Journal of Electroanalytical Chemistry 641 (2010) 104–110

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Journal of Electroanalytical Chemistry

journal homepage: www.elsevier .com/locate / je lechem

Theoretical and experimental study of bi-enzyme electrodes withsubstrate recycling

Neeraj Kohli a, Ilsoon Lee a,*, Rudy J. Richardson b, Robert M. Worden a,*

a Department of Chemical Engineering and Materials Science, Michigan State University, East Lansing, MI-48824, USAb Toxicology Program, Department of Environmental Health Sciences, School of Public Health, The University of Michigan, Ann Arbor, MI 48109-2029, USA

a r t i c l e i n f o

Article history:Received 18 August 2009Received in revised form 8 December 2009Accepted 10 December 2009Available online 16 December 2009

Keywords:Bi-enzyme electrodeElectrochemicalNESTSubstrate recyclingSignal amplificationTheoretical model

1572-6657/$ - see front matter � 2010 Published bydoi:10.1016/j.jelechem.2009.12.010

* Corresponding authors. Fax: +1 517 432 1105.E-mail addresses: leeil@egr.msu.edu (I.

(R.M. Worden).

a b s t r a c t

The range of analytes for which biosensors can be developed can be increased substantially by couplingmultiple enzyme activities into reaction pathways. The sensitivity of the biosensors can also be increased(or amplified) dramatically by incorporating a substrate-recycling scheme. For low concentrations of sub-strate, this paper presents a theoretical model for a bi-enzyme biosensor that achieves signal amplifica-tion via substrate recycling. The bi-enzyme electrode was fabricated by co-immobilizing two enzymes:tyrosinase and NEST (neuropathy target esterase domain). The model was validated by assembling thebi-enzyme interface on a rotating disk electrode and measuring the biosensor’s response to phenyl val-erate substrate under varying rotating speeds. The model can help quantify the influences of mass trans-port, partition coefficients, enzymes, and electron-transfer kinetics on the metrological characteristics ofthe bi-enzyme electrode. This information can help optimize the performance of biosensors that use sub-strate recycling.

� 2010 Published by Elsevier B.V.

1. Introduction

Biosensors based on enzymes are becoming popular in variousfields of analytical chemistry because of their high selectivity,specificity and low cost for mass production. Enzyme electrodeshave been developed for many applications such as electrochemi-cal immunoassays, monitoring of nutrients, and detection of pollu-tants [1–3].

The range of analytes for which reporting interfaces (biosen-sors) can be developed can be increased substantially by couplingmultiple enzyme activities into reaction pathways. For example,the NEST (neuropathy target esterase (NTE) domain) biosensor (de-scribed recently in one of our publication) [4], couples NEST ester-ase activity with two tyrosinase oxidation activities: cresolaseactivity and catecholase activity, resulting in an electrochemicaldetection of phenyl valerate.

The sensitivity of the reporting interfaces can be increased sub-stantially by incorporating a substrate-recycling scheme. In thesesensors, an analyte that is oxidized or reduced at the electrode iselectrochemically recycled so that it can interact with the electrodemore than once, thus amplifying the electrode’s signal. The shuttleanalyte can be either the analyte of interest or a compound that isproduced by an additional enzyme reaction. Amplification by sub-

Elsevier B.V.

Lee), worden@egr.msu.edu

strate recycling has been achieved by several mechanisms. Onemethod uses a chemical reaction to regenerate the enzyme’s sub-strate [1]. Another method uses a second enzymatic reaction,which converts the enzyme’s product back to the substrate [5]. Athird mechanism is based on electrochemically recycling the reac-tion product back to the substrate [6,7].

Mathematical models can be used to analyze the simultaneousmass transfer and reaction steps that occur in biosensors that usesubstrate recycling in order to improve their metrological charac-teristics. Such a theoretical analysis can help elucidate the rate-limiting step(s) and evaluate the performance characteristics ofsubstrate-recycling biosensors. Gorton et al. [9] theoretically con-sidered and experimentally demonstrated the various rate limitingsteps for tyrosinase enzyme modified electrodes with substraterecycling. This model assumed that diffusional resistance withinthe enzyme layer was negligible. Coche-Guérente et al., in a seriesof papers, presented a theoretical model for an immobilized en-zyme layer with an electrochemical substrate-recycling scheme[6–8] This model, which was applied to tyrosinase modified elec-trodes, includes the influence of diffusion, partition coefficient, en-zyme, and electron-transfer kinetics. However, these theoreticalanalyses have been limited to single-enzyme electrodes and arethus not suitable for bi-enzyme electrodes.

