Model of an immobilized enzyme conductimetric urea biosensor

Biosensors & Bioelectronics Vol. 11, No. 10, pp. 967-979, 1996 1996 Elsevier Science Limited Printed in Great Britain. All rights reserved 0956--5663/96/$15.00

ELSEVIER ADVANCED TECHNOLOGY

Model of an immobilized enzyme conductimetric urea biosensor Norman F. Sheppard, Jr* & David J. Mears The Johns Hopkins University, School of Medicine, Baltimore, MD 21218, USA Tel: [1] (410) 516 7506 Fax: [1] (410) 516 4771

&

Anthony Guiseppi-Elie AAI-ABTECH, 1273 Quarry Commons Drive, Yardley, PA 19067, USA (Received 4 May 1995; accepted 10 November 1995)

Abstract: A model for predicting the response of a conductimetric urea

biosensor was developed and validated experimentally. The biosensor under consideration is formed by immobilizing the enzyme urease onto the surface of a planar interdigitated electrode array. The enzymatic hydrolysis of urea produces ionic products, such as ammonium and bicarbonate ions, which increase the electrical conductivity of the solution proximal to the electrode array. The model combines an analysis of the diffusive transport and enzymatic hydrolysis of urea in the vicinity of the biosensor surface with an electric fields model for calculating interelectrode impedance. To validate the model, urea biosensors were constructed by immobilizing urease to the interdigit space of microfabricated interdigitated electrodes. The responses of these sensors were investigated in urea solutions prepared in deionized water, at concentrations ranging from 10 tzM to 5 mM. Using reasonable estimates for the parameters, the predictions of the model were in good agreement with the experimental data over the entire range of concentrations. © 1996 Elsevier Science Limited Keywords: conductimetric sensor, urease, urea biosensor, modelling, interdigitated electrode

INTRODUCTION The operation of conductimetric biosensors is based on the ability of the catalytic action of an enzyme or the affinity of antibodies or receptor

* To whom correspondence should be addressed.

proteins to modify the electrical impedance of a suitably configured set of electrodes. Biosensors for neurotoxins have been created by incorporating acetylcholine receptors into lipid or polymer membranes (Vales et al., 1988; Taylor et al., 1988). Enzyme-based conductimetric sensors rely on a change in solution conductivity when the substrate is converted to product. A number of 967

N.F. Sheppard, Jr et al.

Biosensors & Bioelectronics

investigators have described conductimetric urea sensors (Cullen et al., 1990; Mikkelsen & Rechnitz, 1989; Pethig, 1991; Watson etal., 1988; Jacobs et al., 1994; Nyamsi Hendji et al., 1994; Dzydevich et aI., 1994). Urease immobilized to the electrode surface catalyzes the hydrolysis of urea, in an overall reaction leading to the formation of ammonium, bicarbonate and hydroxide ions: urease

urea + 3 n 2 0

)

(1)

2 NH4 + + HCO3- + O H The charged products of the above reaction increase the solution conductivity in the vicinity of the sensor surface. Urease-tagged antibodies have been used to construct a conductimetric immunosensor (Thompson et al., 1991). Interdigitated electrode arrays modified with electroconductive polymers that change impedance as the polymer reacts with the products of oxidoreductase enzymes may be used in high conductance solutions (Nishizawa et al., 1992; Hoa et al., 1992). Conductimetric sensors are found in a wide variety of sensing applications (Janata et al., 1994), and often use planar interdigitated electrode arrays as the transducer. Standard integrated circuit fabrication methods can be used to manufacture the electrodes, so miniature sensors with areas of the order of square millimeters are readily obtained. A sensor is formed by coating the electrode array with thin films responsive to the analyte of interest. To date, the calibration of conductimetric sensors has been largely empirical. The relationship between the measured impedance (or a related quantity) and the analyte concentration is determined experimentally. There have, however, been reports where finite difference (Fouke et al., 1988; Lee, 1982) solutions to Laplace's equation have been used to relate the properties of the sensing layer to electrode impedance. Analytical treatments (Endres & Drost, 1991; Zhou et al., 1988) led to relationships for the capacitance of interdigitated arrays coated with a thin film for gas sensing. The model of Zaretsky (Zaretsky et al., 1988a,b) is a more general solution of the electric fields problem, permitting the calculation of the complex impedance of an interdigitated electrode array coated with multiple layers of material. This contribution describes a model to predict the response of a conductimetric urea biosensor 968

constructed by immobilizing urease at the surface of a planar interdigitated electrode array. A transport model describing the temporal and spatial evolution of reaction products in the vicinity of the electrode was developed to predict the electrical conductivity of the fluid in the halfspace above the electrode array. A solution of Laplace's equation for the interdigitated electrode array geometry (Zaretsky et al., 1988a) permits computation of interelectrode impedance given the fluid conductivity. The model predictions were compared with the experimentally measured sensitivity and response time of a conductimetric urea microsensor formed by immobilizing urease to the surface of the interdigitated electrode array. To facilitate comparison of the experiments with the model predictions, the enzyme was immobilized by covalent binding to the interdigit surface via a crosslinker, creating an enzyme layer which is very thin relative to the electrode dimensions. Furthermore, the devices were evaluated in urea solutions prepared in deionized water, to eliminate background conductivity from buffer salts. The model allows one to determine sensor behaviour and optimize sensor design, and can easily be adapted for conductimetric biosensors incorporating other enzyme/substrate systems.

