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Current—potential responses for a tetrahemic protein: a method of determining the individual half-wave potentials of cytochrome c3 from desulfovibrio desulfuricans strain Norway
CURRENT-POTENTIAL RESPONSES FOR A TETRAHEMIC PROTEIN: A METHOD OF DETERMINING THE INDIVIDUAL HALF-WAVE POTENTIALS OF CYTOCHROME cg FROM DESULFOVIBRIO DESULFURICANS STRAIN NORWAY P.
BIANCO
and J. HALADJIAN
Laboratoirede Cbimieet Electrochimie des Complexes,Universitbde Provence, Place.VictorHugo, 13331, Marseilleckdex 3, France (Received 9 July 1980)
Abstract-A tetrahemicprotein,cytochromecS from Desu&eibriodesulfuriconsstrah Norway, is studied by differentialpulse polarogrsphyand linearsweep voltammetryat bang@ mercuryelectrode.A graphical subtractivemethod applied to the current-potentialcurves is describedand the four individual rcdox potentialsare dckrmined.Both seriesof experimentsleadto two fit sets of valuescorrespondingto reversible electrodeprocesses.The relationshipbetween these redox potentialsand the structuraldata is discussed.
INTRODUCI’lON Cytochromes cI constitute a unique class of polyhcmic protdns which contain four hemes per molecule (M m 13,000) and have negative redox potentials[I]. From epr and nmr stud&s on some of these cytochromes it appears that the four hemes are in nonequivalent sites[ZJ; four redox midpoints potentials withnvaluesnearoflhavebcenmessuredinthecase of cytochame cg from Desulfovibrio vulgaris strain Hildenborough[3]. The di&rences between the hemc environments have been reported recently by Haser et a1.[4] who have solved the molecular structure at 2.5 A resolution of cytochromc cj from D. desulfuricalls strain Norway. In previous works we have studied the electrochemical behaviour of thii cytocatome cj by differmtial pulse polarography (dpp)[S] and cyclic voltammetry[6]. Two well-separated and one bad-resolved reduction steps have bum detected. It is thus likely that cytochrome cJ from D. desu@ricans has several close half-wave potentials. The knowledge of the individual redox potentials is very useful to understand the biological reactions in which cytochromes cg arc involved as electron carriers ofthe sulfate-reducing bacteria chains. The characterization of the different electroactive sites is not easy for polycentre molecules and their electrochemical behaviour has been the subject of a number of studies[7, a]. The differences in half-wave potentials between the successive reactions depend on several factors, eg structural changes of the molecule. In the case of identical ccntrea, electron transfers follow simpte statistics; a general analysis of this case has been given recently by Flanagan et al.[8]. For cytochrome cj from D. oulgmis strain Miyazaki which contains four non-equivalent redox sites, the voltammetric behaviaur has been anaIysed by using digital simulations[9, 101. The case of cytochrome c5 from D. desu(Wcanr
strain Norway is more specially attractive since the two main steps are well-separated by about O.l8V[5]. In the present paper we report a method for the analysis of current-potential curves obtained by dpp or linear sweep voltammetry (Iw) techniques. The approach used for the four ekctroactive cc&es molecule isbasedonthcfactthattheexperime@aloverallNms can be regarded as the summation of four individual curves. If each individual curve am be resolved from the overall curve, conciusions can be drawn on the halfwave potcntiaIs, reversibility and n value of the individual electron transfers.
