin Moles Fe(III) in core/moles apoferritin = # atoms Fe/molecule ferritin [5.55 × 10᎑7 moles Fe(III) in core]/(9.39 × 10᎑10 moles apoferritin) = 591 atoms Fe/molecule ferritin
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Each student did the experiment at a different reductant concentration. The reduction reaction was prepared in 25-mL volumetric flasks. To each flask was added 2 mL of 2.5 M sodium acetate, 2 mL of 12.5 mM ferrozine, and ca. 9 mL of distilled H2O. In addition, DHF was added for a final concentration that varied between 0.04 and 0.30 mM. Each solution was mixed well; 1 mL of 5.0 mg/mL ferritin (final concentration: 0.20 mg/mL) was added; and timing was initiated. The reaction was diluted to the mark and mixed again, and an aliquot removed. The aliquot was placed in a spectrophotometer cell and the absorbance recorded at 562 nm. The absorbance was read approximately every minute for 6 min, with the elapsed time for each reading noted accurately. A plot of [Fe(II)] vs. time gave a straight line whose slope equaled the initial rate of Fe(II) release (Fig. 4A). A plot of the initial rate of iron release vs. the initial concentration of reductant shows saturation behavior (Fig. 4B) (18). For the saturation curves, we used the initial-rate method, which monitors the first 10% of the reaction where concentration vs. time plots are linear. In this experiment, using the initialrate method, students calculated the amount of Fe(II) released over the time course of the reaction at a particular DHF concentration and, using their previous calculation of the total amount of iron in the iron-mineral core for their ferritin sample, determined the percentage of the total amount of iron released from the iron-mineral core during that time. It 12
[Fe2+ ] / 10–5 M
10 8 6 4 2
(A)
0
Initial Rate/10–5 M min–1
0
1
2
3
4 5 Time/min
6
7
8
0.015
0.010
0.005
(B)
0
0.1
0.2 [DHF] / 10–3 M
0.3
Figure 4. (A) Kinetics of Fe(II) release from ferritin following reduction by dihydroxyfumarate. (A) Plot of the concentration of Fe(II) released versus time at various DHF concentrations: (䊊) 0.0125 mM; (䊉) 0.025 mM; ( 䊏) 0.05 mM; (䉬 ) 0.1 mM; (䉱) 0.2 mM; and (䉲) 0.3 mM DHF. (B) Plot of initial rate of Fe(II) released versus the concentration of DHF in the reaction. The curve was fit to the logarithmic function Y = m 0 + m 1*log(x ).
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is clear from the kinetic studies that reduction of ferritin does not lead to a flood of free iron. Instead, the iron is metered out in a controlled fashion, so that it is provided on an “as needed” basis for biosynthesis. Using the conditions presented above, the time courses are short enough that each student can determine the initial rate of Fe(II) release at different concentrations of DHF. A plot of initial rate vs. [DHF] reveals the apparent saturation kinetics of the reduction process and could serve as an introduction to complex kinetic behavior (17, 18). Alternatively, this experiment lends itself to group activities where the students share the data gathered for different [DHF] and observe the saturation kinetics from the shared data. The Molecular-Graphics Tutorial The tutorial is a prelaboratory exercise that is to be completed before the second week. Our goal is to introduce students to the basic concepts of three-dimensional structures and structure–function relationships and to give them a better understanding of the iron-release process before the second lab period. Students are given a list of questions to review before going through the tutorial and the same questions are interspersed throughout the tutorial, along with hints and answers to guide the students. In addition, pdb files of the compounds used in the experiment are available for the students to download and view interactively using an appropriate molecular viewing package such as Rasmol (19). In this tutorial we chose to emphasize three major points: (i) the differences between the two types of channels found in ferritin; (ii) the size and shape of the different Fe(II) compounds and how they relate to the size and shapes of the channels and (iii) the relationship between different types of structural representations, such as two-dimensional, stick, CPK, and ribbon. The tutorial has full-color three-dimensional visualizations and schematic drawings, but detail is lost when reproduced as gray-scale images; therefore, we will not present them all. Full-color images are available.4
Differences between the Two Channel Types in Ferritin The structures of the amino acid residues that line the two types of channels in the protein are displayed to reveal that the 3-fold channel (Fig. 2) is lined with polar groups and is therefore hydrophilic, while the 4-fold channel (Fig. 3) is lined with nonpolar groups and is therefore hydrophobic. The amino acids are also displayed separately (not shown here) and it can be seen that all of them contain polar groups, which seems to lead to a contradiction. However, we use that apparent contradiction as a starting point for discussing how amino acids link together to form peptides. By visualizing the structural differences between the two channels, the different roles the channels have on the process of iron release will be emphasized. A typical question asked will lead the students to predict that Fe(II) would have a higher affinity for polar groups than for nonpolar groups and therefore the Fe(II) enters and leaves the protein by the 3-fold channel because it is lined by polar groups. Size and Geometry of Fe(II) Compounds The CPK representations of the residues lining the channels reveal the size of the channel openings and show size restriction on the compounds that can traverse the channels.
