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Promotion of the electrochemical response of some negatively charged proteins at an edge-plane graphite electrode by various redox inert cations: an electrochemical manifestation of Frumkin adsorption
307
J. Electroanal. Chem., 324 (1992) 307-323 Elsevier Sequoia S.A., Lausanne
JEC 01877
Promotion of the electrochemical response of some negatively charged proteins at an edge-plane graphite electrode by various redox inert cations: an electrochemical manifestation of Frumkin adsorption Dipankar Datta
l
Department of Inorganic Chemistry, Indinn Association for the Cultivation of Science, Calcutta 700 032 (India)
H. Allen 0. Hill Inorganic Chemistry Laboratory, University of Oxford, South Parks Road, Oxford OX1 3QR (UK)
Hiroaki Nakayama Laboratory of Chemistry, Kagawa Nutrition College, Sakado, Saitama 350-02 (Japan) (Received 30 April 1991; in revised form 25 June 1991)
Promotion of the cyclic voltammetric response of several small negatively charged metalloproteins P at an edge-plane graphite (EPG) electrode E by various inorganic cations M at pH 8 has been interpreted in terms of hvo equilibria: P+MK-PM E+PM -
KC4
EPM
The first equilibrium, where a 1: 1 protein-cation complex PM is formed, occurs in the bulk, while the second takes place at the electrode surface. The value of the equilibrium constant K depends on the cation charge and the charge on the cation binding site of the protein. A simple mode1 for understanding the interactions in the inorganic ion pairs in an aqueous medium has been developed. The mode1 is extended to compare the association of the inorganic ions with various proteins in an aqueous medium and is used to estimate K. The adsorption of the protein-metal ion complex on the electrode surface (the second equilibrium) is assumed to be weak (i.e. the equilibrium constant K& is small) and reversible. It is found that only EPM, the PM species adsorbed on the electrode surface, is electro-
l
To whom correspondence
0022-0728/92/$05.00
should be addressed.
0 1992 - Elsevier Sequoia S.A. All rights reserved
active. The experimental consequences of the two equilibria are discussed. The adsorption pattern is found to obey the Frumkin isotherm. The standard Gibbs energies of adsorption AC&,, have been calculated specifically for U4Fe-4S] ferredoxin in the presence of various cations. The magnitude of the AG$, values, which are found to lie within the range - 13.4 to 22.2 kJ mol- * for 2/4Fe-As] ferredoxin, suggests physical adsorption of the protein. The AC& values for the various cations are found to vary linearly with .z2/r where z is the charge on the cation and r is its ionic radius. It is concluded that the role of the cation is to induce a reversible weak adsorption of a negatively charged protein suitable for electron transfer on an EPG surface at pH 8. Speculations are made on the nature of the adsorption.
INTRODUCTION
The electron transfer behaviour of various negatively charged proteins at an edge-plane graphite (EPG) electrode has been extensively studied by Hill and coworkers using dc cyclic voltammetry [l-6]. The nature of the electrochemical response obtained under various experimental conditions can be explained by invoking radial diffusion (microscopic model for the electrode) or linear diffusion (macroscopic model for the electrode) [l]. A number of studies [7-161 have shown the existence of C-OH functions at the polished surface of an EPG electrode. The electrode surface is believed [3] to be negatively charged at pH > 5.6. For cytochrome c, which is positively charged at pH 8, direct electron transfer is achieved at an EPG electrode at pH 8, but no such electrochemistry is observed for plastocyanin, rubredoxin, 2Fe-2s ferredoxin or 2[4Fe-4S] ferredoxin, presumably because of the negative charge on them at pH 8. Thus electrostatic effects seem to play an important role in bringing about a suitable interaction between the electrode surface and the proteins for electron transfer to occur. However, it was possible to achieve electrochemical responses for the various negatively charged proteins in the presence of some cations (inorganic or organic) which are redox inert in the potential range of interest [6]. These cations are believed to reduce the electrostatic repulsions between the electrode surface and the proteins, and they are termed “promoters”. The ability of a cation to promote an electrochemical response seems to depend on its charge and size. The degree of effectiveness of promotion is measured by the concentration of a cation needed to give rise to the same magnitude of peak current in a cyclic voltammetric experiment at the same scan rate for a given concentration of a protein solution. The amount required for obtaining the maximum peak current is called the “promotion concentration”. For a particular protein, the general order of the promotion concentration for various inorganic cations is found to be as follows [6]: Li+> Na+> K+> Cs+> Mg2+> Ca2+> Ba2+> Fe(o-phen):+ > Cr(NH&+ > Pt(NH&+. Some selected data [6] are given in Table 1 for 2[4Fe-4S] ferredoxin (from Clostridium pasteurianum), which is the most extensively studied system. In this paper we try to understand the role of various inorganic cations in promoting the electrochemical responses of various negatively charged proteins. Before we do so, it is necessary to understand the interactions between these ions and the various proteins.