EXPERIMENTAL Cytochrome C~from D. desadfiriccansstraiu Norway was prepared and purified as previously described11 I]. AU experiments were conducted in 0.01 M Tris-HCI buffer (pH 7.6) which served also as supporting electrolyte. The concentration of the cytochrome cj solution was 18.4pM. Dpp experimenta were performed with a PAR 174A analystr coupkd with a Sefram X-Y recorder. Since it has been shown by Chris& et ul.[l2] that experimental conditions in dpp must be carefUlly selected to obtain responses aacurately rekcting the true instantaneous currents for which the equations in this paper are derived, it proved necessary to use a slow scan rate (0.2 mV s - *). A small pulse amplitude AE ( = - 5 mV) was selected to increase the peaks resolution. The drop time was S s and the mercury flow 0.80 mg s- l. As indicated by the PAR operating manual the pulse is applied to the drop for 57 ms before the drop is dislodged and the current is sampled during 17 ms before application of the pulse and again at the ad of the pulse. These data will he Wed in our further calculations. Linear sweep voltammetq at stationary electrode was performed with a PAR 175 Universal Programmer aad a PAR 173 Potentiostat coupled
P.
1002
BMNCO AND J. HALADJIAN
with a PAR 176 converter. We utilized a Metrohm hanging mercury drop electrode (area = O.O22cm*). The voltammogram obtained at tr = 0.050 V s- ’ has been chosen for calculations. Throughout the present paper, all potentials are given us silversilver chloride (satd. NaCI) electrode reference unless otherwise speci6&, potentials YS normal hydrogen electrode @he) are obtained by adding 0.200 V[13] to the previous values. Experiments were made at 25 _C0.05”C.
RESULTS Determination
of the d$usion
coescient
Do
EIV
The calculations of currents need the knowledge of the diffusion coefficient D, relative to the oxidized species. This coefficient has been determined simultaneously by direct current polarography using the Ilkovic equation and by normal pulse polarography using the Brinkman and Los relationship[14]. Both methods are in very good agreement and give 0.80 f 0.05 x 10-6cm2s-1. Method for the analysis of the experimenral dpp and lsv
cuwes Since cytochrome c3 is a tetrahemic molecule, we shall first assume that the experimental dpp and ISU curves are in each case the summation of four individual curves relative to reversible monoelectronic processes. The equations of these individual curves are obtained from theoretical treatmentgl5, 163. From correct summations of the four similar curves corresponding respectively to the four electroactive centres, the original overall dpp polarogram and Isu voltammogram can be reconstituted only for a welldelined set of half-wave potential values. From a practical point of view, we have adopted a graphical subtractive method which is very similar for both voltammetric techniques used in the present work. Details are given below for each specific case.
E/V
Fig. 1. (a) dp polarogram of cytochromc cj from D. desadfiians strain Nonvav (18.4uM in 0.01 M Tris-HCIbut&r pH 7.6 c~pcri&til C&G;0 calculated points; -thex&cal dp polarograms for a moae&ctro& mcniblt transferequation (I). (b) Irvoltammogramofcytocbrome C~ from D. desulfuricans strainNorway (18.4pM in O.OlMTriaHCl buffer pH 7.6): experimentalcurve; l eakulated points; ---- theoretical 1s voltammogramsfor a monoekctrotic reversibletransfi~-equation (4).
where 7 is the time in the drop life before the pulse is applied and 6 the pulse duration; u is given by o2 = exp[(nF/RT)AE]
(2)
and E, by Diflerential
pulse polarography
The solid curve with two peaks (1) and (2) in Fig. la is the experimental dp polarogram (after subtraction of the background contribution) which will be analysed in the following treatment. Several treatmentsC17, 181 and a digital simulation method[19] have been proposed to evaluate the dpp current response. Recently Birke[lS] has developed a rigorous theory for reversible electron transfer processes with an extension to quasi-reversible and irreversible cases. In the present paper we shall use the equation established by this author: in the case of a reversible electrode process the dpp current is @en by i = 0g5~~~z/3(r+~)z13~‘~2~~-‘ 0 ~2~-‘12
L
(I - 02)E,
(I +Ey)(l +dE,) 1
s1 = exp[(aFIRZXE
-
E,,,)l
(3)
E is the potential before the application of the pulse
