J. Chem. SOC. Faraday Trans I 1986,82 1033-1050 Electrochemical Sensors Theory and Experiment W. J. Albery," P. N. Bartlett,? A. E. G. Cass D. H. Craston and B. G. D. Haggett Department of Chemistry and Centre for Biotechnology Imperial College of Science and Technology South Kensington London S W7 2A Y A comparison is made of potentiometric and amperometric sensors. For amperometric sensors there are advantages in using the wall-jet system with ring-disc or packed-bed electrodes. Particular applications to the determi- nation of proteins root death total iron and the concentration of NO; are described. Enzyme electrodes using organic salts are capable of the direct oxidation of the enzyme itself. A theoretical description is presented. Experiments with glucose oxidase show that the transport of glucose through the membrane is the rate-limiting step.By contrast with a sensor for choline using choline oxidase we find that the transport of substrate through the membrane and the unsaturated enzyme kinetics are each partially rate- limiting. Electrodes made of conducting organic salts also oxidise NADH. For an ethanol sensor using ethanol dehydrogenase we find that the rate-limiting steps are those involving homogeneous enzyme kinetics. There are two main methods for constructing electrochemical sensors potentiometry and amperometry. In the first local equilibrium is set up at the sensor interface and the electrode or membrane potential is measured. In the second the electrode potential is used to drive an electrode reaction and the current resulting from that reaction is measured.The features of these two alternative approaches are compared in table 1. Potentiometric sensors require rapid electrode kinetics while with amperometric sensors sluggish electrochemical reactions can be switched on by the electrode potential ; typically the electrochemical rate constant increases by a power of 10 for every 120 mV increase in electrode potential. Potentiometric sensors whether they are the classical ion-selective electrodes or integrated devices such as ISFETs and CHEMFETs suffer from another disadvantage. The potentiometric signal can be corrupted by mV of noise. Percentage errors are summarised in table 2. On the other hand because there is no net consumption of analyte a potentiometric sensor does not perturb the analyte concentration; mass transport is unimportant.This is not true for the amperometric sensor where if the mass transport is not controlled then the current i will be given by the general form of the Albery equation i = f[N L(dUGC/dt)] where N is the number of windows open in the laboratory L is the number of lorries (trucks) passing outside and dUGC/dt is a complicated periodic function describing the visitations of the University Grants Committee. Controlled Hydrodynamic Voltammetry One way of avoiding the complexities of solving the Albery equation is to use an electrode with controlled hydrodynamics. The most widely used electrode of this type is the rotating-disc electrode. While this electrode is convenient for the investigation of f- Now at the Department of Chemistry and Molecular Sciences University of Warwick Coventry CV4 7AL.35-2 1033 1034 Electrochemical Sensors Theory and Experiment Table 1. Comparison of potentiometric and amperometric sensors method of operation electrode kinetics response mass transport sensitivity Table 2. Errors in concentration for potentiometric sensors AE/mV error (%) n = l ca. amperometric po ten tiome tric measure potential a t i = O must be fast measure transport- limited current electrode potential can drive reaction c is linear function of current giving c is exponential function of EF/RT giving good dynamic range but making c sensitive to errors in measurement of E normal dynamic range and normal response to errors in measure- ment of i must be controlled unimportant mol dm-3 mol dm-3 ca.2 5 electrode mechanism it is not so suitable for application to flow-through sensors. ChanneP3 or wall-jet electrode^^-^ are to be preferred. The wall-jet system is superior to the channel electrode for the following two reasons. First a higher percentage of the analyte reaches the electrode (ca. 7% compared with ca. 0.5% ). Secondly there is a smaller dead space since there is no need for a lead-in length to establish the correct hydrodynamics. A further advantage is that a packed-bed electrode can be easily inserted