Journal of Chemical Education • Vol. 75 No. 4 April 1998 • JChemEd.chem.wisc.edu
In the Laboratory
Students are asked to recall that Fe(II) enters and leaves the protein by the 3-fold channel, that the iron-removal reaction occurs in aqueous solution, and that the soluble species for Fe(II) in aqueous solution is Fe(H2O)62+. They are then asked: What are the geometric structures of the complexes that Fe(II) forms in the channel and outside the protein shell before it reacts with the indicator ferrozine? The three-dimensional model of the Fe(H2O)62+ complex enables students to observe that the complex forms an octahedron (90° bond angles). While the precise method and molecular form that Fe(II) uses to traverse the 3-fold channel are uncertain, students should predict that Fe(H2O)62+ is probably too large to fit through the 3-fold channel. Therefore, Fe(II) is not coordinated to all six water ligands while traversing the channel, but is probably coordinated to some water ligands and to some carboxylate groups attached to the amino acid residues lining the channel. Once outside the channel, the Fe(II) ions are then coordinated to six water ligands.
Different Graphical Representations of Molecules Students should be familiar with chemical formulas and their two-dimensional representations. We show two-dimensional representations next to three-dimensional ones to help students develop structural intuition. One three-dimensional model is the stick representation, which shows the atomic connectivity and is probably the easiest to relate back to the two-dimensional model. The CPK model represents the atoms as spheres, where the radius of the sphere is equal to the van der Waals radius of the atom, and gives an approximation of the volume occupied by the atoms. The ribbon is a common representation for proteins and peptides. It traces only the backbone of the molecule, and represents the secondary structures of the protein (α-helices or β-sheets). We produced a glossary of species used in the experiment where the various compounds (such as DHF, ferrozine, and the ligand– metal complex) were placed next to the protein to show the relative sizes of the species involved. Conclusion We have developed an experiment that teaches fundamental chemical principles in the context of a relevant biological application. This experiment serves as an introduction to absorption spectroscopy and Beer’s law, expands the applications of redox chemistry to living systems, and introduces the concept of metal chelation. The main purposes of the computer tutorial were to enable students to develop an understanding of molecular shape, to relate shape to function, and to compare and associate conventional three-dimensional and two-dimensional representations. From a biological viewpoint, the students learn that mechanisms for iron storage and iron release are based on fundamental chemical principles of structure and reactivity. Acknowledgments The development of this experiment was supported by National Science Foundation Division of Undergraduate Education Grant DUE-9455918 to the ChemLinks program and by a grant from the Howard Hughes Medical Institute through the Undergraduate Biological Sciences Education program, grant HHMI 71195-502005 to Washington Uni-
versity. Molecular-modeling calculations were performed in the Washington University Department of Chemistry Computer Facility. We thank M. Pinske for the improved purification procedure for DHF.2 Notes 1. A copy of the complete laboratory procedure as well as questions and reports sheets used by Washington University students is available at the address: www.chemistry.wustl.edu/EduDev/Ferritin. 2. An improved purification procedure for DHF has been developed. The DHF is dissolved in the minimum amount of MeOH. The solution turns black. The yellow insoluble material is filtered off by gravity filtration. Cold water is added to the black methanol until white crystals begin to form. After standing overnight in a refrigerator, white purified crystals of DHF are collected by filtration. 3. Computational results were obtained using software programs from Molecular Simulations, Inc., of San Diego. Dynamic calculations were performed with the Discover program, using the ESFF forcefield, and graphical displays were printed out from the Insight II molecular modeling system. 4. The complete Internet address for the ferritin tutorial is: www.chemistry.wustl.edu/EduDev/Ferritin/FerritinTutorial.html.
