Accumulation and Reactivity of the Redox Protein Cytochrome c in

The concentration of cytochrome c in the membrane, 24 mM, is very high compared to the solution ... Inorganic Solids; Sequeira, C. A. C., Hudson, M. J...
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Langmuir 2003, 19, 4327-4331

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Accumulation and Reactivity of the Redox Protein Cytochrome c in Mesoporous Films of TiO2 Phytate Katy J. McKenzie and Frank Marken* Department of Chemistry, Loughborough University, Loughborough, Leicestershire, LE11 3TU, United Kingdom Received November 3, 2002. In Final Form: February 26, 2003 The formation of well-defined nanofilm deposits of TiO2 nanoparticle phytates based on the “directed assembly” methodology is demonstrated. Alternate exposure of a tin-doped indium oxide electrode surface to aqueous solutions of TiO2 nanoparticles (3-4% in HNO3, ca. 6 nm diameter) and phytic acid (40 mM, at pH 3) causes layer-by-layer growth of a three-dimensional mesoporous structure. Cytochrome c in aqueous phosphate buffer (pH 7) is readily accumulated into the mesoporous TiO2 phytate film predominantly due to electrostatic binding of the positively charged protein to the negatively charged interfacial phytic acid. Voltammetric data for the reversible reduction and reoxidation of cytochrome c suggest strong adsorption and “ideal” thin film behavior over a wide range of conditions. Voltammetric data are analyzed quantitatively based on the model of a finite diffusion zone. For a TiO2 phytate modified electrode immersed in aqueous 0.1 M phosphate buffer (pH 7), strong accumulation (a 3 order of magnitude increase in concentration) of cytochrome c, an apparent standard rate constant for electron transfer, k0apparent ) 3 × 10-8 m s-1, and an effective diffusion coefficient for cytochrome c within the mesoporous structure, Deffective ) 2 × 10-14 m2 s-1, are obtained. The redox processes within the nanoporous membrane, which are relatively insensitive to impurities and strongly affected by the electrolyte concentration in the aqueous buffer solution, are proposed to be dominated by electron “hopping” between adjacent cytochrome c molecules.

1. Introduction

Chart 1

1

Mesoporous materials are of considerable interest as protective hosts for biological molecules and assemblies.2 Many approaches for the formation of mesoporous structures exist,3 and in particular the recently emerged methods based on layer-by-layer deposition of nanoparticles and ionomers4,5 have attracted attention. We have employed the layer-by-layer assembly strategy to make mesoporous films6 on electrode surfaces by alternate exposure of the electrode surface to solutions of (i) metal oxide nanoparticles and (ii) polydentate binder molecules such as phytic acid (see Chart 1 and Scheme 1). This strategy is versatile and allows mesoporous films to be formed with adjustable thickness and different types of layers. The layer-by-layer deposition of nanoparticles with a polymeric binder has been employed extensively (in particular by Rubner and co-workers7) for the formation of thin porous films,8 nanodevices,9 photonic devices,10 and, for example, for the three-dimensional patterning of * To whom correspondence should be addressed. Tel: 01509 22 2551. Fax: 01509 22 3925. E-mail: [email protected]. (1) See for example: Multifunctional Mesoporous Inorganic Solids; Sequeira, C. A. C., Hudson, M. J., Eds.; Kluwer Academic: London, 1993. (2) Deere, J.; Magner, E.; Wall, J. G.; Hodnett, B. K. J. Phys. Chem. B 2002, 106, 7340. (3) See for example: Brinker, C. J.; Scherer, G. W. Sol-Gel Science; Academic Press: Boston, 1990. (4) Shipway, A. N.; Katz, E.; Willner, I. ChemPhysChem 2000, 1, 18. (5) Kulesza, P. J.; Chojak, M.; Miecznikowski, K.; Lewera, A.; Malik, M. A.; Kuhn, A. Electrochem. Commun. 2002, 4, 510. (6) McKenzie, K. J.; Marken, F.; Hyde, M.; Compton, R. G. New J. Chem. 2002, 26, 625. (7) See for example: Joly, S.; Kane, R.; Radzilowski, L.; Wang, T.; Wu, A.; Cohen, R. E.; Thomas, E. L.; Rubner, M. F. Langmuir 2000, 16, 1354. (8) Wang, T. C.; Rubner, M. F.; Cohen, R. E. Langmuir 2002, 18, 3370. (9) Kovtyukhova, N. I.; Martin, B. R.; Mbindyo, J. K. N.; Mallouk, T. E.; Cabassi, M.; Mayer, T. S. Mater. Sci. Eng., C 2002, 19, 255. (10) Shiratori, S.; Ito, T. Mol. Cryst. Liq. Cryst. 2001, 371, 143.

