determination of substrate concentrations by a computerized enzyme electrode

Determination of Substrate Concentrations by a Computerized Enzyme Electrode

J. P. KERNEVEZ, L. KONATE, and J. L. ROMETTE, U. T. C., BP 233, 60206 Compi2gne. France

Summary

A numerical treatment of the signal produced by an electrode onto which an artificial enzyme membrane is mounted can give the concentration of the substrate (glucose, saccharose, lactose, amino acids, etc.) in solution. In the example of a glucose analyzer, in which glucose oxidase catalyzes the oxidation of glucose, the computer receives PO, level data from the electrode and calculates the glucose concentration. The transient electrode signal, measured as the enzyme membrane is exposed to a solution of glucose, is least-square approximated by a third-degree polynomial whose slope at inflection point is characteristic of the external glucose concentration. A calibration procedure provides a cubic spline approximation of glucose concentration as a function of slope, thus enabling automatic measurement of samples. The computer performs the calculations, and actuates valves for air rinsing, introduction of the sample, and water rinsing.

INTRODUCTION

A major problem for the analysis and control of bioengineering systems is to significantly measure data, such as substrate concentrations. A computerized enzyme electrode offers a solution for measuring the concentration of substrate which is specifically consumed by the enzyme coated along the electrode. Immobilized enzyme systems and enzyme electrodes are described in ref. 1. For the realizations hereafter described we employ artificial enzyme membranes obtained by a method previously described.2 To be specific, we focus in the following on a gelatin membrane bearing a glucose oxidase activity, coating a p 0 2 electrode. Then we describe the behavior of substrate concentrations within the membrane and, in particular, how oxygen partial pres- sure along the electrode varies with time. We next show how this membrane is sequentially exposed to air, sample and water in each measurement cycle. Then we indicate the treatment of the corresponding electrode signal to ob- tain the slope at an inflection point. The calibration of the glucose electrode, leading to a cubic spline representation of concentration as a function of this slope, is also indicated. Following this, we depict the system configuration. This synthesized concentration sensor is used for measuring glucose samples as described in next-to-last section, which is followed by experimental results.

Biotechnology and Bioengineering, Vol. XXV, Pp. 845-855 (1983) 0 1983 John Wiley & Sons, Inc. CCC OOO6-3592/83/030845-11$02.10

846 KERNEVEZ, KONATE, AND ROMETTE

GLUCOSE OXIDASE MEMBRANE

The stoichiometric equation representing the reaction in a glucose oxidase enzyme membrane is:

glucose oxidase Glucose + O2 > gluconic acid + H202

The reaction rate is given by: 1

1+-

where S and A denote glucose and oxygen concentrations, Ks and KA are Mi- chaelis constants for each substrate, and V, is the maximal velocity. The partial differential equations governing glucose and oxygen concentrations inside the membrane are3

v = VM K S I K A

A S

as a2s at a x 2

+ v = o

aa a=a at a x 2

-a- + v = o -

forO<x < 1 and t > 0, where

1 1 x

1 + - + - S a

v = a

Here s = S/Ks and a = A/Ks are dimensionless concentrations of glucose and oxygen and the units of space and time are respectively the membrane thickness L and the characteristic time for diffusion:

e = L V D ~

where Ds is the glucose diffusion coefficient of the membrane. The dimensionless parameters a, A, and u are, respectively:

QL = DA/Ds

where DA is the oxygen diffusion coefficient of the membrane,

h = KA/Ks

and

a = e VM/Ks.

Equations (1) must be supplemented with initial and boundary conditions. For example,

s(x, O ) = O and a(x, O ) = a o for 0 < x < 1 (2)

SUBSTRATE DETERMINATION WITH AN ENZYME ELECTRODE 847

and

s(O,t)=y and a ( O , t ) = a b for t > O (3)

as da - ( 1 , t ) = - (1, t ) = 0. ax ax (4)

Herey denotes the glucose concentration in the surrounding bath, ab is the oxygen concentration at x = 0 within the membrane (different from oxygen concentration in the bath), and the no-flux conditions (4) express that the electrode is impervious to glucose and oxygen.

