www.elsevier.nl/locate/jelechem Journal of Electroanalytical Chemistry 469 (1999) 123 – 131
Diffusionless electron transfer of microperoxidase-11 on gold electrodes Tautgirdas Ruzgas a,*, Adolfas Gaigalas b, Lo Gorton a a
Department of Analytical Chemistry, Lund Uni6ersity, PO Box 124, S-22100 Lund, Sweden b Biotechnology Di6ision, NIST, Gaithersburg, MD 20899 USA
Received 13 January 1999; received in revised form 12 April 1999; accepted 23 April 1999
Abstract Microperoxidase-11, MP-11, is made by proteolytic digestion of cytochrome c, cyt. c. It consists of a polypeptide of 11 amino residues attached covalently to the heme. Given that MP-11 has a more exposed heme than the complete protein, it would seem that electron transfer, ET, between immobilized MP-11 and electrodes would be at least as fast as for intact cyt. c. However, while the maximal heterogeneous ET rate for immobilized cyt. c is around 1000 s − 1, that reported previously for immobilized MP-11 does not exceed 20 s − 1. This work attempts to understand this difference in measured ET rates. The MP-11 was immobilized on gold electrodes using several protocols: (electrode A) the immobilization was done following a previously published carbodiimide based recipe yielding ET rates of the order of 20 s − 1; (B) MP-11 was bound to gold electrodes by Lomant’s reagent and gave an ET rate close to 4000 s − 1; (C) physisorbed MP-11 on gold electrodes with a self assembled monolayer, SAM, of alkane thiols gave an ET rate approaching 2000 s − 1 for the shortest length alkane thiol. Inspection of the immobilization chemistries suggests that the procedure employed in producing electrodes B and C are likely to lead to a monolayer or less of immobilized MP-11 while the procedure employed for electrode A may lead to a film comprised of a multilayer of MP-11. The presence of such a film on electrode A complicates the ET process since the MP-11 in the layer adjacent to the electrode could have fast ET rates while the MP-11 in the outer layers may have significantly slower ET rates. The net result would be an apparent ET rate constant which is much smaller than the value for the first layer. The measurements and calculations are presented in support of such an interpretation. © 1999 Elsevier Science S.A. All rights reserved. Keywords: Hemepeptide; Microperoxidase-11; Electrocatalysis; Peptide-modified electrodes; Interfacial electron-transfer
1. Introduction Porphyrins have considerable potential in medicine for clinical application [1,2], in material science for analytical application [3,4] and for construction of photoelectronic devices [5,6]. The poor aqueous solubility of porphyrins, their high tendency to aggregate and chemical instability are serious constraints [7,8]. Covalent coupling of porphyrins to short polypeptides or artificial proteins increases the robustness of porphyrinbased systems [9–11]. In this context heme peptides produced by proteolytic digestion of cyt. c exhibit * Corresponding author. Tel.: +46-46-2228191; fax: + 46-462224544. E-mail address:
[email protected] (T. Ruzgas)
superior characteristics too [12]. The structure of the heme peptide frequently also called microperoxidase-11, MP-11, due to its peroxidase activity, is presented in Fig. 1. Heme peptides having polypeptide of 6, 8, or 9 amino acids can also be obtained by proteolytic digestion of cyt. c [12]. Heme peptide molecules have several superficial and very attractive properties compared with those of porphyrin. These are: aqueous solubility, a weaker tendency to aggregation, the availability of a few chemical functionalities for covalent coupling or modification, as well as relative simplicity of the structure exhibiting enzymatic activity (peroxidase) which is beneficial for a simplified theoretical description of different phenomena, e.g., structure-function relationship [12,13], or modeling of a biomolecule behavior at interfaces, i.e. adsorption on solid surfaces [14,15], electrochemi-
0022-0728/99/$ - see front matter © 1999 Elsevier Science S.A. All rights reserved. PII: S 0 0 2 2 - 0 7 2 8 ( 9 9 ) 0 0 1 9 4 - 1
