of 0.87%, and for 18 assays conducted on differcnt days, of 2.74%, The accuracy and precision of the modified method were determined by adding known amotints of d-panthrnol to aqueous extracts of samples of two pharmaceutical product!s containing dpanthenol, a liqriid and a capsule prcparation. The mean recovery f standard deviation based on 10 determinations for thc former was 99.9 =t 2.3%, and for the latter was 100.9 f 4.6%. The method was further evaluated by adding d-panthenol to aqueous extracts of each of 10 complex multivitamin samples containing no d-panthenol in the proportion of 3.00 mg. of d-panthcnol per tablet or capsule. Five of the products contained calcium pantothenate. The results of duplicate analyses are given in Table 1 together with values obtained by the two methods of Schmall and Wollish (6). Ap-
proximately 100% recovery for all samples was obtained by the propowd method. Recoveries by the other two methods were markedly poorer in most samples, and, in some instances, the final solutions were so highly colored that they could not be assayed colorimetrically. The ninhydrin reaction appeared to be influenced to a greater extent than the naphthoquinone reagent by highly colored extracts. Another serirs of 10 samples, which had previously been assaycd by Rogers and Campbell in this laboratory using both their microbiological method (6) and that of Bird and McCready (I), gave comparable results by the proposed method, as shown in Table 11. The proposed preliminary solvent extraction togcther with the modified naphthoquinonc procedure is accurate, simplc, and applicable to a wide variety of complex multivitamin preparations.
Most interfering substances present in these preparations are eliminated by ammonium sulfate precipitation or solvent extraction. Although this method requires preliminary extraction, it is suita,ble for routine work. LITERATURE CITED
(1) Bird, 0. D.,McCready, L., ANAL. CHEM.30,2045 (1958). (2) De Ritter, E., Rubin, S. H.,Ibid., 21, 823 (1949). (3) Folk. 0..J . Biol. Chcm. 51. 377 (4) Frame, E.G.,Russell, J. A,, Wilhelmi, A. E.,Ibid. 149, 255 (1943). (5) Campbell, J. A., ANAL. . . nouers, 6. G., CHEM.32, i662’(196oj. (6) Schmall, M.,Wollish, E. G., Ibid., 29, 1,509 _ _ . (1967). . - , (7) Weiss, M. S., Sonnerfeld, J., De Ritter, E., Rubin, S. H.,Ibid., 23, 1687 (1951). \ -
RECEIVED for review January 6, 1961. Accepted April 21, 1961.
Quantitative Analysis by an Automatic Potentiometric Reaction Rate Method Specific Enzymatic Determination of Glucose H. V. MALMSTADT and H. L. PARDUE Departmenf of Chemisfry and Chemical Engineering, University of Illinois, Urbana, 111.
b An automatic potentiometric reaction rate method i s described and shown t o b e sensitive, simple, rapid, and accurate for quantitative determinations and directly applicable for the selective determination o f glucose. Changes in electromotive force (e.m.f,) of a concentration cell are followed automatically b y a measurement system, and a value related t o concentration o f sought-for constituent i s r e a d off a dial. A beaker can serve as the reference compartment o f the cell, and a short test tube immersed in the beaker as the sample compartment. The test tube has a small fiber sealed in the bottom t o provide electrical contact between sample and reference solutions, but does not allow mixing. Platinum electrodes sensitive to iodine concentration, one in each compartment, complete the cell for the glucose determination. Glucose is oxidized selectively in the presence o f a specific enzyme to produce hydrogen peroxide a t a rate proportional to the glucose concentration. As the hydrogen peroxide forms it reacts immediately with iodide in the presence of a molybdenum catalyst t o form iodine, and the change o f iodine concentra1046
ANALYTICAL CHEMISTRY
tion in the sample compartment changes the cell e m f . Commercial equipment and an auxiliary relay system are combined easily t o provide automatic results within 1 minute from the start o f the reaction. Glucose concentrations between 5 and 500 p.p.m. in a total volume o f 2 ml. were determined with relative errors of about 1% throughout the whole ran,ge. For samples between 5 and 50 p.p.m., only lo-’ gram o f glucose react during the measurement interval, so that the precision in terms of the amount gram. reacted i s about
T
of precision nullpoint potentiometry (PNPP) has demonstrated the uscfulness of precise potentiometric measurements for quantitative determinations, especially in the micro range (6,6). With the PNPP method, it has been possible in many cases to determine constituents a t the part per million level with reproducibility and accuracy of 0.1%. Its high sensitivity and precision led the authors to consider the use of precision potentiometric measurements for following the rate of change of a reactant or product HE DEVELOPMENT
related to the concentration of a soughtfor constituent. Recent work by the authors (6) demonstrated the application of PNPP for iodometric procedures, including its application for the determination of micro amounts of hydrogen peroxide. The work of Malmstadt and Hicks ( 4 ) with B spectrophotomctric reaction-rate procedure showed that within a few seconds after the start of the reaction, the rate of change of hydrogen peroxide from the specific oxidation of glucose was proportional to the glucose concentration, a t least over a fewfold range. I t seemed feasible, therefore, to devise a procedure where the hydrogen peroxide formed in the glucose reaction would combine immediately with iodide to form iodine, which could be determined continuously by a potentiometric technique. It was originally thought that a concentration null point could be maintained continuously during a reaction. For the glucose determination it was plannrd to generate iodine electrolytically in the reference compartment at a rate equal to the rate of formation of iodine by the reaction of glucose in the sample compartment. However, this
THERMOMETER REFERENCE STIRRING ROD CE ELECTRODE STIRRING ROD E ELECTROOE
SAMPLE SOCN REFERENCE SOLN WATER JACKET BLACK BAKELITE PLATFORM
WA TER I N
Figure 1. Concentration cell determination of glucose
