Improved apparatus for the differential measurement of pH: Applications to the measurement of glucose

ANALYTICAL

BIOCHEMISTRY

Improved

112, 287-294 (1981)

Apparatus Applications

ANDREA MOSCA, GUILIO WALTER S. FRIAUF,* Cattedra

for the Differential Measurement to the Measurement of Glucose

of pH:

Dow, MASSIMO LUZZANA, LUIGI Ross1 BERNARDI, ROBERT L. BERGER,~,’ HARRY P. HOPKINS, JR.,+ AND VIRGINIA CAREYS

di Chimica

Biologica. Facolta di Medicina, Universita di Milano, Ospedale San Raffaele. *Biomedical Engineering and Instrumentation Branch, Division of Research Services, National Institutes of Health, and tLaboratory of Technical Development, Section on Biophysical Instrumentation, National Heart, Lung, and Blood Institute, Bethesda, Maryland 20205; and $Department of Chemistry, Georgia State University, Atlanta, Georgia 30303

Milan,

Italy;

Received October 16, 1980 Two improved systems for the determination of the difference in pH between two solutions at the same temperature are described, both of which have a long-term stability of a 1 x 10m4pH unit and a peak-to-peak noise level of 5 x 10m5pH unit when operated in the differential mode. The cells are constructed of Delrin which has been found to be inert in biological fluids. These cells, with a volume of 1 ml, can be electrically connected to each other via a dialysis membrane and are thermostated during the duration of the pH measurements to ?O.Ol”C. In a second configuration, combination microelectrodes are inserted into each cell; thus the dialysis membrane is not necessary. To demonstrate the application of these systems to reactions of biological interest where pH changes occur, we investigated the hexokinase-catalyzed reaction between ATP and glucose in a phosphate buffer. The concentrations of glucose determined from the observed changes in pH by a numerical solution to the equilibrium equations are in excellent agreement with the analytical values.

Some years ago we described an electrometric method (1) which used two glass electrodes for differential pH measurements (2). Although it was shown that with this technique it was possible to measure pH differences of about +5 x 10e5 pH unit, very few applications, especially to reactions of biological interest, have so far been reported. Notable exceptions are the studies of Busch and Freyer (3) and Busch el al. differential titration (41, who recorded curves of proteins and other compounds with a system similar to ours. Our experience in the use of the previous differential pH apparatus (1) established several practical limitations to its routine ’ To whom correspondence

should be addressed.

use. The main difficulties were: (a) the use of large (lo-mm diameter) electrodes required a large volume of solution (8 to 10 ml in each cell), (b) the fact that the cells were not anaerobic, (c) the calibration of the system required removal of the test solutions from the two cells, and (d) the junction between the two cells was not thermostated or easily renewable. In this paper we describe two new systems capable of determining the difference in pH between two l-ml samples. Either system can be operated anaerobically and can be maintained at a constant temperature (-+O.Ol”C) during the course of the measurements. In the first system, a liquid junction constructed of a semipermeable membrane provides a suitable electrical 287

0003-2697/81/060287-08$02.00/O Copyright All rights

0 1981 by Academic Press. Inc. of reproduction III any form reserved.

288

MOSCA

connection between the two solutions without appreciable mixing of the two solutions. Two glass electrodes, one in each solution, allows us to determine the difference in pH between the two solutions. We have also found that just as reliable differential pH values can be obtained with the new pH meter in a system where the liquid junction is not present. Here, two completely separate cells in the thermostated block are each equipped with a combination micropH electrode and the differential pH values are derived electronically from the subtraction mode of the pH meter. Both apparatus are shown to be capable of following the pH change caused by the hexokinase-catalyzed adenosine 5’-triphosphate (ATP)-glucose reaction in a phosphate buffer when the glucose concentration is in the range 1-18 mM. From a mathematical analysis of the equilibrium equations, we have shown that this system can be used to monitor glucose in biological fluids. MATERIALS

