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ANALYTICAL CHEMISTRY, VOL. 5 1 . NO. 1, JANUARY 1 9 7 9
LITERATURE CITED
(10) P. R. Coulet, C. Godinot, and D. C. Gautheron, Biochim. Biophys. Acta, 391, 272 (1975). (1 1) J. M. Engasser, P. R. Coulet, and D. C. Gautheron. J. Bioi. Chem., 252, 7919 (1977). (12) J. M. Brillouet, P. R . Coulet, and D. C. Gautheron, Biotechnol. Bioeng., 16, 1821 (1976). (13) J. M. Brillouet, P. R. Coulet, and D. C. Gautheron, Biotechnol. Bioeng., 19, 125 (1977).
(1) G. G. Guilbault, in "Immobilized Enzymes, Antigens, Antibodies and Peptides"; H. H. Weetali, Ed., M. Dekker New York. 1975, p 293. (21 , . K . Camman. in "Das Arbeiten mit Ionenselectiven Electroden". Sorinaer Veriag, New York, 1977, and Fresenius Z.Anal. Chem., 287, 1 {19?7), (3) L. C. Clark and C. Lyons, Ann. N .Y Acad. Sci., 102, 29 (1962). (4) G. G. Guilbault and G. J. Lubrano, Anal. Chim. Acta, 64, 439 (1973). (5) D. R. ThBvenot, P. R. Coulet, R. Sternberg, and D. C. Gautheron, in "Enzyme Engineering" Vol. 4 , Plenum, New York. 1978, p 219. (6) D. R . Thevenot, P. R . Coulet, R . Sternbera. and D. C. Gautheron, Bioelectrochem. Bioenerg., 5, 541 (1978) (7) P. R. Coulet, J. H. Julliard, and D. C. Gautheron, French patent (ANVAR) 73-23-283, publ. number 2.235, 133 (1973). (8) P. R . Couiet. J. H. Julliard, and D. C. Gautheron, Biotechnol. Bioeng., 16, 1055 (1974). (9) T. E. Barman, in "Enzyme Handbook", VOI. 1 Springer-verlag, New York, 1969, p 112.
RECEIVED for review July 25, 1978. Accepted October 11, 1978. This investigation was supported in part by "Dglggation GBngrale la Recherche Scientifique e t Technique" Grant 76.7.0920.
Potentiometric Enzyme Electrode for Lactate Toshio Shinbo"' and Masaaki Sugiura National Chemical Laboratory for Industry, Hiratsuka Branch, Hiratsuka, Japan
Naoki Kamo Faculty of Pharmaceutical Sciences, Hokkaido University, Sapporo, Japan
A potentiometric enzyme electrode for lactate is developed. The enzyme electrode is constructed by coating the sensor membrane of the redox electrode with a film of enzyme-gelatin gel layer. The enzyme used is lactate dehydrogenase which catalyzes the oxidation of lactate by ferricyanide. The change in the concentration ratio of ferricyanide to ferrocyanide is monitored by the redox electrode which is a membrane electrode sensitive to redox potential of the solution. A plot of the potential of enzyme electrode vs. !og [lactate] gives an S-shaped curve which depends on enzyme quantity and ferricyanide concentration. A relation between the enzyme electrode poteniial and substrate concentration is derived semitheoretically. The equation explains the results successfully.
Enzymes have been used widely in the field of analytical chemistry owing to their substrate specificity ( I ) . The enzyme electrode, one of many useful analytic a1 devices. is a n electrochemical sensor made by combination of a n enzyme reaction with an electrode. T h e enzymc electrode enables us t o determine the concentration of a specific organic species continuously and easily. Many enzymc electrodes have been reported in the past decade. which are classified in two groups; (1) T h e change in concentration of a charged substance produced by a n enzyme reaction is measured potentiometrically with use of the ion-selective electrode (2-6). (2) T h e amount of current caused by oxidation or reduction of a product or a reactant of t h e reaction is measured polarographically ( 7 -13). For enzymes catalvzing t h e oxidationreduction reaction. the polarographic method has mainly been employed (7-13). In t h e present paper. we report a new potentiometric enzyme electrode with use of t h e eii7yme catalyzing the I Present address, National Chemical I aboratory for Industry. Hiratsuka Branch. 1-3-4 Nishiyawata. Hira rqukashi, Kanagawaken, .Japan.
