Anal. Chem. 2000, 72, 2937-2942
Analysis of Ternary Mixtures with a Single Dynamic Microbial Sensor and Chemometrics Using a Nonlinear Multivariate Calibration Volker Plegge,†,‡ Michael Slama,†,‡ Benno Su 1 selbeck,§ Dietrich Wienke,| Friedrich Spener,⊥ † Meinhard Knoll, and Christiane Zaborosch*,†
Institut fu¨r Chemo- und Biosensorik, Mendelstrasse 7, D-48149 Mu¨nster, Germany, Zentrum fu¨r Informationsverarbeitung, Westfa¨lische Wilhelms-Universita¨t Mu¨nster, Einsteinstrasse 60, D-48149 Mu¨nster, Germany, DSM Research, P.O. Box 18, NL-6160 MD Geleen, The Netherlands, and Institut fu¨r Biochemie, Westfa¨lische Wilhelms-Universita¨t Mu¨nster, Wilhelm-Klemm-Strasse 2, D-48149 Mu¨nster, Germany
An amperometric biosensor based on immobilized bacterial cells of Alcaligenes eutrophus KT02 and an oxygen electrode was integrated in a flow-through system. Because microorganisms metabolize various organic analytes in a specific manner, the sensor shows for different pure analytes distinct time-dependent oxygen consumption rates that can be treated as characteristic patterns. This behavior is conserved also when the biosensor is exposed to a mixture of these organic analytes; the sensor with a particular type of microorganisms responds with a total signal. The respiration curves as time-dependent amplitudes were subdivided into several time channels. This procedure creates an additional data dimension and makes the single sensor ”dynamic”. Using multivariate calibration models with only one single biosensor, simultaneous quantitative analysis of ternary mixtures of acetate, L-lactate, and succinate was realized. A nonlinear algorithm that compensated for conceivable interactions of the analytes was superior to a partial least-squares algorithm. Each analyte was predicted more precisely by the nonlinear approach resulting in root-mean-square errors of prediction of 0.20 mg/L for acetate, 0.43 mg/L for L-lactate, and 0.73 mg/L for succinate. The development of sensors allowing multiparameter analysis has been limited by the fact that usually sensors are chosen as selective as possible for the determination of a single analyte and cross-reactivities of these sensors are not desirable. One solution is the construction of an array of several selective sensors in combination with mathematical models for data analysis.1 With this approach, arrays consisting of different chemically modified electrodes have already been tested for multicomponent analysis.2-6 * Corresponding author. E-mail:
[email protected]. † Institut fu ¨ r Chemo- und Biosensorik. ‡ These authors contributed equally to this work. § Zentrum fu ¨ r Informationsverarbeitung, Universita¨t Mu ¨ nster. | DSM Research. ⊥ Institut fu ¨ r Biochemie, Universita¨t Mu ¨ nster. (1) Carey, W. P. Trends Anal. Chem. 1994, 13, 210-218. (2) Otto, M.; Thomas, J. D. R. Anal. Chem. 1985, 57, 2647-2651. (3) Beebe, K.; Uerz, D.; Sandifer, J.; Kowalski, B. Anal. Chem. 1988, 60, 66-71. 10.1021/ac991034w CCC: $19.00 Published on Web 05/12/2000
© 2000 American Chemical Society
Furthermore, various gas sensors either as metal-oxide arrays7,8 or as an array of piezoelectric quartz crystals9 have used this approach. A different method deals with an interpretation of time-resolved signals of flow-through systems. Recently, this kinetic approach was used successfully in spectroscopy.10-15 Flow injection analyzers (FIAs) are described to offer a precise and rapid method for liquid analysis. However, only a few sensors were combined with FIAs for multicomponent analysis of mixtures.16-19 All of these methods are based on the classical approach of an array of different selective sensors to span a space for first-order multivariate calibration. Recently, we built a first-order instrument for multivariate calibration with only a single microbial sensor that was integrated in a