AND METHODS

Differential pH Cell for Apparatus I

An enlarged view of the first apparatus used for differential pH determinations is shown in Fig. 1A. It consists of two symmetrical Delrin reaction cells, each containing a glass electrode, a magnetic stirrer, and a stopper. The two electrodes are symmetrically positioned on the side of each cell and sealed by 0 rings. The stoppers are similar to those used in the apparatus described by Rossi-Bernardi ef al. (2) for measurement of the oxygen dissociation curve of blood. With this configuration, the contents of the two cells are anaerobic for all practical purposes. The pH electrodes, specially developed by Dr. W. Ingold AG, Zurich (Ingold electrode type 205) for this work, are made of low-resistance glass (50 to 60 Ma at 25°C) and are 5 mm in diameter. The electrodes are connected to the pH meter with a cable containing a conducting graphite layer to reduce microphonics. The

ET AL.

FIG. 1. Diagram of the differential pH apparatus. Section A shows the details of the cell and electrode arrangement from the outlet port side. Section B shows the path of the solution and the membrane connection from the inlet side. 3 and 3’, Inlet ports; 2 and 2’, Dehin plastic block used to support a dialysis membrane; 4 and 4’, outlet ports; 5, brass or aluminum thermostating block; 6 and 6’, ports for circulating thermostating fluids; 1, stirring motor; 7, Dehin cells; 8, Dehin stoppers; 9, dialysis membrane.

Ag/AgCl inner electrode is very short and is protected from light by a gold shield, a feature found to be essential in order to eliminate spurious drifts of pH readings caused by variations in light intensity. The inner compartment of the glass electrode is filled with a gel, thereby eliminating erratic potentials caused by movement of the air bubble usually present inside electrodes of conventional design. The physical arrangement of the junction between the two electrodes is also shown in Fig. 1 in the section labeled B. The liquid junction (labeled 9 in B) between the two cells is made of a disk of standard dialysis tubing just at the end of the “v” part of the input channels 3 and 3’. The membrane is held in place by the Dehin blocks (Fig. lB, 2 and 2’) which are held together by four screws. Channels are drilled from the solution entry ports, labeled 3 and 3’, so that each solution is in contact with only one side of the membrane. Since only small ions can pass through a typical membrane (M, cutoff 6000-8000) an electrical contact is established between the two solutions. A

DIFFERENTIAL

pH MEASUREMENT OFFSET

289

APPARATUS TC

PH CHAN

I REF.-

DIFFERENTIAL AMPLIFIER

1+ INPUT Cl RCUIT

/

FILTER

SUETRACTOR

\

OFFSET PH CHIN.

2

DIFFERENTIAL

4

6

xl OR xl0 GAIN

TC FILTER

TC I -

FILTER

8

REF

A

4 99K -12v

t15v

50K IOT

3: K

SLOPE

LH0042CH

FIG. 2. (A) Schematic of the differential pH amplifier used in this work. (B) Details of the input circuits. AU critical resistors, i. e., those marked with a *, are Vishay (? 25 ppm/“C, 2 0.1%) (Vishay Resistive Systems Group, Manerin, Pa.).

typical membrane has a resistance of 50 kR. All parts in contact with the solution are insulated from ground. The two outlets, labeled 4 and 4’ in Fig. lA, are connected to silicone rubber tubing so that the waste solutions can be discharged into separate glass bottles. True ground is established by a gold wire sealed into the silicone rubber tubing of one of the waste outlets. The Dehin cells fit snugly into a brass or aluminum (Fig. lA, 5) through which thermo-

stating fluid can be circulated through tubes 6 and 6’. With the temperature of the thermostating fluid equal to 25°C & O.l”C, the temperature of the solutions inside the cells varies less than *O.OlC over the time period of the measurements. The electronic circuitry was designed to have a rapid response and an extremely stable output so we could exploit the fast response of several new pH electrodes that have recently become available (5). The de-