Literature Cited 1. Bertini, I.; Gray, H. B.; Lippard, S. J.; Valentine, J. S. Bioinorganic Chemistry; University Science Books: Mill Valley, CA 1994. 2. Griffiths, E. In Iron and Infection: Molecular, Physiological, and Clinical Apects; Bullen, J.; Griffiths, E., Ed.; Wiley: Chichester, 1987; pp 1–25. 3. Ford, G. C.; Harrison, P. M.; Rice, D. W.; Smith, J. M. A.; Treffry, A.; White, J. L.; Yariv, J. Philos. Trans. R. Soc. London, Ser. B 1984, 304, 551–565. 4. Theil, E. C. Annu. Rev. Biochem. 1987, 56, 289–316. 5. Harrison, P. M.; Andrews, S. D.; Artymiuk, P. J.; Ford, G. C.; Guest, J. R.; Hirzmann, J.; Lawson, D. M.; Livingstone, J. C.; Smith, J. M. A.; Treffry, A.; Yewdall, S. J. In Probing Structure– Function Relations in Ferritin and Bacterioferritin, Vol. 36; Sykes, A. G., Ed.; Academic: San Diego, 1991; pp 449–486. 6. Harrison, P. M.; Andrews, S. C.; Artymiuk, P. J.; Ford, G. C.; Lawson, D. M.; Smith, J. M. A.; Treffry, A.; White, J. L. In Iron Transport and Storage; Ponka, P.; Schulman, H. M.; Woodworth, R. C., Eds.; CRC: Boca Raton, FL, 1990; pp 81–101. 7. Rice, D. W.; Ford, G. C.; White, J. L.; Smith, J. M. A.; Harrison, P. M. In Advanced Inorganic Biochemistry; Eichorn, G. L.; Marzilli, L.; Theil, E. C., Eds.; Elsevier: New York, 1983; Vol. 5, pp 39– 50. 8. Lawson, D. M.; Artymiuk, P. J.; Yewdall, S. J.; Smith, J. M. A.; Livingstone, J. C.; Treffry, A.; Luzzago, A.; Levi, S.; Arosio, P.; Cesareni, G.; Thomas, C. D.; Shaw, W. V.; Harrison, P. M. Nature 1991, 349, 541–544. 9. Treffry, A. B.; Erika R.; Hechel, D.; Hodson, N. W.; Nowik, I.; Yewdall, S. J.; Harrison, P. M. Biochem. J. 1993, 296, 721–728. 10. Funk, F.; Lenders, J.-P.; Crichton, R. R.; Schneider, W. Eur. J. Biochem. 1985, 152, 167–172. 11. Macara, I. G.; Hoy, T. G.; Harrison, P. M. Biochem. J. 1972, 126, 343. 12. Cowan, J. W. Inorganic Biochemistry; VCH: New York, 1993. 13. Crichton, R. R.; Charloteaux-Wauters, M. Eur. J. Biochem. 1987, 164, 485–506. 14. Boyer, R. F.; Clark, H. F.; LaRoche, A. P. J. Inorg. Chem. 1988, 32, 171–181. 15. Discover User Guide; MSI: San Diego, CA, 1995. 16. Stookey, L. L. Anal. Chem. 1970, 42, 779–781. 17. Boyer, R. F.; Grabill, T. W.; Petrovich, R. M. Anal. Biochem. 1988, 174, 17–22. 18. Cornish-Bowden, A.; Wharton, C. W. Enzyme Kinetics; IRL: Oxford, 1988. 19. Sayle, R. A.; Milner-White, E. J. Trends Biochem. Sci. 1995, 20, 374.
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