p1541_vol 84_9.pdf

8/11/2019 p1541_vol 84_9.pdf

1/5

Research: Science and Education

www.JCE.DivCHED.org Vol. 84 No. 9 September 2007 Journal of Chemical Education 1541

Many, if not most, of the college students who takechemistry courses are motivated by chemistrys importancein biology and medicine. Effective teaching can take advan-tage of such interests by relating chemical principles to medi-cal practices. This helps to maintain student interest andattention.

Diabetes has become increasingly prevalent in developedcountries in recent decades. The Centers for Disease Con-trol estimates the U.S. diabetic population at over 20 mil-

lion, about 7% of the total population (1).The A1cbloodtest is the principal means used to assess long-term controlof blood glucose concentration, and the CDC recommendsat least semiannual A1cblood testing for all diabetic patients.The utility of this test derives from basic principles of chemi-cal equilibrium and kinetics, and its results directly correlatewith complications of diabetes that arise from spontaneousinteractions of functional groups in carbohydrates and pro-teins. The A1c test therefore provides useful and relevant il-lustrations of general principles in introductory chemistrycourses, and the related chemistry provides interesting mate-rial involving organic reactions.

GlucoseGlucose (blood sugar) provides a textbook example of

the famous Paracelsian principle that

All substances are poisons; there is none which is not apoison. The right dose differentiates a poison from aremedy. Paracelsus(14931541)

A healthy person maintains a blood glucose concentrationof 90 20 mgdL (5 1 mM) through feedback mecha-nisms involving peptide hormones: insulin, which reducesthe concentration, and glucagon and epinephrine, which raiseit. If the concentration of glucose in blood falls below 50mgdL, hypoglycemia, which can lead to coma and death,results. On the other hand, diabetic patients suffer from hy-perglycemia owing to insulin deficiency or insulin resistance.The excess glucose is not immediately toxic, but its high con-centration results in slow reactions in which it becomesbonded to various proteins throughout the body (vide infra).Affected organs include the blood vessels, leading to coro-nary heart disease; eyes, leading to cataracts and retinopa-thy; kidneys, leading to nephropathy; and nerves, leading toneuropathy and limb necrosis (2).

Maintenance of a stable glucose concentration is a re-markable feat, given that an average person processes about160 grams of glucose per day, 120 grams in the brain alone.About 20 grams of free glucose is available in body fluids at

a given time, and an additional 180200 grams is stored asglycogen (polyglucose) in cells (3).

Instantaneous blood glucose concentrations can readilybe measured in a droplet of blood using ingenious devicesthat rely on glucose oxidase-catalyzed oxidation of glucoseto gluconic acid and hydrogen peroxide,

followed by colorimetric determination of the peroxide con-centration,1

where HRP is horseradish peroxidase. However, the bloodglucose concentration changes rapidly and frequently, risingupon food consumption and falling with physical activity,and it would be necessary to monitor the instantaneous con-centration almost continually to ascertain a meaningful av-erage glucose concentration. This is clearly inconvenient andimpractical. Instead, the A1ctest has been developed to pro-vide a measure of blood glucose concentration averaged overa period of several weeks. Maintaining a low average glucoseconcentration over the long term is a high priority, as thedamaging effects of excess glucose, owing to its binding toproteins (glycation), can be severe. The A1c test assaysglycation of a specific protein, hemoglobin (Hb), as a mea-sure of overall protein glycation.

There are many clinical methods of measuring hemo-globin glycation, which is reported as percent of total hemo-globin bearing glycosyl groups. The methods vary inspecificity for the Hb A1cisomer. One group of methods (cat-ion-exchange chromatography, agar gel electrophoresis) isbased on the reduced positive charge of the glycated protein,and the other group (boronate affinity chromatography, im-munoassay) is based on structural differences. The referencemethod, used since 1978, is a HPLC cation exchangemethod. The clinical goals and outcomes defined by the19831993 Diabetes Control and Complications Trial werebased on the results from use of that reference method, and

The A1cBlood Test: An Illustration of Principlesfrom General and Organic Chemistry W

Robert C. Kerber

Department of Chemistry, SUNY at Stony Brook, Long Island, NY 11794-3400; [email protected]