Equations (1)-(4) model a glucose oxidase membrane coated along an electrode and immersed inside a solution of glucose at concentrationy (Fig. 1). In eq. (2), a. represents the saturation value of oxygen inside the membrane after air rinsing. The first condition in eq. (2) means that the membrane is initially empty of glucose. But as soon as the membrane surface (x = 0) is exposed to a glucose solution, glucose diffuses into the membrane, where it is consumed, together with 02. Consequently, the O2 concentration decreases inside the membrane and particularly along the electrode. More precisely, the concentration profiles of glucose and oxygen evolve as indicated in Figures 2 and 3, where besides each profile we have indicated the corresponding time. Oxygen along the electrode evolves as shown in Figure 4, where the concentration a(1, t ) is plotted versus time t. The shape of this signal, with an inflection point, is important for its numerical treatment.

GLUCOSE ELECTRODE

In enzyme electrodes, an immobilized enzyme system is associated to an electrochemical sensor. This association was realized for the first time in 1962 by Clark and Lyons4 for glucose titration by using glucose oxidase immobilized between two cuprophane sheets. Their system was improved some years later

GLUCOSE SOLUTION

0

ACTIVE ENZYME

LAYER

PO2 SENSOR

- X

Fig. 1. Glucose oxidase membrane separates a pOz gas sensor from a well-stirred solution of glucose.


SPACE I

Fig. 2. Calculated glucose concentration profiles within the membrane 2.5 (dimensionless concentrations, abscissae, and times).

0 SPACE I

Fig. 2. Calculated glucose concentration profiles within the membrane 2.5 (dimensionless concentrations, abscissae, and times).

01 02

04

0 6

08

1

12

?A

16

18

2

24

28 32 -

0 1 SPm

attimesO.l,0.2, . . . ,

Fig. 3. Calculated oxygen concentration profiles within the membrane at times 0.1, 0.2, . . . , 3.2 (dimensionless boundary value is uh = 0.5).


T l f l E

Fig. 4. Plot of the calculated oxygen concentration a ( 1 , t ) as a function of time for eight different glucose concentrations in the sample.

by Updyke and Hicks5 who fixed together a film made of polyacrylamide gel bearing glucose activity and a p 0 2 differential measurement setup.

The sensor of the glucose electrode6 was a Clark electrode allowing an amperometric measurement of O2 concentration (Radiometer E 5046/0). The sensor was connected to a “p02 analyzer” (Radiometer PHM 71). The selective hydrophobic film used was a polypropylene membrane with a thickness of 6 pm (Bollore). In order to get good mechanical stability, the active film containing glucose oxidase was coated on the selective film by pouring 1 mL of a solution of enzyme and gelatin on 40 cm2 of the film. The polypropylene was pretreated with a 0.5% lauryl sulfate solution in phosphate buffer 0.05 mol/L, pH 7.5. The solution of protein was prepared from 240 bloom gelatin (from Bone-Rousselot) solubilized at 50 mg/mL and 50°C in distilled water. After solubilization, 10 IU/mL were added to the gelatin solution at 25°C. The solution spread on the polypropylene was dried at 25°C for 4 h and then immersed in 2.5% glutaraldehyde in 0.05 mol/L phosphate buffer, pH 7.5, for 2 min.

The sensor bearing the selective-active composite membrane was settled in a cell (Radiometer D 616 or magnetic cell) and exposed sequentially to air rinsing, to a sample containing glucose and to phosphate buffer rinsing (Fig. 5). Air rinsing has the effect of saturating the membrane with oxygen, exposing the membrane to a solution of glucose is modelled by conditions (1)-(4) and represented by the curves of Figures 2, 3, and 4. Finally, water rinsing removes the remaining glucose from the membrane. The electrode signal during such a cycle is as shown in Figure 5. Under software control, the air valve is opened


ELECTRODE

lrSt phase I 2nd phase 3rd phase lrst phase I

I I I

air rinsing sample liquid rinsing air rinsing I I b *

TIME

Fig. 5. (resp. 2, 3).