METHODS Sensor construction

Interdigitated electrode arrays (IME-1550-FD-PPt) were obtained from AAI-ABETCH (Yardley, PA, USA). As illustrated in Fig. 1, each electrode consists of 50 'fingers', 15 ~m wide and approximately 5 mm long. The spacing between adjacent electrodes was 15 Ixm. Polyimide tape was used to mask the electrodes, except for a 4.25 mm diameter circle in the center of the array. The electrodes are formed from films of 0.02 ~m of chrome and 0.10 ~m of platinum sequentially deposited on a borosilicate glass substrate by electron-beam evaporation. The arrays were cleaned in a Branson 1200 Ultrasonic Cleaner by sequential washing---first in acetone, followed by 2-propanol and finally in Omnisolve water. Prior to silanization, the devices were cleaned for 5 rain in a UV/ozone cleaner, UV_ Clean (Boekel Industries, PA), to remove adventitiously adsorbed organics. Chemi-

Biosensors & Bioelectronics

A conductimetric urea biosensor

Delrin Rod Electrode 1 Electrode 2 Electrode 3 Electrode 4

Epoxy

Encapsulant

Interdigitated Array 1

C~l

lcm

='

Interdigit Area dth Immobilized Enzyme

Interdigitated Array 2 13orosilicate Glass Substrate

Polvimide i ape

Fig. 1. Schematic illustration o f interdigitated electrode array used to construct conductimetric urea biosensor.

cally cleaned devices were then immersed for 10 min in a freshly prepared solution of 1% 3aminopropyltrimethoxysilane (Aldrich, Milwaukee, WI) in 95% ethanol/5% water. The adsorbed and hydrogen bonded silanol layer was rinsed profusely with ethanol then cured at ll0°C for 10 min before being solvent cleaned again using the protocol above. Following surface modification, the devices were each made the working electrode in a threeelectrode electrochemical cell in which a clean Pt mesh electrode served as the counter electrode. Cathodic cleaning of the platinum electrodes was then carried out by repeatedly cycling from - 1 to - 2 V with respect to a Ag/AgC1 reference for 3 min in phosphate buffered saline, to remove any aminosilane bound to the electrode. Platinum black was then electrolytically deposited from a solution of platinic chloride and lead acetate. A current density of 50 mA/cm 2 was passed for 40 s to produce a deposit that was clearly visible under an optical microscope. The enzyme urease was immobilized to the aminosilane modified interdigit space by immersion of the sensor into a freshly prepared solution containing 1 mg/ml N-hydroxysulfosuccinimide (Sulof-NHS), 20 mg/ml 1-ethyl-3-(3dimethylaminopropyl)carbodiimide-HC1 (EDC) and 1 mg/ml urease (Type C-3 from Jack Beans, Sigma, St. Louis, MO) in pH 7.2 sodium phosphate (0.2 M) buffer. The devices were gently agitated and allowed to incubate for 3 h at room temperature. Following immobilization, sensors were rinsed profusely with pH 7.2 sodium phosphate buffer, and the electrodes cathodically

cleaned according to the procedure described above, to remove any enzyme adsorbed to the platinized electrodes. The sensors were rinsed and stored in pH 7.2 sodium phosphate buffer at 4°C.

Sensor testing Evaluation of the urea sensors was carried out in a magnetically stirred, thermostatted cell at 25°C. Urea solutions of specified concentration were made by dilution of a 1 M stock solution of urea (Sigma, St. Louis, MO) in deionized water. The cell was filled with 75 ml of the urea solution and allowed to come to temperature. Prior to the tests, sensors were removed from storage in phosphate buffer, rinsed thoroughly with deionized water, and temporarily stored in deionized water for the duration of the experiment. To approximate a step change in urea concentration, a trial was initiated by removing a sensor from the deionized water, then quickly immersing it into the cell. The series equivalent resistance and reactance of the interdigitated electrode array were measured using an HP 4192A LF impedance analyzer, at a frequency of 1 kHz and an amplitude of 50 mV. Data were recorded, beginning 5 s prior to sensor immersion in the urea solution, for a period of up to 5 min. The sensor was rinsed and stored in deionized water between sample measurements. Following completion of concentration-dependent urea responses, individual sensors were returned to lower concentrations and the measurements repeated. Triplicate runs indicated no statistically 969

N.F. Sheppard, Jr et al.

Biosensors & Bioelectronics

significant variation in responses over the period of 24 h required to perform such experiments. Measurements performed after storage in pH 7.2 sodium phosphate buffer indicated a loss of approximately 25% activity over a 3 week period.

CONDUCTIMETRIC SENSOR MODEL FORMULATION The operation of the conductimetric urea biosensor, immersed in an aqueous solution containing urea, is illustrated schematically in Fig. 2. Urea in the bulk analyte solution diffuses through a concentration boundary layer to the surface of the sensor, where its hydrolysis is catalyzed by the urease immobilized to the sensor surface. Charged and uncharged products of this reaction diffuse away to the bulk solution and may undergo further reaction, for example, the dissolution of carbon dioxide to form carbonic acid. Ions formed by these reactions increase the electrical conductivity of the solution at the sensor surface. This conductivity change is detected by a change in the electrical conductance of the interdigitated electrode array, which depends on the spatio-termporal distribution of the conductivity of the solution proximal to the sensor surface. Due to the nature of the fringing electric