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cal redox conversion [16], and catalysis in organic solvents [17,18]. In addition to the aforementioned properties, the fact that the active site (iron protoporphyrin IX) is not shielded by a polypeptide is recognized in electrochemical studies of ET of heme peptides [19 – 23]. An obvious possibility of direct contact between an electrode and the heme in microperoxidase is expected to result in an easy realization of a fast ET between an electrode and the heme peptide. Rapid interfacial electron exchange is undoubtedly important for construction of fuel cells [24,25], high efficiency artificial photosynthesis systems [26] or sensors for determination of rapidly degrading analytes such as oxygen radicals and nitric oxide [4,27]. A number of electrochemical investigations have been conducted to determine ET rates between electrodes and heme peptides. The experimental systems can be sorted into two approaches, i.e. the electrochemical study of surface confined microperoxidases (physisorbed or attached covalently) [21,23,28,29] and electrolysis of soluble species [16,22,30]. The kinetic investigations of surface confined MP-11 are briefly summarized below. The first electrochemical measurement of the interfacial ET kinetics on MP-11 immobilized covalently at gold modified with a short thiol, cystamine, was performed by Lo¨tzbeyer et al. The rate constant for ET
Fig. 1. Structure of the heme peptide MP-11 formed by enzymatic digestion of cyt. c. The number of amino acid residues from 11 to 21 corresponds to that number in the cyt. c polypeptide sequence. The side chains of amino acids are also included.
between MP-11 and gold was found to be equal to 12 s − 1 in 0.1 M phosphate buffer pH 7 [29]. It was inferred that the attachment of MP-11 to the cystamine monolayer could proceed via covalent linkage of the carboxylic residue of the peptide or, alternatively, through coupling of the propionic acid groups of the protoporphyrin IX. Later, chronoamperometric measurements were interpreted in the frame of these assumptions with the following conclusion: MP-11 molecules are attached to the cystamine modified gold by the two above mentioned coupling modes with about 50 to 50% distribution and exhibit interfacial ET exchange constants of 8.5 and 16 s − 1 [21]. Several other procedures were tested for immobilization of MP-11 on gold modified with short thiols resulting in interfacial ET rate constants of 0.58–0.86 s − 1 [19]. The highest ET rate constant for MP-11 immobilized on gold modified with cystamine was registered to be 20 s − 1 [31]. These heterogeneous ET rates are surprisingly low if compared with the rates observed for physisorbed hemin or cyt. c electrodes. Hemin adsorbed on glassy carbon or basal plane pyrolytic graphite electrodes exhibits heterogeneous ET constants higher than 4000 s − 1 [32,33]. The heterogeneous ET constants for cyt. c adsorbed on gold modified with short thiols were found to be close to 1000 s − 1 [34–36]. It could be understood that for cyt. c the correct orientation on the electrode is crucial to ensure rapid heterogeneous ET and undoubtedly it drops drastically if a recipe for chemical immobilization does not ensure correct orientation. As an illustration of that might be the fact that cyt. c immobilized covalently on a gold electrode modified with N-acetyl-cysteine exhibits 0.8–3.4 s − 1 interfacial ET [37] while cyt. c adsorbed physically on the same surface shows an ET rate between 400 and 920 s − 1 [36]. The same speculation about incorrect orientation resulting in a remote location of the heme from the electrode cannot, however, be accepted to rationalize slow heterogeneous ET rates (as summarized above) of MP-11 affixed covalently to the gold through carboxylic functionalities of protoporphyrin IX. The main motivation for the experimental work described here was to study heterogeneous ET of MP-11 in order to understand whether heme peptides could exhibit high interfacial ET rates, i.e. the rates close to those observed for cyt. c or hemin modified electrodes. For that, three electrode designs have been prepared and examined: (A) MP-11 immobilized on gold modified with cystamine, following the procedure of Lo¨tzbeyer et al. [29], (B) MP-11 immobilized through amino functionalities of the polypeptide using Lomant’s reagent, and (C) MP-11 physisorbed on hydrophobic alkane thiol modified gold electrodes.