AE. Other symbols have their usual meaning (i/A, m/gs-‘, D,/cm2s-‘, c/molccm-‘). The theoretical current-potential curves corresponding to a reversible process where II electrons are exchanged can be calculated from (1). Firstly we assume that the four electroactive centres are ihdependent and we propose to evaluate the four half-wave potentials relative to the reduction of ihdividual sites. By using (1) it appears that the calculated dp polarogram for a monoelectronic reversible process (the dashed curve with E,, = - 0.365 V in Fig. 2a) and peak (1) are in fairly good agreement. Since the theoretical dp polarogram relative to a monoelectronic reversible process is known, this curve can he successively subtracted from the experimental curve: polarograms relative to the thne, two then one remaining electronscan be constructed by difference. Fig. 2 shows the successive subtractions from the less to the most negative potentials. For the peak (1) E,, value is
Current-potential responses for a tetrahemic protein
1003
Table 1. Calculated half-wave potentials 0s. nhe* of cytochrome cJ from D. Desulfuricans strain Norway __--
dppt lsu :
EkI
E*2
- 0.165 -0.172
- 0.305 - 0.307
Ehd
Ehd
IV
-0.365 - 0.362
-0.400 - 0.397
f 0.00s i 0.010
____~
E, represents the half-wave potential expressed us nhe. +After application of the Parry and Osteryoung relationship[17] E, = I?,,,-$AE. :After application of the relatlonshjp E, = E,i, l
- 9931. E/V
is the experimental Is voltammogram (after subtraction of the background contribution) which will be analysed in the following treatment. It is well known that the theoretical single scan current-potential curve obtained with a hide can bc calculated, for a reversible process, by using the equation of Nicholson and Shain[ 161 i = 602a3’2ADf’2~1’2~[~‘+0.16D1i2(nv)-1~2r~i~]
Fig. 2. Successive subtractions method applied to dp polarogram of eytochrome c3 from D. desulfuricms strain Norway (18.4rM in O.OlM Tris-HCl buffer pH 7.6). (a) experimental curve; (b), (c), (d) polarograms obtained after successive subtractions of the theoretical poiarogxam corresponding to a monoelectronic reversible process calculated from (I). ---- theoretical polarograms from (1).
obtained unambiguously. The presence of a shoulder on the experimental polarogram is a useful indication to resolve the overall curve and to determine Es2 value. After subtraction of the curves relative to the two first reduction steps (corresponding to E,, and E,,, values) the resulting curve exhibits only one peak (Fig, 2c). The determination of E,s and E,_.,seems to be less easy. In fact the experimental curve constitutes the envelope of two partial polarograms and thus reduces this difficulty. The curve obtained after the fast subtraction fits well the theoretical polarogram corresponding to a monoelectronic exchange (Fig. Zd). Thus a set of peak potentiai values can be obtained rather quickly and with a very good approximation from these successive subtractions. A refinement of these values has been then performed on the basis of the best agreement between the experimental and calculated dp.polarograms The best calculated points obtained after the summation of tbe four individual currents at each given potential are shown in Fig. la; the best fit values for the corresponding individual half-wave potentials are collected in Table 1. It will be noted that the pot&al values given in our previous works[5,6] are purely experimental results relative to peaks overlapping several close redox processes. They can thus differ a little from the present data resulting
from calculations.
Linear sweep oolrammetry
(lsv)
The solid curve with two waves (.l) and (2) in Fig. lb
(4) where A is the electrode area (cm2), r the radius of the hmde (cm) and u the scan rate (V s- I)_ x’ and 4 are functions tabulated by Nicholson and Sham. Other symbols have their usual meaning (i/A, D,/cm’s-‘, c/mole I I). Since these function tables are limited towards negative potentials, the descending branch of the voltammograms can be calculated by using treatment proposed by Polcyin and Shain[ZO]. The calculated Isu curve for a monoelectronic fast exchange (the dashed curve with E,, = - 0.4OOV in Fig 3a) fits very well the experimental wave (1). We suppose as previously for the treatment of dpp curves that the four electroactive centres are independent. To calculate the four individual peak potentials, a similar subtractive method from the less to the most negative potentials has been employed (Fig. 3); it has led to a first set of values after suocessive subtractions of the curve relative to a monoelectronic process. A retinement of these peak potential values has been then performed on the basis of the best agreement between the experimental and calculated voltammograms. The best calculated points are shown in Fig. lb; the best fit values for the corresponding half-wave potentials are given in Table 1.