just upstream of the jet to give a double electrode system.The wall-jet system is illustrated in fig. 1. In some applications it is desirable to have a double electrode system. The central disc electrode is surrounded by a concentric ring electrode to make a ring-disc electrode. The rotating ring-disc has been developed over a number of years. Recently we have ShownlO that by simple transformations involving the geometry of the electrode the theory developed for the rotating system9 may be extended to the channel and wall-jet regimes. The collection efficiency and titration curves depend on two geometric parameters a and B which in their turn depend on the radii of the ring-disc electrode i t . rl the radius of the disc rz the inner radius of the ring and r3 the outer radius of the ring. Definitions of a and /3 in terms of the three radii for the three different hydrodynamic regimes are collected in table 3.40 n = 2 AE/mV error (%) 7 19 2 5 10 10 9 3 19 1035 Ag/AgCI reference elect rod e P (r3/r2I3 - (r2/r1I3 W. J. Albery et al. Fig. 1. A wall-jet electrode. The inset shows the flow pattern. Table 3. Definitions of the ring-disc geometric parameters a and P a @2/rA3 - 1 (r2/r1)9/8 - 1 rotating ring-disc wall-jet ring-disc double channela (r3/r1)gls - (r2/r,)9/s (12 /wl ('3/'2)-('2/'1) a In this case measuring from the upstream edge of the upstream electrode the gap lies between 1 and 1 and the downstream edge of the collecting electrode is at 13. Bromine Microtitrations We have shownll l2 that the wall-jet ring-disc electrode may be used to determine the concentrations of proteins by microtitration with bromine.The detector is designed to be used with an h.p.1.c. column where the column is being used to separate a mixture of proteins. We have found that a typical protein molecule P will react rapidly with several hundred molecules of bromine upstream disc electrode 2Br- + Br + 2e solution P + nBr + PBr, downstream ring electrode Br + 2e + 2Br-. The unreacted bromine is measured on the ring electrode. Fig. 2 shows the response of the ring current to increase bromine generation on the disc. The insets show the concentration patterns in the vicinity of the ring-disc electrode. The displacement of the titration curve to higher disc currents is proportional to the concentration of protein in the solution.Typical results for cytochrome c are shown in fig. 3. We have shown that 1036 0 Electrochemical Sensors Theory and Experiment Fig. 2. Ring current us. disc current curves for a bromine microtitration. The insets show the bromine zone spreading from the disc electrode. The displacement of the curve from the collection efficiency line observed in the absence of protein is proportional to the concentration of protein P. 8 12 i&A Fig. 3. Typical titration curves obtained after the addition of successive aliquots of cytochrome c. many proteins can be determined in this way.12 Furthermore by carrying out the titration at different pH one can obtain information that is characteristic of the particular protein.Another application of the bromine titration technique arises in the monitoring of nutrient solutions used to grow crops such as tomatoes by hydroponics. Here if root death occurs there is a release of organic material into the nutrient film that is flowing over the roots of the plants. This release can be measured as an increased consumption of bromine. Typical results for the murder of a busy lizzy plant are shown in fig. 4. 13.5 Fig. 4. Titration curves obtained during the demise of a busy lizzy. iD/CtA 180 5 4 9.0 ’% 4.5 solution in - Besides wishing to have an early indication of root death it is desirable for the horticulturalist to be able to monitor the principle nutrients in the nutrient film.An important trace element is iron which is present as the EDTA complexes of both FeII and FeIII. Using the packed-bed wall-jet electrode shown in fig. 5 where the packed Packed-bed Wall-Jet Electrodes W. J. Albery et al. 1037 135 315 225 solution out t packed bed counter compartment 270 counter electrode wall j e t disc electrode c 2 I ( Ag /Ag CI Fig. 5. The packed-bed wall-jet electrode (PBWJE). 1038 12 10 2 ’ 8 1 6 4 2 Electrochemical Sensors Theory and Experiment 0’ 0’ 8 1.5 6 0 4 6 2 4 2 Fig. 6. Typical results for the determination of total iron in hydroponic solutions using a PBWJE. 