Simultaneous Spectrophotometric Determination of Fructose and Glucose Mixtures by Differential Reaction Rates Application to Blood Serum Analysis LOUIS J. PAPA, HARRY B. MARK, Jr., and CHARLES
N.
REILLEY
Deparfment of Chemistry, University of North Carolina, Chapel Hill, N. C. ,An analytical method for the simultaneous determination of fructose and glucose in aqueous media and in blood serum based on their differential reaction rates toward acidic ammonium molybdate is presented. Both a single-point and double-point method for obtaining an ana!ysis are applicable. S u c r o s e - f r u c t o s e or sucrose-glucose mixtures can also b e determined by this method.
T
analyticaal determination of miltures of fructose and glucose is important because of their common ovcurrence in nature. Fructose content in blood serum is of considerable interest in the study of such diseases ‘is diabetes ( 1 7 ) . l l o s t of the coloriinetric mpthods in the literature (9, f / t - l S , 20) employ the reaction of a .ingle reagent with both sugars. Becanuse fructose reacts faster than glucose \z ith most common reagents under the m n e conditions, the reaction classically is stopped at a time when the fructost has partially reacted, but the glucose only t o a small, almost negligible extent. The total sugar content is then determined by alloF5 ing the reaction to go to completion or using a n entirely different method. These methods, therefore, lose much of their potential sensitivity, and :ilso tend to yield poor results when glucose is the major component. Ronting ( 3 ) devised a differential method based on the reaction of these sugars n i t h anthrone. Fructose reacts at room temperature and glucose must be tnlemted to 100’ C. to obtain a reartion. Although acceptable anal) tical results were obtained, the anthrone rwgent is not stsble and the final color itself has a limited stability. The anthrone procedure does not have the sensitivity of the molybdate procedure presented in this paper. Thc method proposed herein is based on the reaction of thcse sugars \+-ith ammonium molybdate in acid media. The sugars reduce the 1Io(VI) t o l\lo(V) t o give the familiar “molybdenum blue” HE
(10,18,24). This color is stable for several hours under the conditions eniployed. Because the reagents and products are stable, this method is suited for kinetic determinations. The actual kinetic methods employed in these determinations are the singlepoint method of Lee and Kolthoff (11) and the double-point method of Garmon and Reilley (4). The accuracy obtained by both methods was similar. The criterion of optimum short time presented by Garmon and Reilley (4) was found to be invalid in the method employed. Other considerations for the selection of this short time are discussed. This method was applied to the determination of these sugars in aqueous media and in blood serum. Sucrose could also be determined in the presence of either of these sugars. REAGENTS
Reagent grades of all chemicals were used, except for fructose and glucose which were Fisher certified reagent. PROCEDURE
For analysis performed by the singlepoint procedure, a knowledge of the total sugar content is necessary and was obtained b y the ferricyanide method [fcr details of the method, see Hoffman (8)I. Aqueous Solutions. T h e reaction solution is prepared b y pipetting 40 ml. of deionized water, 20 ml. of aqueous ammonium molybdate ( 5 grams per 100 ml.), 10 ml. of 8.1N sulfuric acid, a n d 20 i d . of 0.2mM aqueous sugar solution into a 100-ml. volunietric flask. ilfter t h e contents have been mixed b y inversion, 5 ml. of the reaction solution is pipetted into a 15-ml. glass-stoppered centrifuge tube, which is then placed in a constant temperaturp bath of Carbowax 400 piaintained at 100.2” i 0.2” C. After 3 minutes, the tube is sealed with its stopper (lightly greased t o prevent evaporation) and allowed to react for the specified time interval. The tube is then removed from the reaction bath and immersrd in a room tcmpc>rature