DISCUSSION The method presented in this paper leads rather quickly to two sets of half-wave potential values in very good agreement (Table 1). Equations (1) and (4) used for these calculations are relative to uncomplicated reversible electrode processes at dropping and hanging mercury electrodes respectively. It seems thus likely that each electroactive centre of cytochrome c3 from D. desuljuricans exhibits a reversible electron transfer: the four half-wave potentials as determined above are thus very near of the formal redox potentials; for other ionic strengths, compositions of the medium and pH, it is obvious that different values may be observed[21]. Except E,, and to a less extent 15~~which are well-
P.
1004
BIANCOANDJ.
HALADJWN
open to solvent are the most exposed: their accessibilities should be in fact rather similar and the corresponding redox potentials could be in an indistinguishable way (see above) -0.365 and 0.4COV (us nhe). Heme “3” is the less accessible, it could thus correspond to E,, = - 0.165 V, and heme “1” which lies in an intermediary situation to E,, = - 0.305 V. By using the Stellwagen relationship[22] Eb (V) = - 0.015P + 0.345 where P is the per cent exposure of the heme, the following values are obtained from the less to the most exposed heme: 34,43,47 and 50%.
Acknowledgements-We are greatly indebted to Dr. M. Bruschi from the Laboratoire de Chimie J&&&me du CNRS of Marseille for a gift of purified protein sample.
REFERENCES
-05
-06
-07
-06
Fig 3. Successive subtractions method applied to Is voltammogram of cytochrome c, from D. desulfiricanr strain Norway (18.4gM in O.OlM Tris-HCI buffer pH 7.6). (a) experimental cum; (b), (c). (d) voltammograms obtained after successive subtractions of the theoretical voltammogram corresponding to a monoelectronic reversibk process calculated from (4). --- theoretical voltammograms from (4). it is to note that E,, and E,, differ only from 35 mV. This value can be compared with the difference between the formal potentials for the first and last pair of oxidation states in a molecule with identical n reducible centres as given by Flanagan et nL[8]: separated,
A = Ef -El
= (2RT/F)
In n
ie 35.7 mV for n = 2. It seems thus that these two hemes 3 and 4 should be rather identical and that in their case the electron transfers follow simple statistics. This is not the same when the three hemes 2,3 and 4 are considered (A = 56.4 mV; our data lead to 95 mV). This result suggests that the four hemes ofcytochrome cJ are in non-equivalent sites. It is now interesting to correlate the potential values as determined above with the results from strwtural data (4). As pointed out by SteUwagen[22], the redox potential of a heme becomes more and more negative when its per cent exposure to solvent increases. In the present case it appears from (4) that hemes “2” and “4’ (as symbolized in ref. (4)) which tie in a groove largely
1. J. Le Gall, D. Der VarIanian and H. D. Peck, Current Topics in Bioenergerics 9.237 (1979). 2. D, Der Vartanian and I. Le Gall, Biochim. Biophys. Acta z-46, 79 (1974). 3. D. Der Vartanian, A. Xavier and J. Le Gall, Biochimie 60, 321 (1978). 4. R. Haser, M. Pierrot. M. Frey, F. Payan, J. P. Astier, M. Bruschi and J. Lc Gall, Nature 282.806 (1979). 5. P. Bianco and J. Haladjian, Biochim. Biophys. Acru 545, 86 (1979). 6. P. Bianco, G. Fauque and J. Haladjian, Bioeleerrochem. Bioenerg. 6, 385 (1979). 7. F. Ammar and J. hi. Saveant, 1. electroanal. Chem. 47, 115 (1973). 8. J. B. Flanagan, S. Margel, A. J. Bard and F. C. Anson, J. Am. Chenr. Sot. 100,4248 (1978). 9. K. Niki, T. Yagi, H. Inokuchi and K. Kimura, .I. Rm. them. Sot. 101.3335 (1979). 10. W. Sokol. D. Evans, K. Niki and T. Yagi, J. electround. Chem. 108, 107 (1980). II. M. Bruchi, C. E. Hatchikian, L. A. Golovkva and .I. Le Gall, 1. Baeterioi. 129, 30 (1977). 