Products of Chemistryedited by

George B. KauffmanCalifornia State University

Fresno, CA 93740
http://www.jce.divched.org/http://www.jce.divched.org/Journal/Issues/2007/http://www.jce.divched.org/Journal/http://www.jce.divched.org/Journal/Issues/2007/Sep/abs1541.htmlhttp://www.jce.divched.org/Journal/Issues/2007/Sep/abs1541.htmlhttp://www.jce.divched.org/Journal/http://www.jce.divched.org/Journal/Issues/2007/http://www.jce.divched.org/

8/11/2019 p1541_vol 84_9.pdf

2/5


1542 Journal of Chemical Education Vol. 84 No. 9 September 2007 www.JCE.DivCHED.org

alternative methods are supposed to be calibrated to the samescale. Recommended glycated hemoglobin levels are below7%, with intervention recommended if they exceed 8% (2c).

The key point to be made in an introductory chemistrycourse is that knowing that the rate of glycation is directlydependent on the glucose concentration allows determina-tion of an effective average concentration, despite wide short-term variations. A high average glucose concentration is

deduced directly from detection of large quantities of glycatedhemoglobin. As pointed out by a referee, this dependencecan also be presented as an application of Le Chteliers prin-ciple, as long as the rates are sufficient to ensure that theglycation reactions are at equilibrium. From either the ki-netic or the equilibrium perspective, the dependence of thequantity of glycated hemoglobin on the average blood glu-cose concentration should be evident, even in the absence ofdetailed mechanistic modeling.

Hemoglobin

Hemoglobin is the protein, found in the red blood cells

(erythrocytes), that carries oxygen from the lungs to the tis-sues of the body. Human hemoglobin is a tetrameric assem-blage of four polypeptide chains, two designated !and two", each bound to a heme unit by coordination of a histidineside chain with an ironheme moiety. Every milliliter ofblood has approximately 5 billion erythrocytes, and eacherythrocyte is packed with 280 million molecules of hemo-globin (4).The concentration of hemoglobin molecules inred blood cells is so high (340 mgmL, 2.3 mM) that theyalmost could be said to be on the verge of crystallization.The !2"2tetramers, spheroids of axial dimensions 65 by 55by 50 , are only 10 apart on the average (5).

Also at relatively high concentration within the eryth-

rocyte is glucose, whose transport across the cell membraneis facilitated by transporter proteins. This maintains the in-tracellular glucose concentration close to that in the serumoutside (6).Consequently, the erythrocyte interior providesa space where glucose and a specific protein, hemoglobin,come together in high concentrations, a favorable conditionfor a bimolecular reaction.

Early studies of hemoglobins by ion-exchange chroma-tography had revealed ubiquitous minor components withreduced positive charges relative to unmodified hemoglobin.The principal component that met these criteria was desig-nated hemoglobin A1c (7). This component constituted 57% of the total hemoglobins in normal patients, but thequantity rose as high as 20% in diabetic patients. Hemoglo-bin A1cwas eventually identified as a product of spontane-ous reaction of normal hemoglobin with glucose (2).

Kinetics and Mechanism of Glycation

Glycation provides an example of a biologically impor-tant reaction that is not enzyme-catalyzed. Initial reaction ofglucose and hemoglobin involves reversible formation of animine:

RCH(OH)CH N(Hb) + H2O

RCH(OH)CHO + (Hb)NH2k+1

k#1 (1)

This is followed by a less reversible, exergonic tautomeriza-tion of the imine to an aminoketone (a deoxyfructose de-rivative), often referred to as an Amadori rearrangement:

k+2

k#2

RC( O)CH2NH2(Hb)+

H+

+ RCH(OH)CH N(Hb)(2)

The kinetics of hemoglobin glycation has been studiedboth in vitro and in vivo (810).Results are complicated bythe simultaneous reaction of the glucose at several of the ac-cessible amine side chains in hemoglobin (there are elevenlysines and one N-terminal valine on each of the four chainsof the !2"2 tetramer). Fortunately, a set of parallel second-order reactions between a given pair of reactants shows over-all second-order behavior that can be described by acomposite rate constant. Individual rate constants (if needed)can then be determined from product ratios (11).The over-all rate of reaction is also affected by various ligands that bindto hemoglobin, including phosphate ions (12),organic phos-phates (13),and oxygen (13a, 14).