Scheme 1

surfaces.11 The use of a molecular binder such as phytic acid, in contrast to employing a polymeric binder, results in a more rigid and open mesoporous structure with a minimum of “soft matter” within the solid (metal oxide) framework.6 One important application of mesoporous membranes is that of providing a protected nanoreactor environment for biological processes, for example, in enzyme catalysis12 and in electroanalysis.13 Thin mesoporous membranes applied to suitable electrode surfaces allow proteins to be immobilized and biocatalytic processes to be driven electrochemically.14 It has been demonstrated in elegant work by Rusling and co-workers that myoglobin and other (11) Hua, F.; Cui, T. H.; Lvov, Y. Langmuir 2002, 18, 6712. (12) Zhang, Z.; Chouchane, S.; Magliozzo, R. S.; Rusling, J. F. Anal. Chem. 2002, 74, 163. (13) Hu, N. Pure Appl. Chem. 2001, 73, 1979. (14) See for example: Armstrong, F. A.; Wilson, G. S. Electrochim. Acta 2000, 45, 2623.

10.1021/la0267903 CCC: $25.00 © 2003 American Chemical Society Published on Web 04/11/2003

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heme proteins may be readily adsorbed into active film deposits made from manganese oxide nanoparticles15,16 or clays.17 Furthermore, the ability of TiO2 nanoparticle derivatized surfaces to interact with biomolecules is well established.18 Li et al. demonstrated the adsorption of heme proteins including cytochrome c on nanocrystalline TiO2 surfaces.19 Gra¨tzel et al.20 showed that DNA adsorbs onto thin layers of TiO2 nanoparticles. The effect of a porous alumina membrane on the electron transfer from a glassy carbon electrode to cytochrome c was studied by Ikeda and co-workers.21 Recently, Durrant and co-workers reported the electrochemistry of cytochrome c adsorbed directly into heat-activated films of ZnO and TiO2 (anatase).22 The structural unit responsible for the electron exchange in cytochrome c is the covalently bound heme c, which contains an Fe(III/II) redox center (eq 1). This redox center is embedded in an approximately 3.4 nm diameter protein shell with an overall +9 molecular charge at pH 7 (for ferricytochrome c) and with a considerable dipole moment.23,24 The electrostatic interaction between the positive end of cytochrome c and the biological substrate (cytochrome reductase or cytochrome oxidase) is crucial for the fast transfer of electrons.

FeIII(cyt c) + e- f FeII(cyt c)

(1)