system provcd difficult and a more simple and practic:al techniquc was developed. The techniquc involvcs the measurement of the time required for the pseudo first ordcr reaction to produw a small fixed amount of product. Precision potentiometric rneasuremcnts are used to indicate whcn the fixcd amount of product has been produrcd. The conccntrntion of the rate-dctcrmining reactant is proportional to the reciprocal of the measurcd reaction time. I t s h o ~ l dbe cmph:rsiznd that the new technique is not a P N P P procedure, but that it does depcnd on certain characteristics inherrnt in thc P N P P method. It does rely on prccision POtentiomt:tric measurerncnts capable of an accuracy of 0.02 mv. Also, the measurcments are made in the rcgion of a concentration null point where junction potcntials are negligible. In developing the reaction rate method, it was considered dcsirable to make the rate measurement within a short period, preferably a few seconds, after the start of the reaction in order that the measurements would be cornpletcd before the conccntration of sought-for constituent had chnngcd significantly from its original concentration. To simplify a.nd spced up the me:Lsurements, a precision rtutoinatic measurement system was dcveloped which presents the data on a rcadout dial. In comparison with other selective glucose procedures, thc new method provides thc advantages of much greater speed (3, 7 ) and increased sensitivity (4), as well as tht: rlimination of the rather expcnsive pcroxidssc cnzyme used to catalyze the H,Oz-dye reaction in the usual spcctrophotomctric procerlurcs. Trmperature and pH effects for the glucose system have also been studied and the results presented. Although the measurement method
for
potentiometric
can be presented in a general way, details are presented here for the specific glucose method for which experimental data were obtained. The development of equations for othcr applications is obvious. GENERAL CONSIDERATIONS
The specific oxidation of glucose can be made to produce iodine at a rate proportional t o the glucose,concentration, and the iodine can be readily detected by the platinum electrodes in t h e concentration cell. The important net reactions are shown in Equations 1 and 2. Glucose 01 glucose oxidase Chemical Reactions.
+
+
HIOX
4
+
gluconic acid HZOI (1) 2 H + 21- molybdate(V1)
+
+
---+
11 2H2O ( 2 ) Reaction 2 is very fast and is considered instantaneous compared to Reaction 1, which is the ratedetermining step.
Figure 2.
The concentrations of reactants are all large relative to glucose, and remain essentially constant so as to provide a pseudo first-order reaction with respect to glucose. Potentiometric measurements are used to measure the rate of formation of iodine. Under specified conditions, the reciprocal of the time required for the reaction to produce enough iodinc in one half of a concentration cell to change the e.m.f. of the cell by a preselected amount is proportional to the glucose concentration. Concentration Cell. A concentration cell similar to the one illustrated in Figure 1 is the heart of the new potentiometric method. The beaker contains a reference solution and the small tube contains the sample. Both solutions contain similar electrodes which are sensitive to the same species in the solutions. Howevcr, the electrode-sensitive species remains a t a constant concentration in the refcrenee compartment and changcs continuously in thc samplc compartment. This provides a continuously changing c.m.f. related to the rate of change of the electrode-sensitive species in the sample, which is related to thc conccntration of sought-for constituent undergoing a continuous reaction. In this work the electrode-sensitive species is iodine and the sought-for constituent is glucose. The response of this cell for different glucose concentrations i R shown by the recorded curves in Figure 2. The initial rapid increase in e.m.f. results from a decrease in iodide concentration when the sample is added in the sample tube. After this initial jump the increase results from the specific oxidation of glucose. Cell Response. Although the rate of change of iodine concentration is essentially constant during a recorded interval, the curves show a logarithmic relationship between e.m.f. and time. This is expected from the logarithmic relationship between e.m.f.
Recorded curves of time vs. cell e.m.f. for glucose reaction VOL. 33, NO. E, JULY 1961
1041
and concentration aa expressed in Equation 3 for the iodine-iodide system.
k In [IS]R
+ hEi + a.1+ k In LIS (3)
where k is a temperature dependent constant from the Nernst equation, ( ~ I - ) R , (ar-ls, (.fr*)s, bb, and (149 are the activities, activity coefficients, and concentrations for the reference and sample solutions, and and AE,are junction and assymetry potentials. If conditions are adjusted so that the quantity in large brackets in Equation 3 remains constant from sample to sample and the electrode response is rapid and reproducible, thcn a t each value of E, (horizontal lines on Figure 2) all samples have the same iodine concentration. A change from one preselected voltage (E.) to another (Ea) involves the same change in iodine concentration for all samples as given by Equation 4.
(C*)R,
- [Itla" = AIIt]sO-b
(4)
where [ 1 2 ] 5 ~and [I2]? are the sample iodine concentrations a t E a and Eb and AIIz]so+ is the change in iodine concentration producing the voltagc change from E. to Eb. Since the reaction rate is d8erent for different glucose eoncen= trations, the time interval (&-b b t,) between CBs"and CS*is also difTerent for each glucose concentration. The purpose here is to demonstrate how the time intervals are related to the glucose concentration and in turn how the information necessary for quantitative analysis is obtained by potentiometric measurements. Glucose Concentration-Time Interval Relation. If i t is assumed that for each sample changes in iodine concentration during the measurement interval result only from the specific glucose reaction, and that the change of glucose concentration is negligible during the measurement interval, then the rate of change of iodine concentration is constant throughout the interval and the total change in iodine concentration is given by Equation 5.