nater bath to quench the reaction. The solution is allowed to cool t o room temperature (approximately 5 minutes) arid the absorbance is read a t 720 mp. A Beckman Model DU was used; however, a filter instrument could be employed, because the absorbance band has a broad maximum. Water !vas used as the reference solution. Blood Serum. Blood serum noimally contains about 60 t o 120 mg. of sugar per 100 ml. Sufficient serum, usually 5 t o 10 ml., is taken t o give approximately a 0.1 t o 0.4mM sugar solution when diluted t o 250 ml. This concentration range yields convenient absorbances. Before dilution, t h e serum is deproteinized and dephosphated b y the method of Somogyi (21) to avoid precipitation which would otherwise occur upon addition of ammonium molybdate (for every 5 ml. of serum, 10 ml. of 3M barium hydroxide followed by 10 ml. of 3.431 zinc sulfate is added. and the resulting precipitate is separated b y filtration). The filtrate, diluted t o 250 ml., is ready for analysis. This filtrate was employed in the manner described above for the standard aqueous sugar solutions. For the serum analysis reDorted below, fructose-free s e k m samples which had previously been analyzed for glucose content [using a Technicon AutoAnalyzer (Technicon Controls, Inc., Chauncey, K. Y.) employing the ferricyanide method ( S ) ] were employed. Known quantities of fructose were added t o the serum. I
RESULTS AND DISCUSSION
The rates of reaction of the sugars ammonium molybdate were found to be dependent on acid strength of the medium, 2.s shown in Figure 1. At acid normalities of 0.8 and lower, a precipitate develops shortly after one hour, while a t normalities greater than 1 the rate constant rapidly decreases. Thus, a normality of 0.9 was selected for the determinations. At this acid concentration, a precipitate develops only after 5 to 7 hours. Because of this. however, no value of infinite time absorbance for glucose could be obtained, over 7 hours being required for compleI\ itli
VOL. 34, NO. 1 1 , OCTOBER 1962
1443
tion of the reaction. I n 1N acid equimolar fructose and glucose solutions produced the same amount of color on completion of the reaction. Calculations showed that the same amount of color would be produced by equimolar solutions on completion in 0.9.V acid. Sucrose was found to behave in the same way as a 1 to 1 mixture of fructose and glucose. This was t o be expected, because the rate of its hydrolysis to produce fructose and glucose is much faster than the rate of the color-producing reaction. Hence, mixtures of sucrose and fructose or of sucrose and glucose can also be determined by this method. A few examples of glucosesucrose determinations are given in Table I. The scatter of results for these mixtures was greater than for the fructose-glucose mixtures. Single-Point Method. T h e singlepoint method of Lee and Ko!thoff (11) employs a calibration curve constructed by plotting the ratio ( [ C m l - [ C f l ) / ([A10
+ [BIOI
0s.
[Alol([Alo
+ [BIOI
The resulting line is linesr when the reactions have a constant fractional life, as is the case with the systeni studied. [C,] is the concentration of product at infinite time, [C,] is the concentration of product at any time t, and [A], and [BI0are the initial concentrations of the species undergoing reaction. An alternative method is to plot [CtI/([AIo [Bid 2’s. [~4l,/(IAlLl [B],),which is also a linear relationship, as shown below. Because
+
[Ctl
=
[A10(l -
+
+ [ B ] o (-~ e - W )
where (1 - e - h t ) and (1 - e - W ) are the intercepts when [A lo/( [ A ] , [BIo) equals 1 and 0, respectively. Because concentration [C,] is directly proportional t o the absorbance, this method of plotting was adopted.
+
Table 1.