0.5 [ Fe] /mmol dm-3 5 0’ @/ 1.0 15 10 [ NO;]/mmol dm-3 0 Fig.7. Typical results for the amperometric determination of NO; using a PBWJE. bed is made of reticulated vitreous carbon we can reduce all the FeIII to FeII on the packed bed and then use the wall-jet electrode to determine the total iron in the s01ution.l~ Typical results are shown in fig. 6 . The most important nutrient is NO;. Pletcher and Poorabedi14 have shown that NO; can be determined amperometrically on a copper electrode. We have found that good limiting currents can be measured on a fresh copper electrode but that after several minutes the electrode is poisoned. This problem can be overcome15 by using a packed bed of copper chips and a platinum wall-jet electrode. A fresh copper disc is plated from W. J . Albery et al. 1039 Cu2+ generated on the bed electrode.The concentration of NO; is measured from the current on the fresh copper electrode. The copper is stripped off the wall-jet electrode and the cycle is then repeated. Typical results are shown in fig. 7. This method of renewing the surfacq of a solid electrode whenever it is required confers on solid-state electrochemistry the singular advantage so long enjoyed by mercury-drop polarography. Me TCNQ NMP’ Enzyme Electrodes Greater selectivity for compounds of biochemical interest can be obtained by using an enzyme to recognise the target species. An enzyme electrode is usually an amperometric sensor where the rate OF an enzyme-catalysed reaction is measured electrochemically. Many enzymes involved in oxidation and reduction reactions contain redox groups such as iron copper or quinone centres.However these centres are surrounded by a coat of protein and this coat prevents efficient electron transfer to ordinary electrodes. For this reason the first generation of enzyme electrodes used electrochemistry to detect the product of the natural enzyme reaction. The classic example is the glucose sensor using glucose oxidase. The reaction scheme is as follows solution glucose + FAD -+ gluconolactone + FADH FADH + 0 -+ FAD + H,O electrode H,O + 0 + 2H+ + 2e. The device is a fairly complicated one with two membranes one to keep the enzyme in place and one to protect the electrode from being poisoned by the enzyme. Since 0 is involved in the reaction scheme the response of the system is sensitive to the ambient 0 concentration.These disadvantages can be overcome by eliminating the 0 reaction and using instead an electron-transfer mediator. These second-generation enzyme electrodes have been developed for instance by Hill and Higgins.16-18 In their glucose oxidase electrode they use ferrocene/ferrocinium [Fe(Cp),/Fe(Cp)l] as a mediator solution glucose + FAD -+ gluconolactone + FADH FADH + 2Fe(Cp)i + FAD + 2Fe(Cp) + 2H+ electrode 2Fe(Cp) -+ 2Fe(Cp)i + 2e. Our own work has been concerned with the development of third-generation devices in which the enzyme reacts directly on the electrode itself. We have found that conducting organic salts like NMP+TCNQ- (1) are particularly good electrode materials for the direct transfer of electrons to and from enzymes.Similar conclusions have been reached by Kulys et al.199,0 The reaction scheme is as simple as it can be NC Ncm: solution glucose + FAD -+ gluconolactone + FADH NMP+TCNQ- electrode FADH -+ FAD + 2H+ + 2e. Many of these materials were first prepared by Melby21 and their electrochemistry has been investigated by Jaeger and Bard.22’ 23 We have presented elsewhere a general theory for this type of unmediated enzyme electr~de,,~ and we will now summarise the main conclusions of our theoretical approach. Electrochemical Sensors Theory and Experiment 2e 1 Fig. 8. The enzyme electrode. P (p-1 external m ediu m 1040 and also constants25 and kk where The Model Fig. 8 illustrates the enzyme electrode and the kinetic scheme.As regards the enzyme kinetics we assume the following model for a one substrate - one product enzyme which converts substrate S into product P and which in the course of this conversion is itself converted from E into E’ k k-2 k-1 S+E @ ES f k E’P e E’+P. For each step in the above scheme we write K = k,/k- KTD = Kl K2 K3 where KTD describes the overall equilibrium between S + E and P + E’. The transport of S and P through the membrane is described by the mass-transfer rate X is either S or P Dx is the diffusion coefficient and Kx the,partition coefficient of X in the membrane and LM is the thickness of the membrane. The electrode reaction described by