Erythrocytes have an average lifespan of about 120 daysin the body, so the occurrence of glycation reactions leads toa steady-state concentration of glycated hemoglobins. Theirconcentration is directly dependent on the average glucoseconcentration over the weeks prior to the determination. Thisaveraging property is the basis for the usefulness of the A1ctest as a measure of effectiveness of glucose control.

Reported values for the rate and equilibrium constantsfor the steps in reactions 1 and 2 under physiological condi-tions vary widely, but the use of consensus values (k

+1=96106L mol1 s1; k

1=100 106s1; k+2=14.2 106s1;k

2=1.7 106s1) has led to a biokinetic model that agreeswith clinical data relating average glucose concentration to

hemoglobin A1c(10).This set of rate constants may providean interesting example for steady-state or numerical model-ing in a physical chemistry course.2A sample calculation ispresented in the Supplemental Material.W

The second-order kinetics that has been experimentallyverified for glycation of hemoglobin is assumed to apply toother proteins as well. A high result on the A1ctest indicatesa high average concentration of glucose during the weeks pre-vious to the test and therefore a proportionately high levelof glycation of other proteins. Indeed, proteins with a longerresidence time in the body than hemoglobin would undergocontinuous glycation, rather than achieve the steady state thatresults from the regular turnover of hemoglobin. It is theglycation products from other proteins that are responsiblefor the toxic effects of excess glucose; the glycated hemoglo-bin that is measured in the test serves as a convenient indi-cator of the ongoing extent of glycation and therefore anindication of glucose toxicity.

Structures of Glycation Products

The N-terminal valines of the two hemoglobin "-chainsare generally the most reactive glycation sites in vivo, andthe hemoglobin A1cdesignation refers specifically to the stableproduct of eq 2 at these two sites. The enhanced reactivityof these sites relative to the other 46 primary amino groupsof the hemoglobin tetramer probably results from their greater
http://www.jce.divched.org/Journal/http://www.jce.divched.org/Journal/Issues/2007/http://www.jce.divched.org/http://www.jce.divched.org/Journal/Issues/2007/Sep/abs1541.htmlhttp://www.jce.divched.org/Journal/Issues/2007/Sep/abs1541.htmlhttp://www.jce.divched.org/Journal/Issues/2007/Sep/abs1541.htmlhttp://www.jce.divched.org/http://www.jce.divched.org/Journal/Issues/2007/http://www.jce.divched.org/Journal/

8/11/2019 p1541_vol 84_9.pdf

3/5



accessibility and weak basicity [pKaof 6.8 (13a, 15) as com-pared to about 10.5 for a lysine side chain], which leaves thempartly unprotonated and nucleophilic at physiological pH.It has also been argued that the histidine residue adjacent tothe N-terminus of the "-chain enhances its overall reactivityby catalyzing the Amadori rearrangement (13b, 14).

Less prevalent glycated hemoglobins having carbohydratesother than glucose attached to the "-chain N-terminus have

been identified (16), as have isomers of hemoglobin A1cwithglucose attached to the !N-terminus and to lysine residueson either chain (17). Phosphate or organophosphate ions di-rect the site of glycation in favor of the preferred "-terminalvaline, an effect attributed to their enhancement of the rateof the Amadori rearrangement (12, 13b). Intramolecular ca-talysis of Amadori rearrangement by adjacent carboxylategroups has similarly been cited in one rationalization of theenhanced reactivity of certain specific lysine residues (17b, 18).

Recent advances in protein analysis by electrospray andMALDI mass spectrometry promise to accelerate the analy-sis of glycated hemoglobins (19).These methods of analysisshow hemoglobins !-chain to be glycated to about two-thirds

the extent of the "-chain, rather more than suggested by clas-sical methods of analysis (20). Polyglycation of the "-chainsis also evident at higher glucose concentrations (21).

Advanced Glycation End Products, AGEs

The glycated hemoglobin A1cmeasured in the test is nottoxic. But the result is a surrogate for analogous spontane-ous glycations involving other proteins throughout the body.