Observed electrode signal. The time schedule is 25 (resp. 20, 15) seconds for phase 1

until a plateau is attained for the electrode signal. Then it is shut and the sample valve opened. Within seconds after the admission of sample in the measurement cell, the electrode signal is sampled (approximately 30 measurements during 9 s , as shown in the circled points on the curve of Fig. 4). The third phase of the cycle is liquid rinsing which starts at a given time after the be- ginning of the measurements. After a given time, air rinsing resumes, and so on.

APPROXIMATION OF THE ELECTRODE SIGNAL BY A THIRD-ORDER POLYNOMIAL

After a sample has been introduced into the measurement cell, the dotted line electrode signal z ( t ) behaves as arc AB in Figure 4, and is well approximated by a third-order polynomial:

z ( t ) = a0 + alt + a2t2 + a3t3

The coefficients ao, a1, a2, and a3 are obtained by a least-squares method consisting in minimizing the function:

l M J(ao , al, a2, a 3 ) = - c ( z k - 010 - alk - a2k2 - a3k3)2

2 k = l

where z k is the measured value at time t = k ( k = 1, 2, . . . , M ) . The necessary conditions:

aJ/aai = 0, i = 0 , 1 , 2 , 3

can be written asAa = b, where a = [aoala2a3]t and the coefficientsq; ofA and bi of b are given by:


M M

u..= c k’+j and b i= c Z k k i (0 I i , j 5 3) lJ k = l k = l

This fourth-order symmetric linear system is easily solved by a direct method. Once the coefficients a; are obtained, the inflection point and the slope at this point are determined by Z” (t) = 0, whence:

t = -a2/(3a3) and z ’ ( t ) = cxI - a:/(3a3)

It is important to remark that, as numerical and experimental studies have shown, this slope only depends upon the sample (glucose) concentration.

CALIBRATION OF THE GLUCOSE ELECTRODE

Given (m + 1) samples with known glucose concentrationsyo, y l , . . . ,y,, we determined the corresponding slopes xo, xl, . . . , x,,, by the above procedure, thus obtaining a calibration curve as shown in Figure 6. This curve y = f ( x ) is well approximated by cubic spline functions, defined as follows7:

In interval [xi- x l ] , i = 1, 2, . . . , m, f ( x ) is given by the third-degree polynomial

f ( x ) = t y j + (1 - oyi-1 + hjt(1 - t)[(ki-l - d;) ( l - t ) - (kj - dj)t l ,

where

t = (x - X j - I ) / h j , h . 1 = x. 1 - x. 1 - 1 9

d; = (yi -y;-l)/hi,

GLUCOSE

CONCENTRAT I ON

Y i + I

X X 0 SLOPE x i x .

1+ I

Fig. 6. Calibration curve showing the one-to-one correspondence between slopes xi and glucose concentrations yi.


and ko, k l , . . . , k , satisfy the linear tridiagonal system of equations:

hi+lki-l + 2(hj + hi+,)kj + hikj+l) = 3(hidi+l f hi+ldi)

(i = 1, 2, - . . , rn - 1)

and the two additional conditions:

2ko + kl = 3dl and k, - l + 2k, = 3d,-

SYSTEM CONFIGURATION

An Apple I1 Plus Computer system was applied to the automation of enzyme electrode. The system is comprised of an Apple I1 microcomputer (Apple Computer, Inc., Cupertino, CA) with 48K of main memory. The internal peripheral bus of the computer enables addition of the variety of peripheral units. We have added a disk-controller card and parallel interface cards (Apple Computer, Inc.) for the printer and the interface card cage. The interface card cage (U.T.C. Electronic Department, Compiegne, France) is mounted to the computer through a ribbon cable and contains circuit boards for signal con- ditioning and buffering, an analog-to-digital card based upon the DATEL ADC EK 12 B, a pOz analyzer and a 4-bit logical system. A schematic block diagram of the computer-interfaced system is given in Figure 7.