fields produced by the electrode array, only the solution within a finite distance of the surface contributes to the measured electrode array conductance. Operation of the conductimetric urea sensor was modelled by first solving the coupled mass transport and enzyme reaction problem to determine the concentration of ionic products within the boundary layer. The boundary layer was defined to be the distance from the sensor surface beyond which the concentration of urea and products are equal to the bulk values, and will be a function of experimental conditions such as stirring. The concentrations of ionic products were used to calculate the spatial and temporal distribution of electrical conductivity, which was then incorporated into an electric fields model to predict the electrical conductance of the electrode array. To simplify the modelling, the interdigitated electrode array was considered to be infinite in extent, such that concentrations vary in only one dimension; that normal to the electrode array surface. Both the transport and fields problems were treated numerically by dividing the concentration boundary layer above the sensor surface into volume elements having a thickness expressed as a fraction of the characteristic dimension of the electrode array. Referring to Fig. 2, this characteristic distance, A, is the spatial periodicity of the array, that is, the distance between one digit and the next on the same electrode. The spacing between adjacent digits is denoted by 'a'. For the devices used in the experimental portion of this study, these values were nominally 60 and 15/~m, respectively. The finite thickness of the electrodes was neglected, given the 0.11/zm electrode thickness relative to the 15/zm lateral extent of a digit on the array.

immobilized

urease

Transport model Reactions

platinum j digit glass substrate anal~cte J solution I I

~

X

Fig. 2. Schematic cross-section of conductimetric urea sensor, illustrating spatial variation of urea and product concentrations, ionic conductivity, as well as discretization into layers for modelling.

970

The kinetics of the urease catalyzed hydrolysis of urea has been extensively studied, and the reaction rate depends on pH, temperature, ionic strength and buffer composition. The sensor evaluations to validate the model were carried out in deionized water to eliminate the baseline conductivity of a buffer solution. Under these conditions, spectroscopic (Blakeley et al., 1969) and calorimetric (Jespersen, 1975) studies have demonstrated that the initial product of the enzymatic reaction is ammonium carbamate:

Biosensors & Bioelectronics urease

urea + H 2 0

A conductimetric urea biosensor

;H2NCOO- + NH4 +

(2) The carbamate breaks down to form ammonia and carbon dioxide, with a rate constant, k', which is estimated to be 0.22 s -1 at 25 ° (Blakeley et al., 1969). H2NCOO- + H +

k'

>NH3 + C O 2

(3)

Subsequent dissolution of the CO2 yields carbonic acid, with a rate constant k" of 0.12 s -1 (Blakeley et al., 1969). CO2 + H20

k"

>H2CO3

(4)

The products of reactions (2)-(4) are weak acids and bases. As a result, there are buffering reactions that occur in solution as the products are formed and diffuse away from the sensor surface. The three acid-base reactions of concern in the system are NH3 + H 2 0 ~ NH~- + O H - (pKa = 9.3) (5) H2CO3 ~ H + + HCO~-(pKa = 6.4) (6) H C O y ~ H + + CO 2- (pK~ = 10.4) (7) Under the experimental conditions used in this study (urea solutions prepared in deionized water), the pH at the sensor surface will increase towards a steady-state value of nine shortly after the onset of the enzyme catalyzed hydrolysis (Kistiakowsky & Shaw, 1953). Reactions (5)-(7) will reach equilibrium rapidly compared with the time required for diffusion, allowing the acid-base equilibria to be decoupled from the solution of the mass balance equations. Mass balances Within the concentration boundary layer (0 < x < 8), the time- and position-dependent concentrations of urea and the products of the urease catalyzed hydrolysis are described by the following mass balance equations: OC, 02Cu Ot - Du-~Tx2 - R. OCip

Ot

(8)

02C i _

D i

p

i

p ~ y x2 - Rp

and the ith product, respectively, which are functions of time, t, and distance normal to the sensor surface, x. The quantities Du and D~ represent the corresponding diffusivities, and are assumed to be independent of time and space. Equation (9) does not include a term for the transport of ions under the influence of an electric field, since electroneutrality is established within electrolyte solutions on a time scale considerably shorter than the times of interest in this problem. A consequence of the constraint that electroneutrality be maintained within the solution is that the diffusivities of the charged products of reactions (1)-(7) are not independent of each other. This was treated by assigning each ionic product a common, effective diffusion coefficient, Den, representing the effect of electrostatic interactions between the charged species in solution (Eisenberg & Grodzinsky, 1987). The terms Ru and R¢ are reaction terms, representing the rate of disappearance of urea and the products, respectively. (Note that, in general, the product terms R¢ will be negative to represent formation of products.) In the experiments conducted for this study, enzyme was immobilized only at the sensor surface, so the term Ru will be zero except at the sensor surface. The rate of urea consumption at x = 0 is assumed to follow Michaelis-Menten kinetics, i.e. R,Ix=o = Vm~cL + KM

(lO)

where Vmax is the maximum reaction velocity, KM is the Michaelis constant and C~uis the urea concentration at the sensor surface. The use of this expression is justified, since at the relatively low urea concentrations used in the experiments, substrate inhibition is not important (Ramachandran & Perlmutter, 1976). Boundary and initial conditions The following boundary conditions were used. At the edge of the boundary layer, x = ~, all concentrations are equal to the bulk solution values: =

= o p bu,

(11)

(9)

The subscript u denotes urea, while the subscript p denotes a product of the reaction. The quantities C~ and Cip represent the concentrations of urea

At the sensor surface, the flux of reactant (urea) or products to/from the sensor surface is equal to the rate of consumption/production by the enzymatic hydrolysis. 971

N.F. Sheppard, Jr et al.

o0c u Ox ~ =o = Rulx =0

Biosensors & Bioelectronics

(12)

Similarly, the flux of products away from the surface is given by, O' ° G = R~,lx = o POX x=O

(13)