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2. Experimental
2.1. Materials Heme peptide MP-11 was purchased from Sigma, St. Louis, MO, USA. Cystamine (2,2%-diaminodiethyldisulfide), and alkanethiols (1-butane-, 1-hexane-, and 1-decane-thiol) were obtained from Merck, Darmstadt, Germany. Lomant’s reagent, i.e. 3,3%-dithiodipropionic acid di(N-succimidyl ester), and 1-ethyl-3-(3-dimethylaminopropyl) carbodiimide (EDC) were purchased from Fluka, Buchs, Switzerland. Ultrapure water for washing the electrodes and preparing buffer solutions was produced in a Milli-Q system from Millipore, Bedford, MA, USA.
2.2. Electrode preparation Clean gold electrodes were prepared by polishing with 5 mm alumina powder and finishing with 0.05 mm to produce a mirror-like surface. The electrodes were ultrasonicated in water for 5 min to remove bound alumina, and then cleaned electrochemically by linear potential cycling between 1.7 and −0.35 at 0.2 V s − 1 (30 cycles in total) in 1 M sulfuric acid [38]. After that the electrodes were washed with ultrapure water and used immediately to prepare MP-11 modified electrodes by the following three procedures.
2.2.1. Design (A) Gold electrodes with MP-11 attached covalently using EDC cross-linker were prepared according to a procedure described by Lo¨tzbeyer et al. [29]. A clean gold electrode was immersed into a 100 mM solution of cystamine in water for 3 h at room temperature. After that the electrode was washed with water and immersed for 3 h into a mixture of MP-11 and carbodiimide in 0.01 M HEPES buffer, pH 7.5. The concentrations of MP-11 and EDC were 0.3 and 10 mM, respectively. After that the electrode was washed with water and cyclic voltammetry or electroreflectance measurements were performed (see below). 2.2.2. Design (B) Gold electrodes with MP-11 attached covalently through the amino functionalities of the polypeptide chain were prepared by depositing Lomant’s reagent, 3,3%-dithiodipropionic acid di(N-succimidyl ester), on the electrode surface [39]. For that the clean gold electrode was immersed into a solution of Lomant’s reagent for 10 min at 25°C. Lomant’s reagent was dissolved in DMSO at a concentration of 3 mg ml − 1. For immobilization of microperoxidase the electrode was washed with water and left in a 1 mM MP-11 solution in 0.01 M phosphate buffer, pH 7, overnight at + 4°C. After that electrode was washed with water and used for electrochemical studies.
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2.2.3. Design (C) SAM modified electrodes with physisorbed MP-11 were prepared by first depositing an alkane thiol layer on gold. For that clean gold electrodes were kept in a 10 mM thiol solution in ethanol overnight at room temperature, then washed with ethanol and water and immersed into a 1 mM MP-11 solution in 0.01 M phosphate buffer, pH 7, for 0.5 h at +4°C. After that the electrodes were washed with water and used for electrochemical studies. 2.3. Instrumentation Cyclic voltammetry, CV, measurements were performed with an EG&G potentiostat model 263A (Princeton, NJ, USA). A conventional three-electrode electrochemical cell was used throughout all electrochemical measurements. The gold electrode (0.16 cm dia.) was used as the working electrode. A platinum wire and an Ag AgCl KCl (sat) electrode (BAS, West Lafayette, IN, USA) were used as auxiliary and reference electrodes, respectively. All potentials mentioned herein are relative to the saturated Ag AgCl reference electrode potential. The setup for electroreflectance, ER, measurements has been described previously [36,40].