12. J. H. Christie, J. Dsteryoung and R. A. Osteryoung, Anolyt. c/tern. 45, 210 (1973). 13. R. Bates, Determination ofpH p. 286 Wiley, New York (1964). 14. A. Brinkman and J. Los, J. electroanal. Chem. I, 171 ( 1964). 15. R. L. Birke, Analyt. Chem. 50, 1489 (1978). 16. R. S. Nicholson and I. Shaio, Anal. Chem. 36,706 (1964). 17. E. P. Pany and R. A. Gsteryoung, Anal. Chem. 37,1634 (1965). 18. J. H. Christie and R. A. Osteryoung, I. Elertr-I. Gem. 49.301 (1974). 19. J. W. Dilfard and K. W. Hanck, Anal. Chem. 48. 218 (1976). 20 D. S. Polcyia and 1. Shain, Anal. Chem. 38,370 (1966). 21 M. J. Eddowes, H. Elzanowska and H. A. Hill, Biochem Sot. Trans. 7, 735 (1979). 22 E. Stetiwagen, Nature 275, 73 (1978). 23. R. N. Adams, Electrochemistry at Solid Electro&s, p. 126, M. Dekker, New York (1969).
BIANCO
and J. HALADJIAN
Laboratoirede Cbimieet Electrochimie des Complexes,Universitbde Provence, Place.VictorHugo, 13331, Marseilleckdex 3, France (Received 9 July 1980)
Abstract-A tetrahemicprotein,cytochromecS from Desu&eibriodesulfuriconsstrah Norway, is studied by differentialpulse polarogrsphyand linearsweep voltammetryat bang@ mercuryelectrode.A graphical subtractivemethod applied to the current-potentialcurves is describedand the four individual rcdox potentialsare dckrmined.Both seriesof experimentsleadto two fit sets of valuescorrespondingto reversible electrodeprocesses.The relationshipbetween these redox potentialsand the structuraldata is discussed.
INTRODUCI’lON Cytochromes cI constitute a unique class of polyhcmic protdns which contain four hemes per molecule (M m 13,000) and have negative redox potentials[I]. From epr and nmr stud&s on some of these cytochromes it appears that the four hemes are in nonequivalent sites[ZJ; four redox midpoints potentials withnvaluesnearoflhavebcenmessuredinthecase of cytochame cg from Desulfovibrio vulgaris strain Hildenborough[3]. The di&rences between the hemc environments have been reported recently by Haser et a1.[4] who have solved the molecular structure at 2.5 A resolution of cytochromc cj from D. desulfuricalls strain Norway. In previous works we have studied the electrochemical behaviour of thii cytocatome cj by differmtial pulse polarography (dpp)[S] and cyclic voltammetry[6]. Two well-separated and one bad-resolved reduction steps have bum detected. It is thus likely that cytochrome cJ from D. desu@ricans has several close half-wave potentials. The knowledge of the individual redox potentials is very useful to understand the biological reactions in which cytochromes cg arc involved as electron carriers ofthe sulfate-reducing bacteria chains. The characterization of the different electroactive sites is not easy for polycentre molecules and their electrochemical behaviour has been the subject of a number of studies[7, a]. The differences in half-wave potentials between the successive reactions depend on several factors, eg structural changes of the molecule. In the case of identical ccntrea, electron transfers follow simpte statistics; a general analysis of this case has been given recently by Flanagan et al.[8]. For cytochrome cj from D. oulgmis strain Miyazaki which contains four non-equivalent redox sites, the voltammetric behaviaur has been anaIysed by using digital simulations[9, 101. The case of cytochrome c5 from D. desu(Wcanr
strain Norway is more specially attractive since the two main steps are well-separated by about O.l8V[5]. In the present paper we report a method for the analysis of current-potential curves obtained by dpp or linear sweep voltammetry (Iw) techniques. The approach used for the four ekctroactive cc&es molecule isbasedonthcfactthattheexperime@aloverallNms can be regarded as the summation of four individual curves. If each individual curve am be resolved from the overall curve, conciusions can be drawn on the halfwave potcntiaIs, reversibility and n value of the individual electron transfers.