309 TABLE 1 Variation of the cathodic peak current Ipc and peak separation AE, in the first cycle voltammetric scan of 2[4Fe-4S] ferredoxin at an EPG electrode with concentration chl of various inorganic cations at 25°C and pH 8.0; standard Gibbs energy of adsorption and lateral interaction parameter g of a4Fe-4Sl ferredoxin on an EPG surface in presence of various cations together with their ionic radii ra Cation M Mg*+
Ba2+
Fe(o-phen):+
crwH&+
Crien):’
Naf
Cs+
g/RT
r/A
- 13.2 (0.963 d,
- 6.97
0.65 ’
- 16.5 (0.991 d)
- 5.50
1.35 =
- 22.2 (0.941 d)
- 3.30
6.9 g
- 16.4 (0.993 d)
-5.42
3.4 g
- 18.0 (0.972 d,
- 4.54
4.2 g
0.082 0.093 0.103
- 19.5 (1.000 d)
- 2.86
0.95 c
0.082 0.093 0.103
- 20.4 (0.947 d)
- 2.69
1.69 =
I,/
A&/
[PM1b/
‘=“a,, /
PA
mV
mM
kJ mol-’
9 11 13 15 17 20 21 28 e
1.4 1.4 1.7 1.6 1.7 1.8 2.0 2.2
178 132 115 106 106 107 93 86
0.079 0.082 0.082 0.085 0.088 0.090 0.092 _f
4 5 6 7 9 13 e
1.4 1.7 1.8 1.8 1.9 2.4
183 145 115 108 83 80
0.065 0.070 0.072 0.075 0.079 _f
0.50 1.00 1.50 2.00 2.50 =
1.1 1.2 1.6 1.8 1.9
150 150 140 103 92
0.021 0.033 0.043 0.050 0.055
0.26 0.29 0.33 0.35 0.38 0.42 0.46 =
1.3 1.3 1.7 1.8 1.9 1.9 2.1
133 120 93 85 80 80 73
0.074 0.078 0.083 0.085 0.089 0.092 _f
0.20 0.30 0.40 0.50 0.70 =
1.5 1.6 1.8 1.8 1.9
100 73 70 68 65
0.065 0.079 0.091 0.096 0.103
200 300 400
0.8 1.0 1.2
200 193 130
200 300 400
1.2 1.4 1.5
175 130 98
cM/mM
For footnotes see over.
01
1 2
I
I
1
6
IO
I&
1951
Fig. 1. Relation between log K and I z1z2I for inorganic ion pairs (Table 2) in aqueous medium at ionic strength I = 0. Correlation coefficient, 0.985.
ASSOCIATION
IN INORGANIC ION PAIRS AND OF PROTEINS WITH INORGANIC IONS
For inorganic ion pairs, Bjerrum’s equation [19,201 K = O.O0047rN( I zlz2 I e2/~kT)3/py-4 y = I zlz2 I e2/crkT
exp( y) dy
(1)
b = I zlz2 I e2/eakT
relates the association constant K to the charges zi and zz on the ions in a medium of dielectric constant E. In eqn. (11, The closest distance of approach a is an adjustable empirical parameter which may not always have real physical significance. Though several later modifications of this theory have been made [21,22] the essence remains the same. Simply stated, the interactions in inorganic ion pairs are largely electrostatic. However, it is possible to develop a model
Notes to Table 1: Scan rate, 20 mV s-l; geometric surface area of EPG, 0.20 cm’; [ferredoxinl= 150 PM in 5 mM Tricine + 1 mM NaCl. a For definitions of the symbols see text. The peak current and the peak separation data are taken from ref. 6. b For divalent cations, see Fig. 2; for trivalent cations, see Fig. 3; for monovalent cations eqn. (41 is used with the logarithm of association constant equal to 1.586 (eqn. (2); see text). ’ Pauling’s ionic radius (ref. 17, Table l-1). d Correlation coefficient for the plot of In{& /(2.1- I,XPMjl vs. I,. e Promotion concentration. f Not used in the plot of In{& /(2.1- IJPMI) vs. iW since IW > 2.1 ALA. 8 Estimated from space-filling models [181.