-
(dq)
If, as was previously assumed, Reaetion 1 is pseudo first order and Reaction 2 is very fast compared to Reaction 1, then the rate of change of iodine concentration is proportional to the glucose concentration Gas given by Equation 6:
where k' is a pseudo first-order rate constant for Reaction 1. Combining
1042
ANALYTICAL CHEMISTRY
Equations 5 and 6, the glucose concentration is expressed by Equation 7.
Since for all samples the change in iodine concentration and k' are constants, Equation 7 demonstrates that the glucose concentration is proportional to the reciprocal of the time required for the reaction to produce this constant amount of iodine. In this work k' had a value of about 10-4 - ~ values of second-' and A [ [ I ~ ] s ~ had 1X and 5 X lO-'gram per ml. for the 5 to 50- and 50- to 500-p.p.m. ranges, respectively. If k' is known accurately, then an exact value for AIIz]~a-b combined with an experimentally determined value of At,-b will permit calculation of G. The quantity AI12]sa-b is determined from the values of E, and Ea. Potentiometric Evaluation of Concentration Interval. Equation 3 is used to determine the change in iodine concentration necessary to produce the change AEa-b under the experimental conditions. If the quantity in brackets in Equation 3 is assumed to be constant between E. and Eb, then the difference Eb - E . is given by Equation 8.
Substituting for [12]sb in Equation 8 from Equation 4 and rearranging] concentration change from E . to Eb is given by Equation 9. = [12]s0 [exp
(F) -
11 (9)
This equation is combined with Equation 7 to demonstrate the use of potentiometric measurements to determine glucose concentrations. Combined Equations. The relationship between the glucose concentration and the voltage and time intervals measured is given in Equation 10, obtained by substituting the value given for A[Iz],P-~ in Equation 9 into Equation 7 .
This equation shows that the voltage interval measurement preserves the reciprocal relationship betwecn glucose concentration and the time interval. A knowledge of all of the quantities enclosed in the brackets in Equation 10 would permit a calculation of the glucose concentration from a measured time interval. However, it is inconvenient to determine all these qurtntities individually, and a simplified analyt-
ical procedure is based on a comparison
of unknown glucose samples with standards. This procedure provides an empirical evaluation of the quantity in brackets. Comparison Method. If the time intervals 1,' and t y required for two samples X and Y to overcome the same voltage interval are measured under identical conditions SO that the quantity in brackets in Equation 10 is essentially the same for both samples, then Equation 11 follows.
If Y is a standard sample then t h s concentration of X can be calculated from the simple proportionality in Equation 11. As written, Equation 11 is valid for solution concentrations a t the time of the meesurement. However, if conditions are adjusted so that the total reaction before completion of the measurement does not consume an appreciable fraction of the sample, then the concentrations in Equation 11 correspond to initial concentrations, CHOICE OF VARIABLES
Measurement Conditions. T h e first requirement of the measurement is that i t must be reproducible. Recent work with PNPP (6, 6) has demonstrated that if sample and reference solutions are adjusted to have the same high ionic strength and composition, and if measurements are made near a null point, then these measurements can be made reproducible to ~k0.02mv. Under these conditions activities and activity coefficients cancel and 0.and AE,are small and constant and Equation 3 reduces to Equation 12,
E,
=
[Ills k In 1121 R
where the small constant values AEf have been neglected. In this work it was convenient to make the initial measurement a t a null point (E. = 0 on Figure 2). Under these conditions [Ie]R = [Iz]~' and the value of [12]sa depends upon the reference iodine concentration. The choice of this quantity will depend upon the choice of the other parameters in Equation 10. Voltage Interval. For any system the voltage interval should be chosen large enough that the measurement error is small in comparison. In this work a voltage interval of 5.00 mv. was used with a measurement system reproducible to within 0.02 mv. T h e relative error introduced by this system is within 0.4%, w h i.ch is well within an acceptable analysis error of 2%. Time Interval. It was arbitrarily decided to adjust conditions so t h a t
measurement times for the tenfold concentration ranges covered would be between 10 and 100 seconds. Rate Constant. The magnitude of the pseudo first-order rate constant for Reaction 1 depends upon a variety of conditions, including temperature, pH, dissolved oxygen concentration, and enzyme concentration. If the first three parameters are held constant a t predctermined values, then the magnitude of the constant can be varied by varying the enzyme concentration. The magnitude of the rate constant and the measurement time determine the amount of sample consumed during the measurement interval. If a measurement time of 100 seconds and maximum consumption of 1% are chosen for the lowest concentration of glucose to be determined, the maximum value of the rate constant can be calculated from Equation 7. Substituting A[IP]s~-* 5 0.01G (same units) and &-b = 100 seconds, i t follows that k' must be equal to or less than lo-' second. - I Sample Iodine Concentration at E,. Having selected arbitrary values for the other parameters (k is a constant for a given elcctrode reaction and temperature), the value of [I~]s~is specified by the glucose concentration range to be investigated. Since i t has been assumed that the lowest concentration of the range to be studied will have a measurement time of 100 seconds, then at 25' the value of [I2]sa is given by Equation 10 to be 0.05 X GL, where GS is the lowest glucose concentration of the range to be studied. Reference Iodine Concentration, As indicated above, the value of [IZIR will be that calculated for ( 1 ~ 1 9since ~ these quantities are essentially the =me. Initial Sample Iodine Concentration. The voltage interval is measured by permitting the cell e.m.f. to increase from initial negative values through E. = 0 and on up through E, = 5.00 mv. In order that E, may have negative values initially, it follows from Equation 12 that at the start of the reaction the iodine concentration in the sample must be less than that in the refercnre. To establish how great this difference must be, two factors must be considered. First, after initiation of the reaction and before making the first e.m.f. reading ( E a ) ,sufficient time must be provided for a steady state to be established. A minimum premeasurement time of 15 seconds is desirable. Second, the premeasurement time must not be too long, otherwise an appreciable fraction of the sample will be consumed and Equation 11 will not apply for original concentrations. The premeasurement time can be controlled by starting with some iodine
ADDITION
l
I REMOVAL
s ~ ~ E M
RECCENT h SAMPLE
4I
. DATA READOUT
DfVl;C
1
instrument used in this work picked off the measurement interval reproducibly and [I& remained constant for sufficiently long periods. INS1RUMENTATIOH
CONCENTRATION
TEMPERATURE CONTROLLER
MEASUREMENT
------ -
Figure 3. Block diagram of complete instrument for automatic potentiometric determination of glucose
present initially in the sample solution. The amount of iodine present initially depends upon the desired premcasurement time for a given sample glucose concentration and can be calculated using Equation 7. For example, for a maximum premeasurement time of 150 seconds for the lowest concentration, Gb, to be investigated in a range, and assuming a rate const,ant of second-l, the difference between [ 1 2 ]and ~ [I& is calculated from Equation 7 to be 1.5 X 1 0 - 2 G ~ . In this work no iodine was added to the sample solution initially. Effect of [Iz]s on Cell Response. Though the principles described above are satisfactory for selecting solution conditions for a given concentration range, they do not point out clearly the full effect of the sample iodine concentration upon the response of the concentration cell for a given rate of change of iodine concentration. This effect can best be seen by inspection of Equation 13, which is obtained from the differentiated form of Equation 3, assuming t h a t the quantity ju brackets is constant.