2.4. Measurement procedures All electrochemical and electroreflectance measurements were performed in carefully deoxygenated buffer solutions. This was achieved by continuous argon bubbling more than 0.5 h before measurements. High-speed CV ( \5 V s − 1) measurements were performed with solution resistance compensation. The solution resistance was evaluated by using the measurement procedure available with the EG&G potentiostat in its IR compensation mode. For each specific electrode, five successive cyclic voltammograms, CVs, were recorded. The final (fifth) CV was used to calculate the ET parameters. Usually 6–9 different sweep rates were used in the CV measurements with each electrode. The apparent heterogeneous ET rate constant, kET, was determined from the peak separation measurements in CVs by employing Laviron’s diffusionless model [41]. When the signals were noisy due to disabled signal filtering, a special mathematical procedure was employed to reduce errors in the measurement of the peak separation. For this the peak potentials in the CVs were determined by fitting a portion (the part containing current data at 90.2 V from an approximate peak value) of the recorded CV to the sum of a Gaussian and a linear function. The first accounted for the dependence of the faradaic (peak) current on the applied potential while the last was sensitive only to the background charging current and its dependence on the
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electrode potential. This nonlinear least-squares fitting was performed with a commercial program SigmaPlot V. 4.0, Jandel Scientific, San Rafael, CA, USA. The electroreflectance, ER, measurements were carried out using light coming from a monochromator. The source of the light was a 100 W xenon arc lamp. The angle of incidence measured relative to the normal of the electrode surface was about 15° or less. Reflected light from the electrode was measured by a photodiode and the output signal was separated into ac and dc components by appropriate electronic filters. The electroreflectance spectra intensity function was calculated as described previously [36].
3. Results Three electrode designs (A, B, C), specifically, gold electrodes with surface confined MP-11, were prepared with the objective of investigating the effect of immobilization on the measurable kinetic ET properties of this heme peptide. The main principal differences in coupling protocols are the following. The chemical coupling with EDC is meant to result in MP-11 linked covalently to cystamine modified gold electrodes by crosslinking the carboxylic functionality on MP-11 with the amino functional group of cystamine (design A). However, this procedure could result in a multilayer coverage since cross-linking between MP-11 molecules can occur due to the simultaneous presence of MP-11 and EDC in the immobilization solution. The other two protocols (designs B and C) avoid this complication. Chemical coupling of MP-11 through its amines with Lomant’s reagent deposited on gold surface proceeds just on the surface of the electrode, since there is no coupling reagent in solution (design B). Adsorption of MP-11 from diluted solutions also results in a monolayer [14,15]; however, the molecules are, of course, not attached covalently (design C). The stability of the latter electrodes was worse compared with covalently attached systems if kept/stored in buffer solution for a few hours. However in this study the main priority was given to measuring and interpreting heterogeneous ET rates as well as the amounts of MP-11 attached to the surface of the gold electrodes. Preliminary measurements of other characteristics such as stability or formal potential values were performed, however, the results are not discussed in this study. The results concerning heterogeneous ET measurements and surface concentrations are further described for each electrode design (A, B, C) separately. (A) MP-11 was immobilized on gold electrode modified with cystamine by covalent coupling of the carboxylic functionalities on the heme peptide with the amine functionalities of the SAM by using EDC as described elsewhere [29]. After the immobilization pro-
Fig. 2. Electrochemical data obtained with the gold electrodes modified with cystamine and the following covalent attachment of MP-11 using carbodiimide (design A, see methods). (a) A typical cyclic voltammogram at a sweep rate of 2 V s − 1. Buffer solution was 0.1 M sodium phosphate, pH 7. Points represent experimental data. Lines are from the CV generated mathematically using parameters derived from nonlinear least-squares fitting as described in methods. The insert shows the linear dependence of the peak current on the potential sweep rate. (b) Apparent heterogeneous ET rate constant, kET, at different sweep rates. Calculation was based on the difference of the peak potentials evaluated from CVs similar to that shown in (a) and the diffusionless Laviron model.