311
O-05
Fig. 2. Variation in the population of U4Fe-4S] ferredoxin associated with an ion [PM] with the addition of a 1: 2 electrolyte to a 150 PM solution of a4Fe-4S] ferredoxin in 5 mM Tricine + 1 mM NaCl.
without any explicit reference to the nature of the interactions. Figure 1 shows that the linear equation log K = 0.477 I zlz* I + 0.015 incorporating only I zlz2 I, the modulus of the product of the charges on the two ions, can be used to describe the association of inorganic ion pairs in an aqueous medium at ionic strength Z = 0 (Table 2). The examples used in Fig. 1 are essentially the same as those of Tam and Williams [23], in which pure outer-sphere interactions are believed to be involved, i.e. the examples deliberately exclude the possibility of any specific interactions between the two members of an ion pair. In Fig. 1 we have introduced some additional data [24] (Table 2) to give equal
0.10
:
2
e
0.05
:r -
Fig. 3. Variation in the population of 2[4Fe-4S] ferredoxin associated with an ion [PM] with the addition of a 1:3 electrolyte to a 150 PM solution of 2[4Fe-4S] ferredoxin in 5 mM Tricine + 1 mM NaCI.
312
TABLE 2 Representative association constants for some inorganic ion pairs in an aqueous medium at 25°C and ionic strength I = 0 a Cation
Anion
IZtZrl
log(K/M-‘1
[CoWQOH,13+
[Fe(CN1614[Fe(CN),14-
12 12
5.70 5.95
m31:[Fe(CN),13-
12 9 9
5.74 3.70
KdNH3),PY13+
[!?+m3)613+ KowH3),L13+ L = 4-phenylpyridine L = 4-phenylpyridine Ca2+ Ca2+ [Co(NL$),13+ ;$L-L3)613+ [GANH3)sN0212+
[Fe(CN),L’13L’ = 4,4’-bipyridine L’ = 1,2-bis(4-pyridylethane) [Fe(CN),14[Fe(CN),13so;wo,2SO;SO;-
$~3),13+ 2+ Koten)313 + KJoW313 +
so;Clclao;
34 3 3
2.23 1.85 b 1.90 b 1.15
E;2.t Ba2+
so;NO; NO;
2 2
0.85 0.68 0.84
8 6 6 64
4.80 4.64 3.63 2.63 3.56 2.19 2.59
4
2.69
a 1zl.z21is the modulus of the product of the charges on the cation and the anion in an ion pair. The log K data are taken from ref. 24 unless otherwise specified. b From ref. 23.
statistical weight to each type of charge product (except for I zlzz I = 8). Equation (2) gives rise to a standard error of f 0.370 in the estimation of log K at I = 0. In Table 3 we show that, for a number of ion pairs [24,25], the error remains almost the same, i.e. f0.402. Using this linear model for association in inorganic ion pairs in aqueous medium (Bjerrum’s model is non-linear), we can now go on to examine the association of various proteins with various inorganic ions in an aqueous medium. Basically, we re-examine the work of Chapman et al. [26] on mapping the surfaces of various proteins by using different inorganic ions as the probes. The local charges at the binding sites of the proteins listed in Table 4 have been calculated using our model (see Appendix) and match the results reported previously [261 quite well. A notable difference is that, when the total charge product is less than 15, our values are consistently lower than those obtained by Chapman et al. [26] (Table 4) using Bjerrum’s model. This is probably because in eqn. (0, with a = 6 A (the value used by Chapman et al. [26] in their calculations), the association constants for I z1.z2 I < 15 are underestimated. Such problems with Bjerrum’s equation are well known [27]. However, our present results, in conjunction with those of Chapman et al. [26], show that the association of inorganic ions with