Accordingly, the beneficial effects of negatively charged surface functional groups (e.g., nucleic acids,25 carboxylatefunctionalized surfaces,26-28 or dialysis membranes29) on the electron-transfer process between the electrode and cytochrome c have been repeatedly noted. In this study, the layer-by-layer deposition of nanoparticulate titania with phytic acid (see Chart 1) as a molecular binder is demonstrated. Thin mesoporous films ranging from approximately 20 to 2000 nm thickness are formed in this “directed assembly” deposition procedure. The properties of the mesoporous structure are dominated by the negatively charged phytic acid bound to the TiO2 surface. In the presence of cytochrome c, even at low concentrations, very efficient accumulation of the redox protein into the mesoporous structure is observed. The accumulation process is monitored by electrochemical techniques. It is shown that the accumulation process is favored by a low ionic strength. Electron transfer to and from cytochrome c is fast and facile with apparently low interference from impurities. (15) Gao, Q. M.; Suib, S. L.; Rusling, J. F. Chem. Commun. 2002, 2254. (16) Lvov, Y.; Munge, B.; Giraldo, O.; Ichinose, I.; Suib, S. L.; Rusling, J. F. Langmuir 2000, 16, 8850. (17) Zhou, Y. L.; Hu, N. F.; Zeng, Y. H.; Rusling, J. F. Langmuir 2002, 18, 211. (18) See for example: Topoglidis, E.; Campbell, C. J.; Cass, A. E. G.; Durrant, J. R. Langmuir 2001, 17, 7899. (19) Li, Q. W.; Luo, G. A.; Feng, J. Electroanalysis 2001, 13, 359. (20) Meier, K. R.; Gra¨tzel, M. ChemPhysChem 2002, 3, 371. (21) Ikeda, O.; Ohtani, M.; Yamaguchi, T.; Komura, A. Electrochim. Acta 1998, 43, 833. (22) Topoglidis, E.; Cass, A. E. G.; O’Regan, B.; Durrant, J. R. J. Electroanal. Chem. 2001, 517, 20. (23) Stryer, L. Biochemistry; W. H. Freeman: New York, 1995; p 541. (24) Cytochrome c: A Multidisciplinary Approach; Scott, R. A., Mauk, A. G., Eds.; University Science Books: Sausalito, CA, 1996. (25) Lisdat, F.; Ge, B.; Krause, B.; Ehrlich, A.; Bienert, H.; Scheller, F. W. Electroanalysis 2001, 13, 1225. (26) Collinson, M.; Bowden, E. F.; Tarlov, M. J. Langmuir 1992, 8, 1247. (27) Tarlov, M. J.; Bowden, E. F. J. Am. Chem. Soc. 1991, 113, 1847. (28) Avila, A.; Gregory, B. W.; Niki, K.; Cotton, T. M. J. Phys. Chem. B 2000, 104, 2759.(29) Lojou, E.; Bianco, P. J. Electroanal. Chem. 2000, 485, 71.

2. Experimental Section 2.1. Reagents. Horse heart cytochrome c (type VI, Sigma, molecular weight 12 384 g mol-1) was purified by size exclusion chromatography (prepacked Sephadex G-25 M columns, Amersham Pharmacia Biotech AB, Uppsala, Sweden). Phytic acid (dodeca sodium salt) and other reagents (Aldrich) were used as received. Demineralized and filtered water was taken from an Elga water purification system (Elga, High Wycombe, Bucks, U.K.) with a resistivity of not less than 18 MΩ cm. Titania (anatase) sol (30-35% in aqueous HNO3, pH 0-3, TKS-202) was obtained from Tayca Corp., Osaka, Japan. Tin-doped indium oxide (ITO) coated glass (resistivity, 20 Ω 0-1) was obtained from Image Optics Components Ltd. (Basildon, Essex, U.K.) and was cut into 5 mm wide rectangular plates. The electrodes were cleaned by sonicating in ethanol, rinsing with distilled water, and furnace treatment (Elite tube furnace, model TSH 12/65/550) at 500 °C in air for 60 min. 2.2. Instrumentation. Electrochemical experiments were conducted with a PGSTAT 30 Autolab system (Eco Chemie, The Netherlands) in a 5 mL three-electrode cell. The counter electrode was a platinum gauze, the reference electrode was a saturated calomel electrode (SCE, Radiometer), and the working electrode was a modified ITO electrode of typically 0.2 cm2 area. The aqueous solution was thoroughly deaerated with argon (BOC) prior to conducting experiments. Simulation of cyclic voltammograms was performed with the Digisim 2.1 software package (BAS) assuming a finite diffusion zone. For field emission gun scanning electron microscopy (FEGSEM), a Leo 1530 system was used. Samples were prepared by gold sputter coating (ca. 3 nm) prior to analysis. To estimate the film thickness of deposits, the surface was scratched prior to electron microscopy. 2.3. Growth of TiO2 Nanoparticle Phytate Films. Solution A consisted of TiO2 sol (anatase sol, TKS-202, typically 6 nm diameter, 30-37%, acidified with nitric acid, Tayca Corp., Osaka, Japan) which was diluted 10-fold with distilled water. Solution B was prepared by dissolving sodium phytate (Aldrich, see Chart 1) to give a solution 40 mM in water and acidifying with perchloric acid to pH 3. A thin film of TiO2 nanoparticles is deposited by 30 s immersion of the ITO electrode into solution A followed by thorough rinsing with water. Figure 1A shows agglomerates of TiO2 nanoparticles 20-50 nm in size present on the electrode surface as well as some smaller particles. Immersion of this electrode for 30 s in solution B causes phytic acid to adsorb. Rinsing with water concludes the first deposition cycle (see Scheme 1). By repetition of this sequence, a TiO2 phytate film is formed layer-by-layer. The image shown in Figure 1B shows a 10 layer deposit, and Figure 1C shows a 30 layer deposit. The average rate of growth during film formation can be estimated as 27 nm per deposition cycle.