The intermediate glycation products analogous to thedeoxyfructosyl-lysine shown in eq 2 undergo additional slownon-enzymatic reactions, collectively referred to as Maillardreactions that result in functional degradation of the proteins.The complex products of these slow reactions are referred toas advanced glycation end products, AGEs (22).Along withthe mechanisms underlying eqs 1 and 2, the chemistry un-derlying formation of these AGEs provides many group work-

shop problems useful in organic chemistry courses.One such reaction is the oxidation of the deoxyfructosyl-

lysine to carboxymethyl-lysine and erythronic acid (23),

(3)

catalyzed by phosphate and inhibited by metal-chelatingagents; a free-radical mechanism occurring via the enediolhas been suggested (23).The carboxymethyl products are notparticularly toxic, and their formation may actually limit thecompetitive formation of more damaging byproducts (23).

Scheme I. Formation of glyoxal imine intermediates.
http://www.jce.divched.org/http://www.jce.divched.org/Journal/Issues/2007/http://www.jce.divched.org/Journal/http://www.jce.divched.org/Journal/http://www.jce.divched.org/Journal/Issues/2007/http://www.jce.divched.org/

8/11/2019 p1541_vol 84_9.pdf

4/5


1544 Journal of Chemical Education Vol. 84 No. 9 September 2007 www.JCE.DivCHED.org

These more toxic products are the result of formationof highly reactive !-dicarbonyl compounds (!-oxoaldehydes)or imines by a sequence of enolizations, dehydrations, andretro-aldol reactions. These reactions occur slowly in glucosesolutions under physiological conditions, but more rapidlyin the presence of N!-protected lysine or proteins capable ofimine formation (24).Formation of glyoxal imine interme-diates is illustrated in Scheme I. These imines may undergo

hydrolysis to glyoxals or they may condense directly withlysine residues from proteins via transimination reactions toform the various toxic products described below. These al-ternatives are not explicitly shown in Scheme I to reduce com-plexity.

The highly electrophilic !-oxoaldehydes and imines arethe direct precursors to the AGEs (25, 26).They react withparticular facility with the arginine residues of proteins toform heterocyclic products, including imidazolones and py-rimidines (Scheme II) (26, 27).Since arginine residues inproteins have a high probability of occurrence in ligand andsubstrate recognition sites and enzyme active sites, these un-controlled derivatization reactions often lead to functional

disruption (25).Also highly damaging are reactions that result in inad-vertent cross-linking of protein chains, which reduces theirability to carry out normal functions and contributes to cir-culation, joint, and vision problems in diabetics and the aged.One such cross-link is produced by reaction of two lysineresidues from proximate chains with !-oxoaldehydes to forma bis(lysyl)imidazolium cross-link (Scheme III) (27, 28).

The pentosidine cross-link,

similarly forms a stabilized aromatic heterocycle linking twoprotein chains, in this case through an arginine residue onone and a lysine on the other. The five-carbon moiety thatmakes up the rest of the heterocycle derives from a pentose,probably ribose (29).

These protein-altering reactions occur spontaneously,

without enzyme catalysis. The products result in reductionof protein activity and flexibility and hence to cell damage.These altered proteins are found in everyone, and their quan-tity increases with age. But uncontrolled diabetics have un-usually high quantities of circulating glucose, so the quantitiesof AGEs formed in their bodies are significantly higher thanin non-diabetics of the same age. (In this sense, diabetics agefaster.)

Scheme II. Formation of heterocyclic AGEs.

Scheme III. Formation of bis(lysyl)imidazolium cross-links.
http://www.jce.divched.org/Journal/http://www.jce.divched.org/Journal/Issues/2007/http://www.jce.divched.org/http://www.jce.divched.org/http://www.jce.divched.org/Journal/Issues/2007/http://www.jce.divched.org/Journal/

8/11/2019 p1541_vol 84_9.pdf

5/5



Conclusion

The hemoglobin A1ctest provides a convenient measureof long-term average glucose concentration, which indicatesthe extent of ongoing glycation of proteins in the body. For-mation of the glycation products responsible for many of thedebilitating effects of diabetes is directly proportional to theaverage glucose concentration in the bloodstream, which can

be viewed either as a consequence of their second-order re-action (first order each in glucose and in protein) or of LeChteliers principle applied to the equilibria of eqs 1 and 2.

The enhanced occurrence of these spontaneous reactionsin uncontrolled diabetics can be used by teachers in intro-ductory courses to illustrate the consequences of kinetic or-der. The spontaneous nature of these reactions makes themparticularly straightforward examples of the effect of concen-tration on rate in medically relevant reactions. Detailed ki-netic analyses may be carried out in advanced physicalchemistry courses.3The glycation reactions provide interest-ing examples whose mechanisms involve sequences of simplesteps (e.g., imine formation, tautomerization, condensations)that can be worked out by team-learning groups in second-semester organic chemistry courses. The biological and medi-cal relevance of the reactions should provide immediacy andmotivation to the students.