313 TABLE 3 Deviation of the association constants for various inorganic ion pairs in an aqueous medium at 25°C and ionic strength Z = 0 from eqn. (2) a
I ZlZZ I
Theoretical b log(K/M-‘1
Cation
Anion
Experimental log (K/M-‘)
A(log K) ’
9
4.398
Ells+ Lu’f Als+
fFetCN),13[Fe(CN)ipKo(CN),13-
3.65 3.69 4.30
- 0.748 - 0.708 - 0.098
8
3.921
[Pt(en),14+
so:-
3.52 d
- 0.401
6
2.967
Ko(en1313 + Kofpn),l’+ (D-form) bW313 +
so;so;-
2.974 3.084
0.007 0.117
soi-
2.884
- 0.083
ziEm) Ga3+ In3+ Las+ Eu3+ Lus+ Ca2+
so4’ so:so4’ so;so:so;p,o; -
3.01 2.77 3.04 3.50 3.54 3.49 3.40
0.043 - 0.197 0.073 0.533 0.573 0.523 0.433
Be’+ Mn2+ Ni2+ cur+ Zn2+ Cd’+ Mnzf Cos+ Ni2+ Naf
so:so;so;so;so;so;SeO,ZSeOaSe0,2p40;‘,-
2.16 2.20 2.27 2.40 2.23 2.55 2.43 2.70 2.67 2.12
0.147 0.187 0.257 0.387 0.317 0.537 0.417 0.687 0.657 0.107
MNH,),l”
ICr(en),13 + W$NH,),13+
c10; ClO, c10; NO;
1.2 1.0 1.34 1.74
- 0.336 - 0.536 - 0.196 0.204
Mg2+ Ca2+ Zn2+ Sr2+ cur+ Zn2+
B(GH); B(Gf-0; SCNNO; NO; NO;
1.23 1.23 1.33 0.77 0.54 0.42
0.171 0.171 0.271 - 0.289 - 0.519 - 0.639
4
3
2
2.013
1.536
1.059
a 1z1z2 1 is the modulus of the product of the charges on the cation and the anion in an ion pair. The experimental log K data are taken from ref. 24 unless otherwise specified. b Calculated using eqn. (2). ’ A0og K) = experimental log K - theoretical log K; standard deviation, f 0.402. d From ref. 25.
314 TABLE 4 Formation constants for association of inorganic ions with various proteins (in reduced state) at 25°C ionic strength I = 0.10 M (NaCi) and pH 7.5, and the local effective charges on the binding sites of the proteins Protein
Inorganic ion
Io~(K/M-‘)~
Local effective charge b
Charge at binding site a from structure
PCU’ c
]~~*‘]s+ d rPtwH,>alq+ KdNH,),l’+ [Cdo-phen),]” + [Cr(o-phenj313+
4.204 4.342 2.763 2.223 2.246
-3.12(-3.0) - 4.03( - 4.0) - 3.37( - 3.8) - 2.68( - 2.8) - 2.71( - 2.8)
-4
[2Fe-2S] ’
w”15’ d ]Pt(NH 316I [Cow-L,),;:+
-3.28(-3.0) - 4.01( - 4.0) - 3.67( - 4.0) -3.25x-3.5) -3.38(-3.8) -4.15(-4.5)
-3
[Cr(en),13 + [CdNH,),c11*+
4.422 4.322 2.999 2.666 2.771 2.288
2[4Fe-4S]’
PtwH3)J4+ rd~3M3+ DwH3),13+
3.398 2.649 2.326
-3.13(-3.0) - 3.23 -3.0) - 2.81( - 3.0)
ca. -3
Cytochrome b, g
[CO~~*]~’ e
-3.13(-3.0) - 3.W - 4.0) - 3.39(- 3.8) - 3.02(- 3.3)
-3/-4
;zey$$3+
4.220 4.170 2.778 2.490
[Fe(CN),13 - i
2.653
~cdNH3),13+
[PWH3)14’ 3
Cytochrome c h
f
3.71 ka. 4.0)
3/4
’ From ref. 26. b Calculated using eqn. (2) (see Appendix); values obtained by Chapman et al. [26] are given in parentheses. ’ Parsley. d [C$r]5+ -[tNH,),CoNH,Co(NH,),]‘+. e Clo&diwn pasteurimum. f At pH 6.8. 8 Calves’ liver. h Horse heart in oxidized form. ‘1=0.18 M.