3. Results and Discussion 3.1. Accumulation of Cytochrome c into TiO2 Phytate Membranes. Upon immersion of a TiO2 phytate modified electrode into an aqueous 0.1 M phosphate buffer (pH 7) solution containing 0.05 mM cytochrome c, immediately (after typically 10-30 s depending on film thickness) well-defined and strong voltammetric responses for the reduction and reoxidation of the redox protein are detected (see Figure 2). The process is detected at E1/2 ) (1/2)(Epred + Epox) ) 0.01 V versus SCE and attributed to the conversion of ferricytochrome c to ferrocytochrome c (eq 1). The peak current for the voltammetric response (see Figure 2) is in the order of 1 µA for a scan rate of 0.01 V s-1, which is considerably higher compared to the peak current expected for simple diffusion of cytochrome c to the electrode surface (based on the Randles-Sevcik expression30 and a diffusion coefficient31,32 of Dcytc ) 6 ( 2 × 10-11 m2 s-1, the peak current for a diffusion-controlled (30) Bard, A. J.; Faulkner, L. R. Electrochemical Methods: Fundamentals and Applications, 2nd ed.; Wiley: New York, 2001. (31) See for example: Hill, H. A.; Nakagawa, Y.; Marken, F.; Compton, R. G. J. Phys. Chem. 1996, 100, 17395 and references therein.

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Figure 3. Plot of the charge under the reduction peak in cyclic voltammograms (third scan, scan rate of 10 mV s-1) obtained for the reduction of 0.05 mM cytochrome c in 0.1 M aqueous phosphate buffer (pH 7) at a TiO2 phytate film modified ITO electrode as a function of the number of layers deposited.

Figure 4. Cyclic voltammograms (third scan, scan rate of 5 mV s-1) obtained for the reduction of 0.05 mM cytochrome c in 0.1 M aqueous phosphate buffer (pH 7) at a TiO2 phytate film modified ITO electrode (30 layer deposit) (A) immersed in aqueous 0.05 mM cytochrome c and (B) immersed in aqueous phosphate buffer in the absence of cytochrome c.

Figure 1. FEGSEM images showing titanium oxide nanoparticles (ca. 6 nm diameter) deposited layer-by-layer onto the surface of a tin-doped indium oxide electrode. Image A shows the first layer with some agglomerates, image B shows a film formed after deposition of 10 layers of TiO2 and phytic acid, and image C shows a 30 layer deposit of TiO2 and phytic acid. Prior to imaging, the surface was scratched and gold coated.

Figure 2. Cyclic voltammograms (third scan, scan rate of 10 mV s-1) obtained for the reduction of 0.05 mM cytochrome c in 0.1 M aqueous phosphate buffer (pH 7) at a TiO2 phytate film modified ITO electrode: (A) 5 layer deposit, (B) 15 layer deposit, and (C) 50 layer deposit.

one-electron transfer should be Ipred ) 21 nA). This suggests that the voltammetric signal is entirely dominated by the membrane process and in good approximation independent of the solution phase processes. A quantitative explanation of the voltammetric responses based on the model of a finite diffusion zone within the membrane is given below. A bare ITO electrode also allows voltammetric (32) Also compare: Koller, K. B.; Hawkridge, F. M. J. Am. Chem. Soc. 1985, 107, 7412.