flow-through system.20 Due to the individual metabolism of vital whole cells, a microbial sensor that consists of immobilized microorganisms of one species and an oxygen electrode detects various organic analytes with distinct time-dependent oxygen consumption rates. The FIA setup chosen created an additional data dimension (time axis), thus making this single sensor ”dynamic”. In addition, it has been found that the distinct oxygen (4) Beebe, K. R.; Kowalski, B. R. Anal. Chem. 1988, 60, 2273-2278. (5) Forster, R. J.; Regan, F.; Diamond, D. Anal. Chem. 1991, 63, 876-882. (6) Wang, J.; Rayson, G. D.; Lu, Z.; Wu, H. Anal. Chem. 1990, 62, 1924-1927. (7) Wang, X.; Yee, S.; Carey, P. Sens. Actuators, B 1993, 13-14, 458-461. (8) Wang, X.; Carey, W. P.; Yee, S. S. Sens. Actuators, B 1995, 28, 63-70. (9) Hierlemann, A.; Weimar, U.; Kraus, G.; Schweizer-Berberich, M.; Go ¨pel, W. Sens. Actuators, B 1995, 26-27, 126-134. (10) Beck, H. P.; Wiegand, C. Fresenius’ J. Anal. Chem. 1995, 351, 701-707. (11) Hernandez, O.; Jimenez, A. I.; Jimenez, F.; Arias, J. J. Anal. Chim. Acta 1995, 310, 53-61. (12) Saurina, J.; Herna´ndez-Cassou, S. Analyst 1995, 120, 305-312. (13) Saurina, J.; Herna´ndez-Cassou, S.; Tauler, R. Anal. Chim. Acta 1996, 335, 41-49. (14) Blanco, M.; Coello, J.; Iturriaga, H.; Maspoch, S.; Riba, J. Anal. Chem. 1994, 66, 2905-2911. (15) Saurina, J.; Herna´ndez-Cassou, S.; Tauler, R. Anal. Chem. 1997, 69, 23292336. (16) Forster, R. J.; Diamond, D. Anal. Chem. 1992, 64, 1721-1728. (17) Hartnett, M.; Diamond, D.; Barker, P. G. Analyst 1993, 118, 347-354. (18) Hartnett, M.; Diamond, D. Anal. Chem. 1997, 69, 1909-1918. (19) Polster, J.; Prestel, G.; Wollenweber, M.; Kraus, G.; Gauglitz, G. Talanta 1995, 42, 2065-2072. (20) Slama, M.; Zaborosch, C.; Wienke, D.; Spener, F. Anal. Chem. 1996, 68, 3845-3850.
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Table 1. Correlation Coefficients of the Characteristic Respiration Curves of Acetate, L-Lactate, and Succinate for Two Different Sensor Batches A and B batch A
batch B
acetate L-lactate succinate acetate L-lactate succinate batch A acetate 1 L-lactate 0.908 succinate 0.778
1 0.952
batch B acetate 0.995 0.939 L-lactate 0.876 0.991 succinate 0.703 0.919
Figure 1. Setup of flow-through system of the microbial sensor with peristaltic pumps (P1 and P2), a membrane pump (P3), a 3/2-way selection valve (V1), an autosampler (V2), and the microbial sensor (D).
Figure 2. Analyte-characteristic respiration curves of the dynamic microbial sensor: normalized current-time signals for acetate (solid lines), L-lactate (dashed lines) and succinate (dashed-dotted lines). For each analyte, curves were obtained by two different batches of sensors. Sample addition started at k ) 30 s.
consumption-time profiles of two components sum along the time axis to a total resulting time profile. This device is termed a dynamic microbial sensor.20 Multivariate deconvolution and calibration successfully demonstrated that such a single dynamic microbial sensor is able to analyze binary mixtures of, for example, gluconate and acetate or L-serine and L-threonine. This was achieved with a classical linear model using a partial least-squares (PLS) algorithm.20-22 To broaden the application of the single-sensor device, we focused in the present study on simultaneous determination of an increased number of analytes. For this purpose, ternary mixtures of acetate, L-lactate, and succinate were chosen for quantitative analysis. An extended analysis revealed that respiration curves did not behave completely linearly because of various effects. Therefore, we also focused on the development of a (21) Sjoestroem, M.; Wold, S.; Lindberg, W.; Persson, J.; Martens, H. Anal. Chim. Acta 1983, 150, 61-70. (22) Martens, H.; Næs, T. Multivariate Calibration; John Wiley & Sons: Chichester, U.K., 1989.