B
i
j
,I
,
0 4
A. E. C. D. E.
I2
in
16
20
H,SO,
Precipitates after 15 to 60 minutes Precipitates after 1 to 3 hours Precipitates after 3 to 10 hours Precipitates after 10 to 24 hours N o precipitation after 24 hours
Hence, the curve of ratio of absorbance to total sugar concentration us. mole fraction of fructose is the actual calibration curve used. T o prepare such a curve it is necessary to know only the initial concentration of a pure fructose solution and a glucose solution and the absorbance a t the time selected for analysis. Because the relationship is linear, these two points serve to construct the curve. However, as this method is not applicable to measurements a t infinite time, i t was necessary to employ a n independent method to determine the total sugar concentration. The ferricyanide method was chosen (8). This method may yield slightly higher values for total reducing sugar in serum than methods involving deproteinization, if appreciable quantities of glutathione, creatinine, or thioneine are present (as discussed below). The optimum reaction time is calculated from the following equation derived by Lee and Kolthoff (11 ) : t0,t
=
In k,/kb
k o - kb
Determination of Aqueous Sucrose-Glucose Mixtures Total sugar, yo Sucrose, 70 Glucose,
ANALYTICAL CHEMISTRY
08
Normality
Figure 1. Effect of acid strength on rate constant of fructose, k f , toward ammonium molybdate
Method ‘Taken Found Taken Found Taken 10 10.7 90 100 103“ Single point, 25 27 75 1015 t = 77 min. Double point 10 7.5d 90 100 108” t = 41 min. 75 970 25 20, g d t‘ = 120 min. 10 10.8 90 100 101.9c t = 77 min. 25 27.3 75 101. 6c t‘ = 120 min. Determined by ferricyanide method (8); see text. Glucose found by subtracting total sugar found from sucrose found. Sum of sucrose and glucose concentration found. d Values not taken at optimum time (see text).
1444
‘ C
yo
Found 87.3b 746
100.5d
7 6 , Id
91.1
74.3
and for this system it was found to be 77 minutes. The results obtained by this method (Tables I1 and 111) were equally good for aqueous solutions and serum; the average error was rt 4%. Double Point Method. The double-point method or “the method of proportional equations” of Garnion and Reilley (4) consists of making measurements a t two different times, substituting these values into a pair of simultaneous equations, and solving for the concentrations of both components. The equations are:
-
where Pt is any parameter proportional to concentration (in this case absorbance) measured at time t, and P f ’ is the same parameter measured at second time t’. The initial concentrations are expressed as [A10 and [Blo. K,, K b J KO!, and Kbt are the slopes of plots of absorbance us. concentration at times t and t’ and are constants. The values of proportionality constants were calculated from data obtained with the pure sugars in aqueous solution. The same constants were experimentally found to hold in blood serum. The choice of the longer reaction time, t’, is arbitrary, in that no time need be calculated. The greater the extent to which the t n o reactions have taken place a t time t’, the greater mill be the sensitivity of the method, but as the reactions approach completion, a large measure of time is sacrificed for a very small gain in sensitivity. The long time chosen for this method was 120 minutes, a t which time the fructose reaction is essentially completed and the glucose reaction is
approximately 39y0 completed. Once this long time has been selected, an optimum short time can be calculated from the following equation derived by Garmon and Reilley (4):
Table II.
Method Single point, t = 77 min.
