Journal of Electroanalytical Chemistry 649 (2010) 268–276

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Journal of Electroanalytical Chemistry

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Modeling direct electron transfer to a multi-redox center protein:Cytochrome c oxidase

D. Schach a,d, Ch. Nowak a,d, R.B. Gennis b, Sh. Ferguson-Miller c, W. Knoll d, D. Walz e,1, R.L.C. Naumann a,d,*a Max Planck Institute for Polymer Research, Ackermannweg 10, 55128 Mainz, Germanyb University of Illinois, Department of Biochemistry, 600 South Mathews Street, Urbana, IL 61801, USAc Michigan State University Biochemistry and Molecular Biology, East Lansing, MI, USAd Austrian Institute of Technology GmbH, AIT, Donau-City Str. 1, 1220 Vienna, Austriae Biozentrum, University of Basel, Switzerland

a r t i c l e i n f o a b s t r a c t

Article history:Available online 22 July 2010

In honour of Prof. Jacek Lipkowski on theoccasion of his 65th birthday

Keywords:Multi-redox center proteinsCyclic voltammetryModeling of electron transferKinetic coefficientsFour-electron transfer modelSequential and independent mechanism

1572-6657/$ - see front matter � 2010 Elsevier B.V. Adoi:10.1016/j.jelechem.2010.07.009

* Corresponding author. Address: Max Planck InsAckermannweg 10, D-55128 Mainz, Germany. Tel.:6131 379 100.

E-mail addresses: naumannr@mpip-mainz.mp(R.L.C. Naumann).

1 Present address: Lerchenstrasse 21, 4059 Basel, Sw

Direct electron transfer to Cytochrome c Oxidase (CcO) was investigated using fast scan cyclic voltamme-try. The enzyme was tethered to the electrode in a strict orientation by means of a histidine-tag with CuA,the first electron acceptor, directed towards the electrode. A lipid bilayer was then reconstituted in situaround the bound proteins, forming a protein-tethered bilayer lipid membrane. Cyclic voltammogramswere measured under anaerobic conditions at different scan rates with CcO in the non-activated andthe activated state. The activated state was attained after catalytic turnover of the enzyme in the presenceof oxygen. A four-electron transfer model was developed to analyze the data. This enables us to discrim-inate between the mechanisms of sequential and independent electron transfer to the four redox centersCuA, heme a, heme a3 and CuB. Moreover, values of parameters such as standard redox potentials andkinetic coefficients of electron transfer could be obtained. Based on these results we conclude that directelectron transfer to CcO most likely follows the sequential mechanism, thus mimicking the electrontransfer form cytochrome c, the genuine electron donor of CcO.

� 2010 Elsevier B.V. All rights reserved.

1. Introduction

Electrochemistry of multi-redox site proteins has attracted con-siderable attention aiming at a better understanding of electrontransfer (ET) mechanisms of these enzymes. Fast scan voltammetryof protein films directly adsorbed to an electrode was pioneered bythe Armstrong group [1–3]. Alternatively proteins were wired tothe electrode via specific linkers [4], or sophisticated assembliesof different linkers [5,6]. Methods were developed using both elec-trochemical [7] and Marcus theory [8] to analyze catalytic as wellas substrate free ET to these enzymes. In the majority of cases,these methods are based on the assumption that rate constants de-pend on applied potentials provided that kinetics is dominated bydirect electron transfer to the catalytic center [9]. The theory ofelectrochemical reactions of adsorbed species introduced byLaviron is then directly applicable [10]. The simplest case is aone-step electrochemical reaction recorded by linear potential

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titute for Polymer Research,+49 6131 379 157; fax: +49

g.de, dieter.walz@unibas.ch

itzerland.

sweep voltammetry, which can conveniently be analyzed in termsof the Butler–Volmer equation. Laviron developed a method inwhich peak potentials are plotted vs. log of scan rate resulting inthe well-known trumpet plot [11]. Using this formalism, electro-chemical rate constants of substrate-free heterogeneous ET couldbe obtained for a large variety of enzymes [1,2,12,13]. Turnoverrates in the presence of substrates, on the other hand, were deter-mined using the rotating disc electrode. Voltammograms wereanalyzed by Koutecky–Levic-plots also based on the Butler–Volmerequation [1,2,7,9]. In cases where the catalytic center does not ex-change electrons directly with the electrode, a so-called hoppingmechanism was considered. ET to the catalytic center was treatedas a chemical reaction coupled to electron uptake via a number ofredox centers also denoted as redox chain. Square wave voltammo-grams were simulated using the Jellyfit software developed by Jeu-ken et al. [3]. Some simplifications had to be made thus reducingthe number of parameters to a single Eo and ks of the redox chainand the catalytic center each. Several algorithms and programswere developed to simulate bioelectrochemical processes and ana-lyze data under different experimental conditions (for a recent re-view see Ref. [14]).