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1 0.828 0.975 0.993
1 0.916 0.762
1 0.952
1
mathematical model to compensate for these nonlinearities. Such a simple sensor device allows the simultaneous determination of a limited number of known components as required for analysis and monitoring of biotechnological processes, e.g., enzymatic conversions, and offers an alternative to expensive analytical equipment. EXPERIMENTAL SECTION Reagents. The bisulfite-blocked polyurethane prepolymer for immobilization of cells was a research product from the Bundesforschungsanstalt fu¨r Landwirtschaft (Braunschweig, Germany). Tris(hydroxymethyl)aminomethane (ultrapure) was obtained from USB (Cleveland, OH). The remaining chemicals were purchased as analytical grade from Sigma (Deisenhofen, Germany) and used without further purification. All sample solutions were prepared by diluting aliquots of stock solutions (5 g/L) with 50 mM TrisHCl buffer (pH 7.2). The same buffer was also used as the carrier stream in the flow-through system. Microorganism, Cultivation, and Harvesting of Cells. For all experiments, the bacterial strain Alcaligenes eutrophus KT02 (DSM 6519) was used.23 Cells were grown on a rotary shaker at 30 °C in a Tris mineral medium,24 supplemented with 0.4% sodium gluconate and 20 mM nickel chloride. Cells were harvested at the beginning of the stationary phase, centrifuged for 20 min at 5000 rpm and 4 °C, washed in 50 mM potassium phosphate buffer (pH 7.2), and resuspended in the same buffer. The final cell suspension was adjusted to an absorbance of A436 ) 250 to achieve comparable cell loadings. Immobilization. Cells were immobilized within a polyurethane hydrogel.25 The immobilization procedure was described previously.20 An aliquot of 3 µL of the hydrosol mixed with the cell suspension was spread onto a 7 mm2 spot of a gas-permeable polyethylene (PE) membrane (thickness 10 µm; Metra, Radebeul, Germany) and incubated for 30 min at 30 °C in a water vaporsaturated atmosphere, where polymerization to the hydrogel was completed. Microbial Sensor. An oxygen electrode (Pt cathode with a diameter of 0.5 mm and Ag/AgCl reference anode; PGW Medingen, Dresden, Germany) was covered first with a gas-permeable PE membrane onto which the immobilized microorganisms were adhering and then with a capillary pore membrane (pore diameter (23) Timotius, K.; Schlegel, H. G. Nachr. Akad. Wiss. Go¨ettingen, II. Math.-Phys. Kl., 1987, 3, 15-23. (24) Mergeay, M.; Nies, D.; Schlegel, H. G.; Gerits, J.; Charles, P.; Gijsegem, F. V. J. Bacteriol. 1985, 162, 328-334. (25) Vorlop, K.-D.; Muscat, A.; Beyersdorf, J. Biotechnol. Tech. 1992, 6, 483488.
Table 2. Comparison of the Prediction Accuracy of 125 Ternary Mixtures Using Linear PLS with Two Different Calibration Sample Sets and a Nonlinear Regression Methoda rel error (%)b
RMSEP (mg/L) regression model
calibration data set
acetate
L-lactate
succinate
acetate
L-lactate
succinate
PLS PLS nonlinear regression
central composite Box-Behnken Box-Behnken
0.38 0.36 0.20
0.75 0.50 0.43
1.01 0.80 0.73
9.5 9.0 5.0
18.7 12.5 10.7
12.6 10.0 9.1
a Results combine predictions for calibration data and test data. b Error refers to maximum concentration measured: acetate, 4 mg/L; L-lactate, 4 mg/L; succinate, 8 mg/L.
Figure 3. Correlation plots of predicted concentrations for acetate (A), L-lactate (B), and succinate (C) in 125 ternary mixtures, obtained by multicomponent PLS calibration, versus true concentrations. Thirteen samples following the Box-Behnken design and p ) 21 time channels were used for calibration. The box plots show statistics for the 25 predictions of each concentration as follows: 10th percentile, 1st/2nd quartile, median, 3rd/4th quartile, and 90th percentile. Predictions that are located outside this range are marked with circles.