k is assumed to be irreversible. All the primed rate constants are heterogeneous rate constants usually measured in cm s-l.Lower-case letters are used to denote the concentrations of the different species and for S and P the subscripts GO and 0 refer to the concentrations outside and inside the membrane respectively. We assume that the electrolyte layer behind the membrane is so thin (approximately a few pm) that there is no concentration polarisation in this layer. k3 k-3 1041 W. J. Albery et al. 1 I # ' I # 3 $ 1 I- f 2 E'+P 3 - - - - IG E+S - - Fig. 9. Schematic free-energy profile illustrating the free-energy differences associated with each of the 10 possible rate-limiting kinetic terms in eqn (1) to (3) The three terms that make up k,, in eqn (2) are circled and the three terms that make up kcat/& in eqn (3) are boxed.The four terms in the bottom row where the reactants are E+S make up the s term in eqn (1). The rest of the terms are found in the first term of eqn (1). !a The Steady-state Equation In the steady state we find24 that the flux j (usually measured in mol cm-2 s-l) is given by and ex is the total concentration of the enzyme. The expressions for kcat and KM/kcat have been discussed by Albery and Knowles.2s The free-energy diagram in fig. 9 shows how each term in eqn (1)-(3) corresponds to a possible rate-limiting free-energy difference in the enzyme kinetics. The advantage of the reciprocal expressions in eqn (1)-(3) is that the different possible rate-limiting processes are separated in this way.27 We now discuss the various terms in eqn (1).1042 First there are two terms which include L. These terms can only be dominant if the enzyme kinetics are rate-limiting; the first of these terms with kcat corresponds to the saturated enzyme and the second term with KM/kC,; to the unsaturated enzyme. If the flux j becomes close to the limit imposed by transport through the membrane j x kss, then the concentration polarisation means that the enzyme inside the membrane is less saturated than one would expect from the external concentration s,. This effect is described by the first bracket which reduces the significance of the kcat term. Electrochemical Sensors Theory and Experiment Secondly the simple term k'-l will be dominant if the electrode kinetics are rate limiting and if nearly all the enzyme is converted into E'; these conditions arise when the electrode kinetics are slow and there is no product inhibition.The rate constant k occurs in the same bracket as Lk,, since in either case the rate-limiting step involves turnover of the enzyme. Thirdly the other two terms involving k' are also cases where the electrode kinetics are rate-limiting. In the first bracket most of the enzyme is present as either ES or E'P while in the second bracket most of the enzyme is present as E and therefore requires S to be converted into E'. These terms are larger the larger the concentration of P behind the membrane whether this is because of the external concentration (p,) or because of slow transport of the generated P across the membrane ( j/rp).This product inhibition arises because in going from E ES or E'P to E' and thence to the rate-limiting transition state on the electrode P has to be released. This does not apply if E' is the dominant enzyme species when one obtains the simple k-l term. Finally we have the last term on the right of eqn (1). This term will dominate if the transport of S through the membrane is rate-limiting. Under these conditions j does not depend on the enzyme concentration; the kinetics of both the enzyme and the electrode are fast enough to consume S as soon as it passes through the membrane. No Product Inhibition Eqn (1) is a cubic in j but in our view little insight can be obtained by solving the cubic. It is however unlikely that for any system all the terms will be significant.The important application of the analysis is the identification of the rate-limiting process. For this purpose we have considered24 a number of special cases of eqn (1). In particular we take the case where there is no product inhibition. We rearrange eqn (1) into a form which is similar to a Hanes plot2* for the analysis of Michaelis-Menten kinetics In this equation we have introduced the effective electrochemical rate constant for the enzyme electrode at low substrate concentrations k; E where ( 5 ) lkME = KM/(eZ Lkcat) + lk&* We have introduced a