cedure the electrode was washed carefully with water, placed into the electrochemical cell containing 0.1 M phosphate buffer (pH 7.4) and CVs at different potential sweep rates were recorded. The results derived from these measurements are summarized in Fig. 2. A typical CV taken at 2 V s − 1 sweep rate is presented in Fig. 2a. As expected for covalently attached molecules a direct proportionality of peak current on sweep rate confirms the electrochemistry of surface bound MP-11 molecules (insert in Fig. 2a). From the peak separation in CVs taken at different sweep rates, the apparent heterogeneous ET rate constants, kET, were evaluated using Laviron’s diffusionless model [41]. It can be seen that the kET value depends on the sweep rate (Fig. 2b). Due to an observed and unexpected dependence of kET on the sweep rate in CV experiments with MP-11 immobilized covalently, additional experiments were
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performed to confirm that the measured reaction is an electrochemically driven one electron ET process: kET
HemeMP-11(Fe3 + )+e − l HemeMP-11(Fe2 + )
(1)
For this, ER spectra of MP-11 (Fig. 3a) and cyt. c (Fig. 3b) modified electrodes were recorded. ER spectra originate from the difference in an optical absorbency of the reduced and oxidized forms of the redox species [42]. The spectral features of the reduced and oxidized forms of MP-11 can be expected to be very similar to those of cyt. c due to the fact that they are determined by the same iron protopophyrin – polypeptide (though smaller part) from cyt. c. Due to this expected optical similarity the ER spectra should be almost identical for these two molecules if the electrochemical redox process is the same for both. Indeed, a very close similarity of both spectra (Fig. 3) indicates that the reaction of the electrochemical conversion of MP-11 on the electrode is the same as that of cyt. c. There is no doubt that for the latter the electrochemical reaction is an ET process described by Eq. (1), which thus should be the same for heme peptide MP-11 originating from cyt. c. (B) To prepare another electrode design still with covalently immobilized MP-11, gold electrodes were treated with Lomant’s reagent to activate their surface
Fig. 3. Electroreflectance spectra of the gold electrodes modified with (a) cystamine and EDC coupled MP-11 (electrode A, see methods) and (b) N-acetyl-cysteine and adsorbed cyt. c. Experimental conditions and signal processing to obtain intensity function of ER spectra, DR/R, were carefully described previously.
Fig. 4. A typical cyclic voltammogram (dots) of the gold electrodes modified with Lomant’s reagent and following covalent coupling of MP-11 (electrode B, see methods). Buffer solution was 1 M sodium phosphate, pH 7. Sweep rate was 60 V s − 1. Lines represent CV generated using the parameters extracted from fitting the experimental data as described in the text.
for covalent coupling of the heme peptide through its amine functionalities. After immobilization of MP-11, CVs were recorded with sweep rates ranging from 10 to 100 V s − 1. A typical CV at 60 V s − 1 is presented in Fig. 4. From these CVs the heterogeneous ET rate constant and surface coverage of MP-11 were evaluated. The ET constant was estimated from the difference in peak separation and resulted in a value of 3600 s − 1. Integration of the charge passed during the electrochemical oxidation or reduction process of MP-11 gives the possibility of calculating its surface concentration, G. This was found to be equal to 13 pmol cm − 2. (C) The third approach was to study the electrochemistry MP-11 adsorbed on alkane thiol modified gold electrodes, i.e. SAM modified electrodes. SAMs were prepared using three different length alkanethiols: butanethiol, hexanethiol, and decanethiol. After modification of the gold electrodes with the SAMs they were immersed into a MP-11 solution for 0.5 h, subsequently washed carefully with water and immersed into buffer solution for CV measurements of the physisorbed MP11. A typical CV of MP-11 adsorbed on gold modified with hexanethiol is presented in Fig. 5. It can be seen that the electrochemical redox conversion is reversible with almost symmetric anodic and cathodic peaks. From the peak integration the amount of MP-11 adsorbed on the SAM modified electrodes was evaluated. It ranged between 10 and 65 pmol cm − 2. Almost always G values were higher at those electrodes which had been modified with SAMs of shorter thiols. From the peak separation in CVs the ET rate constants were estimated to be equal to 1700, 1010, and 450 s − 1 on butane, hexane, and decane thiol modified gold electrodes, respectively.