0.6 µm, thickness 10 µm; Oxyphen, Dresden, Germany) to increase mechanical stability. The sensor was installed in a flowthrough system (BOD-Module; PGW Medingen, Dresden, Germany) with alternating flows of 50 mM Tris-HCl buffer (pH 7.2) and analyte solution which were both saturated with air by a membrane pump (Figure 1). All measurements were taken at 31 °C and a constant flow rate of 100 mL/h. The platinum cathode was polarized at -800 mV vs an Ag/AgCl anode. The sampling time of 30 s and a signal recovery time of up to about 7 min enabled a throughput of about eight samples/h. The microbial sensors were used directly after preparation. Chemometrics. A total of 125 distinct ternary mixtures of acetate, L-lactate, and succinate were prepared, resulting from all possible variations of single-analyte concentrations as follows: acetate, 0, 1, 2, 3, and 4 mg/L; L-lactate, 0, 1, 2, 3, and 4 mg/L; and succinate, 0, 2, 4, 6, and 8 mg/L. For each sample, the response of the biosensor was recorded at a time resolution (step width) of 5 s, and a measurement vector y ) [y1, y2, y3, ..., yp] and a corresponding concentration vector c ) [c1, c2, c3] were stored. One part of the samples served for multivariate calibration; the remaining set were used as independent test samples. To reduce the number n of calibration samples, two different designs on three levels were compared.26 The central composite design consisted of 15 samples: 8 samples situated in the corner points of a cube spanning the concentration space, 6 samples in the middle of the sides, and 1 sample in the center of the cube. The Box-Behnken design included 13 samples: 12 samples bisecting the edges of a cube and 1 sample in the center of the cube. (26) Otto, M. Chemometrie: Statistik und Computereinsatz in der Analytik; VCH: Weinheim, Germany, 1997.
The multivariate calibration analyses were performed under the operating system DOS/Windows95 (Microsoft, Seattle, WA) on a personal computer (486/66 MHz). The PLS algorithm of the software The Unscrambler 6.0 (Camo, Trondheim, Norway) was applied, whereas the nonlinear multivariate regression was realized with the software package Excel 7.0 (Microsoft, Seattle, WA) using the algorithm described under Results and Discussion. RESULTS AND DISCUSSION A comparison of the normalized respiration curves of the pure analytes indicated that the three substances could be differentiated reliably (Figure 2). Acetate was detected with the shortest response time; the peak maxima of L-lactate and succinate were reached with a few seconds’ delay. Measurements with two different batches of sensors showed that the characteristics of the time-resolved respiration curves were conserved regardless of a minor sensor drift. A correlation analysis of these respiration curves revealed the reproducibility of sensor preparation (Table 1). As expected, the respiration curves for the same analyte when measured with different sensor batches were highly correlated, resulting in a correlation coefficient near 1. Beyond that, correlation coefficients can be used as a measure for the probability of distinction of the different analytes. Acetate should be detectable in the presence of the other two analytes L-lactate and succinate, and vice versa. Difficulties could arise from the similarity between the respiration curves of L-lactate and succinate, with a correlation coefficient of 0.95. In the following, the analysis of a simultaneous determination of different ternary mixtures of acetate, L-lactate, and succinate shows that the analytes L-lactate and succinate might possibly influence each other, and thus affect the quality of prediction. Analytical Chemistry, Vol. 72, No. 13, July 1, 2000
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Figure 4. (A) Current-time curves of the microbial sensor for the pure analytes acetate (1, 2, 3, 4 mg/L; solid lines) and succinate (2, 4, 6, 8 mg/L; dashed-dotted lines). (B) Current values at distinct time channels k with k ) 68 s (0), 90 s (O), 110 s (4), and 125 s (3) for a series of pure analyte solutions of succinate.
Multivariate Calibration. The multivariate calibration was based on a subdata set from the respiration responses of the 125 different mixtures of acetate, L-lactate, and succinate. Calibration samples were chosen according to two different response surface designssa central composite design and a Box-Behnken design.26 The central composite design required n ) 15 calibration samples, whereas n ) 13 calibration samples were sufficient for the BoxBehnken design. Calibrations were done by a PLS algorithm applying the two multifactor designs. The remaining samples of the set were used as independent test samples. The calibration was performed with 21 time channels, which were equally distributed between 50 and 150 s after sample addition started. Within all 125 samples, the error of prediction for each analyte was determined (Table 2). The calibration model based on the Box-Behnken design resulted in lower root-mean-square errors of prediction (RMSEPs) for all analytes. This design required two calibration samples less than the central composite design and showed a more optimized distribution of the calibration samples in the concentration space according our data quality. Thus, in further analysis, only the Box-Behnken calibration design was used. Correlation plots of true and predicted concentrations demonstrated the quality of the predictions of the ternary mixtures 2940 Analytical Chemistry, Vol. 72, No. 13, July 1, 2000
Figure 5. Sensor responses of measurements for pure solutions of L-lactate (A) taken at distinct time channels k with k ) 60 s (0), 72 s (O), 85 s (4) and 100 s (3) in a time interval of 32 min and (B) taken in a time interval of 13.3 h. In (B) different mixtures of acetate, succinate, and L-lactate were measured with a sample throughput of 8 h-1 between the measurements of the five pure L-lactate concentrations at the given time points.