Cytochrome c Oxidase (CcO) is a multi-redox site protein contain-ing the four redox centers CuA, heme a, heme a3 and CuB (Fig. 1). It is

http://dx.doi.org/10.1016/j.jelechem.2010.07.009mailto:naumannr@mpip-mainz.mpg.demailto:dieter.walz@unibas.chhttp://dx.doi.org/10.1016/j.jelechem.2010.07.009http://www.sciencedirect.com/science/journal/15726657http://www.elsevier.com/locate/jelechem

D. Schach et al. / Journal of Electroanalytical Chemistry 649 (2010) 268–276 269

the terminal complex of the respiratory chain, which uses the freeenergy gained from the oxidation of NADH by oxygen to transportprotons across the inner mitochondrial membrane. In CcO electronsare transferred from reduced cytochrome c to CuA, the first electronacceptor, wherefrom they are donated to heme a and the catalyticcenter consisting of heme a3 and CuB [15]. In order to mimic the nat-ural process as closely as possible, we have tethered the CcO to anelectrode in a strict orientation by means of a histidine (his)-tagengineered onto the enzyme (Fig. 1). A lipid bilayer was then recon-stituted in situ around the bound proteins, forming a protein-teth-ered bilayer lipid membrane (ptBLM) [16]. We found that thestructural integrity of the enzyme in the ptBLM is retained. Electronsare transferred between the electrode and the enzyme but only ifCuA faces the electrode. In the presence of oxygen the enzyme dis-played catalytic activity [17]. We obtained evidence that ET betweenthe electrode and the enzyme most likely occurs exclusively via CuA,whereas the catalytic center does not exchange electrons directlywith the electrode. If this is indeed the case the trumpet plot analysisused tentatively in the previous study [17] is not applicable. In orderto clarify this point we have designed a model in which ET to CcO istreated as an electrochemical reaction (to CuA) coupled to threechemical reactions in sequence, in electrochemical terms an ECCCmechanism. We are particularly interested to exclude the possibilitythat electron transfer occurs to each of the four centers indepen-dently (EEEE mechanism). This could be the case if the enzyme wereimmobilized on the electrode in an unspecific orientation, for exam-ple lying more or less flat on the surface. The ECCC mechanism, onthe other hand, would be a perfect mimic of the sequential ET mech-anism induced by the natural electron donor cytochrome c.

2. Materials and methods

2.1. Dithiobis (nitriloacetic acid butylamidyl propionate) (short:DTNTA)

DTNTA was synthesized as described [18], briefly N-(5-amino-1-carboxypentyl) iminoacetic acid (ANTA) was coupled to dithiobis(N-succinimidyl propionate) (DTSP).

Fig. 1. Cytochrome c Oxidase (CcO) from Rh. Sphaeroidis with the his-tag attached to subelectrode. Electrons are transferred via the spacer from the electrode to CuA and from theand that the size of the linker molecules is not to scale.

2.2. Immobilization of the protein

Immobilization of the protein was performed as described [18].Briefly CcO from Rhodobacter sphaeroides with a his-tag engineeredto the C-terminus of subunit II was expressed and purified accord-ing to Hiser et al. [19]. Template stripped gold (TSG) electrodes,used for surface plasmon resonance (SPR) and electrochemistrymeasurements [20], were immersed for 24 h in a solution in dryDMSO of DTNTA and dithiobis (propionic acid) (DTP) mixed at amole ratio of 0.2 (total concentration 2 mg/ml). After rinsing withDMSO, followed by de-ionized water pH = 5, the slides were im-mersed for 30 min in 40 mM NiSO4 in acetate buffer (50 mM,pH = 5.5) followed by thorough rinsing with de-ionized waterpH = 5 to remove the excess NiSO4. Then CcO dissolved in dodecylb-D-maltoside (DDM)-phosphate-buffer (K2HPO4 0.1 M, KCl0.05 M, pH = 8, 0.1%DDM) was adsorbed to the NTA-functionalizedsurface at a final concentration of 10 nM. After 4 h adsorption timethe cell was rinsed with DDM-phosphate buffer. Then a DiPhyPCsolution (40 lM) in DDM-phosphate buffer was added. Dialysiswas performed by adding biobeads (Bio-Rad Laboratories GmbH,Munich, Germany) to the lipid-detergent solution.

2.3. Surface plasmon resonance (SPR)

SPR was performed in a setup using the Kretschmann-configu-ration using a measuring cell designed for use of SPR in a combina-tion with electrochemistry. The glass slide (LaSFN9 glass fromHellma Optik, Jena, refractive index n = 1.85 at 633 nm) was opti-cally matched to the base of a 90� glass prism (LaSFN9). Monochro-matic light from a He/Ne Laser, (Uniphase, San Jose, CA,k = 632.8 nm) was directed through the prism and collected by acustom made photodiode detector. Reflectivity at a fixed angle ofincidence transferred into a thickness yields the time course ofprotein binding and reconstitution.