responses for the reduction of cytochrome c to be detected.33,34 However, in this case the voltammetric response is more sensitive to impurities and deteriorates with time. In contrast, in the presence of the TiO2 phytate membrane, voltammograms are enhanced by accumulation and obtained in a highly reproducible manner. Experiments conducted with uncolumned cytochrome c solutions give similar results. This robust behavior suggests a relatively low sensitivity of the electrode to impurities. Changing the thickness of the TiO2 phytate membrane results in a corresponding change in the voltammetric response (see Figure 2). A plot of the charge under the reduction peak versus the number of layers deposited is shown in Figure 3. Clearly, the amount of cytochrome c accumulated into the TiO2 phytate film increases with the film thickness. This result is consistent with the presence of cytochrome c throughout the film and distributed evenly within the pores. The nonlinear correlation can be attributed to effects due to mass transport within the nanoporous membrane (vide infra). For the case of thicker films, a complete electrolysis of the cytochrome c within the film is not achieved with a scan rate of 10 mV s-1. The bond between cytochrome c and the TiO2 phytate membrane is surprisingly inert. Once the redox protein has been accumulated by adsorption into the membrane, the electrode can be removed, rinsed with distilled water, and reimmersed into a 0.1 M phosphate buffer solution (pH 7). The resulting voltammetric response (see Figure 4) is stable over many potential cycles and only slightly smaller (approximately 30% loss of signal occurs probably due to desorption) compared to the voltammetric response obtained in the presence of 0.05 mM cytochrome c. Therefore, the redox protein appears to be strongly bound to the membrane and unable to quickly re-equilibrate with the solution phase. (33) See for example: Bowden, E. F.; Hawkridge, F. M.; Chlebowski, J. F.; Bancroft, E. E.; Thorpe, C.; Blount, H. N. J. Am. Chem. Soc. 1982, 104, 7641. (34) El Kasmi, A.; Leopold, M. C.; Galligan, R.; Robertson, R. T.; Saavedra, S. S.; El Kacemi, K.; Bowden, E. F. Electrochem. Commun. 2002, 4, 177.

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Figure 5. Cyclic voltammograms (third scan, scan rate of 10 mV s-1) obtained for the reduction of (A) 0.05 mM, (B) 0.1 mM, and (C) 0.2 mM cytochrome c in 0.1 M aqueous phosphate buffer (pH 7) at a TiO2 phytate film modified ITO electrode (10 layer deposit).

Figure 6. Plot of the charge under the reduction peak in cyclic voltammograms (third scan, scan rate of 10 mV s-1) obtained for the reduction of cytochrome c in 0.1 M aqueous phosphate buffer (pH 7) at a 10 layer TiO2 phytate film modified ITO electrode as a function of the cytochrome c concentration.

Figure 7. Cyclic voltammograms (third scan, scan rate of 10 mV s-1) obtained for the reduction of 0.05 mM cytochrome c in (A) 0.5 M, (B) 0.1 M, and (C) 0.02 M aqueous phosphate buffer (pH 7) at a TiO2 phytate film modified ITO electrode (10 layer deposit; a fresh electrode was used for each experiment).

3.2. Cytochrome c Electrochemistry in TiO2 Phytate Membranes: Concentration Effects. There are several crucial parameters affecting the accumulation and mobility of cytochrome c within the TiO2 phytate membrane. Both the concentration of cytochrome c in the aqueous solution phase and the concentration of electrolyte in the aqueous buffer solution are important. Figure 5 shows cyclic voltammograms for the reduction of ferricytochrome c accumulated into a 10 layer (ca. 270 nm) TiO2 phytate membrane. As the concentration of the cytochrome c in the aqueous solution phase is increased, also the voltammetric peak current increases. A plot of the charge under the reduction peak versus the concentration of cytochrome c is shown in Figure 6. An approximately linear relationship (R ) 0.992) is observed (although the reduction process is not going to completion, see Figure 5). With the TiO2 phytate membrane present, reversible and well-defined voltammetric signals are obtained even in the presence of relatively high concentrations of cytochrome c. Even more dramatic than the cytochrome c concentration effect is the buffer concentration effect. Figure 7 shows cyclic voltammograms obtained for the reduction of 0.05 mM cytochrome c at a TiO2 phytate modified ITO electrode (10 layers) immersed in (A) 0.5 M, (B) 0.1 M, and (C) 0.02 M aqueous phosphate buffer at pH 7. When exposed to