(Figure 3). In our setup, each concentration of a given analyte was measured at 25 different concentrations of the other two analytes. The values of these 25 predictions of each concentration are shown in a statistical representation. Boxes with the median inside represent 50% of the predictions, whereas whiskers mark the 10th and 90th percentiles, respectively. Predictions that are located outside this range are marked with circles. Acetate and succinate were predicted in ternary mixtures with an average error relative to the maximum concentration measured of e10%. Prediction of L-lactate was poor, with an error larger than 10%, especially in the low-concentration range (Table 2). Scrutiny of the current-time curves for pure analytes revealed that the time channels, at which maximal sensor responses for acetate were obtained, were independent of the measured concentration (Figure 4A). Previously it had been shown that the signal heights for acetate at distinct time channels were linearly dependent on the concentration.27 In contrast, sensor responses for increased succinate concentrations shifted their maxima to (27) Slama, M.; Zaborosch, C.; Wienke, D.; Spener, F. Sens. Actuators, B 1997, 44, 286-290.
Figure 6. Correlation plots of predicted concentrations for acetate (A), L-lactate (B), and succinate (C) in 125 ternary mixtures, obtained by nonlinear multicomponent calibration, versus true concentrations. Thirteen samples following the Box-Behnken design and p ) 21 time channels were used for calibration. The box plots show statistics for the 25 predictions of each concentration as follows: 10th percentile, 1st/2nd quartile, median, 3rd/4th quartile, and 90th percentile. Predictions that are located outside this range are marked with circles.
later time channels (Figure 4A). This caused a nonlinear dependence of the sensor response from the substrate concentration at distinct time channels. The resulting nonlinear curves show either increasing or decreasing slopes depending on the time channel (Figure 4B). This nonlinearity of microbial sensor signals may result from a concentration-dependent delayed substrate transport by carrier systems in the cell membrane. A decreasing signal within one measurement cycle could be a second cause for a nonlinear behavior of biosensors. Figure 5A shows that the response for L-lactate at a distinct time channel was nearly linear when five increasing concentrations were measured consecutively within 40 min (sample throughput 8 h-1). The reason for the observable nonlinearity is a small shift of the maxima of the current-time curves for increasing concentrations, as seen for succinate. In a second setup, the five concentrations of L-lactate were measured in a time range of 13.3 h (Figure 5B). Between the measurements of the five L-lactate concentrations, different mixtures of acetate, succinate, and L-lactate were measured with a sample throughput of 8 h-1. In this case, the concentration dependences of the signals for the increasing L-lactate concentrations deviated significantly from the ones measured in Figure 5A. This time-dependent behavior presumably reflects a combination of the shifting of the peak maxima and an “aging” of the sensor within the measuring period or a physiologically caused saturation for L-lactate. To overcome the error of prediction resulting from the observed nonlinearities, the classical linear calibration model20 was adjusted by inclusion of additional terms which represent conceivable “interactions” between the analytes j (j ) 1, acetate; j ) 2, L-lactate; j ) 3, succinate):
y(k) ) b1(k) c1 + b2(k) c2 + b3(k) c3 + b4(k) c1c2 + b5(k) c1c3 + b6(k) c2c3 + b7(k) c12 + b8(k) c22 + b9(k) c32 (1) y(k) represents the total signal response at the time channel k, cj the concentrations of the analytes, and bi(k) the sensitivity coefficient for the ith analyte or interaction at the kth time channel. This nonlinear approach was applied to the calibration and prediction of the ternary mixtures. The calibration was performed also with the Box-Behnken subdata set and the same 21 time channels. Correlation plots of true and predicted concentrations
Figure 7. Overlay of the parameters b1 (acetate), b2 (L-lactate), b3 (succinate), and b0 (intercept) for all 21 time channels k estimated by least-squares within the linear model (O) and the nonlinear model (+) both with an included intercept. Plots are based on the full data set.