290

MOSCA

sign also allows pH measurements in grounded metallic containers, such as a stopped-flow apparatus (6,7) where feedback to the solution via the reference electrode is not possible, and in differential pH measurements without use of reference electrodes. Information about all gain and filter settings can be transmitted through a BCD output to a data acquisition system along with the digitized pH signal from the digital panel meter (Model AD2024, Analog Devices, Not-wood, Mass .). Two separate pH measuring circuits are provided in the pH meter with provision for subtracting one signal from the other to provide a differential reading of the pH in the two cells. The signals are unfiltered up to the point of subtraction, as shown in Fig. ZA, so that small differences in filtering will not degrade common mode rejection during pH changes. Each circuit, as well as the differential circuit, has a low pass filter with a selection of time constants ranging from 10 to 500 ms. Both circuits have fixed gains, which provide a sensitivity of 1 V per pH unit and a precision offset that permits the adjustment of the pH output in the range of 6.5 to 7.5. Slight adjustments of gain and offset can compensate for small differences between the electrodes and the variation of the temperature of the pH solution. The differential circuit also includes a separate zero adjustment and 1 x or 10~ gain selection. On the higher gain the overall sensitivity is 10 V/pH unit. At this sensitivity differential pH values can readily be monitored to 1 x lO-4 pH unit with conventional digital voltmeters or panel meters. Differential

pH Cell for Apparatus

II

It is often desirable to monitor the pH of each solution as well as the difference between them. Therefore, in the second apparatus, combination electrodes (Model 41OS, Microelectrodes, Inc., Londonderry , N . H.) are inserted into each cell. This configuration also eliminates the need for any electrical connection between the two solu-

ET AL.

tions. A detailed schematic of the electronic circuit and connections is given in Fig. 2B. The combination electrodes are connected to the electronics with quadaxial cable. The center conductor connects the pH electrode to the non-inverting input of the 42L amplifier (Analog Devices). The first shield is driven by the output of the 42L so as to follow the input voltage. With the voltage between the center conductor and the shield held virtually to zero, it is not necessary to charge the cable capacitance through the high resistance of the pH electrode and suffer a degradation of response. The next shield carries the reference electrode signal and the outer shield is grounded. Since commercial cables and connectors with three shields are not available, triaxial components were used with another shield over the cable connected via a pig tail. The pH input amplifier is an Analog Devices 42L and the reference input amplifier, with a less stringent input current and requirement , is a National Semiconductors, Inc. LHOO42CH. Both are operated in a non-inverting mode with a gain of 3, and are followed by a subtraction circuit with an adjustment for common mode rejection to provide the differential pH signal. This eliminates the large feedback loop found in many conventional pH meters. Elimination of this loop, which includes the reference electrode and solution, is mandatory if fast response is to be achieved. This also allows operation without interference from small solution potentials often created by nearby electronic equipment. In the absence of such potentials, the solution potential will be established at a constant value by leakage thru the lOOO-MR resistor which is connected to ground from the reference electrode input. CHEMICALS

AND SOLUTIONS

Hexokinase (ATP : D-hexose- 6-phosphotransferase, EC 2.7.1.1.) was obtained from Sigma as lyophilized samples sealed in

DIFFERENTIAL

pH MEASUREMENT

vials. Enzymes suspended in concentrated ammonium sulfate or in strong buffers are not recommended for this work, because the addition of these enzyme solutions even in small amounts would change the buffer power of the solutions. The standard buffer used for glucose determination had the composition: KH2P0, (0.008 M), KC1 (0.1 M), ATP (0.002 M), and MgC& (0.004 M). After dissolving the required amount of each solid in water, the pH of the solution was adjusted to 7.46 with 1 M KOH. A fresh solution was prepared every day. Acid and glucose standards were made up by diluting reagent-grade HCl with 0.1 M KC1 and dissolving solid anhydrous D-(+)-glucose in 0.1 M KCl. RESULTS AND DISCUSSION