NTE is a membrane protein found in human neurons and othercells, including lymphocytes [10–13]. Binding of certain organo-phosphorus (OP) compounds to NTE is believed to cause OP-in-duced delayed neuropathy (OPIDN), a type of paralysis for which

N. Kohli et al. / Journal of Electroanalytical Chemistry 641 (2010) 104–110 105

there is no effective treatment. Mutations in NTE have also beenlinked with serious neurological diseases, such as motor neurondisease [14]. Recently, in a publication, we described the develop-ment of a bi-enzyme biosensor interface consisting of two en-zymes: tyrosinase and a catalytically active fragment of NTEknown as NEST [4]. Potential applications of the biosensor includescreening OP compounds for NTE inhibition, and investigating theenzymology of wild type and mutant forms of NTE.

The current paper presents a theoretical model for a bi-enzymerotating disk electrode consisting of NEST and tyrosinase. Themolecular architecture of the bi-enzyme electrode is shown inFig. 1. The NEST protein converts phenyl valerate to phenol, whichis converted to o-quinone by tyrosinase. The o-quinone is electro-chemically reduced to catechol at the electrode’s surface, resultingin current. A portion of the catechol produced is then converted too-quinone by tyrosinase. Catechol thus serves as a shuttle analytethat can undergo successive cycles of enzymatic oxidation-electro-chemical reduction (substrate recycling), resulting in an amplifica-tion of the biosensor’s response.

The theoretical model includes the influence of the mass trans-port, permeation through the enzyme layers, and enzyme kinetics.This model is expressed in dimensionless form to minimize thenumber of constants that must be evaluated. The biosensor wasassembled on a rotating disk electrode, and the biosensor’s perfor-mance was measured at a variety of rotational velocities and sub-strate concentrations to evaluate the constants and validate themodel.

2. Experimental section

2.1. Materials

Thioctic acid, poly-L-lysine (PLL) (molecular weight �15,000),tyrosinase, sodium phosphate (monobasic and dibasic), and so-dium chloride were obtained from Sigma (St. Louis, MO). Ultrapurewater was supplied by a Nanopure-UV four-stage purifier (Barn-stead International, Dubuque, IA); the purifier was equipped witha UV source and a final 0.2 lm filter.

2.2. Preparation of gold electrode

The molecular architecture of the biosensor is shown schemat-ically in Fig. 1. Gold rotating disk electrodes (Metrohm Limited,Herisau, Switzerland) were polished with alumina powder anddipped in a 5 mM solution of thioctic acid in ethanol for 30 min.The electrodes were washed with absolute ethanol, dried undernitrogen and dipped in PLL solution for 45 min. The PLL solutionwas prepared by adding 12 mg of poly-L-lysine in 50 ml of

Fig. 1. Molecular architecture of bi-enzyme electrode. The scheme has beenadapted from Kohli et al. [4].

20 mM phosphate buffer (pH 8.5). The electrodes were then rinsedwith water and dipped in an equimolar solution of tyrosinase andNEST in 0.1 M phosphate buffer for 45 min. The last two steps wererepeated three times to create three bilayers of PLL and tyrosinase/NEST. The electrodes were then washed with water, dried undernitrogen, and dipped in phosphate buffer (0.1 M, pH 7.0) for test-ing. All the experiments were done at room temperature (23–25 �C).

2.3. Preparation of phenyl valerate solution

Phenyl valerate (15 mg) was dissolved in 1 mL of dimethylform-amide (DMF), and 15 mL of water containing 0.03% (v/v) Triton wasadded slowly while swirling the solution. For potential step vol-tammetry experiments, small aliquots of the resulting phenyl aler-ate micellar solution (5.3 mM) were added to the phosphate bufferto obtain the desired concentrations.