2.4. Electrochemistry

Electrochemical measurements were performed using an Auto-lab instrument (PGSTAT302) equipped with an FRA2-module forimpedance measurements, an ECD-module amplifier for low-cur-

unit II immobilized in a protein-tethered bilayer lipid membrane (ptBLM) on a goldre to heme a, heme a3 and CuB. Note that the number of lipids shown is exaggerated,

270 D. Schach et al. / Journal of Electroanalytical Chemistry 649 (2010) 268–276

rents, an ADC750 module for rapid scan measurements and aSCAN-GEN module for analog potential scanning. Electrochemicalimpedance spectroscopy (EIS) data were recorded in a frequencyrange of 50 kHz–3 mHz with an excitation amplitude of 10 mVand a bias potential of 0 V against an Ag|AgCl,KClsat reference elec-trode. Data were analyzed by the complex non-linear fitting algo-rithm supplied in the data processing software ZVIEW (Version 2.6,Scribner Associates, Inc.) Cyclic voltammetry experiments wereconducted with IR drop compensation, particularly at high scanrates. Measurements under anaerobic conditions were performedin a buffer solution containing K2HPO4 0.1 M, KCl 0.05 M, pH = 8and the oxygen trap consisting of glucose (0.3%w/w), glucose oxi-dase (75 lg/ml) and catalase (12.5 lg/ml). This solution wasflushed with Ar purged from oxygen by bubbling through the oxy-gen trap containing buffer solution for 30 min prior to the mea-surements to assure a completely deoxygenated solution. Allelectrochemical measurements were taken in a three electrodeconfiguration with TSG as the working electrode, a Ag|AgCl,KClsatreference, and a platinum wire as the counter electrode. All elec-trode potentials are quoted vs. SHE.

3. Development of models

3.1. General concepts

The complex is considered adsorbed to an electrode, where Cdenotes the surface coverage, i.e. the mole number of protein perunit area. The complex comprises four redox centers, which arenumbered sequentially, and all of them are one electron redox cou-ples. Electron transfer to the complex and within the complex oc-curs, respectively, by transfer of electrons from the electrode to acenter (denoted as ‘‘uptake”) and by exchange of electrons be-tween two centers (denoted as ‘‘exchange”). The various redoxstates (oxidized or reduced) of the centers arising upon electrontransfer are considered as different conformational states of thecomplex, which are numbered sequentially [18]. The kth confor-mation has the probability pk, hence

Rkpk ¼ 1 ð1Þ

where the sum includes all conformational states. The transition be-tween two states k and l is described by the flow

Jk;l ¼ kk;lpk � kl;kpl ð2Þ

The rate coefficients kk,l and kl,k depend on the type of electrontransfer and the centers involved. In the case of electron uptake,they also depend on the applied potential E according to

Kk;lðEÞ ¼ ke;i exp½ðEo;i � EÞ=ð2unÞ� andkl;kðEÞ ¼ ke;i= exp½ðEo;i � EÞ=ð2unÞ� ðuptakeÞ ð3Þ

with the abbreviation

un ¼ RT=F ð4Þ

In Eq. (3), Eo,i denotes the standard potential of the ith center(which is reduced in this transfer), and ke,i is the rate constant ofthe electrochemical reaction. When writing Eq. (3), a symmetricalenergy barrier is assumed. Electron exchange between centers iand j corresponds to a chemical reaction, hence the rate coeffi-cients are independent of E. It is described by a forward rate con-stant ki,j and a backward rate constant which follows fromdetailed balancing [21]

Kk;l ¼ ki;j and kl;k ¼ kj;i exp½ðEo;i � Eo;jÞ=un� ðexchangeÞ ð5Þ

Note that redox interaction is excluded here, i.e. rate constantsof a given electron transfer are not dependent on the redox statesof the other centers not involved in the particular transfer.

The overall probabilities for the ith center in the reduced andoxidized state are, respectively

Pi;red ¼ Rkpkji;red and pi;ox ¼ 1� pi;red ð6Þ

where pk|i,red denotes the probability of the kth conformation withthe ith center reduced. The relation for pi,ox follows from Eq. (1).

The flow of electrons associated with the ith center, expressedas current density ji becomes

ji ¼ �CFR½Jk;lj!i � RJk;lji!� ð7Þ

where Jk,l|?i and Jk,l|i? denote the flows into the ith center and out ofit, respectively. The current density jel flowing through the electrodeis then given by

jel ¼ Riji ¼ �neFRJk;ljup ð8Þ

where Jk,l|up denotes flows pertaining to electron uptake.

3.2. Electron transfer at pseudo-equilibrium

If the change of E with time t is sufficiently slow, i.e. for suffi-ciently small scan rates, the electron transfer processes can easilycope with the change in E irrespective of the particular electronpathways. Hence the centers are always very close to equilibriumwith respect to E (pseudo-equilibrium). This special case will be re-ferred to as ‘‘equilibrated electron transfer”. The Nernst equation

E ¼ Eo;i þun lnðpi;oxjpi;redÞ ð9Þ

then applies to the overall probabilities pi,red and pi,ox, hence (cf. Eq.(6))

pi;red ¼ f1þ exp½ðE� Eo;iÞ=un�g�1 ð10Þ

The current density ji associated with the ith center can be cal-culated as

ji ¼ �CFdpi;red=dt ¼ �ðCFmÞdpi;red=dE

¼ ðCFm=unÞ exp½ðE� Eo;iÞ=un�f1þ exp½ðE� Eo;iÞ=un�g�2 ð11Þ

where

m ¼ dE=dt ð12Þ

denotes the scan rate. Note that m < 0 and m > 0 for the reductive(cathodic) and the oxidative (anodic) branch of a cyclic voltammo-gram, respectively. The absolute value of m commonly used for scanrates will be denoted by |m|.