Initial conditions assume spatially uniform concentrations of all species. The urea concentration was initialized to the value of interest. Deionized water with a pH of approximately seven was used for the experiments, defining initial concentrations of H + and O H - a s 1 0 - 7 M. Concentrations of all products were zero. Solution Finite difference methods were used to solve simultaneously Eqs. (8)-(13), to determine the concentration of urea and products within the boundary layer (0 < x < 8) as a function of time. The region above the biosensor surface was discretized into layers, as pictured in Fig. 2. Because the response of the conductimetric biosensor (i.e. the electrical conductance of the interdigitated electrode array) depends on conductivity changes within a finite distance of the sensor surface (approximately one-third of the periodicity of the electrode array, a/3 (Zaretsky et al., 1988b)), the grid dimensions were scaled to the array geometry. Individual layer thicknesses were chosen to be Ax = A/50, and the number of layers was given by n = 8/Ax, where 8 is the boundary layer thickness. At each time step, discretized versions of Eqs. (8)-(13) were solved for the new concentrations in each segment using the Crank-Nicholson method (Press et al., 1986). After this operation, the equilibria for the three dissociation reactions (Eqs. (5)-(7)) were determined in each segment from the new species concentrations using the Newton-Raphson method for multidimensional non-linear equations (Press et al., 1986). Once this step was completed, the time was incremented and the above steps were repeated. At periodic intervals during the solution, the electrical conductivities of each layer were computed for use in the fields model, using Eq. (14) below: = ~lzilF~,~ i

972

(14)

The quantity ~ is the conductivity of the #h layer at the nth time step, FIs Faraday's constant, and zi and /~i are the valence and mobility of the ith ionic species. The quantity ~ j is the molar concentration of the ith ionic species in the jth layer at the nth time step. The mobilities were assumed to be equal to dilute solution values. The sum is taken over all ions present in solution. The set of conductivities, ~ , at a given time, provides the information from which the conductance of the interdigitated electrode array was computed using the electric fields model described below. Fields model

The interelectrode conductance of the sensors at a specified time during the simulation was calculated using a quasi-analytical solution of the electric field equations for the interdigitated electrode array geometry, formulated by Zaretsky (Zaretsky et al., 1988a,b). The cited electric fields model treats the electrode array as a periodic structure, infinite in extent, and solves Laplace's equation using collocation methods to match the mixed boundary conditions in the plane of the electrodes. Given the geometry of the electrodes and the material properties (permittivity and conductivity) of the half spaces above and below the electrodes, the Laplace solver yields the complex admittance (conductance and capacitance) of the interdigitated electrode array. The electrode geometry is specified by the interelectrode spacing, 'a', and the spatial periodicity, A, which is the distance from the centerline of one electrode digit to the corresponding position on the next digit on the same electrode. The final geometric specification needed to calculate admittance is the meander length, the length of the serpentine path between the two electrodes. To account for non-uniform material properties in the direction normal to the surface of the electrode array, the half-spaces above and below the electrodes can be discretized into a set of layers (Zaretsky et al., 1988a,b). Each layer has a specified thickness and conductivity. In the analysis performed here, the glass substrate was assumed to be perfectly insulating and assigned a conductivity of zero. The half-space above the electrodes, i.e. the urea solution, was represented as the set of layers used in the discretization of the transport problem. The conductivity of each

Biosensors & Bioelectronics

layer at any given time was determined from the overall concentration of ions within the layer, as represented by Eq. (14).

RESULTS AND DISCUSSION

Experimental results The interdigitated electrode array used to construct the urea biosensor forms a conductivity cell, monitoring the conductivity in the sample solution within approximately 20 ~m (;t/3) of the array surface. However, unlike a standard conductivity cell, there is not a direct proportionality between the measured conductance of the electrode array and the solution conductivity. This is due to the finite resistance of the on-chip leads connecting the array to the bond pads. The value of this resistance and the cell constant of the array must both be known or determined to permit comparison of experimental data with the model predictions. The lead resistances and cell constants of the devices were determined experimentally following the platinization step in the preparation of the urea biosensor. The electrodes were immersed in NIST-traceable conductivity standard solutions and the impedance measured. Three standards were used. A linear regression of the real part of the measured impedance versus solution resistivity yielded the on-chip series lead resistance (from the intercept) and the cell constant (from the slope). These results are summarized in Table 1. The measured cell constants of the nominally identical devices differed by as much as 25%. However, closer observation revealed that linewidths of the individual electrode arrays differed due to the extent of platinization that each had received. To verify this was the cause of the differing cell constants, the widths of three representative digits in the center of the array were measured under a

A conductimetric urea biosensor

microscope using a micrometer reticle. Using these line measurements, cell constants were estimated using the fields model described above (Sheppard et al., 1993). These estimated values, K~st, reported in Table 1, agree to within 5% of the measured values. To facilitate comparison of biosensor response data measured using different electrode arrays, the on-chip lead resistance determined above was subtracted from the measured resistance to obtain the electrode array resistance. (The reactance, or imaginary part of the measured impedance, was considerably smaller than the resistance; the phase angles ranges from - 5 ° to -15°.) The on-chip lead resistance, which ranged from 110 to 250/2, is a significant component of the measured resistance only for the most concentrated urea solutions tested; at 5 mM urea, the measured resistance decreased from 30,000/2 to approximately 1000/2 during the course of a run. An apparent solution conductivity was then calculated by dividing the measured cell constant by the electrode array resistance. The term 'apparent' is used in recognition of the fact that the solution conductivity is non-uniform in the vicinity of the electrode. Kme~s CraPP -- Rme~ - Rleaa

(15)

Finally, apparent conductivity measured for a 'blank' run in deionized water containing no urea was subtracted from the data. Figures 3(a-c) are plots of the apparent solution conductivity change as a function of time for the immobilized urease biosensors immersed in urea concentrations ranging from 10 ~M to 5 mM. Each point represents the average and standard deviation of the response of four electrode arrays. At any given concentration, the apparent conductivity increases in a logarithmic fashion, that is, the conductivity increases most rapidly upon immersion in the urea solution, and

TABLE 1 Cell constants for the two arrays on representative IME devices.