2.4. Chronoamperometry and other measurements

The bi-enzyme rotating disk electrodes containing NEST andtyrosinase were maintained at a potential of �100 mV (versus aAg/AgCl reference electrode) using a CHI 660B electrochemicalanalyzer (CH instruments, Austin, TX). To perform electrochemicalmeasurements, the bi-enzyme rotating disk electrodes (area =0.07 cm2) were dipped in 0.1 M phosphate buffer (pH 7.0), andsmall aliquots of phenyl valerate, phenol or catechol solution wereadded. The steady state current was then measured at differentrotating speeds. Ellipsometric measurements were done using aWVASE 32 (J.A. Woollam Co. Inc., Lincoln, NE) ellipsometer. The an-gle of incidence was 75� for all experiments. The refractive indicesof films were assumed to be n = 1.5, k = 0. Unless otherwise stated,all the errors reported in this paper are the standard deviation (r)values determined using four different electrodes.

3. Theoretical model

3.1. Enzyme kinetics

Tyrosinase is a copper-containing oxidase, which possesses twodifferent activities as illustrated in reaction A.

ðAÞ

The second step, known as enzyme’s catecholase activity com-prises three different redox states of copper containing active site:resting form (Emet), reduced form (Ered) and oxidized form (Eoxy).The enzymatic conversion of catechol to o-quinone has beenshown to be represented by the following reaction steps [6–8]:

EdeoxyðCu2þ2 Þ þ O2 ! EoxyðCu4þ

2 � O2�2 Þ k1 ðBÞ

EoxyðCu4þ2 � O2�

2 Þ þ S! EmetðCu4þ2 Þ þ P k2 ðCÞ

EmetðCu4þ2 Þ þ S! EdeoxyðCu2þ

2 Þ þ P k3 ðDÞ

where S represents catechol and P represents o-quinone.At steady-state conditions, it has been shown [6–8] that the

overall rate v can be expressed by the Michaelis–Menten formal-ism (Eq. (1)) with an apparent Michaelis constant Kapp

m = �220 lM.

106 N. Kohli et al. / Journal of Electroanalytical Chemistry 641 (2010) 104–110

v ¼ kcat½Et�½S�Kapp

m þ Sð1Þ

where Et, S and kcat represent the enzyme concentration, catecholconcentration and turnover number, respectively.

Because the experiments conducted in the present study in-volve substrate concentrations around two orders of magnitudeless than Kapp

m , the kinetics can be assumed to be first order relativeto the substrate concentration.

Besides its catecholase activity tyrosinase is also able to cat-alyze ortho-hydroxylation (monophenolase activity, see reactionA) of monophenols to o-diphenols (catechols) that, in turn, areoxidized to corresponding o-quinones (catecholase activity). Be-cause the hydroxylation activity of tyrosinase is expressed inconjunction with oxidation of o-diphenol to its o-quinone, someauthors have defined monophenolase activity as the completeconversion of monophenols to o-quinone. Indeed, the hydroxyl-ation step proceeds and has been shown to be much slowerthan the oxidation of o-diphenol to o-quinone and is thereforeconsidered to be the rate limiting step [6–8]. The enzymaticoxidation of phenol to o-quinone has also been shown to followMichaelis–Menten formalism [6–8], with an apparent Kapp

m of�250 lM.

Similarly, the esterase activity of NTE (or NEST) can convertphenyl valerate to phenol and, for simplicity, this reaction can alsobe assumed to follow Michaelis–Menten formalism.

3.2. Assumptions

Fig. 2 is a schematic representation of a bi-enzyme rotatingdisk electrode, modified with an enzyme layer that containsNEST and tyrosinase, and has a thickness L. Using the sameapproach as one already reported in a theoretical treatment ofbiosensors [6–8], the sequential steps that lead to an electro-chemical signal in the presence of phenyl valerate substrate S1

are as follows:Mass transfer of phenyl valerate (S1), phenol (S2), catechol (S3),

and quinone (Q4) through a stagnant film between the bulk and the

L

δ

Electrode

Enzymes containing layer

Stagnant film

E1

S1

S2

Q4 S3

De

Df

Bulk solution

E2 E3

Fig. 2. Schematic representation of a rotating disk bi-enzyme electrode andprinciple of its functioning in the presence of phenyl valerate substrate. S1, S2, S3

and Q4 denote the substrate phenyl valerate, phenol, catechol and o-quinone,respectively. E1 denotes NEST esterase activity. E2 and E3 denote tyrosinase’sphenolase and catecholase activities, respectively. L denotes the thickness of theenzyme. This picture has been adapted from Coche-Guerente [8].

enzyme layer. For a rotating disk electrode, this film has a thick-ness d ¼ 1:61D1=3

e t1=6x�1=2 (as formulated by Coche-Guerenteet al.) [6], where De, t and x represent the diffusion coefficient,kinematic viscosity and rotation speed, respectively. For simplicity,the diffusion coefficients of S1, S2, S3 and Q4 in the bulk aqueousphase and stagnant film were assumed to be identical (De).