similar parameter in our treatment of modified electrodesz9* 30 and indeed the KM term corresponds to the layer case of that treatment. Secondly we have introduced the equivalent of the Michaelis constant for the enzyme electrode KME where The significance of KME is similar to that of the Michaelis constant in homogeneous enzyme kinetics.For concentrations smaller than KME the system is unsaturated the current is proportional to the concentration of substrate and is governed by the rate constant kkE. For concentrations greater than KME the system becomes saturated and the flux reaches a maximum value. This flux can be characterised by the equivalent of kcat x m I - Q L 1 Y Fig. 10. (A) typical plots of flux against substrate concentration for different values of kdE/kk for the case where there is no product inhibition. For these curves (B) and (C) show the corresponding Hanes plots and plots of eqn (17) respectively. The values of kd/kk are as follows:- (-) 0.00.s,. Because k& describes a flux per unit area it has the usual dimensions (cm s-l) of an electrochemical rate constant. From eqn (5)-(7) we find For an enzyme electrode under unsaturated conditions this equation relates the kinetic description used by enzyme kineticists (kcat/KM) to the electrochemical rate constant (k’) used by electrochemists. The first stage of the analysis is to find kdE by making a Hanes plot of s,/j against Eqn (4) shows that this may be a curve but the limiting value as s + 0 gives [s,/j10 = (kkE)+. Next for values of s,/j significantly greater than [s,/’Jo we calculate values of p where 1.00 (-.-) 0.80 (- - .) 0.50 and (--) 1.0 W. J . Albery et al. I I 0 .o (8) 5 .O 4.0 3.0 2 .o 2.0 I 2.0 4.0 I 1 .o 0 .o 4 .O 1.0 P P = ( .i / s ) / ( j / s ~ ) o G 1. I 1 8.0 I 8.0 6 .O 1 6 .O S IKME s IK*E 2.0 1043 (9) 1044 f T 50 0 Electrochemical Sensors Theory and Experiment 150 5 > 3 E 100 20 10 [glucose] /mmol dm-3 Fig. 11. Variation of current with concentration of glucose for glucose electrodes made of three different salts of TCNQ- m TTF+; 0 NMP+; 0 Q'. Substitution in eqn (4) gives .Y=-=- 1 p-'-1 S A plot of y against p will then determine from the intercept at p = 0 the value of KME and from the intercept at y = 0 the ratio k M E / k $ . The relative importance of the transport and enzyme kinetic terms in eqn (5) for kdE is given by this ratio.If the ratio is unity then the transport of S across the membrane is rate-limiting. If on the other hand the ratio is much less than unity then the unsaturated enzyme kinetics are rate-limiting. Hence this is a valuable diagnostic plot. In the development of these electrodes it is vital to identify the rate-limiting step in the overall performance of the device so that research can be concentrated on improving the membrane the enzyme or the electrode kinetics. Fig. 10 shows typical j us. s curves Hanes plots and plots of eqn (10) for different values of kkE/kk. It is interesting that for the case where transport across the membrane is cleanly rate-limiting we obtain a sharp dog-leg plot of flux against concentration of substrate.This arises because under these conditions neither of the two rate-limiting processes transport or enzyme turnover under saturated conditions depends on the internal substrate concentration so; hence the flux is simply limited by the slower of the two processes. KME 30 100 80 10 I v) 1 .Y - 5 I v - 8 60 W - Y 40 20 0 The results in fig. 11 are analysed by the procedure presented above. The first stage of the analysis is to plot [glucose]/j = 2AF[glucose]/i against [glucose] as given by eqn (4). To compensate for the different areas (A) of the electrodes we carry out the analysis in terms of the current densities ( i / A ) . These plots are shown in fig. 12. From the intercepts I at zero concentration we find the electrochemical rate constant kLE where H Fig.12. Hanes plots28 of the data in fig. 11 for the measurement of glucose using three different salts of TCNQ- 0 TTF+; 0 NMP+; 0 Q+. and TTF Q' We have found that the enzyme glucose oxidase can be oxidised on six different conducting organic salts3' Results for three of the salts showing the variation of current with concentration of glucose are shown in fig. 11. In these salts the anion is TCNQO-; the cations are NMP+ TTF" (2) and Q+ (3). values of kkE are collected in table 4. kk = KsDs/LM. Glucose Electrodes W. J. AIbery et al. 1045 0 0 0 0 0 m o m a 0 10 30 