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Fig. 5. A typical cyclic voltammogram of the gold electrodes modified with SAM and adsorbed MP-11 (electrode C, see methods). SAM was prepared using hexanethiol. Sweep rate was 2 V s − 1. Buffer solution was 1 M sodium phosphate, pH 4.2.
4. Discussion A short summary of the data from the cyclic voltammetry measurements on the three designs of MP-11 modified gold electrodes is presented in Table 1. Before starting to compare the characteristics of the electrodes it should be mentioned that the conditions of measurement were not the same for all three electrode designs (Table 1). The buffer molarity was increased from 0.1 to 1 M to avoid severe potential drops as a result of solution resistance when experiments were done with electrode designs B and C. To be able to extract kinetic information for the electrodes B and C quite high potential sweep rates were necessary, i.e. 1 – 100 V s − 1. The buffer pH was also changed from pH 7 to 4.2 when CV measurements were performed on gold electrodes modified with SAMs and adsorbed MP-11 (design C), because in more basic solutions the electrodes exhibited a decreased stability and the faradaic peaks were broader, sometimes consisting of two overlapping peaks (data are not presented). This was never observed in acidic solutions. The broadening of the peaks in CVs [43] could be caused by strong repulsive interaction
between adsorbed MP-11 molecules. This interaction is minimized in acidic solutions since MP-11 has an acidic isoelectric point, i.e. pI = 4.75 [44]. Simple CV measurements allow rapid estimation of the heterogeneous ET rate constants from peak separation observed at different sweep rates of applied potential when using the procedure described by Laviron for diffusionless heterogeneous kinetics of redox molecules [41]. To use this method correctly one needs to ensure that the surface concentration of redox molecules is equal to a monolayer coverage or less. It can be seen (G in Table 1) that the surface concentration of MP-11 as a result of different immobilization recipes is quite different. The highest G is obtained for electrodes A, where MP-11 is immobilized on cystamine modified electrodes by EDC coupling. Since EDC and MP-11 are present in the immobilization solution at the same time cross-linking can occur. The question then to be answered is, what should the surface concentration of a monolayer coverage for MP-11 be? From ellipsometric measurements a monolayer coverage of MP-11 has been estimated previously to be in the range between 40 and 60 pmol cm − 2 on hydrophobized silicon [14] and platinum [15]. There it was also shown that the maximum surface concentration depended on pH, however, it never exceeded 64 pmol cm − 2. In this context it can be estimated that 3–4 monolayers of MP-11 are present on the gold electrodes prepared by covalent coupling of the heme peptide using EDC. This follows if an amount of 60 pmol cm − 2 is taken as a complete monolayer coverage of MP-11 and compared with the G values of 220 or 280 pmol cm − 2 found after the EDC coupling procedure. It should be noted that the same multilayer coverage could have been concluded for previously studied MP-11 modified electrodes when EDC was used for its immobilization. In some of these cases the G values were even higher than that observed in this study (Table 1, design A), i.e. 240 pmol cm − 2 [29], 300 pmol cm − 2 [17], 320 pmol cm − 2 [21], 600 pmol cm − 2 [23]. The other two designs, covalent coupling of MP-11 by Lomant’s reagent and simple adsorption (designs B and
Table 1 A summary of the electrochemical characteristics derived from the cyclic voltammetry measurements of MP-11 modified gold electrodes a Electrode design
G/pmol cm−2
kET/s−1
E°%/V
Electrolyte
A. Au modified with cystamine and MP-11 coupled covalently with EDC. B. Au modified with Lomant’s reagent and covalent MP-11 coupling. C. Au modified with SAM and physisorbed MP-11. SAM was made using the following alkanethiol: C.1. butanethiol; C.2. hexanethiol; C.3. decanethiol.