McKenzie and Marken

Figure 8. Cyclic voltammograms (third scan, scan rate of (A) 1, (B) 2, (C) 5, (D) 10 mV s-1) obtained for the reduction of 0.05 mM cytochrome c in 0.1 M aqueous phosphate buffer (pH 7) at a TiO2 phytate film modified ITO electrode (30 layer deposit).

the same electrolyte solution, the electrodes give essentially identical voltammetric responses. However, it can be seen in Figure 7 that the cytochrome c accumulation effect is considerably enhanced at a lower concentration of electrolyte. Increasing the concentration of phosphate buffer first reduces the voltammetric response (presumably due to a reduced capability of the membrane to bind the protein) and then completely removes the voltammetric response. The same result is observed when the TiO2 phytate membrane is first “charged” with cytochrome c in aqueous 0.1 M buffer solution and then transferred into the high-concentration buffer solution. The ability of cytochrome c to bind into the membrane, to move within the membrane, and/or to exchange electrons at the electrode surface seems to be dramatically reduced at higher phosphate buffer concentrations. A possibly related effect was observed recently for a porphyrin derivative adsorbed into a TiO2 phytate film.35 The results obtained as a function of phosphate buffer concentrations are consistent with double-layer effects and can be rationalized by comparison with “peptidization” phenomena. Repulsion between like-charged colloidal particles is observed at low electrolyte concentration.36 Therefore, stronger binding between unlike-charged colloidal particles (here positively charged cytochrome c and negatively charged TiO2 phytate) can also be expected at reduced ionic strength. However, alternative interpretations of the voltammetric data based on electrolyte-induced film swelling effects37-39 and/or Donnan potential effects40 are possible. A more detailed discussion is presently unwarranted. 3.3. Cytochrome c Electrochemistry in TiO2 Phytate Membranes: Quantitative Analysis of Voltammetric Data. To achieve a more quantitative understanding of processes within the TiO2 phytate membrane, data from cyclic voltammograms can be compared to data from numerical simulation. Figure 8 shows cyclic voltammograms obtained for the reduction of 0.05 mM cytochrome c at a TiO2 phytate modified electrode (30 layers) immersed in 0.1 M phosphate buffer solution (pH 7) at different scan rates. The shape of voltammograms is indicative of (i) a complete electrolysis at slow scan rates changing to diffusion-dependent signals at higher scan rates and (ii) apparently slow electron transfer (35) Marken, F.; Parkhouse, S. M.; Hoe, L. A.; McKenzie, K. J.; Mortimer, R. J.; Vickers, S. J.; Rowley, N. M. Indian J. Chem., in print. (36) See for example: Evans, D. F.; Wennerstro¨m, H. The Colloidal Domain; Wiley: New York, 1999. (37) Dubas, S. T.; Schlenoff, J. B. Langmuir 2001, 17, 7725. (38) Farhat, T. R.; Schlenoff, J. B. Langmuir 2001, 17, 1184. (39) Forzani, E. S.; Perez, M. A.; Teijelo, M. L.; Calvo, E. J. Langmuir 2002, 18, 9867. (40) Calvo, E. J.; Wolosiuk, A. J. Am. Chem. Soc. 2002, 124, 8490.

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Figure 9. Cyclic voltammograms simulated with the Digisim software package (third scan, scan rate of (A) 1, (B) 2, (C) 5, (D) 10 mV s-1) obtained for a one-electron reduction process under finite diffusion boundary conditions with a layer thickness of 800 nm, a diffusion coefficient of 2 × 10-14 m2 s-1, a concentration of 24 mM, a standard rate constant for electron transfer of 3 × 10-8 m s-1, a transfer coefficient of 0.5, and an equilibrium potential of 0.0 V vs SCE.