This equation exhibita a reciprocal relationship between the total iodine concentration and the rate of change of e.m.f. of the cell. For a constant rate of change of concentration, the slope of an E, us. t plot will decrease as the sample iodine concentration increases until the total concentration becomes very large compared to the rate of change of concentration. When this hamens., contributions to [12]sby are relatively small and the E, 0s. t plot will have a constant slope. As shown on Figure 2, measurements were made in a region of a steep but continuously changing slope. This has the advantage of providing good sensitivity for small changes in iodine concentration, but the disadvantage that the results are quite dependent upon the point at which the measurement is made. This latter point is not a serious limitation since the
' 9 I -
The general functions which are performed to obtain quantitative measurementa are summarized by reference to the block diagram, Figure 3. The reagent and sample are added to the sample compartment of the concentration cell. The solution is stirred rapidly and the changes of e.m.f. are followed b a precision measurement system. T l e data, a function of the reaction rate, are fed to a readout device. The control system regulates reagent and sample delivery, mixing, and solution removal after the measurement is obtained. The stirring unit also rovides for mixing of the solution in t i e reference compartment to provide stability and reproducibility of the reference electrode potential. A temperature controller is necessary to maintain the concentration cell, reagents, and sam les at a constant temperature within 0.1 C. There are several obvious ways of performing the necessary measurements. One method is to use a precise and accurate recording potentiometer and necessary switches to control the above functions. This method provided satisfactory results by measuring the time required for the e.m.f. to change between two preset voltages. The data were obtained from the recorded curvea as illustrated in Figure 2. An automatic and less expensive syatem for obtaining a measurement with direct readout on a dial as well as control of functions is easily provided by combining the Sargent Model Q concentration comparator, an auxiliary rela device, and an electric timer. Wit{ this system i t is merely necassary to push the automatic button on the Model Q comparator and then to read the data off the timer dial. Provision is made for plugging in automatic sample delivery devices, but in the present work samples were added manually by a 1-ml, hypodermic syringe . The Sargent Model Q comparator does not require any internal modifications since input and output circuita can be modified by plugging in the desired circuits a t the auxiliary outlets on the back of the unit. Therefore, the auxiliary relay is built as a small unit with three plugs connecting directly to three outlets on the Model Q comparator. By disconnecting the three plugs the Model Q is again ready for ita other applications, such as for PNPP or aa a titrator. The details of the system are described under the respective units. Measurement and Control System. The schematic diagram for the auxiliary relay system and its connection to the Model Q com arator are illustrated in Figure 4. $he comparator is essentially a very stable high i n p u t impedance amplifier with precision input and output circuits. Included in the output circuit is a sensitive meter
B
VOL. 33, NO. 8, JULY 1961
1043
I”
REFERENCE ELECTRODE
Figure 4. PI. P2E. P3. P4, P5.
Pll. KI. K2.
K3. K4. K5.