EXPERIMENTAL Cytochrome C~from D. desadfiriccansstraiu Norway was prepared and purified as previously described11 I]. AU experiments were conducted in 0.01 M Tris-HCI buffer (pH 7.6) which served also as supporting electrolyte. The concentration of the cytochrome cj solution was 18.4pM. Dpp experimenta were performed with a PAR 174A analystr coupkd with a Sefram X-Y recorder. Since it has been shown by Chris& et ul.[l2] that experimental conditions in dpp must be carefUlly selected to obtain responses aacurately rekcting the true instantaneous currents for which the equations in this paper are derived, it proved necessary to use a slow scan rate (0.2 mV s - *). A small pulse amplitude AE ( = - 5 mV) was selected to increase the peaks resolution. The drop time was S s and the mercury flow 0.80 mg s- l. As indicated by the PAR operating manual the pulse is applied to the drop for 57 ms before the drop is dislodged and the current is sampled during 17 ms before application of the pulse and again at the ad of the pulse. These data will he Wed in our further calculations. Linear sweep voltammetq at stationary electrode was performed with a PAR 175 Universal Programmer aad a PAR 173 Potentiostat coupled
P.
1002
BMNCO AND J. HALADJIAN
with a PAR 176 converter. We utilized a Metrohm hanging mercury drop electrode (area = O.O22cm*). The voltammogram obtained at tr = 0.050 V s- ’ has been chosen for calculations. Throughout the present paper, all potentials are given us silversilver chloride (satd. NaCI) electrode reference unless otherwise speci6&, potentials YS normal hydrogen electrode @he) are obtained by adding 0.200 V[13] to the previous values. Experiments were made at 25 _C0.05”C.
RESULTS Determination
of the d$usion
coescient
Do
EIV
The calculations of currents need the knowledge of the diffusion coefficient D, relative to the oxidized species. This coefficient has been determined simultaneously by direct current polarography using the Ilkovic equation and by normal pulse polarography using the Brinkman and Los relationship[14]. Both methods are in very good agreement and give 0.80 f 0.05 x 10-6cm2s-1. Method for the analysis of the experimenral dpp and lsv
cuwes Since cytochrome c3 is a tetrahemic molecule, we shall first assume that the experimental dpp and ISU curves are in each case the summation of four individual curves relative to reversible monoelectronic processes. The equations of these individual curves are obtained from theoretical treatmentgl5, 163. From correct summations of the four similar curves corresponding respectively to the four electroactive centres, the original overall dpp polarogram and Isu voltammogram can be reconstituted only for a welldelined set of half-wave potential values. From a practical point of view, we have adopted a graphical subtractive method which is very similar for both voltammetric techniques used in the present work. Details are given below for each specific case.
E/V
Fig. 1. (a) dp polarogram of cytochromc cj from D. desadfiians strain Nonvav (18.4uM in 0.01 M Tris-HCIbut&r pH 7.6 c~pcri&til C&G;0 calculated points; -thex&cal dp polarograms for a moae&ctro& mcniblt transferequation (I). (b) Irvoltammogramofcytocbrome C~ from D. desulfuricans strainNorway (18.4pM in O.OlMTriaHCl buffer pH 7.6): experimentalcurve; l eakulated points; ---- theoretical 1s voltammogramsfor a monoekctrotic reversibletransfi~-equation (4).