20 [glucose]/mmol dm-3 1046 K M Eb kMEa kist EC 9 x 10-2 8 x 20 22 11 1.4 x 80 60 4.7 x 10-5 1.3 x 10-5 Calculated from eqn (1 3).a Calculated from eqn (1 1). Calculated from eqn (6). P 0.5 p = Ij/[glucose]. - - I 2 E -. a A 40 20 0 Next the parameter p [eqn (9)] is calculated where From eqn (10) y is plotted against p where 1 (1 -x). Electrochemical Sensors Theory and Experiment Table 4. Results for membrane electrodes /cm s-' /mmol dm-3 electrode material /cm s-' 3.0 x 10-5 TTF+TCNQ- NMP+TCNQ- Q+TCNQ- 1 .o Fig. 13. Plots of the data in fig. 10 according to eqn (13) for the measurement of glucose using three different salts of TCNQ- 0 TTF+; 0 NMP'; 0 Q'. ' = [glucose] p-1- 1 - - K~~ Pk', Plots of eqn (13) for the three electrodes are shown in fig. (13). In each case good straight lines are obtained showing the success of the analysis.The fact that in each case 1047 W. J . Albery et al. 4 I 8 I 2 1 6 1 [choline]/mmol dm-3 Fig. 14. Variation of current with concentration of choline for a choline electrode made of TTF+TCNQ-. Fig. 15. Plot of the data in fig. 14 according to eqn (10). y = 0 when p = 1 means that from eqn (13) we can conclude that kLE = k; and that in eqn (1 1) (14) KM/(eZ Lkcat) Q (kk)-l* This means that at low substrate concentrations the rate-limiting step is the diffusion of glucose through the membrane. The subsequent enzyme and electrode steps are so fast that they are not rate-limiting. This is the most desirable condition for a reliable sensor since the enzyme and electrochemical kinetics do not affect the response of the sensor.As long as this condition is maintained any decay in the enzyme or electrode activity has no effect. The results in fig. 11 show that glucose concentrations can be determined in the range 50 pmol dm-3 to 10 mmol dm-3. The fact that the transport of the glucose through the membrane is rate-limiting explains why the values of khE in table 4 are all so similar and do not depend on the electrode material. Returning to fig. 13 from the intercepts and eqn (13) we can calculate values of KME. Results are collected in table 4. In eqn (6) for K M E we have already shown that the k; 1048 Electrochemical Sensors Theory and Experiment Table 5. NAD-NADH enzyme systems analyte application enzyme alcohol dehydrogenase lactate dehydrogenase malate dehydrogenase alcohol lactate malate glutamate glutamate dehydrogenase glucose glucose dehydrogenase fermentation dairy industry fermentation fermentation food industry fermentation glycerol bile acids clinical fermentation clinical nitrate glycerol dehydrogenase 1 1 hydroxysteroid dehydrogenase nitrate reductase oestradiol oestradiol 17 dehydrogenase agriculture water industry agriculture food industry clinical fermentation amino acids amino acid dehydrogenase clinical food industry transport term dominates the numerator.Taking a value for k, of 800 s-l 32 and a value of L of several pm we find that the denominator in eqn (6) is dominated by the k electrode-kinetic term.Hence we can calculate values of the electrochemical rate constant k' for the oxidation of the enzyme; these values are reported in table 4. It is satisfactory that the three materials in table 4 are indeed excellent electrocatalysts for the direct oxidation of glucose oxidase with electrochemical rate constants k' which are all greater than cm s-l. We have also investigated the stability of the electrode. An electrode was run continuously for 28 days. During that time the response declined by only 20%. At the end of the period of the rate-limiting process was still transport of the glucose through the membrane. The enzyme and electrode kinetics were both still sufficiently rapid to handle the substrate that arrived.These results are very encouraging and show that the system is both stable and robust. Choline Oxidase Another enzyme which can be directly oxidised on TTF+TCNQ- is choline oxidase. Typical results for the variation of current with concentration of choline are shown in fig. 14. The same analysis is applied and fig. 15 shows the p plot. In this case the straight line passes through 2 on the x axis. This shows that in eqn (5) the two terms are equal. The transport through the membrane and the unsaturated enzyme kinetics are equally ra te-limi ting. NADH Systems We have also shown that these materials make good electrodes for the oxidation of NADH.33 Over 250 enzymes use NAD+ as a cofactor and hence we can design sensors using a wide variety of different solution dehydrogenases SH + NAD+ for dehydrogenase - a typical substrate S + NADH SH, + H+ NMP+TCNQ- electrode NADH ___+ NAD+ + H+ + 2e.0.5 0 -4 0 . 