Fig. 7. (a) Computer-interfaced enzyme electrode analysis system and (b) enzyme electrode instrumentation block.

SUBSTRATE DETERMINATION WITH AN ENZYME ELECTRODE

I I I I I I I A I I I

I I I I I

853

Fig. 7 . (continued from previous page)

A SYNTHESIZED CONCENTRATION SENSOR

The Apple I1 was programmed in BASIC, and a routine written in 6502 ma- chine language used to read the inputs from the electrode and actuate the valves. This routine is invoked from the BASIC interpreter. The BASIC pro- gram first initiates a calibration procedure, resulting in a calibration curve, then enters into a measurement phase. For each sample, the slope is computed and used to compute glucose concentration. The results demonstrate that the accuracy is typically better than 1 TO. Sixty analyses per hour are possible in routine work with the same accuracy. The system can be recalibrated at will for selected standard.

EXPERIMENTAL RESULTS: APPLICATIONS TO THE MEASUREMENT OF DIFFERENT PARAMETERS

The glucose sensor based upon the amperometric measurement of oxygen consumed by immobilized glucose oxidase is successfully and widely used in measuring glucose in very small samples (50 p L ) of whole blood or industrial broths. The glucose electrode owes its success to lack of interference from other electroactive species in whole blood and to the high specificity of the immobilized enzyme. The enzyme support have permitted to solve the delicate problem of the variability of the oxygen content of the sample. The glucose sensor represents a good model for the use of oxidase enzyme. It has permitted to extend this technique to the determination of other parameters using oxidase enzyme as active elements such as choline, L-lysine, L-amino acids,

854

PO,

KERNEVEZ, KONATE, AND ROMETTE

I I I I

1 2 3 4

I I , _ . 0 3 0 6 0 9 0

TI111 ( s e c o n d s )

Fig. 8. Typical response of the glucose sensor.

uric acid, etc. It is also used with immobilized invertase and mutarotase in the measurement of saccharose, or with immobilized lactase in the measurement of lactose.

Typical response for a glucose concentration (1 g/L) is given by Figure 8. A calibration curve is shown in Figure 9 for the glucose determination. The stability of the signal has been tested: Results are given for an enzyme membrane stored between each measurement in buffer at 5°C. This study has been also performed successfully in dry conditions during a one-year period.

15

5 w D. 0 -1

v)

0 1 2 3 4

GLUCOSE G/L

Fig. 9. Calibration curve of the glucose sensor: ( 0 ) 2 days, (0) 6 days.


References

1. I. Chibata, Immobilized Enzymes, Research and Development (Wiley, New York, 1978). 2. G. Broun, D. Thomas, G. Gellf, D. Domurado, A. M. Berjonneau, and C. Guillon, Bio-

3. J . P. Kernevez, Enzyme Mathematics (North Holland, Amsterdam, 1980). 4. L. C. Clark and C. Lyons, Ann.' NYAcad. Sci., 102,29 (1962). 5. J . W. Updyke and J. P. Hicks, (1967) Nature, 214,986 (1967). 6. J. L. Romette, B. Froment, and D. Thomas, Clin. Chem. Acta, 95, 249 (1979). 7. G. Dahlquist and A., B$rck, NumbericalMethodr (Prentice Hall, Englewood Cliffs, NJ, 1974). 8. N. D. Tran, J. L. Romette, and D. Thomas, Biotechnol. Bioeng., 25,329 (1983).

technol. Bioeng.. 15, 359 (1973).

Accepted for Publication September 7, 1982

determination of substrate concentrations by a computerized enzyme electrode

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