Determination of Aqueous Fructose-Glucose Mixtures
Total sugar, 7’0 Taken Found 100 low 102= 99“ 97= 97a
loo=
For the system studicd, tOpt = 41 minutes; results calculated from data obtained using this time were poor a t low fructose concentrations (as shown in Tables I1 and 111). This is attributable to the large value of dP,/dt a t the time selected for the determination. As a result of this and any slight nonuniformity of the reaction bath. different rates of heating and quenching for different tubes exist, and this leads to a difference in the effective value of t for the individual tubes. Equation 1 was derived for a minimum d [ A ] , / d P t (at constant t ) . Thus, no account is taken of errors in t itself. I n a n effort t o avoid this scatter, 77 minutes was then selected for the short time, t, because at this time dPtldt is considerably smaller. The combination of 77 and 120 minutes yielded better accuracy and precision a t low fructose concentrations than 41 and 120 minutes. At intermediate fructose concentration levels, the accuracy and precision were comparable for either pair of times (Tables I1 and 111). The analysis of samples containing only glucose gave the same results, within experimental error, with either the ferricyanide (8) or the molybdate method. Interferences. As this method takes advantage of t h e reducing ability of glucose a n d fructose, i t is necessary t o assay t h e interference t h a t would result from t h e presence of other reducing substances. In general, t h e presence of a n y of t h e other reducing sugars or similar compounds will result in error. Ascorbic acid had the same rate constant as fructose, b u t its color equivalence was twice t h a t of fructose. T h e rate constant for the reaction of mannose is approximately t h e same as t h a t of glucose, while that of galactose is soniewhat greater. The presence of more than 4y0 of these sugars will result in noticeable error. Qualitatively, the rate constants of the pentoses, arabinose and ribose, were on the order of t h a t of fructose. Compounds which have rate constants of the same magnitude as fructose would lead to error only in the amount of fructose calculated, while those which have rate constants similar to that of glucose n.ould interfere only with glucose. Any compounds with intermediate rates would be expected t o lead to error in both sugars. Aside from the possible presence of ascorbic acid and the other naturallv
Double point t = 41 min. t’ = 120 min.
Fructose, 70 Taken Found 0
5 10 20
50 80
0 5 3 10.5
20.0 50.0 79.0
Glucose, c/$ Taken Found 100 100b 95 96 i b 90 88.5b 80
50
20
2 5d 95 l0lC 5 7 6d 90 104,8c 10 14 4d 80 106,4c 20 49 7 d 50 98. 3c 50 79 3d 20 99 5. 80 0 100 t = 77 min. 100 101c’ 0 4.4 95 5 t‘ = 120 min. 98 4 c 9.9 90 10 99 7 c 20 19.4 80 99. 4 C 48.8 50 A0 98 8 C 78.8 20 98 8c 80 Determined by ferricyanide method ( 8 ) ; see text. * Glucose found by subtracting total sugar found from fructose found. c Sum of fructose and glucose found. d Values not taken at optimum time (see text).
Table 111.
Method Single point t = 77 min.
100
77.0* 47 06
21.0b
98 jd 97. 2d 92 Od 48. Bd 20 2 d 101 94.0 89.8 80.0
50.0
20.0
Determination of Fructose-Glucose Mixtures in Blood Serum
Total sugar, mg 1100 cc. Fructose, mg /lo0 cc. Glucose, mg./100 CCTaken Found Taken Found Taken Found 180 178“ 0 0 180 17Sb 7 81n 9 8 5 171 172 5b 17@ 18 17 1A2 158 S b -. -- . . 1173 45 45 i 1.35 129 3 b l€Qa 90 89.8 90 92 2‘ ~
Double point t = 41 min. it = 120 min. ~~
~~~~
t = 77 min. t’ = 120 min.
I80 ~-
180
182C 183.8c 192, lC 18lC
181.8C 1i5c
9 18
45 0
4.7d 12.Sd
171 162
36.4d 0 8.5
135 180
9 171 18 18.9 162 177. 8c 45 45.0 135 177.4c 90 89.6 no a Determination by ferricyanide method (8); see text. b Glucose found by subtracting total sugar found from fructose found. c Sum of fructose and glucose found. d Values not taken at optimum time (see text).