Partitioning of S1, S2, S3 and Q4 from the stagnant film intothe enzyme layer. The kinetics of partitioning were assumedto be rapid so that the interfacial concentrations in the filmand enzyme layers remained at equilibrium. In addition, thepartition coefficients (kp) were assumed to be identical for S1,S2, S3 and Q4. Thus, yielding the following equilibriumexpressions.

½S1�L� ¼ kp½S1�Lþ ð2Þ

½S2�L� ¼ kp½S2�Lþ ð3Þ

½S3�L� ¼ kp½S3�Lþ ð4Þ

½Q 4�L� ¼ kp½Q4�Lþ ð5Þ

Diffusion of S1, S2, S3 and Q4 within the enzymatic layer of thicknessL. The enzymatic layer was assumed to behave like a semi-perme-able membrane. The model was simplified by assuming an identicaldiffusion coefficient (Df) for S1, S2, S3 and Q4.

At steady-state conditions, all the substrates S1, S2, S3 and Q4 arepresent in the enzymatic layer, although only S1 is present in thebulk solution. Inside the enzyme layer, for low concentrations ofphenyl valerate, the conversion of phenyl valerate (S1) to phenolcan be given by the following first order equation:

v1 ¼k1½E1�½S1�

K1ð6Þ

where E1 denotes the total concentration of active NEST, and K1 isthe apparent Km value. The rate of conversion of phenol to o-qui-none and catechol to o-quinone has been shown to be given by sim-ilar first order expressions [6–8]:

v2 ¼k2½E2�½S2�

K2ð7Þ

v3 ¼k3½E3�½S3�

K3ð8Þ

where E2 and E3 represent the concentrations of monophenolaseand catecholase active sites, respectively. Electrode potential wasalso assumed to be sufficiently negative so that the electrochemicalreduction step is not rate limiting.

3.3. Model equations

Using the same approach as the one already reported in a the-oretical treatment of biosensors [6–8,15], and also from mass bal-ance that takes into account diffusive flux and chemical reaction,the equations describing the concentrations of phenyl valerate(S1), phenol (S2), catechol (S3), and quinone (Q4), at steady stateare as follows:

@2S1

@x2 �S1

K21

¼ 0 ð9Þ

@2S2

@x2 �S2

K22

þ S1

K21

¼ 0 ð10Þ

@2S3

@x2 �S3

K23

¼ 0 ð11Þ

N. Kohli et al. / Journal of Electroanalytical Chemistry 641 (2010) 104–110 107

@2Q4

@x2 þS2

K22

þ S3

K23

¼ 0 ð12Þ

where x is the distance from electrode surface. As defined below, K1,K2 and K3 represent the reaction lengths [6–8] related to phenylvalerate (S1), phenol (S2), and catechol (S3):

K3 ¼Df K3

k3E3

� �12

K2 ¼Df K2

k2E2

� �12

K1 ¼Df K1

k1E1

� �12

ð13Þ

3.4. Boundary conditions

To determine concentration profiles within the enzyme layer,Eqs. (9)–(12) were solved with the following boundary conditions:

(1) Applied potential is sufficiently negative, so that

½Q 4�x¼0 ¼ 0 ð14Þ

(2) Because phenyl valerate and phenol are not directly electro-active

@S1

@x

� �x¼0¼ 0;

@S2

@x

� �x¼0¼ 0 ð15Þ

(3) Only phenyl valerate is present in the bulk

½S1�x¼1 ¼ S1ð1Þ; ½S2�x¼1 ¼ 0; ½S3�x¼1 ¼ 0; ½Q4�x¼1 ¼ 0 ð16Þ

At steady state, assuming stagnant film theory, the flux of phenylvalerate, phenol, catechol, and quinone across the film (thick-ness = �d) equals that entering the enzyme layer.