3.3. Sequential electron transfer (ECCC mechanism)

Center 1 can take up electrons from the electrode. The othercenters exchange electrons with their neighbors as indicated bythe numbering, i.e. center i exchanges electrons with centersi � 1 and i + 1. Note that the last center has only a preceding neigh-bor. The kinetic scheme of this electron transfer is shown in Fig. 2A,and further details concerning transitions, flows Jk,l, and probabili-ties pk|i,red are given in the Supplementary information. If appliedto CcO the centers 1–4 represent CuA, heme a, heme a3, and CuB,respectively.

3.4. Independent electron transfer (EEEE mechanism)

All centers can take up electrons directly from the electrode butdo not exchange electrons with their neighbors. Since redox inter-action is excluded this model can be represented by four electronuptakes (cf. Eq. (6)), as shown by the kinetic scheme in Fig. 2B. Inthis case no unambiguous assignment of centers 1–4 to the redoxcenters in CcO is possible.

Fig. 2. Kinetic schemes for sequential (A) and independent electron transfer (B). Vertical and horizontal transitions between states represent electron uptake and electronexchange, respectively. All transitions are reversible (see Eq. (2)) but, for graphical reasons, are represented here only by single arrows indicating the positive direction offlows.

D. Schach et al. / Journal of Electroanalytical Chemistry 649 (2010) 268–276 271

3.5. Simulation and parameter fitting

The mathematical description of the models by means of Eqs.(1)–(8) and (12) consists of a set of non-linear differential equa-tions for the probabilities pk, which have to be integrated numer-ically in order to obtain the current densities ji and jel as a functionof E, i.e. to simulate cyclic voltammograms (CVs). A very conve-nient and powerful alternative is to transform the models intoan electrical network representation and to make use of the net-work simulation program Spice for integration [22]. Spice hadbeen introduced earlier to model bioelectrochemical processesacross membranes [23]. Its advantage is not only that no differen-tial equations have to be formulated, but also that it reflects thetopology of the kinetic scheme, and in particular its modular de-sign. New elements can be defined (subcircuits in Spice terminol-ogy) which are programmed for a particular process, e.g. the flowof electron uptake or exchange (Eqs. (2), (3), and (5)). These ele-ments can be repeatedly used and plugged in anywhere in the net-work. This is of particular benefit for complex systems such asmulti-electron transfer systems (cf. Fig. 2A). Spice is in the publicdomain and available for various computer systems. We routinelyuse MacSpice (version 3f5) on Mac computers with OS X (versions10.4.x).

Parameter fitting was performed with the program MODFIT[24]. This code is based on the Marquardt–Levenberg algorithmand does not require analytical expressions for the partial deriva-tives with respect to the parameters but calculates them numeri-cally. It is therefore well suited to cope with Spice simulationsand was implemented in the control structure of the Spice inputfiles. For further information on this routine and details of the Mac-Spice program contact D. Walz (dieter.walz@unibas.ch).

4. Results and discussion

4.1. Characterization of the biomimetic layer system

The CcO from R. sphaeroides with the his-tag attached to subunitII was immobilized on a template stripped gold (TSG) electrode andreconstituted into a ptBLM (Fig. 1). The formation of the CcO layerand the reconstitution of the ptBLM were followed by a combina-tion of SPR and EIS (Fig. 3). The changes in thickness measured bySPR and the electrical parameters measured by EIS are shown inTable 1.

EIS showed a decrease of capacitance from 18.8 lF cm�2 for theCcO/detergent/water layer to 14.9 lF cm�2 for the ptBLM, whilethe resistance increased from 10 to 18 MX cm2. The high resis-tance indicates good electrical sealing properties of the ptBLM.The capacitance values indicate that detergent and water mole-cules residing between the proteins are replaced by lipid bilayerpatches, considering the dielectric constant of lipids (2.2) is smallerthan that of water (80) and proteins. Thereafter, the capacitance isstill dominated by the protein indicating a high surface coverage.

4.2. Cyclic voltammetry measurements

Cyclic voltammetry had shown before that CcO immobilized ina ptBLM undergoes a gradual transition from a non-activated to anactivated state upon catalytic turnover in the presence of oxygen[25]. These states are considered as equivalents to the restingand pulsed states deduced from biochemical data. When the en-zyme is kept for at least 60 min under strictly anaerobic conditionsit is in a non-activated state. The CVs show peaks (Fig. 4A) which

Fig. 3. Immobilization of CcO and reconstitution into the ptBLM. (A) Kinetic trace of the SPR spectrum at a fixed angle of incidence H = 54� showing the binding of the CcO insolubilized form and the reconstitution of a lipid bilayer after the addition of biobeads to the lipid-detergent containing buffer solution. (B) Bode plot and (C) frequencynormalized admittance plot of electrochemical impedance spectra before (solid squares) and after (solid circles) CcO binding and (solid triangles) reconstitution.