WSupplemental Material

This set of rate constants may provide an interesting ex-ample for steady-state or numerical modeling in a physicalchemistry course. A sample calculation is presented in thisissue ofJCE Online.

Notes

1. Use of a related glucometer in an error analysis laboratory

exercise has been suggested by Edmiston, P. L.; Williams, T. R. AnAnalytical Experiment in Error Analysis: Repeated Determinationof Glucose using Commercial Glucometers.J. Chem. Educ.2002,77,377379.

2. A referee reports that he found it a somewhat daunting,but ultimately rewarding challenge to build a spreadsheet to pre-dict the time variance (of glycated and unglycated hemoglobins),based on the rate constants provided...

3. Adapted from ref22.

Literature Cited

1. National Diabetes Fact Sheet, 2005. http://www.cdc.gov/dia-betes/pubs/pdf/ndfs_2005.pdf(accessed Jun 2007).

2. (a) Kilpatrick, E. S.J. Clin. Pathol.2000,53,335339. (b)Pizzorno, J. E.; Murray, M. T. A Textbook of Natural Medi-cine. www.healthy.net/library/books/textbook/section2/glyhem.pdf(accessed Jun 2007). (c) Laboratory Medicine Practice Guide-lines. www.nacb.org/lmpg/diabetes/6_diabetes_hemoglob.pdf (ac-cessed Jun 2007).

3. Garrett, R. H.; Grisham, C. M. Biochemistry, 3rd ed.;Thomson Brooks/Cole: Belmont, CA, 2005; p 705.

4. Dickerson, R. E.; Geis, I. Hemoglobin: Structure, Function, Evolution,and Pathology;Benjamin/Cummings: Menlo Park, CA, 1983; p 21.

5. Dickerson, R. E.; Geis, I. Hemoglobin: Structure, Function, Evo-lution, and Pathology;Benjamin/Cummings: Menlo Park, CA,1983; p 127.

6. Garrett, R. H.; Grisham, C. M. Biochemistry, 3rd ed.;Thomson Brooks/Cole: Belmont, CA, 2005; pp 287289.

7. Bunn, H. F.; Haney, D. N.; Kamin, S.; Gabbay, K. H.; Gal-lop, P. M.J. Clin. Invest.1976,57,16521659.

8. Higgins, P. J.; Bunn, H. F. J. Biol. Chem.1981,256,52045208.

9. Svendsen, P. A.; Christiansen, J. S.; Segaard, U.; Nerup, J.Diabetologia 1981,21,549553.

10. Mortensen, H. B.; Vlund, A. Scand. Lab. Invest. 1988,48,595602.

11. Frost, A. A.; Pearson, R. G. Kinetics and Mechanism; JohnWiley & Sons, Inc.: New York, 1953; pp 151152.

12. (a) Watkins, N. G.; Neglia-Fisher, C. I.; Dyer, D. G.; Thorpe,S. R.; Baynes, J. W. J. Biol. Chem.1987,262, 72077212.(b) Kunika, K.; Itakura, M.; Yamashita, K. Life Sci.1989,45,623630.

13. (a) Lowrey, C. H.; Lyness, S. J.; Soeldner, J. S.J. Biol. Chem.1985,260, 1161111618. (b) Gil, H.; Pea, M.; Vasquez, B.;Uzcategui, J.J. Phys. Org. Chem.2002,15,820825.

14. Bai, Y.; Ueno, H.; Manning, J. M.J. Protein Chem.1989,8,299315.

15. Garner, M. H.; Bogardt, R. A., Jr.; Gurd, F. R. N. J. Biol.Chem.1975,250I, 43984404.

16. Garrick, L. M.; McDonald, M. J.; Shapiro, R.; Bleichman,M.; McManus, M.; Bunn, H. F. Eur. J. Biochem.1980,106,356359.