causing a widening of the peak-to-peak separation. Both effects can be successfully reproduced by assuming a finite diffusion space and suitable values for the concentration of cytochrome c, the effective diffusion coefficient for cytochrome c within the membrane, and an apparent standard rate constant for electron transfer (see Figure 9). The physical interpretation of parameters such as the diffusion coefficient and the standard rate constant obtained by comparison of voltammetric data with numerical simulation data is not immediately obvious. The match between experiment and simulation for several scan rates is very good, but the nature of the processes responsible for the electron transfer is revealed only in part. The concentration of cytochrome c in the membrane, 24 mM, is very high compared to the solution concentration, 0.05 mM, and diffusion effects are likely to be augmented by intermolecular electron transfer. This electron transfer via “hopping” could be even more important if cytochrome c molecules are strongly adsorbed to the surface of the modified TiO2 particles. The lack of loss of cytochrome c from the membrane when immersed in a pure buffer solution (vide supra) suggests that strong adsorption is important. Although lateral mobility of cytochrome c might exist, this is pointing toward the importance of intermolecular electron hopping processes. The effective diffusion coefficient, Deffective ) 2 × 10-14 m2 s-1, is much slower compared to the literature value for the approximate diffusion coefficient of cytochrome c in solution, Dcytc ) 6 × 10-11 m2 s-1. Geometric effects such as those invoked for diffusion in gel environments39 are not sufficient to explain the 3 orders of magnitude change. However, if the process is assumed to be based entirely on intermolecular electron hopping, the Dahms-Ruff equation42,43 can be used to at least estimate the concentration of cytochrome c at the membrane walls (eq 2).

ccytc )

6Deffective kexδ2

(2)

(41) See for example: Zhang, W.; Ma, C. S.; Ciszkowska, M. J. Phys. Chem. B 2001, 105, 3435 and references therein. (42) Dahms, H. J. Phys. Chem. 1968, 72, 362. (43) Ruff, I.; Friedrich, V. J. J. Phys. Chem. 1971, 75, 3297.

In this expression, the concentration of cytochrome c, ccytc, is obtained from Deffective, the approximate bimolecular rate for electron self-exchange,44 kex ) 1.4 × 105 M-1 s-1, and the approximate distance between adjacent redox centers, δ ) 4 nm. The resulting estimate, ccytc ) 53 mM, is very reasonable and therefore lends support to the hypothesis of an electron hopping mechanism. It has to be pointed out that a more careful analysis of the redox exchange mechanism has to go beyond the Dahms-Ruff treatment and requires experimental data obtained with different anions and cations.45 The interpretation of the electron-transfer kinetics between the ITO electrode surface and cytochrome c molecules adsorbed into the membrane is also complicated by the presence of a high concentration of possibly immobilized cytochrome c. The standard rate constant for electron transfer extracted from the simulation, k0apparent ) 3 × 10-8 m s-1, is consistent with quasireversible electron transfer. Usually cytochrome c is observed to undergo very fast heterogeneous electron transfer, in particular at metal electrodes.46 However, for a densely packed layer of cytochrome c in contact with the electrode surface, a distribution of different standard rate constants can be expected depending on the distance, orientation, and location of the redox protein relative to the electrode surface. Even if fast electron transfer to some cytochrome c molecules is possible, the overall standard rate constant will be governed by the average including the slower rate constants. Further experimental work and new approaches for data analysis will be required to provide more insight into the nature of redox processes within the mesoporous TiO2 phytate membrane. 4. Conclusions A directed assembly method for the formation of a mesoporous membrane composed of TiO2 nanoparticles and phytic acid has been described. The resulting membrane very efficiently accumulates cytochrome c from dilute (or concentrated) aqueous solution and allows welldefined voltammograms for the conversion of the ferri- to the ferrocytochrome c and vice versa to be recorded. The simulation model based on mass transport in a finite diffusion zone coupled to quasi-reversible electron transfer at the electrode surface leads to a successful parametrization of the experimental data in terms of an effective diffusion coefficient and an apparent standard rate constant. The redox protein cytochrome c employed in this study may be regarded as a model system for other types of proteins or enzymes, which in future can be accumulated and protected in similar mesoporous membrane environments. Acknowledgment. F.M. thanks the Royal Society for the award of a University Research Fellowship. K.J.M. thanks the EPSRC for a studentship. We are grateful to Tayca Corporation (Osaka, Japan) for the generous gift of titania sols. LA0267903 (44) Concar, D. W.; Hill, H. A. O.; Moore, G. R.; Whitford, D.; Williams, R. J. P. FEBS Lett. 1986, 206, 15. (45) Electroactive Polymer Electrochemistry; Lyons, M. E. G., Ed.; Plenum: New York, 1994. (46) See for example: Nahir, T. M.; Bowden, E. F. Langmuir 2002, 18, 5283.