0003
'00/79~0351-0100$01O O / G
oxidation-reduction reaction. For monitoring t h e progress of such reactions, a new membrane electrode sensitive to redox potential (redox electrode) was developed. T h e sensoimembrane of the redox electrode is a plasticized poly(vinylchloride) membrane containing dibutylferrocene (PVC-Fc membrane). It responds to the redox potential of the solution. T h e enzyme electrode was constructed by coating the sensor membrane of the redox electrode with a film of enzymegelatin gel. T h e enzyme used is lactate dehydrogenase (cytochrome b2, EC 1.1.2.3) which catalyzes the oxidation of lactate in the presence of a n electron acceptor such as ferricyanide;
pyruvate
+ 2Fe(CN):-
+ 2H+
T h e change in t h e concentration ratio of ferricyanide to ferrocyanide in the enzyme gel layer caused by t h e enzyme reaction is detected by t h e redox electrode.. T h e equation relating the potential of the enzyme electrode t o the substrate concentration is derived semitheoretically and it explains the results obtained successfully.
EXPERIMENTAL Materials. Lactate dehydrogenase (cytochrome bp,EC 1.1.2.3; prepared from yeast) and catalase (EC 1.11.1.6) were purchased from Sigma Chemical Co. L-Lactate was purchased from Sigma Chemical Co. and used after neutralization with NaOH. Dibutylferrocene and dioctylphthalate were obtained from Tokyo Kasei Co. (Tokyo, Japan). Gelatin was obtained from Nippi Co. (Tokyo, Japan) and purified by electrodialysis a t room temperature for 30 h. Preparation of PVC-Fc Membrane a n d Redox Electrode. In 10 mL of tetrahydrofuran (THF) were dissolved 250 mg of poly(vinylch1oride) (PVC),500 mg of dioctylphthalate (DOP),and 300 mg of dibutylferrocene (Fc). This solution was poured into a Petri dish (60 cm2 in area) and evaporated slowly a t room temperature to form a thin membrane (0.14.15 mm in thickness). A piece of the PVC-Fc membrane was peeled off and glued to a PVC tube with THF. An AglAgC1 electrode was used as the inner reference electrode which consisted of a silver wire mounted in a glass pipet filled with an agar gel containing 3 M KCI. The CC 1978 American Chemical Society
ANALYTICAL CHEMISTRY, VOL. 51, NO. 1, JANUARY 1979
101
O t I
> E-50W
(a:
(b)
Figure 1. Construction of electrodes. (a) redox electrode, (b) lactate
-loor
enzyme electrode. A, Ag/AgCI electrode, B, Agar gel containing 3 M KCI, C, PVC tube, D,redox compound solution, E, PVC-Fc membrane, F, rubber ring, G, dialysis membrane, H, enzyme-gelatin gel layer
inner reference solution consisted of 50 mM ferricyanide and 50 mM ferrocyanide. The redox electrode is schematically illustrated in Figure l(a). Construction of Lactate Enzyme Electrode. An appropriate amount of lactate dehydrogenase and a small quantity of catalase were dissolved in 0.1 M phosphate buffer solution (pH 6.0) containing 0.1 mM EDTA, 0.1 mM MgSO,, and varying concentrations of K,Fe(CN), and K,Fe(CN)6. The concentration ratio of ferricyanide to ferrocyanide was kept constant a t 4:l (The reason is described in "Results".). This buffer solution was denoted by Fi-Fo solution, hereafter. To the enzyme solution. an equal volume of the Fi-Fo solution containing 5% gelatin was added and mixed. On the PVC-Fc membrane (0.25 cm2) of the redox electrode, 10 pL of the enzyme- gelatin mixture was placed dropwise and spread uniformly. After the mixture was gelated a t 4 "C for 10 min, it was secured in place with a dialysis membrane and a rubber ring (see Figure l(b)). Enzyme Activity Measurement. The activity of lactate dehydrogenase was estimated by the initial rate of reduction of ferricyanide which was determined spectrophotometrically at 420 nm at 25 "C (14). Except for experiments on determination of the optimum p H of activity, the reaction mixture contained 0.1 M Tris-C1 (pH 8.0), 0.1 mM EDTA, 0.1 mM MgSO,, 0.02 M L-lactate and 0.4 mM K,Fe(CN),. The reaction was initiated by addition of a small quantity of the enzyme. The buffers used for determination of optimum pH were 0.1 M Tris-C1 (pH 9.0-5.51, 0.1 M sodium phosphate (pH 7.5-6.01, and 0.1 M sodium acetate (pH 5.5-4.5). The stability of the enzyme at varying pH mas determined as the usual procedure. After the enzyme was incubated in an appropriate buffer for 2 h a t 25 " C under the aerobical condition, the residual activity was measured as described above. The quantity of the enzyme entrapped in gelatin gel was expressed in "units". One