220, 280 (N = 2)
13–112 (Fig. 2b)
−0.355
0.1 M PB, pH 7
13 9 2 (N =2) 10–65
3600 91100 306–2800
−0.345
1 M PB, pH 7 1 M PB, pH 4.2
45 915 (N =8) 54 9 4 (N= 4) 17 97 (N = 10)
1700 9600 1010 9210 450920
−0.230 −0.236 −0.237
a Au, PB, SAM, and N represent gold electrode, phosphate buffer, self assembling monolayer, and number of electrodes studied, respectively. Formal potential values, E°%, are given versus Ag AgCl KCl(sat).
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C, respectively in Table 1) resulted in G values lower than 60 pmol cm − 2 and thus can be treated undoubtedly as systems with monolayer coverage of MP-11 on gold. From Table 1 it follows that the ET rate constants obtained from peak separation in CVs are quite different for our three electrode designs if compared with each other. Design A is characterized by the lowest ET rate constants. It should be noted that lower limits of ET rate constant as well as the G value of electrodes with EDC immobilized MP-11 are in good agreement with previously published results [21,29,31] meaning that in our hands the immobilization procedure resulted in similar electrodes as described elsewhere. The interpretation of the results presented here is, however, completely different for these electrodes. We believe that the ET rate constant estimated at slow sweep rates in CV measurements reflects not the heterogeneous ET rate between MP-11 and the electrode, but is characteristic of the electron exchange rate between the MP-11 molecules residing in different layers. As a support for this is the fact that the ET rate constant increases at higher potential sweep rates. Such behavior can be expected from cyclic voltammetry measurements if one considers an idealized model of the film of MP-11 (i.e. three monolayers) immobilized on a gold electrode. Theoretical treatment of this model and some conclusions derived from this model system are illustrated below. The model is an idealized representation of the film of MP-11 immobilized on the gold electrode. To model ET transitions between MP-11 molecules in the film, the latter is split into three identical monolayers of MP-11 molecules. The ET rate constants between the layers are given by a single potential independent constant, kL, while the ET rate constants between the layer adjacent to the electrode and the electrode will be given by kred(E) and kox(E) both of which depend on the applied potential, E. Fig. 6 gives a schematic representation of the model which is described mathematically as: (f0 =kred(E)(1−f0)− kox(E)f0 +kL f1(1 − f0) (t −kL f0(1− f1) (f1 = −kL f1(1−f0)−kL f1(1 − f2) +kL f0(1 − f1) (t + kL f2(1− f1) (f2 = −kL f2(1−f1)+kL f1(1 − f2) (2) (t where f0, f1, and f2 are the fractions of reduced MP-11 molecules in each layer, respectively. It is assumed that each layer has the same number of MP-11 molecules. The potential dependent rate constants are written as [45]:
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Fig. 6. Experimentally observed dependence () of the peak potentials difference, DEP, on sweep rate from cyclic voltammetry measurements with the gold/crosslinked MP-11 electrodes (A, see methods). Line represents theoretically generated DEP-sweep rate dependence using heterogeneous ET constant 1000 s − 1 and interlayer ET constant 40 s − 1 (for modeling details see discussion). A schematic presentation of an idealized film, consisting of three monolayers of crosslinked MP-11, used for the calculations of the theoretical DEP values is included.