Table 1Thickness changes Dd from SPR data and electrical properties from impedancespectroscopy (capacitance, C, and resistance, R) of the protein/lipid layer before andafter CcO binding and reconstitution into a ptBLM.

Layer Dd (nm) C (lF cm�2) R (MX cm2)

Spacer molecule 2.3 22.4 6.8CcO 9.7 18.8 10.0Lipid bilayer 2.1 14.9 18.7

272 D. Schach et al. / Journal of Electroanalytical Chemistry 649 (2010) 268–276

are in the range of midpoint potentials of the redox centers CuA,heme a and heme a3 known from biochemical literature [26]. Thepeak height changes linearly with scan rate as required for ad-sorbed species (inset of Fig. 4A). When changing to an air-saturatedsolution, the peaks at positive potentials disappear and are re-placed by two peaks at �240 and �530 mV (Fig. 4B). From theamplified current density of these peaks we conclude that theenzyme starts to work under turnover conditions. The peak at�530 mV had been identified in a control experiment to be dueto the reduction of protons [17]. The peak at �240 mV was attrib-uted to continuous (catalytic) electron transfer from the electrodeto the redox centers, although the potential is shifted by more than400 mV in the negative direction vs. the midpoint potentials of theredox centers. When returning to anaerobic conditions the peak at�240 mV persists but with a reduced current density (Fig. 4C andD). The peak height changes linearly with scan rate as required foran adsorbed species (inset of Fig. 4C) indicating a nonrecurring ET.The enzyme is in what we call the activated state. Most impor-tantly, potentiometric titrations of this state followed by surface-enhanced IR absorption spectroscopy have confirmed that the

reduction of the four redox centers does take place in this particu-lar potential range [25].

4.3. Analysis of cyclic voltammograms

4.3.1. CcO in the activated stateIntegrating the current density i of the baseline-corrected CVs

shown in Fig. 4C and D over the range of applied potential E yieldsan estimate of the surface coverage of CcO molecules per unit area.For a complex with four redox centers

C ¼Zðj=mÞdE=ð4FÞ ð13Þ

The results listed in Table 2 shows some variation with |m| andsomewhat higher values for the reductive branch than for the oxi-dative branch, as observed earlier [17]. Hence a factor

fp ¼ C=C0 ð14Þ

is introduced (see Table 2) and used to scale all j data to a commonvalue C0 which then can be fitted.

Even at the lowest scan rate (0.05 V s�1) the peak in the reduc-tive branch is displaced to a more negative potential with respectto the peak in the oxidative branch. This is a frequently observedphenomenon for redox proteins [27]. It can be accounted for bymeans of a quantity DEps called peak separation, which is commonto all centers and defined as

DEps ¼ ðEp;ox;i � Ep;red;iÞ=2 ð15Þ

where Ep,ox,i and Ep,red,i denote, respectively, the peak potentials ofthe ith center in the oxidative and reductive branch at pseudo-equi-librium of electron transfer (cf. Section 3.2).

-60

-30

0

30

60

90

E / V vs SHE

j / µ

A c

m-2

A

0 5 10 15 20 25 30j /

µA

cm

/ Vs

-400

-200

0

200

400

-0.6 -0.4 -0.2 0.0 0.2 0.4 0.6 0.8 -0.6 -0.4 -0.2 0.0 0.2 0.4 0.6

-0.6 -0.4 -0.2 0.0 0.2 0.4 0.6-1.0 -0.8 -0.6 -0.4 -0.2 0.0 0.2 0.4 0.6-300

-250

-200

-150

-100

-50

0

50

j / µ

A c

m-2

E / V vs. SHE

B

-80

-60

-40

-20

0

20

40

60

j / µ

A c

m-2

E / V vs. SHE

C

-250-200-150-100-50

050

100150

0 1 2 3 4 5 6 7 8 9

j / µ

A c

m

/ Vs

-600

-400

-200

0

200

400

j / µ

A c

m-2

E / V vs SHE

D

Fig. 4. Cyclic voltammograms of CcO immobilized in a ptBLM via his-tag on subunit II (see Fig. 1) (A) under anaerobic conditions before activation, scan rate/(V s�1) 0.05(open squares), 0.1 (open circles), 0.2 (open triangles), 0.4 (solid squares), 0.8 (solid circles), 1.6 (solid triangles); (B) upon evolution of the protein catalytic activity underaerobic conditions, i.e. activation [1st (squares), 5th (triangles), 10th (circles), and 20th scan (diamonds) at scan rate 0.05 V s�1]; and (C and D) under anaerobic conditionsafter activation, scan rate/(V s�1) 0.05 (open squares), 0.1 (open circles), 0.2 (open triangles), 0.4 (solid squares), 0.8 (solid circles), and 1 (solid triangles) for (C), 1 (opensquares), 2 (open circles), 4 (open triangles), and 8 (solid squares) for (D). The insets in A and C show that peak heights increase linearly with scan rate in accordance with ETto adsorbed species.