unit is defined as the amount of the enzyme which catalyzes reduction of 1 pmol of ferricyanide in 1 min a t 25 "C in the solution containing 0.1 M Tris-C1 (pH 8.01, 0.1 mM EDTA, 0.1 mM MgSO,, 0.02 M L-lactate and 0.4 mM K,Fe(CNI6. Potentiometric Measurements of the Redox Electrode and t h e Lactate Enzyme Electrode. The potential difference between the redox electrode and a reference electrode (Type N o 201 OA-05T, Hitachi-Horiba, Tokyo. Japan) was measured at 25 "C with a vihrating reed electrometer (Model TR-8434, Takeda Riken. Tokyo, Japan) connected to a pen-writing recorder. The same apparatus was used for the lactate enzyme electrode. The enzyme electrode was immersed in 10 mL of Fi-Fo solution and the st,eady potential ( E )was recorded. The solution was stirred magnetically and maintained at 20 "C. When an aliquot of lactate solution was pipetted into the solution, the potential changed in negative direction and reached a steady value ( E7 . The magnitude (absolute value) of the potential change, i.e. (E E'I, is denoted by AE. hereafter. The enzyme electrode was stored in Fi-Fo snlrition a t 4 "C. ~
RESULTS Redox Electrode. When two solutions of different redox potential were separated hy t h e PVC-Fc membrane, t h e magnitude of the membrane potential generated depended
-'5f
,
-2
-J
-1 0 1 2 Log ([Fwricyonide]/I:Frrrocyonide!:
Figure 2. Plots of the potential of redox electrode vs. log ([ferricyanide] / [ferrocyanide]) for various total concentrations of ferricyanide and ferrocyanide. The total concentration of ferricyanide and ferrocyanide is, 0 , 100 mM, A , 20 mM, 0 , 2 mM, 0, 0.4 mM
on the redox potential difference across the membrane. In Figure 2, the potential of the redox electrode is plotted vs. log ([ferricyanide]/[ferrocyanide]). For the data points of the respective lines, t h e total concentration of ferricyanide and ferrocyanide was kept constant. The plots in Figure 2 gave a straight line with a slope of 52 niV per decade of [ferricyanide]/ [ferrocyanide] a t least in the range of [ferricyanide] / [ferrocyanide] between 0.01 and 4. T h e electrode must be used in this region. Therefore, the concentration ratio of ferricyanide to ferrocyanide in Fi-Fo solution was chosen as 4, because the enzyme reaction decreased this ratio. In the linear region, the electrode potential, E , can he expressed as:
E=Eo+
52 log ([ferricyanide] / [ferrocyanide]) (in mV)
As the total concentration of ferricyanide and ferrocyanide in a test solution increased, E" became larger in the positive direction. E" also depended on the concentrations of electrolytes present in the test solution. T h e influence of pH on E" was investigated by changing the pH of the solution . 0.2 m h l containing 0.1 M KCI, 0.2 m M K , 3 F e ( C N Rand K,Fe(CN),. T h e pH of the solution was adjusted hy adding HC1 or NaOH. KC1 was added t o eliminate t h e effect of change in ion concentration of E". T h e pH of the solution had almost no effect on E" except at low p H (less than 4 ) . Lactate E n z y m e Electrode. Tt is reported that at constant lactate concentration the rate of rediiction of ferricyanide catalyzed by lactate dehydrogenase is nearly independent of acceptor concentration down to ahout 0.1 mM. Le., the reaction is of zeroth order with respect to acceptor concentration (1.5, 16). We obtained t h e same results. T h e optimum p H was found to he 8. This value was essentially the same as that reported by previous investigators (1.5). L,actate dehydrogenase, however, was unstable at optimum p H under the aerobical condition and it lost ahout 30%' of' its activity in 2 h at 25 "C. In contrast. the enzyme retained almost all activit,y within 2 h at pH 6.0. Further storage a t p H 6.0 led to a decrease in activity. hut addition of a small quantity of catalase diminished inactivation of t h e enzyme. Taking these ohservations into account. lactate dehydrogenase was always used together with a small quantity of catalase and the pH of the enzyme gel was maintained at, 6.0. Figure 3(a) and (h) show plots of potential change of enzyme vs. concentration of lactate in logarithmic scale electrode (2) for various Fi-Fo solutions. Addition of lactate to Fi-Fo solution into which the enzyme electrode was immersed shifted
102
ANALYTICAL CHEMISTRY, VOL. 51, NO. 1, JANUARY 1979
r-
1
a1
I
75t
W
a
t I
25t
-2
-1
-3
-L
.cq (Lacrate M 1
L -1
8
-2
-3 Log !Lactate hd
-4
-
-3
;
751
25.