occurring sugars, the reducing compounds glutathione, creatinine, and thioneine are commonly found in blood serum (6, 7’. 21). However, according to Tierney and Peters (dS), Benedict and Gottschall (I), Peters and Van Slyke ( I S ) , and Hawk, Oser, and Summerson ( 5 ) , these compounds are found only in small quantities in blood serum. Hill and Kessler (6, 7‘) f o w d t h a t normal serum analyzed by a glucose-oxidase method gave values for glucose content which were very close t o those found by the ferricyanide method (8) (which gives only “total reduction power” content). Deproteination of the serum by the method of Somogyi (21) considerably lessens the content of these reducing amino acids and peptides ( I S , 21). Also Spell (22) has found that glucose determinations using both the ferricyanide ( 8 ) and a cupric tartrate-phosphomolybdate
177.3d 171 . O d 155.7d 81 3 . 3 56 1
32 8 87.8
method (20) which involved deproteination agreed within experimental error. Somogyi (21) and Smelo, Kern, and Drabkin (19) have shown t h a t the concentration of these compounds is not affected b y pathological or physiological conditions that greatly alter the sugar concentration in blood and, hence, their occurrence in large concentration is not t o be expected. The major source of interference for blood serum analysis is, therefore, the presence of other sugars, including disaccharides (2) which are not removed by the deproteination procedure ( I S ) . No more than a 4Y0 total content of other sugars can be tolerated. The presence of such substances as phosphate and arsenate, which form heteropoly acids with molybdate, alter the rate of formation of molybdenum blue b y the reaction with reducing agents (IO.24), such as sugars (12). VOL. 34, NO. 1 1 , OCTOBER 1962
1445
Because blood serum contains large quantities of phosphate, the resulting change in the rates introduces considerable error. This problem is circumvented by the precipitation of phosphate as a barium salt in the deproteinizatioii step. As in any kinetic method, care must be taken to eliminate or correct for any such species which alters the rates. CONCLUSIONS
The single- and double-point methods are comparable for fructose concentrations of 10% and greater. As expected, the single-point method yields better results a t fructose levels belom- lo%, The single-point method requires a previous determination of total sugar concentration and this is a decided handicap, especially because the total sugar concentration must be determined by a n independent method. No such limitation exists in the double-point method. I n the double-point method, the criterion for choice of a n optimum short time must take into account all the sources of error arising from the conditions peculiar to the reaction employed. I n a subsequent paper each of the factors contributing to error in the double-
point method will bc discussed and criteria for selecting an optimum short time will be presented. ACKNO W LEDGMEN’I
The authors express their appreciation to Louis G. Welt and John B. Hill. Memorial Hospital, University of North Carolina, for their valuable suggestions and helpful discussions of the problems involved in blood serum analysis. LITERATURE CITED
(1,)henedict, S. R., Gottschall, G., J . Biol. Chem. 99, 729 (1933). 12) Best. J. W..drch. Phusiol. Neerland ‘ 3, 222’(1919).‘ (3) Bonting, S.L., Arch. Biochem. Biophys. 52, 272 (1954). (4) Garmon, R. G., Reilley, C. N., ANAL. CHEM.34, 600 (1962).
(5) Hawk, P. B., Oser, B. L., Summerson, IT.€I., “Practical Physiological Chemistry,” 13th ed., p. 557, McGraw-Hill, New Yorlr, 3954. (6) Hill, J. B., Memorial Hospital, University of North Carolina, Chapel Hill, N. C., private communication. (.7 ,) Hill. J. B.. Kessler. G.. J . Lab. Clin. M e d . 57. 970 il961).’ (8) Hoffmkn, IT?. S.,3.Biol. Chem. 120, 51 (1937). (9) Jordan, R. C., Pryde, J., Riochem. J . 32, 279 (1938).