ELECTRODE
Concentration comparator-auxiliary relay control system
Amphenol 18-8P male plug Polarized two-prong male plug which plugs into socket at back of Sargent stirring unlt Standard octal rocket Standard 1 15-volt a x . female sockets Amber neon pilot light SPDT, 1 15-volt a.c. relay DPDT, rachet impulse relay, Potter and Brumtleld, 1 15-volt a x . SPST, 1 15-volt a.c. relay 3PS1, 1 15-volt a.c. Amperite thermostatic delay relay, 1 15 C 2
relay system around which the prescnt automatic systcm is designcd. The general operation of the combined units is as follows: When the automatic button on the comparator is pushed, 115 VAC is put across the twoprong valve outlet at thc back of the unit. This voltage remains on the valve outlet until the input voltage El reaches zero, at which timc the 115 VAC is immcdiatcly removed by operation of the meter rclny. However, with the auxiliary relay systcm connected, the above on-off cyclc r:iuscs the :tddcd relay to immcdiritcly rcwtivntc the comptlrtltor which again puts 115 VAC a t the two-prong vdvc: outlvt rtnd simultaneously starts n tirricLr :ind applies a fixed bizis voltngc E,, lit the input. Again the 115 VAC rrmnins at the outlet until the input volt:i.gr reaches zero, by thc cc11 voltngc E, changing continuously tn ovrrc:omc’ the applicd bias. The rrmoval of the 1 1 5 VAC for the secoiid timt: stops the tinirr and all relays are movcd bark t,o their original positions and arr rcndy for the next sample to be run. Thr net result of thc two on-off cyclrs is a time interval 1, (Equation 11) which is n function of the reaction rate and glurosc concentration for sample x. Thc bins voltage applied is equal to the voltnge interval Eh - E, on Figure 2 (Ed = E b - Ea). Model Q Concentration Comparator. A brief discussion of the schematic of the Model Q is desirable a t this point. A portion of the input circuit is reproduced to illustrate connection to the auxiliary relay 1044
GMPLE
ANALYTICAL CHEMISTRY
B
system and to show thr relationship between the input voltage to the amplifier Et and the cell, E,, and bias, Ea, voltagrs. If poles B and Ii on P1 are shorted, then the bins E d is bypassed and Et = E,, but if B and H are diseonnrc+ed, thcn E d is applied and Et = E, Ed. The systrm is arrangcd 80 that a positivr going potential a t H will overcome the negative bias Ed introduced, thus bringing E1 equal to zero. The approarh of El to zero controls the on-off cydes described above. Th(, two-prong valve outlet is a polarized plug and caution must be observed to assure ronnrction of the low side of the auxiliary relay system to low sidr of thr cornparator. Pin 7 of the octal outlet socket, P3, is ronnrctrd to the high sidr of the comparator. Pins 1 and 8 of this socket ronnrct through thr mcter relay and load relay roils of the cornparator, the othcr end of which connects to the low sidc of the linc, SO thnt, connection of 1 and 8 to 7 activates thrsr roils and thus the comparator. Auxiliary Relay System. T h e functions of 1’1, P2E, and P 3 have been describrd. P 4 provides for a sample and rengcnt addition system. The addition system must bc designcd t o rarry out the drsirrd scyurnre of evrnts when h e voltage I$ apphrd and remains connected, and to reset when it is removed. P 5 provides for connection of a data readout drvicr operating on line voltage. The pilot light P L l indicates when P 5 is activated. Combined Operation. For the pur-
+
pose of this discussion it is assumed that a continuously changing c.m.f. is applied across points G and H of PI. I t is also assumed that with the relay system contacts as shown in Figure 4, point G has a constant reference potential and point H is nrgativc with respect to point G but is changing in a positive direction to approach thc value of point G. When the start button on the comparator is pressed, thr metcr and load relays are activated to provide line voltage at P2R. This linc voltage activates K1 and R2 closing contacts f-e, c-a, and h-b and brcaking contacts j-g and c-d. Closing contacts j - e nnd c-u provides line voltage across 1’4, which remains until K1 is deactivated, Closing h-b shorts out the bias E d so that thc input to the chopper amplifier is equal to the cell e.m.f. applied across G-H. Opening contactsf-g and c-d prevrnts activation of K3 and P5. The system remains in this state (Ed = E, and P4 activated) until the potential of point I€ reaches that of point G ( E 1 = O), at which point the meter relay deactivates the load relay of thc concentration comparator, removing line voltage from P2E and dcactivating K1 and K2. Whrn K1 is deactivated, contact j moves to the normally closrd position, breaking contacts f-e and niaking f-g. Contacts c-a and h-b rcniain closed until K 2 is again activatcd. ’I’hc rcsult is that K 3 is activated, closing contacts k-1 and activating K4 which closw contacts n-q, m-p, and r-R. Closing m - p and n-q rractivatcs the aompnrritor meter and load rclays to providr linc voltage at P 2 E q a i n and activating 111 and K2. Activation of 112 sirnultancously breaks contacts c-a and h-b and makes rontarts c-d so that thc bins is applird a t the comjxmtor input (El = E, Ed) and the timer is stnrtcd simultancously. Activation of K1 brctks contacts j - g and makrs contacts f-e. Howcvcr, since c-a is brokcn, P 4 is not activated on this half cycle. J h a k i n g of f-g drnctivatcs R3 so that k-1 is brokrn. However, note t,hat although k-1 is broken, K4 is sustainorl in the r~rtivatrtl stntc by the closing of r-s and rrniniiis so until contarts t - 1 ~ break. ‘l’hrsr contnets are controlled by IC5 wfiich has it 2-srcaond delay after bring ac:tiv:itctl hy thr srcond pulsr at 1’2E. ’l’hr rrsult of this is that thc com1):irntor is hrld in the activated stnt,r for 2 srronds. This is ncccssnry to nvoid tlifhwltirs of trmsicnts producrtl by oprrntion of thc rrlriys during the off-on scqucncr. \l’hcn contitcts t-u brcak, K4 is dcrwtivatrd nnd n-q and nz-p rrturn to their norm:ilfy opcn positions. This total scqirncr of cvrnts (escrpt for the 2-sr!:ond drlay rclny) takes plarc in lcss thnn the minimum measurablr time of 0.02 sc:cwid. The rchy systrni rrinnins i n this state until Et is again ccliinl t o zrro (En has been ovrrvome by E,), tit nfhic:h point line vo1t:igr is again romoved from P2E, so that Z i l nnd K 2 arc drnctiwitcd, and linr volt,:igo is rrniovrd from 1’5, Contact f moves bnck to g, 1 bwk to u, and the systcm is Icft as shown in Figurc 4, ready for the nest sctmplc. The nrt rrsult of this Ycqurnrc of
+
TO 115 V A.C.