Measured cell constant, gmeas(cm-1) Series lead resistance, Rlc,a (ll) Normalized spacing, 2a/A (%) Estimated cell constant, Kcst (cm-1)

Device 1 Array 2

Device 1 Array 1

Device 2 Array 2

Device 2 Array 1

0.0432 246 42.8 0.044

0.0420 138 42.4 0.044

0.0541 182 57.1 0.054

0.0503 111 53.4 0.051

973

N.F. Sheppard, Jr et al.

Biosensors & Bioelectronics 6

Cu (raM)

40 a

E v

~5

6

3 0 10 0

,~TI]

~

2

12

0.5

.>_

o

<

1.50

-2

0

2 4 1/[Urea] (raM"1)

6

Fig. 4. Lineweaver-Burke plot constructed from initial rate of change of conductivity data in Fig. 3.

2.5 .

~

0.05

Simulation results

1.00.5-

~,~'~

_, , ~ . a 4 4 , 4 + ¢ ~

0.0

41.5

i 20

i 40

i 60

, 80

]oo, °.°2

, 100

Time (sees)

Fig. 3. Apparent conductivity, as measured by interdigitated electrode array, as a function of time for urea biosensors immersed in urea solutions prepared in deionized water. Panel a: (A) 1 raM, (0) 2 raM, (11) 5 raM; panel b: (&) 0.1 raM, (0) 0.2 raM, (11) 0.5 raM; panel c: (A) 10 I~M, (0) 20 t~M, ( I ) 50 t~M. Points indicate experimental measurements, solid curves represent results of simulations.

increases less rapidly as time evolves. The response is directly proportional to the urea concentration, increasing most rapidly and to the highest level at the highest urea concentration. At the lowest concentrations, presented in Fig. 3(c), the apparent conductivity of the solution decreases slightly upon immersion of the sensor in the urea solution. The data from the first 10 s of each trial were taken as representative of the initial reaction velocity and used to estimate the kinetic parameters of the enzyme immobilized to the sensor. (Note that the data points presented in Fig. 3 represent only one in five of those actually acquired.) Figure 4 is a double reciprocal plot of initial slope (in units of pS cm -1 s -1) versus urea concentration, using data obtained in the range of 0.2-5 mM. The apparent value of KM determined from this construction is 4.0 mM. The maximum activity corresponds to a rate of change of conductivity of 5.3/~S cm -1 s -1. 974

rr T--

4.5-

0.2 0.1

2.0- C 1.5Q_

~

To validate the model of the conductimetric urea sensor, reasonable estimates of the model parameters were made and used to predict the response of the sensor under conditions corresponding to those used to obtain the experimental results presented in Fig. 3, The adjustable parameters in the model include the diffusivities of urea and its hydrolysis products, the kinetics of the immobilized enzyme as described by the Michaelis-Menten kinetic parameters KM and vm~, and the boundary layer thickness, 8. Given the number of parameters and the model complexity, the formulation of a non-linear regression to obtain 'best-fit' parameter values was not deemed worthwhile at the present time. The diffusivity of urea in aqueous solution is 1.38 x 10 -5 cm2/s ( R a t n e r & Miller, 1973). As discussed above, a single diffusion coefficient was assigned to each of the ionic products of the urea hydrolysis. This simplifies the analytical treatment while satisfying the constraint that electroneutrality be maintained. This effective diffusion coefficient was approximated as the geometric mean of the diffusivities of the products of reaction (1), a value equal to 1.94 x 10 -5 crn2/ s. The diffusivities of dissolved ammonia and carbon dioxide were taken as 2.0 x 10 -s and 1.96 x 10 -5 cm2/s, respectively. The kinetics of the urease catalyzed hydrolysis of urea at the surface of the sensor was represented by the Michaelis-Menten expression, Eq. (10). The use of this expression is justified by the relatively low urea concentrations used in the experiments, where inhibition observed at high concentrations is not important. The value

Biosensors & Bioelectronics

of the Michaelis constant, KM, for urease immobilized to various supports is reported to range from 3 to 20 mM (Carr & Bowers, 1980; Owusu et al., 1985). For the purposes of the simulation, the value obtained from the Lineweaver-Burk analysis of the experimental data (Fig. 4), 4.0 mM, was used. A value for the reaction velocity parameter Vmax was estimated by assuming a surface coverage of urease of 1 ng/ mm 2, which represents the amount of protein immobilized to a glass surface using a similar, but not identical, immobilization procedure (Bhatia et al., 1989). This surface coverage was multiplied by the manufacturer's stated activity of the urease preparation (870,000 units/g) and corrected for the fact that urease is only immobilized to the exposed glass substrate of the electrode array, which represents 50% of the area. This analysis yields an estimated surface reaction rate, Vm~,, of 3.6 x 10 -1° mol cm -2 s -1. The implicit assumption that no enzyme activity is lost upon immobilization is compensated by the fact that the immobilization procedure used in this work is likely to yield a greater surface coverage (due to urease to urease coupling) than the cited procedure (Bhatia et al., 1989). The boundary layer thickness, a key parameter in the model, is difficult to determine experimentally. An order of magnitude estimate for this parameter was obtained using boundary layer theory (Schlichting, 1979), assuming that fluid flow across the sensor in the stirred cell could be represented by flow across a flat plate at zero incidence. A fluid velocity of 2.5 cm/s across the face of the 1 cm sensor substrate was estimated using a tracer dye and gave a boundary layer thickness ('displacement thickness') of 770/~M. The temporal evolution of the interdigitated electrode array conductance was computed at each of the urea concentrations tested experimentally using the parameters specified above. At low urea concentrations (100 ~M or less), these calculations predicted a more rapid increase in the apparent solution conductivity than was observed experimentally. This discrepancy appears to be due to the absorption of atmospheric carbon dioxide by the tested urea solutions. Neutralization of the resultant carbonic acid by the basic products of the urea hydrolysis leads to a less rapid increase, and under some conditions a decrease, in the conductivity of the urea solution at the sensor surface. The sequence of reactions consisting of (i) the complete hydrolysis