where 7 is the time in the drop life before the pulse is applied and 6 the pulse duration; u is given by o2 = exp[(nF/RT)AE]
(2)
and E, by Diflerential
pulse polarography
The solid curve with two peaks (1) and (2) in Fig. la is the experimental dp polarogram (after subtraction of the background contribution) which will be analysed in the following treatment. Several treatmentsC17, 181 and a digital simulation method[19] have been proposed to evaluate the dpp current response. Recently Birke[lS] has developed a rigorous theory for reversible electron transfer processes with an extension to quasi-reversible and irreversible cases. In the present paper we shall use the equation established by this author: in the case of a reversible electrode process the dpp current is @en by i = 0g5~~~z/3(r+~)z13~‘~2~~-‘ 0 ~2~-‘12
L
(I - 02)E,
(I +Ey)(l +dE,) 1
s1 = exp[(aFIRZXE
-
E,,,)l
(3)
E is the potential before the application of the pulse
AE. Other symbols have their usual meaning (i/A, m/gs-‘, D,/cm2s-‘, c/molccm-‘). The theoretical current-potential curves corresponding to a reversible process where II electrons are exchanged can be calculated from (1). Firstly we assume that the four electroactive centres are ihdependent and we propose to evaluate the four half-wave potentials relative to the reduction of ihdividual sites. By using (1) it appears that the calculated dp polarogram for a monoelectronic reversible process (the dashed curve with E,, = - 0.365 V in Fig. 2a) and peak (1) are in fairly good agreement. Since the theoretical dp polarogram relative to a monoelectronic reversible process is known, this curve can he successively subtracted from the experimental curve: polarograms relative to the thne, two then one remaining electronscan be constructed by difference. Fig. 2 shows the successive subtractions from the less to the most negative potentials. For the peak (1) E,, value is
Current-potential responses for a tetrahemic protein
1003
Table 1. Calculated half-wave potentials 0s. nhe* of cytochrome cJ from D. Desulfuricans strain Norway __--
dppt lsu :
EkI
E*2
- 0.165 -0.172
- 0.305 - 0.307
Ehd
Ehd
IV
-0.365 - 0.362
-0.400 - 0.397
f 0.00s i 0.010
____~
E, represents the half-wave potential expressed us nhe. +After application of the Parry and Osteryoung relationship[17] E, = I?,,,-$AE. :After application of the relatlonshjp E, = E,i, l
- 9931. E/V
is the experimental Is voltammogram (after subtraction of the background contribution) which will be analysed in the following treatment. It is well known that the theoretical single scan current-potential curve obtained with a hide can bc calculated, for a reversible process, by using the equation of Nicholson and Shain[ 161 i = 602a3’2ADf’2~1’2~[~‘+0.16D1i2(nv)-1~2r~i~]
Fig. 2. Successive subtractions method applied to dp polarogram of eytochrome c3 from D. desulfuricms strain Norway (18.4rM in O.OlM Tris-HCl buffer pH 7.6). (a) experimental curve; (b), (c), (d) polarograms obtained after successive subtractions of the theoretical poiarogxam corresponding to a monoelectronic reversible process calculated from (I). ---- theoretical polarograms from (1).
obtained unambiguously. The presence of a shoulder on the experimental polarogram is a useful indication to resolve the overall curve and to determine Es2 value. After subtraction of the curves relative to the two first reduction steps (corresponding to E,, and E,,, values) the resulting curve exhibits only one peak (Fig, 2c). The determination of E,s and E,_.,seems to be less easy. In fact the experimental curve constitutes the envelope of two partial polarograms and thus reduces this difficulty. The curve obtained after the fast subtraction fits well the theoretical polarogram corresponding to a monoelectronic exchange (Fig. Zd). Thus a set of peak potentiai values can be obtained rather quickly and with a very good approximation from these successive subtractions. A refinement of these values has been then performed on the basis of the best agreement between the experimental and calculated dp.polarograms The best calculated points obtained after the summation of tbe four individual currents at each given potential are shown in Fig. la; the best fit values for the corresponding individual half-wave potentials are collected in Table 1. It will be noted that the pot&al values given in our previous works[5,6] are purely experimental results relative to peaks overlapping several close redox processes. They can thus differ a little from the present data resulting
from calculations.