TO GENERATOR ELECTRODES
Figure 5. of iodine 81,
5. . R. S.
SI,SI
Timer.
Current source for electrolytic generation
45-volt B batteries DPST toggle switch 90 K resistor SPDT switch controlled by timer Time delay timer (Industrial Timer Corp., TD-SM, 1 15/60)
rvents H i that the time required for the changing e.m.f. across G-H to overcome the bias E d has been measured. Application of this system to the measurement of reaction rates follows from the discussion in the previous section. Points H and G are connected to the sample and reference electrodes, respectively, to provide the continuously changing e.m.f. and the value of E d is adjusted on the zero adjust helipot of the concentration comparator to have the desired value ( E , - Ea = -5.00 mv.). Stirring Unit. T h e stirring motor for the Sargent electrotitrator, Model E (E. H. Sargent and Co., Chicago, Ill.), equipped with a stirring rod ( A A ) was used for the reference stirrer. The sample stirring unit consisted of a small motor of about 1200 r.p.m. mounted above the sample compartment and connected to a '/a-inch glass rod flattened on the end to give good stirring efficiency. The reference stirrer was controlled by the reagent selector switch on the concentration comparator. Data Read-Out Device. The data rcad-out device was a timer (Model S-10, The Standard Electric Time Co., Springfield 2, Mass.) which vould be read to the nearest 0.02 second and had a manua,l reset lever which was pushed after the time was rcitd off for each determination. Autoinatic electrical reset could bc obtained tLt the start of each determination by c-onnrcting a reset solenoid into P4. Addition and Removal System for Reagent and Sample. Reagents and sn.mp1e.r wcrc added mnnually to the mniplc compartment of the concentration cell using 1-cc. hypodcrmic syringes reproducible to *0.002 ml. 'l'he si1mple compartmeirt ~ l t cmpf,ied s aft,vr c:ompletion of each dcteriiiination hy means of an nspirator t,itbe with :I finr tip nearly touching the bottoni of the compartnicnt. 'I'his tip W:LH rcwovcd during runs. Comentration Cell. l'hc cwiiwnh t i o i i (:(*I1 is shown in 1~igiii.c'1 . The HI1111J)1l! Holution is contaiiicd i n an isolatioii compartment imiiiersctl i n t,lw refvrcmcc Holution contained in n wiLt,er-jiii~k(.tcicl100-ml. tall form Iwitkcr.
Figure 6.
The cell is thermostated by circulating water from a constant temperature reservoir through the water jacket surrounding the beaker. The isolation compartment has a sealed-in asbestos fiber to provide electrical contact between the sample and reference solutions without permitting significant mixin The platinum electrodes supplied wit% the comparator are conditioned as described earlier (6) before, use. The water-jacketed beaker was supported on the Bakelite platform of the electrotitrator stand. Current Source. Iodine solutions were prepared by electrolytic generation using the current source shown in Figure 5. This source uses two 45 V B batteries in series as a source and uses an electrical timer (Jndustrial Timer Corp., Newark 4, N. J., Model TD-SM) to terminate automatically the flow of generation current after a preselected generation time has becn completed. The desired generation time (0 to 5 minutes) is dialed on the timer. When 81and SI' are closed, the timer and generation current start simultaneously and continue until the preselected time is completed, a t which point Sz opens and generation stops. The generator electrode system was the same RS dcscribed previously (6). REAGENTS
All reagents were prepared in demineralized water. Buffer-Catalyst Solution. This solution is prepared by dissolvin 82 grams of potassium dihydrogen ptosphate, 42 grams of potassium monohydrogen phosphate, and 13 grams of ammonium molybdate ((NH&Mo,O2~.4Hz0J in water and diluting to 1 liter. This solution is stable indefinitely. Enzyme Solution. This solution is prepared by dissolving 1.6 grams of glucose oxidase (U'orthington Biochemicxl Corp., Freehold, N. J., 15,000 units) in water, filtering through Whntman No. I filter paper, and diluting to 250 ml. This solution is stablr for several days when stored at '5 C.
Plots of read-out vs. glucose Concentration
Iodide Solution. This solution is prepared fresh once daily by dissolving 50 grams of potassium iodide in water and diluting to 125 ml. Iodine-Iodide Solutions. These solutions are prepared once daily by electrolytic generation of iodine in the iodide solution. The time of generation depends upon the glucose concentration range of interest. For the 5- to 50-p.p.m. range, iodine is generated for 60 seconds a t 1.0 ma. in 25 ml. of the iodide solution. For the 50- to 500-p.p.m. range, iodine is generated for 300 seconds a t 1.0 ma. in 25 ml. of the iodide solution. Glucose Standards. Standard glucose solutions were pre ared by dilution of a 1000-p.p.m. g ucose solution prepared by dissolving 1.000 gram of Baker's C.P. dextrose (anhydrous powder) in water and diluting to 1 liter.