kred(E)= k0 exp − anF
E(t)−E°% RT
kox(E)= k0 exp (1−a)nF
E(t)− E°% RT
(3)
Here n= 1 is the number of transferred electrons and a= 0.5 is the transfer coefficient. E°% is the midpoint potential in the CV, R is the gas constant, F is the Faraday constant, and T is the absolute temperature. The two rate constants kL and k0 were adjusted to obtain the mathematically derived dependence of the separation of the two peak potentials at different potential sweep rates close to that observed experimentally (Fig. 6). For this, theoretical CVs were generated by the following dimensionless current–potential dependence using the expression:
I(t)= (1− f0(t)) exp − anF
− f0(t)exp (1−a)nF
E(t)− E°% RT
E(t)− E°% RT
(4)
where f0(t) was the solution obtained from Eq. (2) and Eq. (3). The equations were solved numerically with a potential which was swept linearly from − 0.5 to −0.2 V and then back to −0.5 V resulting in theoretically predicted CVs. Then, the peak potential values (E ox P and E red P ) were obtained by fitting the current peaks in these theoretical CVs to quadratic polynomials. Finally, by subtracting the two peak potentials the difference, red DEP = E ox P − E P , was estimated. A first calculation, corresponding to the first CV (non-stationary initial potential sweep) was performed to obtain starting f0, f1,
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and f2 values for the theoretical calculation of a second CV whose resulting DEP was used in the comparison to the experimental CV measurements. The width of the theoretical current peaks was smaller than that measured experimentally (Fig. 2). Fig. 6 presents the calculated and measured DEP values. To generate theoretical DEP close to the experimental values k0 =1000 s − 1 and kL = 40 s − 1 were used. If we used only two layers to model the MP-11 film, we could not obtain sufficiently large DEP using k0 =1000s − 1. The model was implemented using Mathcad 7.0; the program describing the model is available upon request. The main conclusion from this mathematical treatment of an idealized model is that it actually demonstrates that results observed experimentally for design A electrodes can be obtained from multilayer modified MP-11 electrodes. The rate constants k0 and kL generating a theoretical DEP similar to that observed experimentally are also surprisingly close to that estimated for multilayer (A) and monolayer (B and C) MP-11 modified electrodes. An attempt was made to estimate the upper limit of the ET rate constant for A electrodes with ER measurements. However, the results were similar to those derived from CV measurements. The higher the potential modulation frequency, the higher were the observed ET rates. It was possible to observe strong ER signals at 1111 Hz modulation frequency (Fig. 7) which definitely would be impossible for systems with a heterogeneous ET constant of 20 s − 1 [42].
5. Conclusions
MP-11 are immobilized on electrodes by the method of carbodiimide coupling of heme peptides to cystamine modified electrodes. The observed dependence of the ET rate constant on potential sweep rate during CV measurements and theoretical treatment of the ET for a three-layer idealized system confirms that the rate constant estimated from slow sweep voltammetry measurements reflects the interlayer ET process, but not the heterogeneous electrode/MP-11 electron exchange rate. In this context the use of Laviron’s diffusionless model for calculations of heterogeneous ET rate constants of multilayer redox systems should be strongly discouraged. From further experimental data observed on monolayer systems (electrodes B and C) it could be concluded that the ET rate constant between MP-11 and the gold electrode should be more than 1000 s − 1. From the data obtained with SAM modified electrodes with adsorbed MP-11 (C, Table 1) it can be seen that the ET rate constant decreases with increasing thickness of the SAM. Further studies are in progress to estimate the dependence of the ET rate constant on the distance for surface confined MP-11 on SAM modified electrodes. Acknowledgements Dr. Vincent Vilker at NIST is acknowledged for providing electroreflectance measurement facilities to conduct this study as well as for a consistent questioning of the quality of electrochemical measurements and their correct interpretation. TR is grateful for financial support from the EU (DIAMONDS BIO4-CT97-2199) and the Royal Swedish Academy of Science.
Three electrode designs with surface confined MP-11 species were prepared and studied by cyclic voltammetry. High amounts, i.e. equivalent to 3 – 4 monolayers of
References
Fig. 7. Electroreflectance voltammogram of the gold electrode modified with cystamine and EDC coupled MP-11 (electrode A). Ac modulation amplitude and frequency were 20 mV and 1111 Hz, respectively. Electrode was irradiated with light of l=414 nm. The electrolyte solution was 0.1 M phosphate buffer, pH 7.
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