Linear sweep oolrammetry
(lsv)
The solid curve with two waves (.l) and (2) in Fig. lb
(4) where A is the electrode area (cm2), r the radius of the hmde (cm) and u the scan rate (V s- I)_ x’ and 4 are functions tabulated by Nicholson and Sham. Other symbols have their usual meaning (i/A, D,/cm’s-‘, c/mole I I). Since these function tables are limited towards negative potentials, the descending branch of the voltammograms can be calculated by using treatment proposed by Polcyin and Shain[ZO]. The calculated Isu curve for a monoelectronic fast exchange (the dashed curve with E,, = - 0.4OOV in Fig 3a) fits very well the experimental wave (1). We suppose as previously for the treatment of dpp curves that the four electroactive centres are independent. To calculate the four individual peak potentials, a similar subtractive method from the less to the most negative potentials has been employed (Fig. 3); it has led to a first set of values after suocessive subtractions of the curve relative to a monoelectronic process. A retinement of these peak potential values has been then performed on the basis of the best agreement between the experimental and calculated voltammograms. The best calculated points are shown in Fig. lb; the best fit values for the corresponding half-wave potentials are given in Table 1.
DISCUSSION The method presented in this paper leads rather quickly to two sets of half-wave potential values in very good agreement (Table 1). Equations (1) and (4) used for these calculations are relative to uncomplicated reversible electrode processes at dropping and hanging mercury electrodes respectively. It seems thus likely that each electroactive centre of cytochrome c3 from D. desuljuricans exhibits a reversible electron transfer: the four half-wave potentials as determined above are thus very near of the formal redox potentials; for other ionic strengths, compositions of the medium and pH, it is obvious that different values may be observed[21]. Except E,, and to a less extent 15~~which are well-
P.
1004
BIANCOANDJ.
HALADJWN
open to solvent are the most exposed: their accessibilities should be in fact rather similar and the corresponding redox potentials could be in an indistinguishable way (see above) -0.365 and 0.4COV (us nhe). Heme “3” is the less accessible, it could thus correspond to E,, = - 0.165 V, and heme “1” which lies in an intermediary situation to E,, = - 0.305 V. By using the Stellwagen relationship[22] Eb (V) = - 0.015P + 0.345 where P is the per cent exposure of the heme, the following values are obtained from the less to the most exposed heme: 34,43,47 and 50%.
Acknowledgements-We are greatly indebted to Dr. M. Bruschi from the Laboratoire de Chimie J&&&me du CNRS of Marseille for a gift of purified protein sample.
REFERENCES
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Fig 3. Successive subtractions method applied to Is voltammogram of cytochrome c, from D. desulfiricanr strain Norway (18.4gM in O.OlM Tris-HCI buffer pH 7.6). (a) experimental cum; (b), (c). (d) voltammograms obtained after successive subtractions of the theoretical voltammogram corresponding to a monoelectronic reversibk process calculated from (4). --- theoretical voltammograms from (4). it is to note that E,, and E,, differ only from 35 mV. This value can be compared with the difference between the formal potentials for the first and last pair of oxidation states in a molecule with identical n reducible centres as given by Flanagan et nL[8]: separated,
A = Ef -El
= (2RT/F)
In n
ie 35.7 mV for n = 2. It seems thus that these two hemes 3 and 4 should be rather identical and that in their case the electron transfers follow simple statistics. This is not the same when the three hemes 2,3 and 4 are considered (A = 56.4 mV; our data lead to 95 mV). This result suggests that the four hemes ofcytochrome cJ are in non-equivalent sites. It is now interesting to correlate the potential values as determined above with the results from strwtural data (4). As pointed out by SteUwagen[22], the redox potential of a heme becomes more and more negative when its per cent exposure to solvent increases. In the present case it appears from (4) that hemes “2” and “4’ (as symbolized in ref. (4)) which tie in a groove largely
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