Df@S1

@x

� �x¼L�¼ De

kpdkpS1ð1Þ � ½S1�x¼L�� �

ð17Þ

Df@S2

@x

� �x¼L�¼ � De

kpd½S2�x¼L� ð18Þ

Df@S3

@x

� �x¼L�¼ � De

kpd½S3�x¼L� ð19Þ

Df@Q 4

@x

� �x¼L�¼ � De

kpd½Q 4�x¼L� ð20Þ

From the law of conservation of mass, for any x inside the en-zyme layer:

½Q 4� þ ½S1� þ ½S2� þ ½S3� ¼ kpS1ð1Þ ð21Þ

Current density ¼ J ¼ iA¼ �nFDf

@S3

@x

� �x¼0¼ nFDf

@Q 4

@x

� �x¼0

ð22Þ

Solution of Eqs. (9)–(12) gave the following analytical expres-sions for concentration profiles of phenyl valerate (S1), phenol(S2), catechol (S3), and quinone (Q4).

S1 ¼kpS1ð1Þ

Pmh1me

sinh h1 þ cosh h1cosh

xK1

� �ð23Þ

S2 ¼kpS1ð1Þ

Pmh1me

sinh h1 þ cosh h1

h21

h22 � h2

1

!cosh

xK1

� ��

�Pmh1

mesinh h1 þ cosh h1

Pmh2me

sinh h2 þ cosh h2

!cosh

xK2

#ð24Þ

S3 ¼ kpS1ð1Þ 1� 1Pmh1

mesinh h1þcosh h1

� 1Pmh1

mesinh h1þcosh h1

h21

h22�h2

1

!"

� 1�Pmh1

mesinh h1þcosh h1

Pmh2me

sinh h2þcosh h2

!#

� coshx

K3�

Pmh3me

sinh h3þcosh h3

Pmh3me

cosh h3þ sinh h3sinh

xK3

" #ð25Þ

Q4 ¼ kpS1ð1Þ � S1 � S2 � S3 ð26Þ

where

me ¼De

dPm ¼

kpDf

Lh1 ¼

LK1

; h2 ¼L

K2; h3 ¼

LK3

me is the mass transfer coefficient across the stagnant film, and Pm

denotes the permeability inside the enzyme layer. The ratio Pmme

,which compares the mass transfer in enzyme layer to that in bulk,is also known as the Sherwood number. The dimensionless param-eters h1, h2, and h3, also known as the Thiele modulus, compare theenzymatic reaction rates of phenyl valerate, phenol, and catecholsubstrates, respectively, with their diffusion in the enzymatic layerof thickness L.

The cathodic current sensitivity (Scpv) of the electrode toward

phenyl valerate substrate can then be derived from Eqs. (25) and(22):

Scpv ¼

Jpv

S1ð1Þ

¼ 2FPmh3 1� 1Pmh1

mesinh h1 þ cosh h1

� 1Pmh1

mesinh h1 þ cosh h1

"

� h21

h22 � h2

1

!� 1�

Pmh1me

sinh h1 þ cosh h1

Pmh2me

sinh h2 þ cosh h2

!#

�Pmh3

mesinh h3 þ cosh h3

Pmh3me

cosh h3 þ sinh h3

" #ð27Þ

where S1ð1Þ denotes the bulk phenyl valerate concentration. Thisequation demonstrates that the bio-electrode response is affectedby the rate of mass transport in the stagnant film (me) and the en-zyme layer (Pm), as well as by the enzymatic activities toward phe-nyl valerate (h1), phenol (h2), and catechol (h3). Eq. (27) was derivedassuming that only phenyl valerate is present in the bulk. However,if only phenol is present in the bulk, then it has been shown that thefollowing relation can be derived [6–8]:

Scph ¼

Jph

S2ð1Þ¼ 2FPmh3 1� 1

Pmme

h2 sinh h2 þ cosh h2

!

�Pmme

h3 sinh h3 þ cosh h3

Pmme

h3 cosh h3 þ sinh h3

!ð28Þ

where Scph denote the cathodic current sensitivity of the electrode in

the presence of phenol, and S2ð1Þ phenol bulk concentration. Sim-ilarly, if only catechol is present in the bulk, then it has been shownthat the following relations related to cathodic and anodic currentsensitivities can be derived [6,7]:

Scct ¼

Jcct

S3ð1Þ¼ �2FPm

1� Pmh3me

sinh h3 � cosh h3

Pmme

cosh h3 þ sinh h3h3

ð29Þ

Sact ¼

Jact

S3ð1Þ¼ 2FPm

1Pmme

cosh h3 þ sinh h3h3

ð30Þ

where Scct denotes the sensitivity of the electrode in the presence of

catechol at an applied potential of �0.1 V (where the major contri-bution to current comes from the reduction of o-quinone), and Sa

ct

108 N. Kohli et al. / Journal of Electroanalytical Chemistry 641 (2010) 104–110

denotes the sensitivity at an applied potential of 0.5 V (where themajor contribution to current comes from oxidation of catechol thatcould not be converted to o-quinone by tyrosinase). For rotatingdisk electrodes we can assume me to be given by the following Le-vich equation [6,7]:

me ¼D2=3

e

1:613m1=6x�1=2 ð31Þ

On rearranging Eqs. (29) and (31) and substituting the value of me

from Eq. (31), the following relations can be obtained. The followingrelations were used by us (data shown in the next section) to vali-date the model and also estimate some parameters.

Scct

Sact

¼ ð�1þ cosh h3Þ þ ð1:613PmD�2=3e m1=6h3 sinh h3Þx�

12 ð32Þ

1Sa

ct

¼ 12FPm

sinh h3

h3

� �þ 1:613

D�2=3e m1=6 cosh h3

2F

!x�1

2 ð33Þ

240

260

/mol

)

3.5. Validation of the model

The model was validated using bi-enzyme electrodes contain-ing NEST and tyrosinase. Four electrodes (A, B, C, and D) were used,and the steady state cathodic and anodic current sensitivities, Sc

ct

and Sact ; were measured at two different catechol concentrations

(3 and 5 lM), under varying electrode rotation speeds. Similarly,the cathodic current sensitivities, Sc

ph and Scpv ; were also measured

at different phenol (3 and 5 lM) and phenyl valerate concentra-tions (3 and 5 lM). While the cathodic sensitivity, Sc

ct ; remainedpractically constant with rotation rate, Sc

ph and Scpv ; decreased with

rotation rate.

y = 0.0155x + 0.00093R2 = 0.9818

0

0.001

0.002

0.003

0.004

0.05 0.07 0.09 0.11 0.13 0.15-1/2 (rad-1/2s1/2)

1/S c

ta (m

olA-1

cm-1

)

y = 46.641x + 2.1358R2 = 0.9853

0123456789

10

0.05 0.07 0.09 0.11 0.13 0.15-1/2 (rad-1/2s1/2)

S ctc /S

cta

a

b

Fig. 3. Reciprocal plots of Sact and Sc

ctSa

ctversus the square root of rotation rate for

electrode A.

Fig. 3 shows reciprocal plots of Sact and Sc

ctSa

ctversus the square root

of rotation rate. Both plots, as predicted by the model (Eqs. (32)and (33)), showed linearity with coefficients of determination(R2) greater than 0.98, suggesting that the model reasonably repre-sents the electro-enzymatic processes occurring in the presence ofcatechol. From the slopes and intercepts of the fitted lines inFigs. 3a and 3b, Eqs. (32) and (33) can be used to determineh3 = 1.81 (±0.2), Pm = 0.0091 (±0.0015) cm/s and De = 2.2(±1.2 � 10�5) cm2/s. Alternatively, De can be determined separatelyusing a Levich plot of data obtained from a bare gold electrode. Theobtained value of De compares well with published values of De forcatechol [6,7].

Fig. 4 shows the current sensitivity to phenol as a function ofelectrode rotation speed. The sensitivity of the electrode was foundto decrease with increasing rotation rates. In principle, Eq. (28)could be fitted to the data shown in Fig. 4 and used to determineh2, Pm, and h3. However, the rotating disk electrode system usedby us can give data points at only six rotation speeds. To get morereliable values of the parameters, the values of Pm and h3 obtainedwith catechol present in the bulk solution were used, and Eq. (28)was fitted to the data in Fig. 1.4 to give a best fit value of h2 = 0.23(±0.05).

Fig. 5 shows the current sensitivity to phenyl valerate as a func-tion of electrode rotation speed. Like phenol, the sensitivity of theelectrode to phenyl valerate decreased with increasing rotationrate. Eq. (27) was fitted to the experimental data using the previ-

50 100 150 200 250 300 350

160

180

200

220

Cur

rent

(Acm

w (radian/s)

Fig. 4. Cathodic sensitivity, Scph ; in the presence of phenol as a function of rotation

rate.

50 100 150 200 250 300 35060

80

100

120

140

160

180

Cur

rent

(Acm

/mol

)

w (radians/s)

Fig. 5. Cathodic sensitivity, Scpv ; in the presence of phenyl valerate as a function of

rotation rate.