P
PROCEDURE
Preparation of Equipment. TJnitR A and B of the concentration comparator are connected as described in the instruction manual for the instrument. Plugs P 1 and P3 of thc auxiliary relay system are connected to matching sockets on the back of unit A . Plug P 2 E is connected to the two-prong female socket on the back of unit B. With the white input lead (pin G) connected to the reference electrode and thc black lead connected to the sample electrode, increases in iodine concentration in the sample compartment will cause the meter needle to move from left to right on the mcter face. With the reagent selector switch in position 1, the on-off cycle will be produced through unit B to P 2 E when the automatic button is pressed and the null point (E. on Figure 2) has been reached. The bias voltage (E,) is obtained from the input of unit A by setting the zero adjust Helipot to the desired value. With the function switch set on the PNPP osition (10 mv. either side of zero), a [ias of - 5 mv. is obtained with the zero adjust Helipot set on 2.5. Since it is desirable to keep the reference solution stirred to maintain temperature equilibrium, the reagent selecVOL. 33,
NO. 8, JULY 1961
1045
tor switch was left in position 1 through-
out a series of samples. The stirring motor for the sample solution was provided with an individual switch so that it could be turned off between samples. The auxiliary relay contacts should be as shown in Figure 3 before starting a series. If the system is not as shown, then a single application and removal of line voltage a t P2E will assure that all contacts are in their proper positions. Preparation of Reference Solution. T h e reference solution is prepared once daily by mixing buffer-catalyst, appropriate iodine-iodide solutions, and water in ratios of 1: 1:3. This solution is brought to temperature equilibrium in the water-jacketed beaker before any samples are run. Characteristics of electrodes and isolation compartments can be evaluated by placing a portion of this solution in the sample compartment and observing the bucking voltage required on the zero adjust to bring the meter needle to zero. This value should not exceed a few tenths of 1 mv. Preparation of Composite Reagent. T o avoid the necessity for adding more than one reagent in the analysis step, a composite reagent is prepared for each concentration range as fol-
lows.
For the 5- to 50-p.p.m. range, mix buffer-catalyst, iodide, and enzyme aolutions in ratios of 2: 2: 1. For the 50- to 500-p.p.m. range, mix buffer-catalyst, iodide, and enzyme solutions and water in ratios of 4: 4: 1: 1. The temperature of this composite reagent should be adjusted to the analysis temperature before any analses are begun. This reagent should e replaced every 2 to 3 hours for best results Should i t be desirable to decrease the premeasurement time for either range, this can be done by starting with some iodinc in the composite reagent initially. T o do this it is convenient to add an appropriate amount of the iodine-iodide solution to the composite reagent, a t the same time reducing the amount of iodide solution added by a corresponding
g
I
Table 1. ~l~~~~ Concn., P.P.M.
Reproducibility of Automatic Results for Glucose Direct Time Readout, Sec. ti
tt
Coeff.
of Var., Is
5%
5- to 50-p.p.m. range 5 10 20 30 40
50
50 100 200
300
400
600
1046
146.5 150.0 149.6 66.6 67.1 69.2 35.0 34.0 34.8 22.7 22.6 22.3 16.5 17.0 16.7 13.3 13.8 13.3
0.9 2.0 1.5 0.9 1.5 1.8
50- to 500-p.p.m. range 91.5 91.0 89.6 43.6 43.4 43.4 21.9 22.2 21.9 14.4 14.4 14.5 10.7 10.7 10.9 9.04 9.15 9.02
1.1 0.3 0.8 0.0 1.1 0.8
ANALYTICAL CHEMISTRY
%
amount so that the total iodide concentration is not changed. Analysis Step. The sample compartment and associated electrode and stirrer are rinsed first with 0.5 ml. of water and then 0.5 ml. of composite reagent betwcen each sample by injecting each from a wash bottle or syringe and then removing by inserting the aspirator tube. After the rinse is completed, 1.00 ml. of the composite reagent is placed in the sample compartment, the sample stirrer is started, and the automatic switch on the comparator is prcssed. Then 1.00 ml. of the sample is added. From this point the instrument completes the measurement automatically and the time interval can be read from the timer. After the time interval has been recorded, the timer is reset to zero and the procedure repeated for the next sample. After the twofold dilution of the composite reagent by the addition of the sample, the reference and sample solutions have identical ionic strengths and compositions except for the amounts of glucose and enzyme present in the sample. Unknown glucose concentrations are calculated by comparison with a standard solution using Equation 11 or determined from a working curve similar to Figure 6. RESULTS A N D DISCUSSION
Quantitative Data. Table I shows the results as read directly from the timer of the automatic system for a typical series of determinations. For both the 5- to 50-p.p.m. and 50- to 500p.p.m. ranges, single determinations of six diffcrent concentrations were run successively. Then the determinations were repeated. The data indicate that reproducibility for each sample is within 1 to 2%, which is also typical of many similar series run over several weeks. The reciprocal of the average readout values from Table I are plotted against concentration in Figure 6. The results show that Equations 10 and 11 are valid within a few per cent over the two concentration ranges. For the 5- to 50p.p.m. range, the straight line does not quite pass through zero because of the small but significant amount of glucose which has reacted when the measurement was completed for the samples on the low end of the range. These data illustrntc that if glucose samples cover a tenfold range, it is necessary under the given conditions to use a working curve if an accuracy of 1 to 2% is desired. For many npplicntions it is only necessary to determine glucose over a fcwfold ronccntration range. In these cases it is convenient to use only one standard and to assume direct proportionality bctween glucose concentration and reciprocal of time. Results calculated on this basis are given in Table 11. The data are taken from thc automatic
results given in Table I, but it is aasumed that the 30- to 300-p.p.m. glucose samples are standards for the low and high ranges, respectively, and results for the other samples are calculated using the simple proportionality of Equation 11. These data indicate that over a fourfold concentration range it is not necessary to plot a working curve to obtain good accuracy. This was verified by many other sets of data.
Table II. Automatic Glucose Results on a Single Standard Reciprocal Time, pg. Glucose in Second-' Sample Error, X 10' Taken Calcd.' yo Range I* 14.7 28.9 44.4 60.0
20 40 60 80
19.8 39.0 . . a
81.0
-1.0 -2.5
0.0
+1.3
Range 2 b 23.0 46.5 69.4 92.0
200 400 600 800
199 394
...