A conductimetric urea biosensor

of urea according to Eq. (1), followed by (ii) neutralization of a proton by the hydroxide formed, results in the net formation of ammonium and bicarbonate ions, and the loss of a proton. The mobilities of ammonium and bicarbonate sum to less than the proton mobility, so that the net conductivity change of the solution following these reactions is negative. The conductivity of the solution will continue to decrease as long as protons are the dominant charge carrier in the solution. This decrease is most apparent in the 20/zM data presented in Fig. 3(c). At higher urea concentrations, where the acid is neutralized much more rapidly, the effect is not apparent in the experimental data. To account for CO2 absorption in the model, the initial conditions were changed to reflect a concentration of carbonic acid of 2.5/~M, which is approximately one-third of the concentration expected for a solution equilibrated with atmospheric C O 2 (West, 1990). Figure 5 presents a comparison of the model predictions with and without the background CO2, together with the 20/.~M data. The simulation with the background carbonic acid exhibits the initial decrease in conductivity observed experimentally, and subsequently increases at a rate comparable with that observed experimentally. Simulations of the entire set of experiments, incorporating a background concentration of 2.5/zM CO2, are presented as the solid curves in Figs. 3(a-c). The predictions provide an excellent representation of the measured responses, particularly considering the two and a half orders of magnitude range

1.2

.~_=~

1~

w/o CO2

wl CO 2

8


~

0.4-

0-

-0.2

0

.

20

40 60 Time (sees)

,

80

.

1O0

Fig. 5. Apparent conductivity change as a function of time of immersion in a 20 IzM urea solution. Solid points represent experimentally measured values from four interdigitated electrode arrays. Solid curves represent simulations with and without 2.5 IzM dissolved C02.

975

N.F. Sheppard, Jr et al.

Biosensors & Bioelectronics

of urea concentration studied, and the fact that no iterative optimization of the model parameters was attempted. The model was used to examine the sensitivity of the conductimetric urea biosensor response to a number of design and operational parameters, including enzyme kinetics, boundary layer thickness and the geometry of the interdigitated electrode array. The output of the mass transport section of the model demonstrates that, under the experimental conditions used in this study, the response of the conductimetric urea biosensor is reaction rate limited. Figure 6 presents the steadystate urea concentration and conductivity as a function of position within the boundary layer for a 1 mM initial urea concentration. The urea concentration at the sensor surface only reaches 75% of the bulk value at steady state, indicating that sensor operation is reaction rate limited. This is also reflected in the dimensionless Thiele modulus, tk, a ratio of reaction rate to diffusion rate, given by, Ru~2

(16)

DuC,,

62-

where Ru is the reaction velocity expressed by Eq. (10), and c~ is the bulk urea concentration. Using the parameters estimated above, the Thiele modulus, 4~, ranges from 0.13 to 0.20 over the range of urea concentrations considered in this study. The conductivity change due to urea

1

-0.1

0.9

-0.08~

~0.8-

o.o6 8

~0.70 o t~ 0.6-

-0.04"~ ._N

t-

hydrolysis decreases from a maximum at the sensor surface to zero (by definition) at the boundary layer/analyte solution interface. The simulation results presented in Fig. 6 have been normalized by the conductivity change that would result from complete conversion of all of the urea in solution according to Eq. (1). At steady state, the value of this normalized conductivity at the sensor surface is approximately 7%, indicating that the conductimetric biosensor as presently configured is relatively inefficient at transducing the urea concentration into an electrical signal. Incorporation of the enzyme into a transduction element such as a conducting polymer (Nishizawa et aL, 1992; Hoa et al., 1992) or responsive hydrogel (Sheppard et al., 1995) as a means of improving transduction efficiency warrants investigation. The boundary layer thickness, 8, is an important factor controlling both the magnitude and kinetics of the sensor response. As presently configured, the response of the sensor will depend on the flow rate of the analyte solution across the sensor surface, through changes in the boundary layer thickness. Figure 7 illustrates the effect of the boundary layer thickness, 8, on the response of a sensor immersed in I mM urea. For comparison, the simulated response of Fig. 3(a), calculated using an estimated boundary layer thickness of 770 ~m, is presented together with calculations representing boundary layer thicknesses of one half and one quarter of this value. Decreasing the thickness of the boundary layer improves the response time of the sensor, but also decreases

(~m) 201'1 mM

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0:6

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Fig. 6. Spatial variation of urea and conductivity across the diffusion boundary layer, for an interdigitated electrode array immersed in 1 mM urea under the conditions of Fig. 3. Dashed line represents profile after 90 s elapsed time, corresponding to the last data point in Fig. 3. Solid line represents profile after 360 s, when steady state has been reached.