Table 2Surface coverage C and scaling factor fp for activated CcO. For C and fp see Eqs. (13)and (14), respectively. Red and ox refer to the reductive (cathodic) and oxidative(anodic) branch of CVs, respectively.

|m| (V s�1) C (pmol cm�2) fp for C0 = 6 pmol cm�2

Red Ox Red Ox

0.05 8.468 4.849 1.411 0.8080.1 7.616 5.438 1.269 0.9060.2 8.698 5.337 1.450 0.8900.4 7.544 5.719 1.257 0.9530.8 6.694 5.243 1.116 0.8741 8.366 5.210 1.394 0.8682 10.42 6.808 1.737 1.1354 10.37 5.222 1.728 0.8708 9.780 4.210 1.630 0.702

D. Schach et al. / Journal of Electroanalytical Chemistry 649 (2010) 268–276 273

Since the current densities j increase with increasing scan rates(see inset of Fig. 4C) parameters were fitted to the m-normalizedCVs, i.e. j/|m|, which yields about equal weights for all CVs in thefitting procedure and avoids a dominance of CVs at higher scanrates. An estimate for the standard potentials Eo,i and the peak sep-aration DEps was obtained by fitting these parameters to bothbranches of the CV at the lowest scan rate (0.05 V s�1) using themodel of equilibrated ET (see Table 3, 2nd column). They wereused as initial values in the subsequent fitting of parameters toall CVs with the model of sequential ET. The assignment of valuesto the Eo,i’s was also permutated since, in contrast to the model of

sequential ET, the model of equilibrated ET is insensitive to the se-quence of Eo,i values and hence does not provide any evidence inthis respect. Attempts to fit all parameters simultaneously failed,the iterative procedure did not converge because the rate constantski,j for electron exchange were set to increasingly higher values ineach iteration step. This indicates that the electron exchange reac-tions are so much faster than electron uptake that they cannot beresolved. Therefore a large and fixed value (10,000 s�1) was as-signed to the pertinent rate constants.

When fitting Eo,i’s and ke,1 with a fixed value of 39.2 mV for DEps,a stable result could be achieved but only if the initial values�233 mV and �292 mV were assigned to Eo,1 and Eo,2, respectively.The assignment of the other values (�252 mV and�170 mV) to Eo,3and Eo,4 proved to be less crucial, however, Eo,3 = �170 mV yieldsclearly a better fit (Table 3, 3rd column). This is corroborated whenfitting Eo,i’s and DEps with ke,1 fixed to 370 s�1 (Table 3, 4th col-umn). The quality of fit between experimental and simulated CVsis illustrated by the examples shown in Fig. 5.

All attempts to fit parameters using the model of independentET failed, the iterative procedure did never converge. The reasonfor this becomes evident if parameters are fitted to reductive andoxidative branch of the CVs separately. Convergence could onlybe achieved using fixed Eo,i’s values, taken from the equilibratedET model. The quality of fit between experimental and simulatedCVs is similar to that shown in Fig. 5, however, the ke,i values thusobtained are significantly different for each branch (see Table 3,5th and 6th column). This explains why convergence is not

Table 3Parameter values fitted to CVs of the activated CcO at pH 8 using different ET models. The uncertainty of fitted values based on variance analysis [21] is indicated by ±, valueswithout ± were fixed in the fitting procedure. Red and ox refer to the reductive (cathodic) and oxidative (anodic) branch of CVs, respectively.

Model |m| (V s�1) branch Equilibrated ET 0.05 red and ox Sequential ET 0.05–8 red and ox Independent ET 0.05–8

Red Ox

C0 (pmol cm�2) 6.094 ± 0.05 5.883 ± 0.03 5.867 ± 0.03 6.035 ± 0.03 5.968 ± 0.03Eo,1 (mV) �91.5 ± 1.8 �238.5 ± 0.7 �236.4 ± 0.7 �292 �292ke,1 (s�1) – 368 ± 14 370 40.9 ± 2.1 124 ± 15Eo,2 (mV) �252.1 ± 3.0 �296.4 ± 0.9 �292.5 ± 0.8 �252 �252k1,2 (s�1) – 10,000 10,000 – –ke,2 (s�1) – – 69.7 ± 5.4 17.2 ± 0.9Eo,3 (mV) �233.2 ± 2.8 �175.5 ± 1.0 �173.3 ± 1.0 �233 �233k2,3 (s�1) – 10,000 10,000 – –ke,3 (s�1) – – 93.5 ± 8.5 103 ± 11Eo,4 (mV) �169.5 ± 1.4 �253.5 ± 1.1 �252.1 ± 1.1 �170 �170k3,4 (s�1) – 10,000 10,000 – –ke,4 (s�1) – – 85.0 ± 6.0 19.6 ± 1.0DEps (mV) 39.2 ± 0.6 39.2 44.2 ± 0.4 48.1 ± 0.5 39.8 ± 0.6

274 D. Schach et al. / Journal of Electroanalytical Chemistry 649 (2010) 268–276

obtained if both branches are taken into account simultaneously.But it also means that the model of independent ET can be rejectedbecause, according to basic physico-chemical principles, rate con-stants of electrochemical reactions have to be independent of thedirection in which E is changed. We therefore conclude that elec-tron transfer in the activated CcO follows the sequential pathway.