-0.6 -1.6 0.0 0.0
800 From Equation 11, using the 30- and 300-p.p.m. eamples as standards for rangea 1 and 2, respectively. b Ranges 1 and 2 refer to experimental conditions for the 5- to 60- and 60- to 500. p.p,m. ranges, respectively. Q
I n the 5- to 50-p.p.m. range, the reference iodine concentrations is only 2.5 X 104M. Therefore air oxidation of iodide can significantly change the iodine concentration over a period of hours, and it is desirable to check the calibration frequently with a standard glucose solution. These data were obtained a t 25.0' C. at a pH of 6.1. For best results it is necessary that both composite reagent and sample be a t 25.0' C. before starting the reaction. The effects of temperature and pH on the reaction rate are shown by the following results. pH Dependence. The effect of p H on the reaction rate was studied in phosphate buffers from p H 3 to 7. The total salt concentration was kept constant as the p H was varied. The results represented on an arbitrary rate scale in Figure 7 show a rather broad maximum in the region of pH 6. Comparable results have been reported by Keilin and Hnrtree (I) and Kingsley and Getehell (J), who obtained maxima a t pH's 5.6 and 7.0, respectively. Adjustment of the pH to within this region should give maximum freedom from errors resulting from deviations in solution pH. At very low pH values the enzyme preparation oxidizes iodide rapidly. Temperature Dependence. The effect of temperature on the rate of
30L
Figure 7. Effect of pH upon rate of glucose oxidation in presence of glucose oxidase
Reaction 1 was studied and results are presented in Figure 8. These results show a rapid increase in reaction rate with increased temperature up to 40" C. and after t h a t a very rapid decrease. At the temperature of 25' C. where the procedure was developed, the temperature coefficient is about 10% per degree centigrade, so that control to 0.1' C. reduces errors due to temperature variations to within 1%. Higher temperatures which give some increase in sensitivity may prove to be advantageous for very low glucose concentrations. Iodine-Hydrogen Peroxide Reaction. Under the conditions of this work, Reaction 2 was shown t o be sufficiently rapid to give accurate and precise analyses a t reaction rates 20 times larger than the largest one reported here. Interferences. Reaction 1 is relatively free of interferences. Keilin and Hartrce (2) have demonstrated that the enzyme is very specific for the d-form of glucose, other sugars bcing less than 1% as reactive. I t was demonstrated here that many anions, including the halides, sulfatc, nitrate, and phosphate, do not interfere with this reaction. At enzyme concentrations fiveto tenfold higher than that suggested in this work, some component in the enzyme preparation reacts with iodine a t a finite rate, causing a negative value dE for -zc a t zero glucose concentrations. However, under the conditions used for this work this was not a serious problem. Oxidizing and reducing agents which react very rapidly with iodide or iodine should cause little error if the amounts of iodine produced in the sample solution do not interfere significantly with the premeasurement time. However, slow
so
TEMPERATURE (DEG. C)
45
Figure 8. Effect of temperature upon rate of glucose oxidation in presence of glucose oxidase
nonspecific redox reactions forming iodine might introduce errors. This method depends upon the ionic strength remaining constant in the sample and reference solutions. If ssmp1e.s of widcly differing ionic strengths are encountered the quantity in brackets in Equation 3 might vary from sample to sample. However, this effect can be corrected by working with a very high ionic strength, which makes differences in the samples insignificant, or by increasing the sample iodine concentration to a point where the E, us. 1 curves are linear and the measurement becomes independent of the point a t which it is made. Alternate Analysis Method. As was mentioned earlier, several methods are available for making the rate measurement potentiometrically. Developmental work on the method described here demonstrated that the slope of the E us. t curve measured a t any point was proportional to the glucose concentration. This is shown in Equation 14, obtained by substituting for d L l s from Equation 6 into Equation 13.
-2r
corded curves and also by various electronic methods. However, in general the methods for automation and direct readout are not as simple as with the time interval procedure. Generalizations. This method should be applicable to other reactions where iodine is produced or removed at a rate dependent upon the concentration of some sought-for constituent. This would of course include other enzyme-substrate reactions producing hydrogen peroxide. The method should have general application for various other electrodeactive species which are produced or consumed by specific chemical reactions. The method has been applied to the determination of glucose in deprotcinized blood serum samples. Work in this area is continuing and will be published a t a future date. ACKNOWLEDGMENT
This investigation was carried out during the tenure of a Predoctoral Fellowship from the National Heart Institute, United States Public Health Service. LITERATURE CITED
This expression can be applied for quantitative work by making the slope measurement always at the same value of [IZ]8. Under these conditions, different glucose concentrations can be related by a simple proportionality. If the potentiometric measurement is made under the conditions described for P N P P (6),then mcnsurcment at the same value of E, for each sample is equivalent to measurement a t the value of [IzIs. The slopes can be obtained from re-
(1) Keilin, D., Hartree, E. F., Biochem. J. 42,221 (1948). (2) Zbid., 50, 331 (1951-52). (3) Kingsley, G . R., Getchell, G., Clin. Chem. 6. 466 f l a R * ) (4) Malmstadt,. H. V.. Hicks. G. P.. 394'( 1960). ' \A""",.
V., Pardue, H. L.,
V., Winefordner, J. . . D. Anal. C h . Acta 20, 283 (1959). (7) . . dalomon. r,. L.. ,Johnson.' J. E.. ANAL. CHEM.3 1 ,'453 ( 1959). RECEIVED for review February 2, 1961.
Accepted April 6, 1961.
VOL. 33, NO. 8, JULY 1961
1047