976

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Fig. 7. Simulation of apparent conductivity change as a function of time of immersion in a 1 mM urea solution, for boundary layer thicknesses of 770, 385 and 192.5 lgn.

Biosensors & Bioelectronics

A conductimetric urea biosensor

the magnitude of the steady-state conductivity change. The diminished response is due to the reaction rate limited kinetics of the sensor. For a given urea concentration, the diffusive flux of urea hydrolysis products away from the sensor will be essentially independent of boundary layer thickness. As the boundary layer thickness is reduced, there will be a proportionate reduction in product concentrations at the sensor surface such that the concentration gradient remains constant. The result, that the apparent conductivity change is proportional to the boundary layer thickness, is reflected in the simulation results presented in Fig. 8. The geometry of the interdigitated electrode array used to construct the biosensor influences the magnitude of the response, but not the kinetics, which is determined solely by the reaction rate and mass transport. The response is defined here as the apparent conductivity change measured by the biosensor following immersion in the urea solution. A change only in the lateral extent of the array, effected by modifying the length of the digits or the number of digits, will not affect this response. These changes in electrode geometry will, however, increase or decrease the apparent cell constant of the electrode array, resulting in a proportionate change in the measured resistance, as described by Eq. (15). A more interesting case to consider is miniaturization of the sensor, by reducing the digit width and/or interdigit spacing. If these are reduced proportionately, while maintaining the original length of the digits, then the cell constant will remain unchanged (Sheppard et al., 1993). Figure 8 illustrates the effect of decreasing the

10 °

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~

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0

0

g0

160

150

260

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(~rn) Fig. 8. Steady-state apparent conductivity change as a function of boundary layer thickness, for interdigitated electrode arrays of differing spatial wavelength, A.

spatial wavelength of the interdigitated electrode array, A. The figure is a plot of the steady-state, apparent conductivity change versus boundary layer thickness, for devices having A values of 20, 40 and 60 (used in the experiments) ~m, and immersed in a 1 mM urea solution. Decreasing A increases the magnitude of the response; the progressively smaller volume of electrolyte sampled by the miniaturized sensor has a higher average conductivity since, as shown in Fig. 6, the conductivity decreases with distance from the sensor surface. However, for the boundary layer thicknesses of 100 ~m or more expected in practice, the analysis presented in Fig. 8 suggests that the steady-state conductivity changes will differ by less than 5% for the three different devices. This recognition, that equivalent performance can be expected from the interdigitated electrode arrays having spatial periodicity, A, less than the boundary layer thickness, 8, can facilitate the design and miniaturization of this type of sensor.

CONCLUSION A model has been developed to predict the response of a conductimetric urea biosensor formed by immobilizing urease to the interdigit space of a planar interdigitated electrode array. The model combines an analysis of urea mass transport and enzymatic hydrolysis with an electric fields model describing the interelectrode conductance of an interdigitated electrode array. To validate the model, urea sensors were constructed by immobilizing urease onto the interdigit space of planar interdigitated electrode arrays. The sensors had very rapid response times and were sensitive to urea concentrations from 10 ~m to 5 mM in deionized water. The predictions of the model, based on reasonable estimates for the adjustable parameters, were in good agreement with the experimental data. The effect of altering sensor design parameters such as boundary layer length and background conductance can be examined with the model. Extensions of the model can be used to examine sensor behavior with different buffering systems and immobilization methods, as well as sensors incorporating different enzyme/substrate pairs. The utility of the model presented above is that it demonstrates, for the first time, that the transport modelling which has long been applied 977

N.F. Sheppard, Jr et al. to the operation of potentiometric and amperometric enzyme based biosensors can be applied to modelling conductimetric biosensor operation. Given the success of the model at reproducing the admittedly idealized experimental conditions, factors such as enzyme immobilized within a gel layer and more complex sample matrices having a significant background conductivity can be analyzed for the design of a practical sensor.

ACKNOWLEDGMENTS This work was supported by a National Science Foundation Presidential Young Investigator Award to NFS (ECS-9058419). A . G . E . thanks Allage Associates, Inc. for support.

REFERENCES Bhatia, S., Shriver-Lake, L., Prior, K., Georger, J., Calvert, J., Bredehorst, R. & Ligler, F. (1989). Use of thiol-terminal silanes and heterobifunctional crosslinkers for immobilization of enzymes on silica surfaces. Anal. Chem., 178, 408-413. Blakeley, R. L., Hinds, J. A., Kunze, H. E., Webb, E. C. & Zerner, B. (1969). Jack bean urease (EC3.5.1.5). Demonstration of a carbamoyltransfer reaction and inhibition by hydroxamic acids. Biochem., 8, 1991-2000. Carr, P. W. & Bowers, L. D. (1980). Immobilized Enzymes in Analytical and Clinical Chemistry. John Wiley & Sons, New York. Cullen, D. C., Sethi, R. S. & Lowe, C. R. (1990). Multianalyte miniature conductance biosensor. Anal. Chim. Acta, 231, 33-40. Dzydevich, S. V., Shul'ga, A. A., Soldatkin, A. P., Hendji, A. M., Jaffrezic-Renault, N. & Martelet, C. (1994). Conductometric biosensors based on cholinesterases for sensitive detection of pesticides. Electroanalysis (N.Y.), 6, 752-758. Eisenberg, S. R. & Grodzinsky, A. J. (1987). The kinetics of chemically induced nonequilibrium swelling of articular cartilage and corneal stroma. J. Biomech. Eng., 109, 79-89. Endres, H. R. & Drost, S. (1991). Optimization of the geometry of gas-sensitive interdigital capacitors. Sensors & Actuators B, 4, 95-98. Fouke, J. M., Wolin, A. D., Saunders, K. G., Neuman, M. R. & McFadden, E. R., Jr. (1988). Sensor of measuring surface fluid conductivity in vivo. IEEE Trans. Biomed. Eng., 35, 877-881. H o a , D. T., Kumar, T. N. S., Punekar, N. S., Srinivasa, R. S., Lal, R. & Contractor, A. Q. 978