The long-term stability of the difference in pH between the two glass electrodes when the cells were filled with a KH2P0, solution (1 X 10m4 M in KH,P04 and 0.1 M in KCl) was similar to that previously reported, i.e., -+ 0.0001 pH unit in 24 h with a peak-to-peak noise of -e 5 x 10d5 pH unit. In this apparatus the minimum number of hydrogen ions that theoretically can be detected in the 1.09-ml volume is 3 x lo-l2 mol. To achieve this sensitivity and to obtain the required stability of the difference in potential between the two solutions, the solutions in the cells must be connected to ground only through gold wires. Otherwise, loop currents will develop through various parts of the apparatus and make the pH readings unstable. Stirring of the solutions did not affect the pH readings. Determination of Glucose

When glucose is placed in a solution of ATP where the enzyme hexokinase is present, adenosine 5’-diphosphate (ADP) and glucose 6-phosphate (G-6-PY are formed and the equilibrium 2 Abbreviation

used: G-6-P, glucose 6phosphate.

291

APPARATUS

Glucose + ATP e G-6-P + ADP

[l]

is readily established. Since the pK, values of ATP (7.68,4.00) (8,9) differ from those of G-6-P (6.55, 4.00) (8,9) and ADP (7.20, 3.95) (8,9), the pH of the solution changes when glucose is added. This change in pH provides a simple means of determining the concentration of glucose in the sample before the reaction occurs. Formally, the reaction may be written with balanced charges on either side as ATP-

+ glucose Z$ G-6-P- + ADP2-

[2]

or ATP4- + glucose * G-6-P”

+ ADP-

+ H+.

[3]

The latter shows that hydrogen ions are released in this reaction when ATP4- is the predominant ATP species in solution; this is the situation around pH 7.5. Goldberg (8) reports AC” for reaction [3] to be 16.7 kJ mol-l; thus, the reaction of glucose with ATP at pH 7.5 should be nearly stoichiometric. The actual reaction that occurs in solution at pH 7.5 can be written symbolically as glucose + XATP zs XG-6-P + ZADP + n H+,

[4]

where CATP, ZADP, and XG-6-P represent all of the different charged species in the solution for ATP, ADP, and G-6-P, respectively, and n is the number of hydrogen ions produced in the solution. Clearly, the addition of glucose to a solution of ATP with hexokinase present will cause the pH of the solution to change to a lower value. But, what is the relationship between the pH change and the moles of glucose added? To find such a relationship we must perform a complete analysis on the equilibrium equations before and after the addition of glucose. This is complicated by the fact that magnesium ions must be present for the activation of hexokinase. Unfortunately, most of the species in the solution before and after the addition of glucose form com-

292

MOSCA

plexes with Mgz+ ions and these equilibria must be included in the analysis. Since the initial solution which we employed in the experiments described here contains ATP, inorganic phosphate, MgCl, , and KCl, one must include at least six equilibria in the analysis:

ATP3-

ATP3- 2 ATP4-

+ H+,

PI

H,POi

+ H+,

bl

2 HP@,-

+ Mg2+ 2 MgATP-,

AK+ = [ATF-]

+ [MgATF’-]

[71 + [HPO;-]

The fractions of ATP and inorganic phosphate in each form shown in Eq. [ 1 l] can be calculated from the pH, the free Mg2+ con[ATI’-y[ATP],,

= (1 + [H+YK,

The appropriate K values to be used in Eq. [12] can be calculated at the ionic strength of the solution from the equations given by Goldberg (9). Since initially neither the ionic strength nor the [Mg2+] is known, we have employed an iterative procedure (9) to find the fraction of ATP in the ATT’- form. A similar procedure was followed to find the other fractions needed in the calculations. Once these fractions are known, we can establish the concentration of each species in solution from total concentration of ATP, Mg, and inorganic phosphate. After the addition of glucose to the solution, five new equilibria must be included in the analysis of the ionic equilibria, i.e., K, ADP2- z+ ADP3-

+ H+,

KlO G-6-P- _ G-6-P2- + H+, KE ADP2- + Mg2+ _ MgADP, G-6-P2- + Mg2+ 2

MgG-6-P,

D31 P41

WI WI

ET

AL.

ATP4-

+ Mg2+ 2 MgATP2-,

PI

HP@,-

+ Mg2+ 2 MgHP04,

[91

H,O 2 H+ + OH-.