N. Kohli et al. / Journal of Electroanalytical Chemistry 641 (2010) 104–110 109

ously determined Pm, h2, and h3 parameters (h3 = 1.81, h2 = 0.23,Pm = 0.0091 cm/s). A best fit value of h1 = 1.1 (±0.25) was obtained.

To summarize the results, the average values of Pm, h1, h2 and h3

were 0.0091 cm/s, 1.1, 0.23 and 1.81, respectively. The thickness ofthe interface (L) as measured using an ellipsometer was 25 nm. Ifwe assume the partition coefficient, kp, to be 1, then the value ofDf, using the relation, Pm ¼

Df kp

L ; would be 2.27 � 10�8 cm2/s.Although these calculations are approximate, they suggest thatthe diffusion in the enzyme film is roughly three orders of magni-tude slower than in bulk electrolyte. Similar effects have alreadybeen reported in layered polyelectrolyte films by Coche-Guerenteet al. [6–8] Assuming that the immobilized tyrosinase has the samekinetic constants as in the homogeneous solution, the concentra-tions [E2] and [E3] of monophenolase and catecholase active sitescan be determined using the following relations:

ðk2=K2Þ½E2� ¼Df h

22

L2 ð34Þ

ðk3=K3Þ½E3� ¼Df h

23

L2 ð35Þ

Table 1 shows the calculated values of [E2] and [E3] along with thereported values of kinetic constants used to determine them [6–8].

Table 1Kinetic characteristics of tyrosinase immobilized in bi-enzyme electrode. Values of kand K were obtained from the literature [8]. However, enzyme concentration wascalculated using Eqs. (34) and (35) (see text).

Monophenolase activity Catecholase activity

K (mol/cm3) (2.5 ± 0.3) � 10�7 (2.2 ± 0.2) � 10�7

k (s�1) 20 ± 2 760 ± 30k/K (mol�1 cm3 s�1) 8.4 � 107 3.45 � 109

Enzyme concentration(mol/cm3)

2.29 � 10�6 3.45 � 10�6

Phenyl Valerate

0.2

0.3

0.4

0.5

0 0.2 0.4 0.6 0.8 1

Con

cent

ratio

n/S 1

()

0

0.01

0.02

0.03

0.04

0.05

0.06

0 0.2 0.4 0.6 0.8 1x/L

x/L

Con

cent

ratio

n/S

1()

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

Con

cent

ratio

n/S

1()

catecholquinonephenol

a

b

Fig. 6. Concentration profiles of: (a) phenyl valerate (b) phenol, catechol and o-quinone normalized to phenyl valerate bulk concentration (S1ð1Þ) as a function ofrelative position (x/L) within the bi-enzyme interface.

Although these calculations are coarse approximations, they sug-gest that monophenolase active sites represent only 66% of the cat-echolase sites and about 40% of the total sites.

3.6. Simulations and discussions

Fig. 6 shows the simulated concentration profiles of phenyl val-erate, phenol, catechol, and o-quinone normalized to phenyl valer-ate bulk concentration (S1ð1Þ) as a function of relative position (x/L) within the interface. The concentration profile was simulatedusing Eqs. (23)–(26), along with the experimentally determinedvalues of different parameters (Pm = 0.0091 cm/s, h1 = 1.1,h2 = 0.23, h3 = 1.81, x = 500 rpm and De = 2.2 � 10�5 cm2/s). As ex-pected, the concentration of o-quinone, and the concentration gra-dients of phenyl valerate @S1

@x

� and phenol concentration ð@S2

@x Þ; at theelectrode surface (x = 0) are zero.

The model’s predictions help explain the observed (Fig. 5) de-crease in current with increasing rotation rates in the presenceof phenyl valerate. The electrochemical transduction step regen-erates catechol from o-quinone. A portion of the catechol is lostby diffusion through the stagnant film, and the remainder is oxi-dized to o-quinone, which increases the sensor’s output. As theelectrode rotation rate increases, the film mass transfer coeffi-cient also increases and an increasing fraction of the catecholis lost. Consequently, less catechol is recycled to o-quinone,and the o-quinone concentration at the electrode is reduced,leading to lower sensitivity for phenyl valerate detection. Consis-tent with this mechanism, Fig. 7 shows that the predicted con-centration gradient of o-quinone at x = 0 decreases as therotation rate increases.