17. (a) Bunn, H. F.; Shapiro, R.; McManus, M.; Garrick. L;McDonald, M. J.; Gallop, P. M.; Gabbay, K. H.J. Biol. Chem.1979,254, 38923898. (b) Shapiro, R.; McManus, M. J.;Zalut, C.; Bunn, H. F.J. Biol. Chem. 1980,255,31203127.(c) Neglia, C. I.; Cohen, H. J.; Garber, A. R.; Thorpe, S. R.;Baynes, J. W.J. Biol. Chem.1985,260,54065410.

18. Acharya, A. S.; Roy, R. P.; Dorai, B.J. Protein Chem.1991,10,345358.

19. Miedema, K. Clinical Chemistry1997,

43,705707.20. (a) Roberts, N. B.; Green, B. N.; Morris, M. Clinical Chemis-try1997, 43,771778. (b) Lapolla, A.; Tubaro, M.; Reitano,R.; Arico, N. C.; Ragazzi, E.; Seraglia, R.; Vogliardi, S.; Traldi,P.; Fedele, D. Diabetologia2004,47,17121715.

21. Peterson, K. P.; Pavlovich, J. G.; Goldstein, D.; Little, R.; En-gland, J.; Peterson, C. M. Clinical Chemistry1998,44,19511958.

22. Singh, R.; Barden, A.; Mori, T.; Beilin, L. Diabetologia2001,44,129146.

23. Ahmed, M. U.; Thorpe, S. R.; Baynes, J. W. J. Biol. Chem.1986,261,48894894.

24. Thornalley, P. J.; Langborg, A.; Minhas, H. S. Biochem. J.1999,344,109116.

25. (a) Thornalley, P. J. Ann. N. Y. Acad. Sci.2005,1043,111117. (b) Niwa, T.J. Chrom. B: Biomed. Sci. Appl. 1999,731,2336.

26. Oya, T.; Hattori, N.; Mizuno, Y.; Miyata, S.; Maeda, S.; Osawa,T.; Uchida, K.J. Biol. Chem.1999,274,1849218502.

27. Thornalley, P. J.; Battah, S.; Ahmed, N.; Karachalias, N.;Agalou, S.; Babaei-Jadidi, R.; Dawnay, A. Biochem. J.2003,375,581592.

28. Brinkmann, E.; Wells-Knecht, K. J.; Thorpe, S. R.; Baynes,J. W.J. Chem. Soc., Perkins Trans I1995,28172818.

29. (a) Grandhee, S.; Monnier, V. M.J. Biol. Chem. 1991,266,1164911653. (b) Biemel, K. M.; Reihl, O.; Conrad, J.;Lederer, M. O.J. Biol. Chem.2001,276,2340523412.
http://www.jce.divched.org/http://www.jce.divched.org/Journal/Issues/2007/http://www.jce.divched.org/Journal/http://www.jce.divched.org/Journal/Issues/2007/Sep/abs1541.htmlhttp://www.jce.divched.org/Journal/Issues/2007/Sep/abs1541.htmlhttp://www.jce.divched.org/Journal/Issues/2002/Mar/abs377.htmlhttp://www.jce.divched.org/Journal/Issues/2002/Mar/abs377.htmlhttp://www.jce.divched.org/Journal/Issues/2002/Mar/abs377.htmlhttp://www.cdc.gov/diabetes/pubs/pdf/ndfs_2005.pdfhttp://www.cdc.gov/diabetes/pubs/pdf/ndfs_2005.pdfhttp://www.cdc.gov/diabetes/pubs/pdf/ndfs_2005.pdfhttp://www.healthy.net/library/books/textbook/section2/glyhem.pdfhttp://www.nacb.org/lmpg/diabetes/6_diabetes_hemoglob.pdfhttp://www.nacb.org/lmpg/diabetes/6_diabetes_hemoglob.pdfhttp://www.healthy.net/library/books/textbook/section2/glyhem.pdfhttp://www.cdc.gov/diabetes/pubs/pdf/ndfs_2005.pdfhttp://www.cdc.gov/diabetes/pubs/pdf/ndfs_2005.pdfhttp://www.jce.divched.org/Journal/Issues/2002/Mar/abs377.htmlhttp://www.jce.divched.org/Journal/Issues/2002/Mar/abs377.htmlhttp://www.jce.divched.org/Journal/Issues/2007/Sep/abs1541.htmlhttp://www.jce.divched.org/Journal/http://www.jce.divched.org/Journal/Issues/2007/http://www.jce.divched.org/

Documents

p1541_vol 84_9.pdf