4.3.2. CcO in the non-activated stateA similarly detailed analysis as in the case of the activated CcO

is not possible for the CVs of non-activated CcO (Fig. 4A). The base-line-corrected CVs yield on integration (Eq. (13)) values for the sur-face coverage C which are of similar magnitude for reductive and

-0.4 -0.3 -0.2 -0.1 0.0

-20.0

-15.0

-10.0

-5.0

0.0

5.0

10.0

15.0

jν-1 /

µC

cm

-2V

-1

E / V vs. SHE

A

-0.4 -0.3 -0.2 -0.1 0.0

-20.0

-15.0

-10.0

-5.0

0.0

5.0

10.0

15.0

jν-1 /

µC

cm

-2V

-1

E / V vs. SHE

B

C

Fig. 5. Experimental and simulated CVs for activated CcO at pH 8. Baseline-corrected andata (solid circles), the simulated total current density (solid line) and the components reCuB (solid triangles) are plotted vs. the applied potential E. CVs were simulated with the m

oxidative branch for scan rates up to 0.4 V/s but increase consider-ably for higher scan rates (Table 4). However, even the values atlow scan rates are far too large compared to C for a densely packedlayer of CcO (see below). Moreover, the CVs span a broader poten-tial range as in the case of activated CcO (see Fig. 6). We considerthis in terms of additional processes, which we were not able toidentify as yet. Hence we cannot separate their contribution tothe CVs, but we can check whether part of the CVs is attributableto the redox centers. To this end we have used the sequential ETmodel found to be the most likely, and restricted the analysis tothe current density in the potential range between 0.1 and 0.3 Vfor m 6 0.4 V/s.

-0.5 -0.4 -0.3 -0.2 -0.1 0.0 0.1 0.2-25.0

-20.0

-15.0

-10.0

-5.0

0.0

5.0

10.0

15.0

jν-1 /

µC

cm

-2V

-1

E / V vs SHE

d m-normalized CVs at scan rates 0.05 (A), 0.4 (B), and 2 V s�1 (C). The experimentalsulting from CuA (open squares), heme a (open circles), heme a3 (open triangles), and

odel of sequential ET and the fitted parameter values listed in Table 3 (4th column).

Table 4Surface coverage C and scaling factor fp for non-activated CcO. For C and fp see Eqs.(13) and (14), respectively. Red and ox refer to the reductive (cathodic) and oxidative(anodic) branch of CVs, respectively.

|m| (V s�1) C (pmol cm�2) fp for C0 = 12 pmol cm�2

Red Ox Red Ox

0.05 13.50 15.53 1.125 1.2940.1 13.43 13.79 1.120 1.1490.2 14.10 14.11 1.175 1.1760.4 17.67 16.45 1.472 1.3710.8 34.10 22.78 2.842 1.8991.6 27.22 14.78 2.268 1.2323.2 43.17 30.34 3.597 2.5296.4 59.32 59.05 4.943 4.921

12.8 67.54 51.91 5.628 4.326

-0.2 -0.1 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7

-15.0

-10.0

-5.0

0.0

5.0

10.0

15.0

jν-1 /

µC

cm

-2V

-1

E / V vs. SHE

A

-0.2 -0.1 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7-15.0

-10.0

-5.0

0.0

5.0

10.0

15.0

jν-1 /

µC

cm

-2V

-1

E / V vs. SHE

B

Fig. 6. Experimental and simulated CVs for non-activated CcO at pH 8. Baseline-corrected and m-normalized CVs at scan rates 0.05 (A) and 0.2 V s�1 (B). Theexperimental data (solid line), the simulated total current density (solid circles) andthe components resulting from CuA (solid triangles), heme a (open circles), heme a3(open triangles), and CuB (open squares) are plotted vs. the applied potential E. CVswere simulated with the model of sequential ET and the fitted parameter valueslisted in Table 5.

Table 5Parameter values fitted to CVs of the non-activatedCcO at pH 8 using the sequential ET model. Theuncertainty of fitted values based on varianceanalysis [21] is indicated by ±, values without ±were fixed in the fitting procedure. Only experi-mental data within the range of E indicated bylimits were included.

|m | (V s�1) 0.05–0.4

Limits for E 0.1–0.3 VC0 (pmol cm�2) 5.788 ± 0.037Eo,1 (mV) 201.8 ± 1.0ke,1 (s�1) 370Eo,2 (mV) 138.8 ± 1.0k1,2 (s�1) 10,000Eo,3 (mV) 302.9 ± 1.8k2,3 (s�1) 10,000Eo,4 (mV) 257.3 ± 1.0k3,4 (s�1) 10,000DEps (mV) 0

D. Schach et al. / Journal of Electroanalytical Chemistry 649 (2010) 268–276 275

When fitting the parameters, large and fixed values for the elec-tron exchange reactions had again to be used. Moreover, the valueof ke,1 had to be fixed, and the value found for the activated CcOwas then assigned to this parameter. DEps oscillated around a verysmall value in successive iteration steps and hence was set to 0.The result thus obtained is illustrated in Fig. 6 for two scan rates.The fitted values of parameters (Table 5) are obviously less reliablethan those for the activated CcO (Table 3). Nevertheless, the valueof C0 is reasonable and comparable to those for activated CcO,while the Eo,i values fall into the range known from biochemical lit-erature [26]. Using different fixed values for ke,1 had little effect on

the quality of fit and the fitted parameter values. Hence we cannotdecide upon a definite rate constant, but it seems to be of the sameorder of magnitude as for the activated CcO. In view of these find-ings we conclude that the CVs of non-activated CcO are indeedcompatible with the model of sequential ET.