01 -1
-2 -3 Log (Lactate M
-4
Figure 3. Plots of the enzyme electrode potential ( L E )vs log [lactate] for various Fi-Fo solutions. Addition of varying concentration of lactate to Fi-Fo solution led to the decrease in the enzyme electrode potential The absolute value of this potential change was denoted by LE(detai1s in text). (a) Enzyme quantity is 0.006 unit. Ferricyanide concentration in Fi-Fo solution is: 0, 20 rnM, A, 10 rnM, 0 ,2 mM, A, 0.8 mM, 0 , 0.32 mM. (b) Enzyme quanti?, IS 0.016 unit. Ferricyanide concentration in Fi-Fo solution is: 0, 20 mM, A , 15 mM, 0, 10 mM, A ,5 mM, 0 , 2 rnM
the electrode potential in the negative direction. This potential change indicates the decrease in the value of log ([ferricyanide] /[ferrocyanide]) due to the enzyme reaction, because the redox electrode did not respond to lactate or pyruvate in the range less than 10-1 M. The steady potential was found in 20-30 min after pipetting lactate. As described above, the absolute value of the potential deflection was denoted by AE. Plots of 1E vs. log [lactate] give an S-shaped curve, as shown in Figure 3, to which theoretical consideration is made in "Discussion". When ferricyanide concentration in Fi-Fo solution was increased under the condition t h a t the enzyme quantity was kept constant, AE became smaller a t a given substrate concentration. Higher enzyme activities resulted in steeper slopes. Figure 4 shows the dependence of A E on t h e quantity of the enzyme.
DISCUSSION Redox Electrode. Hinkle (17) has reported that addition of dibutylferrocene to the phospholipid membrane which separates oxidizing and reducing solutions generates membrane potential. Figure 2 reveals that the plasticized PVC membrane containing dibutylferrocene also generates the membrane potential corresponding to the difference of the redox potential. T h e mechanism of generation of membrane
Figure 4. Dependence of the enzyme electrode potential ( A € ) on enzyme quantity. The ordinate has the same meaning as in Figure 3. The concentration of ferricyanide in Fi-Fo solution is 20 mM. Enzyme quantity is: 0, 0.031 unit, A , 0.016 unit, 0, 0.006 unit
potential in this system can be explained as follows. At the interface between the reducing solution (R phase) and the membrane (M phase), Fc is reduced to a neutral form, FC(,,d), while a t the interface between the oxidizing solution (0phase) and M phase, Fc is oxidized to a cation, Fe+(oxl.If it is assumed t h a t the PVC-Fc membrane is permeable predominantly to FC[,,d) and Fc+(,,), the accumulation of positive and negative charges is caused in R and 0 phases due to the redox reaction, respectively. The accumulation of charges supresses the redox reaction a t interfaces and apparent equilibrium is attained. The membrane potential in this stage is approximately equal to the redox potential difference between both sides of the membrane. As shown in Figure 2, the slope in the linear portion was 52 mV per decade of [ferricyanide] / [ferrocyanide] which was a little smaller than a Nernstian value of 59 mV. The reason for the deviation from the ideal value is not clear a t present, b u t the most possible explanation is t h a t the membrane leaks inorganic ions slightly other than Fc+[,,). This leakage of the membrane may also explain the result that the value of Eo was affected by the presence of electrolytes. On this aspect, we are now performing further experiments. Lactate Enzyme Electrode. The change in the potential of the lactate enzyme electrode is due to the change in the value of [ferricyanide]/ [ferrocyanide] in the enzyme gel layer. When the electrode is immersed in a substrate solution, the fluxes of substrate, acceptor, and products are caused by diffusion and by the enzyme-catalyzed reaction. Then, the following equations are set up in accordance with the mass-conservation law;