3 2 3 0.2 0.1 3 0 Fig. 16. Variation of current with concentration of ethanol for an ethanol electrode made of 0 A . 0.3 - - \ -0 c( - I i 6 0.1 - W. J . Albery et al. 6 [ ethanol]/mmol dm-3 0 I NMP+TCNQ-. fi 0.4 0 " - 0 I 0.2 P m 0.2 1 0 Fig. 17. Plot of the data in fig. 16 according to eqn (10). In table 5 we collect together some examples of the possible application of this type of sensor. In fig. 16 we show results obtained for an ethanol sensor using ethanol dehydroogenase. Application of the analysis gives the p plot shown in fig.17. In this case a horizontal straight line is obtained. This means that the unsaturated enzyme kinetics are rate-limiting. Hence in the three cases described here we have shown how the p plot can discriminate between the glucose electrode where transport is rate-limiting (fig. 13) the ethanol electrode where enzyme kinetics are rate-limiting (fig. 17) and the choline electrode where both processes are partially rate limiting (fig. 15). We believe that such analysis leading to the identification of the rate-limiting step is essential for a proper understanding of these devices. We are grateful to the following colleagues who carried out some of the experimental work reported in this paper Dr L. R. Svanberg on protein titrations Mrs M.M. P. Net0 and Mr C. P. Jones on the determination of iron and NO, respectively Mr B. J. Driscoll 1049 9 12 0 0.6 Electrochemical Sensors Theory and Experiment on choline oxidase and Mr K. W. Sim on ethanol dehydrogenase. We thank the S.E.R.C. the A.F.R.C. the Gulbenkian Foundation Pharmacia B.P. and Genetics International for financial support. 1050 References 1 W. J. Blaedel C. L. Olson and L. R. Sharma Anal. Chem. 1963 35 2100. 2 W. J. Blaedel and L. N. Klatt Anal. Chem. 1968 40 512. 3 R. Braun J. Electroanal. Chem. 1968 19 23. 4 J. Yamada and H. Matsuda J. Electroanal. Chem. 1973 44 189. 5 B. Fleet and C. J. Little J. Chromatogr. Sci. 1974 12 747. 6 M. Varadi and E. Pungor Anal. Chim. Acta 1977 94 351.7 A. N. Frumkin and L. I. Nekrasov Dokl. Akad. Nauk SSSR 1959,126 115. 8 W. J. Albery and S. Bruckenstein Trans. Faraday Soc. 1966 62 1920. 9 W. J. Albery and M. L. Hitchman Ring-Disc Electrodes (Clarendon Press Oxford 1971). 10 W. J. Albery and C. M. A. Brett J. Electroanal. Chem. 1983 148 201. 11 W. J. Albery L. R. Svanberg and P. Wood J. Electroanal. Chem. 1984 162 29. 12 W. J. Albery L. R. Svanberg and P. Wood J. Electroanal. Chem. 1984 162,45. 13 W. J. Albery and M. M. P. M. Neto Portugaliae Electrochimica Acta 1985 3 67. 14 D. Pletcher and Z. Poorabedi Electrochim. Acta 1979 24 1253. 15 W. J. Albery B. G. D. Haggett C. P. Jones M. J. Pritchard and L. R. Svanberg J. Electroanal. Chem. 28 C. S. Hanes Biochem. J. 1932 26 1406. 1985,188,257. 16 A.E. G. Cass G. Davis G. D. Francis H. A. 0. Hill W. J. Aston I. J. Higgins E. V. Plotkin L. D. L. Scott and A. P. F. Turner Anal. Chem. 1984 56 667. 17 A. E. G. Cass G. Davis H. A. 0. Hill I. J. Higgins E. V. Plotkin A. P. F. Turner and W. J. Aston in Charge and Field Eflects in Biosystems ed. M. J. Allen and P. N. R. Usherwood (UK Abacus Press London 1984) p. 475. 18 A. E. G. Cass G. Davis H. A. 0. Hill and D. J. Nancarrow Biochim. Biophys. Acta to be published. 19 J. J. Kulys A. S. Samalius and G. J. S. Svirmickas FEBS Lett. 1980 114 7. 20 J. J. Kulys and A. S. Samalius Bioelectrochemistry and Bioenergetics 1983 10 385. 21 L. R. Melby Can. J. Chem. 1965 3 1448. 22 C. D. Jaeger and A. J. Bard J. Am. Chem. Soc. 1979 101 1690. 23 C. D. Jaeger and A. J. Bard J. Am. Chem. Soc. 1980 102 5435. 24 W. J. Albery and P. N. Bartlett J. Electroanal. Chem. 1985 194 211. 25 W. J. Albery Electrode Kinetics (Clarendon Press Oxford 1975) p. 58. 26 W. J. Albery and J. R. Knowles Biochemistry 1976 15 5631. 27 W. J. Albery and J. R. Knowles Biochemistry 1976 15 5588. 29 W. J. Albery and A. R. Hillman Annu. Rep. Progr. Chem. Sect. C 1981 377. 30 W. J. Albery and A. R. Hillman J. Electroanal. Chem. 1984 170,27. 31 W. J. Albery P. N. Bartlett and D. H. Craston J. Electroanal. Chem. 1985 194 223. 32 M. K. Weibel and H. J. Bright J. Biol. Chem. 1971 246,2734. 33 W. J. Albery and P. N. Bartlett J. Chem. Soc. Chem. Commun. 1984 234. Paper 511880; Received 21st October 1985