(10) Kitson, R. E., Mellon, M. G., INL). EKG.CHEM., A N A L . ED. 16, 468 (1944). (11) Lee, T. S.,Kolthoff, I. M., A n n . N . Y . Acad. Sci. 53, 1093 (1951). (12) Lo, C., Chu, L. J., IND.ENG.CHEM., ~ A L ED. . 16, 637 (1944). (13) Peters, J. P., Van Slyke, I’. D.. “Quantitative Clinical Chemistry,” Vol. 1, 2nd ed., pp. 160, 792, William and Willtins, Baltimore, 1946. (14) Poe, C. F., Edson, F. G., IXD. ENG. CHEM.,ANAL. ED.4, 300 (1932). (15) Reineclte, R., J . Bid. Chem. 142, 487 (1942). (16) Roe, J. H., Ibid. 107, 15 (1934). (17) Scott, L. D., Riochem. J . 29, 1013 (1938). (18) Scott, L. D., J . Lab. Clin. Tiled. 19, 523 (1934). (19) Smelo, L. S., Kern, F. M., Drablcin, D. L., J . Biol.Chem. 125, 461 (1938)., (20) Snell, F. D., Snell, C. I., “Colorimetric Methods of Analysis,” Vol. 3, 3rd ed., I). 196. Van Nostrand, New Yorlr, 1952. (21) Somogyi, M., J . Biol. Chem. 80, 73:3 (1928); 83, 137 (1937); 160, 69 (1945). ( 2 2 ) Spell, C. R., Emory and Henry College, Emory, Va., private communication. (?3) Tierney, N. A., Peters, J. P., J . Clin. Invest. 22, 595 (1943). (24) Woods, J. T., .Mellon, M. G., IND. ENG. CAEY., ANAL. ED. 13, 760 I 1941). RECEIVEDfor review April 19, 1962. Accepted July 26, 1962. Research supported in part by Sational Institutes of Health Grant RG-8349.
Theory of Diffusion Limited Charge-Transfer Processes i n EIect roa na Iytica I Tech niq ues W. H. REINMUTH Departmenf of Chemistry, Columbia Uriversity, New York 27, N. Y . ,The theory of charge-transfer processes proceeding under conditions of semi-infinite linear diffusion is discussed. Formulation of the Fick’s law boundary value problem and its conversion to the integro-differential equation describing the potential-currenttime relation is followed by a cataloging of some general approaches to explicit solutions. These approaches are exemplified by application to specific problems corresponding to techniques of analytical interest. Implications of the results and limitations of the approaches are pointed out.
I
liavc contributed to the theory of electroanalytical techniques in the time since the common acceptance of Fick’s law of diffusion and the various expressions relating current, potential, and coiicentrations a t solution electrode interfaces. I n a fair majority of cases, the problems to be solved take the forms of linear differential or integro-differentia1 equaNSUMERABLE
1446
WORKERS
ANALYTICAL CHEMISTRY
tioiiy. Piqycss on problems of this bypc has Iiern rapid particularly since the first applicatioiib of I ~ p l a c etransformation tcrhiiiques bj, Brdickn and Koutecky ( 3 ) i n 19-17, However! nonlinear cquatioiis or q u a t i o n s with \.arial)lc corficicnt,s arise, on considcration of terhniqws in whirl1 a controlled varying imtential is appli(~dto a crll, and evcn in controlled current tecliniques whcn doublc In and ohmic Imtrntial lo tred. Thcse caws arc inhcrently less susccptiblc to t>heinor? co~iiinonniathematicnl inethods. Progrtss on problems of this type has hccii correspondingly slower, and thc approaches devised have been leas widely nl)l)licable and their basrs less con~inonlyrecognized. For this reason it appeared profitable t o examine the gencral theoretical basis of clectroaiialyticnl terhniques and to catalog some of the approaches which have been applied to the derivation of explicit potential-current-time relations. T h e limitations of space and time precluded a complctely geiicral
discussion, a i d the following is limited to diffusion limited charge-transfer proccsscs involving only soluble species at stationary planar electrodes. All of the methods discussed are applicable in principle, however, to other cases. References in the following sections have been chosen more on the basis of inathcmatical than chemical importaiicc. The reader is rcferred to a recent m i e n - by Randles ( 2 5 ) for a more chemically oriented discussion of similar subj w t matter. DIFFUSIONAL PROBLEM
Coni.ider a geimxlizetl clectrode reaction of thc form
0
+
11c -+
li
nith c w h species soluble in one of the phases separated by the solution-electrode interface. Assume that if either or both of the species accuniulate preferentially at the interface at equilibrium-Le., adsorb in the general sense-this accumulation is either