Fig. 8 shows the simulated current sensitivity, Scpv ; as a function

of amount of NEST esterase activity (h1) and tyrosinase’s catecho-lase activity (h3), assuming Pm = 0.0091 cm/s and x = 500 rpm. Atlow h1 values, Sc

pv increases as h1 increases, indicating that the NESTactivity is rate limiting. However, as h1 increases, the Sc

pv curve ap-proaches an asymptote, indicating that the biosensor response isbecoming limited by the catechol recycling (h3). For a given, h1,the current sensitivity Sc

pv increases with h3, because at higher val-ues of catecholase activity, enzymatic recycling of o-quinone be-comes more and more efficient, leading to amplified responses orhigher sensitivities.

The amplification factor (AF) can be defined as the ratio of cur-rent sensitivities in the presence (Sc

pv) and absence of catecholaseactivity Sc

pv ;h3¼0

�.

AF ¼Sc

pv

Scpv ;h3¼0

ð36Þ

0

0.005

0.01

0.015

0.02

0.025

0.03

0.035

0 0.2 0.4 0.6 0.8 1 1.2x/L

Nor

mal

ised

con

cent

ratio

n

500 rpm

1000 rpm

1500 rpm2000 rpm2500 rpm3000 rpm

Fig. 7. Concentration profile of o-quinone normalized to phenyl valerate bulkconcentration (S1ð1Þ) at various rotation rates.

Fig. 8. Current sensitivity, Scpv ; as a function of amount of NEST esterase activity (h1)

and tyrosinase’s catecholase activity (h3).

0

5

10

15

20

25

0 2 4 6 8 10 12

Ampl

ifica

tion

Fact

or

Amplification in bi-enzyme electrode

3

Fig. 9. Signal amplification in bi-enzyme electrode due to the recycling of catechol.For simulation, the following values of different parameters were used.Pm = 0.0091 cm/s, De = 2.2 � 10�5 cm2/s, x = 500 rpm.

110 N. Kohli et al. / Journal of Electroanalytical Chemistry 641 (2010) 104–110

The following relation for the AF can be derived from Eqs. (27) and(36). This equation shows that AF is a function of Thiele modulus h3

and the ratio Pmme

, which is the reciprocal of the Sherwood number.

AF ¼ 1þ Pm

me

� �h3

Pmme

h3 sinh h3 þ cosh h3

Pmme

h3 cosh h3 þ sinh h3

!ð37Þ

Fig. 9 shows predicted AF values as a function of h3, assuming exper-imentally realistic values of Pm = 0.0091 cm/s and x = 500 rpm.Amplification increases with h3 and, depending upon the rotationrate, very high amplification factors can be achieved. The mathe-matical model predicts a signal amplification of about 2.5-fold viarecycling for our bi-enzyme electrode at a rotation speed of500 rpm.

Collectively, the results of this study present an importantcontribution from the point of view of optimization of bi-enzymebiosensors that involve substrate recycling. The results suggeststrategies that can be used to increase biosensor sensitivity. For

the NEST biosensor, increasing the tyrosinase concentration anddecreasing the mass transfer coefficient give higher signals for a gi-ven NEST loading. This result is interesting because tyrosinase isrelatively inexpensive and commercially available, while NEST isnot commercially available, and its expression and purification re-quires special expertise. In order to achieve higher signals, we arecurrently exploring different ways of increasing tyrosinase loadingon the surface. We are also looking at the possibility of using thisinterface as a sensor for detecting NEST inhibitors such as neuro-pathic organophosphorus compounds.

4. Conclusions

This paper presented a theoretical treatment for bi-enzymeelectrodes with substrate recycling. The model was validated bystudying the response of bi-enzyme rotating disk electrode con-sisting of two enzymes, NEST and tyrosinase, to phenyl valerate,phenol and catechol under varying rotating speeds. The validatedmodel helped us determine and quantify the influence of impor-tant parameters such as mass transport in the bulk and enzymelayer, partition coefficients, enzyme kinetics and catechol recyclingon the sensitivity of the sensor. This information can be helpful foroptimizing the metrological characteristics of bi-enzymeelectrodes.

Acknowledgment

This work was funded in part by the National Science Founda-tion (0609164, 0756703, 0832730), the US Army Research Office(DAAD19-02-1-0388), the University Research Corridor, and theMSU Foundation.

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