Biosensors & Bioelectronics (1992). Biosensor based on conducting polymers. Anal. Chem., 64, 2645-2646. Jacobs, P., Suls, J. & Sansen, W. (1994). Performance of a planar differential-conductivity sensor for urea. Sensors & Actuators B, 20, 193-198. Janata, J., Josowicz, M. & DeVaney, D. M. (1994). Chemical Sensors. Anal. Chem., 66, 207R-228R. Jespersen, N. D. (1975). A thermoehemical study of the hydrolysis of urea by urease. J. Am. Chem. Soc., 97, 1662-1667. Kistiakowsky, G. B. & Shaw, W. H. R. (1953). Ureolytic activity of urease at pH 8.9. J. Am. Chem. Soc., 75, 2751-2754. Lee, H. L. (1982). Optimization of a Resin Cure Sensor. Massachusetts Institute of Technology. Mikkelsen, S. R. & Rechnitz, G. A. (1989). Conductometric transducers for enzyme-based biosensors. Anal. Chem., 61, 1737-1742. Nishizawa, M., Matsue, T. & Uchida, I. (1992). Penicillin sensor based on a microarray electrode coated with pH-responsive polypyrrole. Anal. Chem., 64, 2642-2644. Nyamsi Hendji, A. M., Jaffrezic-Renault, N., Martelet, C., Shul'ga, A. A., Dzydevich, S. V., Soldatkin, A. P. & El'skaya, A. V. (1994). Enzyme biosensor based on a micromachined interdigitated conductometric transducer: application to the detection of urea, glucose, acetyl- and butyrylcholine chlorides. Sensors Actuators B, 21, 123-129. Owusu, R. K., Trewhella, M. J. & Finch, A. (1985). Flow microcalorimetric study of immobilized enzyme kinetics using the urea-immobilized urease system. Biochim. Biophys. Acta, 830, 282-287. Pethig, R. (1991). Dielectric-based biosensor. Biochem. Soc. Trans., 19, 21-25. Press, W. H., Flannery, B. P., Teukolsky, S. A. & Vetterling, W. T. (1986). Numerical Recipes. Cambridge University Press, Cambridge. Ramachandran, K. B. & Perlmutter, D. D. (1976). Effects of immobilization on the kinetics of enzyme-catalyzed reactions. II. Urease in a packed-column differential reactor system. Biotech. Bioeng., 18, 685-699. Ratner, B. D. & Miller, I. F. (1973). Transport through crosslinked poly(2-hydroxyethyl methacrylate) hydrogel membranes. J. Biomed. Mater. Res., 7, 353-367. Schlichting, H. (1979). Boundary-layer Theory, McGraw-Hill, New York. Sheppard, Jr., N. F., Lesho, M. J., McNally, P. & Francomacaro, A. S. (1995). Microfabricated conductimetric pH Sensor. Sensors & Actuators B (Chemical), 28, 95-102. Sheppard, Jr., N. F., Tucker, R. C. & Wu, C. (1993). Electrical conductivity measurements using microfabricated interdigitated electrodes. Anal. Chem., 65, 1199-1202.

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microfabricated interdigitated electrodes. Anal. Chem., 65, 1199-1202. Taylor, R. F., Marenchic, I. G. & Cook, E. J. (1988). An acetylcholine receptor-based biosensor for the detection of cholinergic agents. Anal. Chim. Acta, 213, 131-138. Thompson, J. C., Mazoh, J. A., Hochberg, A., Tseng, S. Y. & Seago, J. L. (1991). Enzyme-amplified rate couductimetric assay. Anal. Biochem., 194, 295-301. Valdes, J. J., Wall, Jr., J. G., Chambers, J. P. & Eldefrawi, M. E. (1988). A receptor-based capacitive biosensor. Johns Hopkins A P L Tech. Digest, 9, 4-10. Watson, L. D., Maynard, P., Cullen, D. C., Sethi, R. S., Brettle, J. & Lowe, C. R. (1988). A microelectronic conductimetric biosensor. Biosensots, 3, 101-115.

A conductimetric urea biosensor

West, J. B. (1990). Respiratory Physiology. Williams and Wilkins, New York. Zaretsky, M. C., Li, P. & Melcher, J. R. (1988a). Estimation of thickness, complex bulk permittivity and surface conductivity using interdigital dielectrometry. Proc. IEEE Symposium on Electrical Insulation, Cambridge, MA, 1988. IEEE Press, Piscataway, NJ, pp. 162-166. Zaretsky, M. C., Mouyad, L. & Melcher, J. R. (1988b). Continuum properties from interdigital electrode dielectrometry. IEEE Trans. Elec. Ins., 23, 897-917. Zhou, G., Kowel, S. T. & Srinivasan, M. P. (1988). A capacitance sensor for on-line monitoring of ultrathin polymeric film growth. IEEE Trans. Components, Hybrids, Manufact. Technol., 11, 184-190.

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