dS,"/dt =
U,
+ PL(S,
-
SIm)
(i = 1,2, 3)
(I)
where S,", a,,P,and S,stand for the concentration of i in the enzyme gel layer, the production of i due t o the enzyme reaction, the permeability coefficient of i in the dialysis-gelatin membrane and the concentration of i in the bulk solution, respectively. Subscripts 1, 2, and 3 represent lactate (substrate), ferricyanide (acceptor), and ferrocyanide (product), respectively. This set of equations is solved under the following assumptions ( 4 ) : (1) T h e enzyme reaction obeys Michaelis-Menten kinetics. (2) T h e rate of the enzyme reaction is independent of ferricyanide concentration as described above and the presence of ferrocyanide does not affect the reaction rate. (3) The concentrations of substrate, acceptor and products in the bulk solution are kept constant. According to the above assumptions and the stoichiometry of the reaction, u, is expressed as follows: a1 = -VS1"/(K
a3
+ Slm)
(24
= 2a1 = -2VS,"/(K
+ SI")
(2b)
= -2a1 = 2VS,rn/(K
+ Slm)
(2c)
ANALYTICAL CHEMISTRY, VOL. 51, NO. 1, JANUARY 1979
103
Substituting Equation 10 into Equations 8 and 9, we obtain
.
szm
I
=
sz
2(V/K)PlSl P2[P1+ ( V / K ) I
-
~
(11)
73i Next, we consider the case where SI>> K , Equations 3, 4, and 5 are approximated as follows:
-- i50! W 4
1
-v + PI(s1- SIrn) = 0 -2v + P& S;!m) = 0 2v + P,(S, Sp)= 0
4 0
(14)
-
I -I
(13)
(15)
-
-2
-3
-4
From Equations 14 and 15, we obtain
-5
Log [Lac:ate, N )
(16)
T h e electrode potential in the absence of lactate is given as Equation 18;
E = E"
+ 52 log ( S 2 / S 3 )
(18)
When lactate is present in the bulk solution, the electrode potential is given as
'
251-
0
E ' = E"
E' = RO -2
-3
(19)
Then we obtain the following equations with use of Equations 11, 12, 16, 17, and 19
I -1
+ 52 log (Sgm/Sgm)
+
-4
Log ( Lactate M )
Figure 5. Calculated curves and experimental points for the response of the enzyme electrode. Solid lines represent values calculated from Equations 24 and 25 (a) As the values of cy and 3, CY = 1.0 and p = 2.5 are used. Experimental points are the same as in Figure 3(a). (b) cy = 2.0 and p = 6.4 are used. Experimental points are the same as in Figure 3(b)
and
sz
where V and K are the maximum rate and Michaelis constant, respectively. Substitution of Equation 2 into Equation 1 yields Equations 3, 4, and 5:
dSl"/dt = - V S l m / ( K + S I m ) dS,"/dt dS,"/dt
+ Pl(S1 - SI") = - 2 V S l m / ( K + Si") + P2(S, S2"') = 2VSI"/(K + SI") + PS(S3 S g m ) -
-
(3)
s 3
equations with use of Equation 6
- S3m)
(21)
and
1E = 5 2
=0
(7)
=0
(8)
=0
(9)
Equation 7 is recast to give
(10)
log S2(s3+ S,(SZ -
B)
(S,>> K )
(23)
where
CY
- S2m)
(SI>> K )
Therefore, 1E ( = [ E - E l ) is expressed as follows;
K , Equations 3, 4,and 5 are reduced to the following set of - Slm)
-
(5)
(i = 1, 2 , 3 ) (6) We consider the two cases where S1 > K . First, for the case where S,is dilute compared with K , i.e., S1