WI

When an amount of KOH is added to such a solution to adjust the pH to 7.46, the total concentration of K+ is increased by some amount (M+). At this point, the introduction of the mass balance equations into the charge balance equation gives + [MgHP04]

+ (K, - x[H+12)/[H+].

[ll]

centration, and equilibrium expressions. For example the fraction of ATP in the ATP+ form can be calculated as + [Mg2+][H+]K,IK1

ADP3-

+ [Mg2+]K,)-‘.

WI

MgADP-.

r171

+ Mg2+ 2

Knowing the new pH value after the addition of glucose to the buffer, we can evaluate the fraction of each ionic species present in the same manner as described for the original solution. Assuming that the reaction goes to completion, the initial concentration of glucose before the reaction is equal to the concentration of ADP or G-6-P at the end of the reaction. The substitution of the mass balance equations into the charge balance equation for the solution after the addition of glucose gives an equation which also contains the term AK+: AK+ = [ATF’-]

+ [MgATF’-]

+ [MgHPO,]

+ [ADF-]

+ [MgADP-]

+ [G-6?-]

+ [HPO:-]

+ [Mg G-6-P] + [Kg-

[H+12Y[H+].

[18]

DIFFERENTIAL

pH

MEASUREMENT

When this term is eliminated from the two equations ([ 1 l] and [ 181) we obtain an expression for the concentration of glucose before the reaction which can be solved by an iterative procedure (9). In these calculations the hydrogen ion activity obtained from the pH values was converted to the hydrogen ion concentration by dividing by the activity coefficient determined from an empirical equation (lo), which relates the activity coefficient to the ionic strength of the solution. All calculations were performed on a PDP8 computer using a Basic program which is available upon request. In order to test the validity of this procedure, known quantities of glucose were added to a solution that was 0.002 M in ATP, 0.004 M in MgCl,, 0.0087 M in inorganic phosphate, and 0.1 M in KCI. The concentration of glucose before the reaction was calculated from the initial pH, the pH after the addition of glucose, and the known concentrations as described above. These values are listed in Table 1 for comparison with the glucose concentration determined from the dilution factors. In all experiments the calculated value is within 4% of the known value, which is remarkable considering that the pK values are from several sources, and an empirical equation is used for evaluation of the activity coefficient of the hydrogen ion. Since some deviations are positive and others are negative, these differences are probably due to errors in the absolute pH and the ApH values. Where duplicate measurements are available, we see that l-10% change in ApH produces approximately the same percentage change in the calculated glucose concentration. We have also investigated the effect on the calculated glucose values of the solution by varying the concentrations of (i) acid groups with pK, values around 7.0 which would affect the pH of the buffer before the reaction, (ii) neutral salts that merely change the ionic strength of the solution, and (iii) (3) Mg2+ ions, while retaining the same values of the initial and final

293

APPARATUS TABLE

1

COMPARISQN OF CALCULATED GLUCOSE CONCENTRATION WITH TRUE VALUE WHEN THE CONCENTRATIONS IN THE BUFFER ARE [ATP] = 0.002 M; [M&l,] = 0.004 M; [p,L = 0.0087 M; [KCI] = 0.100 M

GlUCOSe” (mM) 2.77 5.55 II.11 16.65 22.2 27.75 16.65 16.65 16.65 16.65

PH

~PH

Calculated ghC0%? (C x 1V)

Actual ghCOSe~ (C x I@)

P~~C.Zl&ig~ difference

7.430

0.0060 2.629 2.518 0.0069 2.970 0.0128 5.217 5.045 0.0258 10.28 10.09 0.0254 10.11 0.0378 15.06 15.13 0.0498 19.97 20.18 19.77 0.0493 0.0620 25.09 25.22 [PO,] = 0.009; all others the same as above 0.0378 15.67 15.13 [KCI] = 0.12; all others the same as above 0.0378 15.11 15.13 [MgCI,] = 0.405; all others the same as above 0.0378 14.26 15.13 Change all PK., values by 1 SD 0.0378 15.80 15.13 Arbitrary change in pH by 0.01

a Concentration of glucose in the 0.1 M KCI solution added solution in the pH cell. b Concentration of glucose in the pH cell before reaction.