revealed the deviations from true values (Figure 6). The use of the nonlinear approach significantly improved the quality of prediction for acetate, which resulted in good and equally distributed predictions of the unknown test samples. Also, in the case of L-lactate and succinate, lower errors of prediction with a more equal distribution of the predicted values were achieved. A few predictions deviated clearly from the true values. These outliers can be caused by the Newton algorithm that was applied to solve eq 1. Sometimes this algorithm for fitting the variables, here concentrations, was not able to find the global minimum. Thus, the outliers could be understood as a problem of data inhomogeneity. The linear model and the nonlinear one with interaction terms cannot be compared only by their results in predicting unknown concentrations but also more directly by their ability to explain the calibration data set or the full data set itself. To check the Analytical Chemistry, Vol. 72, No. 13, July 1, 2000
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not shown). This again shows that the Box-Behnken design was well chosen and that it is possible to realize a good model selection based on a carefully selected subset of all possible combinations of concentrations. A quantitative comparison of the prediction accuracy of both multivariate calibration methods, PLS and the nonlinear method, can be found in Table 2. Each analyte was predicted more precisely by the nonlinear approach, even if mentioned outliers were included. The RMSEPs were 0.20 mg/L for acetate, 0.43 mg/L for L-lactate, and 0.73 mg/L for succinate. In comparison to those of the used PLS algorithm, the RMSEPs were reduced between 9% and 44%, which demonstrated the advantages of the nonlinear approach.
Figure 8. Parameters b4 ([acetate][L-lactate]) (+), b5 ([acetate][succinate]) (3), b6 ([L-lactate][succinate]) (]), b7 ([acetate]2) (O), b8 ([Llactate]2) (4), and b9 ([succinate]2) (0) for all 21 time channels k estimated by least-squares within the nonlinear model with an intercept term included. Plots are based on the full data set.
linear model, an intercept term (b0(k)) was included:
y(k) ) b0(k) + b1(k) c1 + b2(k) c2 + b3(k) c3
(2)
The parameters bi(k), (i ) 0, 1, 2, 3) were estimated within the linear regression approach by least-squares for all time channels k and represented graphically with different plots for the analytes and the intercept (Figure 7, circles). The figure shows a strong deviation of the intercept at the different time channels from 0, the value which is expected from the experimental design. This is an indication that the linear model does not fit the data very well. To analyze the quality of the nonlinear model, we also included an intercept b0(k) in eq 1. The parameters bi(k) (i ) 0, ..., 9) were also estimated by least-squares for every k. The first four parameters b0-b3, which are comparable to those of the linear model, were overlayed in the plots of Figure 7 (marked with crosses). Now the intercept term was much closer to its expected value 0 and the parameters for L-lactate have changed significantly. This corresponded to the observed quadratic behavior of L-lactate already revealed in Figure 5B. In Figure 8 the additional six parameters b4-b9 resulting from the nonlinear fit are shown. It is obvious that only the parameters b4 for the product [acetate] [L-lactate], b7 for [acetate]2, and b8 for [L-lactate]2 are different from 0 for relevant time channels, which is a further argument for the suitabilty of the nonlinear approach. The plots in Figures 7 and 8 were based on the full data set. The use of the smaller calibration data set did not change the parameter estimates significantly (data
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CONCLUSIONS The present study demonstrates the feasibility of multicomponent analysis with a single biosensor containing one microbial species. Characteristic respiration kinetics of such a microbial species for and cross-sensitivities to several analytes were exploited to realize a dynamic microbial sensor as a first-order multivariate instrument. A simultaneous quantitative analysis of different ternary mixtures of acetate, L-lactate, and succinate was achieved with this sensor. Application of a classical PLS algorithm resulted in sound predictions, but the nonlinear approach enabled an even more precise analysis. The improvements of 9% -44% in precision upon applying a few nonlinear terms compared to classical linear regression in partial least-squares have been significant. By this extension, various nonlinearity-causing effects, such as aging, physiological saturation of the microbial sensor, or delayed substrate transport through the cell membrane, can be compensated. Generally, nonlinear calibration models require an increased number of calibration samples to describe correctly the curved data space in comparison to linear models. However, with our sensor concept, three analytes can be determined quantitatively by one measurement with a single sensor. Further development for complex mixture analysis, namely to build an array of dynamic microbial sensors using different microbial strains as a secondorder instrument, is currently under investigation. ACKNOWLEDGMENT This work was supported by a grant from the Deutsche Forschungsgemeinschaft (ZA 219/1-1). We are grateful to K.-D. Vorlop (FAL Braunschweig, Germany) for kindly providing the poly(carbamoyl sulfonate) prepolymer.
Received for review September 8, 1999. Accepted March 17, 2000. AC991034W