5. Conclusions

An analysis of ET to a multi-redox site protein was performedusing modeling based on rigorous electrochemical theory. Themodels implicitly account for position and shape of the contribu-tions of individual redox centers to the overall current density.Both cathodic and anodic branches of baseline-corrected CVs takenover a broad range of scan rates between 0.05 and 8 V s�1 wereanalyzed.

The analysis provides strong evidence that direct ET to CcO inthe activated state follows the sequential model (ECCC mecha-nism). Thus direct ET, in other words electronic wiring can be con-sidered as equivalent to ET from the genuine electron donor of CcO,i.e. cytochrome c. Independent ET to each center separately (EEEEmechanism) can be excluded since the analysis failed when bothbranches of the CVs were used simultaneously. Moreover, the val-ues for the electrochemical rate constants obtained when analyz-ing the two branches separately are significantly different thusviolating basic physico-chemical principles. In the case of non-acti-vated CcO, discrimination between the two mechanisms is not pos-sible because of the interference of other processes. However, an E-range restricted analysis showed that the CVs are still compatiblewith sequential ET.

The electrochemical rate constant for ET to CuA is well in therange found for other proteins [1–3]. The discrepancy to the resultreported previously [17] is most certainly due to differences inpreparations of CcO obtained from different sources. This is consis-tent with the finding that the preparation used previously could betransferred to the activated state much more easily. Intra-proteinelectron exchange is known to be much faster than ET to CuA,hence the pertinent rate constants could not be fitted. ET betweenthese centers is then always close to equilibrium, which can besimulated by assigning large and constant values to the rate con-stants. The Eo,i values found for non-activated CcO are of limitedreliability due to the E-range restricted analysis, yet they are in linewith data in the biochemical literature [26]. The reliable Eo,i valuesfound for activated CcO are negatively shifted thus indicatingsubstantial differences between the two states of CcO. In fact, 2DIR has revealed major conformational changes in the proteinaccompanying the transition from the non-activated to the

276 D. Schach et al. / Journal of Electroanalytical Chemistry 649 (2010) 268–276

activated state [28]. Hence we attribute the shift in Eo’s to an al-tered environment of the redox centers. Considerable changes inEm’s of hemes due to different environments was documented byMulti-Conformation Continuum Electrostatics calculations [29],and experimentally demonstrated for the BM3 heme domain ofP450, an enzyme with a catalytic cycle similar to CcO [30,31].

The average value for the surface coverage C (�7 pmol cm�2)obtained from the values presented in Table 2, as well as the fittedvalues for C0 (Tables 3 and 5) are in reasonable agreement with6 pmol cm�2 estimated for a densely packed monolayer of CcO.For this estimate we assumed an ellipsoidal disk of 4.5 nm �7.0 nm for the in-plane dimension of CcO, which can be deducedfrom crystal structure data of R. sphaeroides [32]. We therefore con-clude that the ptBLM consists of a densely packed monolayer ofCcO interspersed with a small number of lipid molecules, as alsoindicated by the EIS and SPR measurements. In this arrangementthe CcO molecules should be well ordered and in the orientationdepicted in Fig. 1, which explains why an independent ET to thecenters is not possible.

Information on the exact pathway of electrons in CcO embed-ded in a ptBLM is important for several aspects. Spectro-electro-chemical measurements using surface-enhanced IR absorptionspectroscopy have revealed conformational changes that cruciallydepend on the pathway of the electrons through the enzyme[25]. The analysis of time-resolved spectro-electrochemical mea-surements performed in our laboratory requires a well-definedmodel for ET. Finally, knowing that ET follows the genuine path-way in CcO facilitates the investigation of the catalytic turnoverof CcO in the presence of oxygen. Work along this line is currentlyin progress.

Appendix A. Supplementary material

Supplementary data associated with this article can be found, inthe online version, at doi:10.1016/j.jelechem.2010.07.009.

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http://dx.doi.org/10.1016/j.jelechem.2010.07.009

Modeling direct electron transfer to a multi-redox center protein: Cytochrome c oxidaseIntroductionMaterials and methodsDithiobis (nitriloacetic acid butylamidyl propionate) (short: DTNTA)Immobilization of the proteinSurface plasmon resonance (SPR)Electrochemistry

Development of modelsGeneral conceptsElectron transfer at pseudo-equilibriumSequential electron transfer (ECCC mechanism)Independent electron transfer (EEEE mechanism)Simulation and parameter fitting

Results and discussionCharacterization of the biomimetic layer systemCyclic voltammetry measurementsAnalysis of cyclic voltammogramsCcO in the activated stateCcO in the non-activated state

ConclusionsSupplementary materialReferences