+4.2 +3.2 11.8 +0.2 -0.46 -1.0 -2.0 -0.5 +3.4 -0.1 -5.7 f4.3

IO the

pH. We repeated the calculations for the 16.65 mM glucose solution with arbitrary changes in the concentrations of the inorganic phosphate, KCl, and MgCl, . The glucose values calculated after increasing only one of these without changing the others are given in Table 1 for the 16.65 mM glucose solution. Changing the inorganic phosphate by nearly 5% to 0.009 M causes the calculated glucose value to increase by 4%. Increasing the KC1 concentration by 20% has virtually no effect on the value of glucose determined by this method. If the MgCl, concentration is increased by 25% to the 0.005 M, the calculated value of glucose rises by only 4.9%. The effects of the uncertainties associated with the pK, values and measured pH values on the calculated value of glucose were also investigated for the 16.65 mM glucose solution. When the experimental standard deviations for the pKa values are added to the pK,‘s used in this analysis, the calculated concentration changes by

294

MOSCA

4%. If the absolute value of the initial pH is lowered by 0.01 pH unit, then the glucose concentration is calculated as 1.6% higher than the originally calculated value. CONCLUSIONS

We have described two simple systems for making differential pH measurements down to +O.OOOl pH unit. Either of these systems can be employed to determine glucose in aqueous solutions by following the change in pH caused by the hexokinasecatalyzed ATP-glucose reaction. Our analysis of the equilibria involved shows that glucose can be monitored by this procedure without a standard curve, if the concentrations of the components in the buffer are known to within several percent. It should be noted that the range of glucose concentrations studied in this work extends from a glucose concentration of 0.05 to 0.25 mM. Since the original sample was diluted in a 1: 100 ratio, these concentrations correspond to 5 to 25 mM glucose in the undiluted sample, which is the range found in normal and pathological human blood samples. For the determination of glucose in whole blood or plasma, however, account must be taken of the buffer power of the added sample. Generally this value is not known, but the additional acid should not change the calculated value by more than 4-5%, as was seen when the total PO, concentration was arbitrarily changed by 3%. This complication in the

ET AL.

determination of glucose in blood can be overcome by using the addition of a glucose standard to the solution after the addition of the blood. Since this method does not depend on photometric mesurements, solutions that are turbid or highly light absorbing can be readily analyzed for glucose. This procedure should also be applicable to the determination of any substrate involved in an enzyme-catalyzed reaction that releases or absorbs hydrogen ions. ACKNOWLEDGMENT This study was supported in part by a contract from the Consiglio Mazionale delle Ricerche, Rome, Italy.

REFERENCES 1. Luzzana, M., Perrella, M., and Rossi-Bemardi, L. (1971) Anal. Biochem. 43, 556-563. 2. Rossi-Bemardi, L., Luzzana, M., Samaja, M., Davi, M., DaRiva-Ricci, D., Minoli, J., Seaton, B., and Berger, R. L. (1975) Clin. Chem. 21, 1747-1753.

Busch, N., and Freyer, P. (1977)Anal. Biochem. 79, 212-216. 4. Busch, N., Freyer, P., and Szameit, H. (1978) Anal. Chem. 50, 2166-2167. 5. Berger, R. L., (1978) Biophys. J. 24, 2. 6. Crandall, E. D., and Forster, R. E. (1978) 3.

Biophys.

J. 24, 35.

Crandall, E. D., Klocke, R. A., and Forster, R. E., (1971) J. Gen. Physioi. 57, 666. 8. Goldberg, R. N., (1975) Biophys. Chem. 3, 192. 9. Goldberg, R. N., (1976) Biophys. Chem. 4, 215. 10. Andersen, 0. S. (1980) in Blood pH and Gases (Anton, H. J., ed.), p. 17 Maas Univ. Press, Utrecht. 7.