proteins essentially
A very important result which emerges from this exercise is that eqn. (2) can be used to describe the interactions of various ions with the proteins, and the association constant is determined mainly by the product of the charge on the inorganic ion and the local effective charge on the binding sites of the proteins. The model based on eqn. (2) is worked out explicitly for a4Fe-G] ferredoxin obtained from Chtridium pasteutinum as an example to elucidate the variation
315
in the population of the 1: 1 protein-cation complex in a given aqueous solution at a given pH. The logarithm of the association constants K of 2[4Fe-4S] ferredoxin with a divalent cation and a trivalent cation at ionic strength Z = 0 are calculated from eqn. (2) as 2.967 M-’ and 4.398 M-i respectively, assuming the local charge at the binding site to be -3 (Table 4). The dependence of log K on the ionic strength [28] is given by log K, = log Kc,,,,, - 1.018 I .zlz* I {[V/(
1 + Z1’2)] - 0.31)
(3)
Thus we can calculate the equilibrium concentration [PM] of the protein P associated with a metal-ion complex M for any equilibrium concentration [PI of the protein and [Ml of the ion: P+M-
K
PM
(4) Figures 2 and 3 show the variations of [PM] when 1:2 and 1:3 electrolytes respectively are added to a 150 PM solution of 24Fe-4S] ferredoxin in 5 mM Tricine (pK = 8.1) at pH 8.0 in the presence of 1 mM NaCl. The contribution of the protein to the ionic strength of the solution is calculated by considering the net charge on the protein at pH 8.0 (- 10 in the case of a4Fe-4S] ferredoxin [29]) to be made up of discrete charges 1301. The curves (Figs. 2 and 3) show that, as expected, the concentration of PM is higher for an M3+ ion than that for an M2+ ion when the same amount of the two ions is considered. However, there is an important difference between the inorganic ion pairs and the protein-inorganic ion complexes. An inorganic ion, which is much smaller in size than a protein molecule, probably rolls around on the surface of a protein molecule as revealed from NMR studies of the binding of Cr(NH,)i+ to plastocyanin [31]. This phenomenon is similar to the rolling of a substrate molecule on an enzyme molecule [32]. ADSORPTION
As stated in the Introduction, in a cyclic voltammetric experiment the various negatively charged proteins do not show any electrochemical response at pH 8 at a polished EPG electrode unless a “promoter” is added to the solution. At concentrations much lower than the “promotion concentration” radial diffusion takes place [1,61, giving rise to sigmoidal voltammograms. For our purpose we have chosen those concentrations of promoters where linear diffusion predominates. In the region of linear diffusion, voltammograms show two important features [6,33]: up to a scan rate u of 200 mV s-i the cathodic peak current Zpc is proportional to u112, i.e. the plot of Z, versus u112 is a straight line which passes through the origin, and the anodic peak current Z,, is almost equal to ZW, i.e. Zpc/Zpa= 1. If we assume that only the 1: 1 protein-cation complex PM is electro-active, the situation represents a chemical reaction C, preceding the electron transfer E,, i.e. a C,E, mechanism operates here. Depending on its nature, this chemical reaction can affect the nemstian behaviour of the electron transfer process in various ways
316
(ref. 34, Ch. 11; ref. 35, Ch. 6). In cyclic voltammetry, two diagnostic features of a C,E, mechanism are as follows: (i) Z& ‘1’ decreases as u increases, and (ii) Z,,JZpa increases with u and is always greater than or equal to unity. In our case, since Zpc is proportional to z#/* and Z&Z,, = 1 for scan rates up to 200 mV s-l, it is clear that the preceding reaction has little effect on the nernstian behaviour of the electron transfer process. In fact it is well known that, when the equilibrium constant of the preceding reaction (in our case, reaction (4)) is greater than or equal to 20 M-‘, the electrochemical response appears as an unperturbed nemstian behaviour (ref. 34, Chll; ref. 36). In our case the minimum value of K (for the association of monovalent cations with 4[4Fe-4S] ferredoxin) is 38.5 M-i. Thus the equilibrium (4) lies so far to the right that we expect an unvitiated electron transfer behaviour of PM alone to be reflected in the cyclic voltammograms. For a planar electrode in the experimental conditions chosen here, we can expect the cyclic voltammetric data to obey the Randles-Sevcik equation [37,381 ZPC = 2 *69 x 105D~‘2~,Av1’2
(5)
where Zpc is in amperes, u is in V s -I, the area A of the electrode is in cm*, the bulk concentration c,, of the oxidized species is in mol cmm3 and the diffusion coefficient D, of the oxidized species is in cm s -l. Actually this equation is meant for a reversible electron transfer process. As revealed by the AE, values given in Table 1, our process can be said to be only quasi-reversible. However, as mentioned earlier we have observed a proportionality between Zpc and ul/* up to v=200 mV s- ‘. Thus we can say that an equation like eqn. (51, where the numerical constant is different, is applicable in our case (ref. 35, Ch. 6). From the above discussion it follows that, in our case, the C,E, mechanism leads to the fact that the observed Zpc should be directly proportional to the bulk equilibrium concentration [PM], of the 1: 1 protein-cation complex for a particular scan rate at a given EPG electrode (neglecting the small variations in the diffusion coefficient of PM for a particular protein P with Ml. From the IF data given in Table 1 we find that when the response is fully promoted, the average of the maximum cathodic peak current I,,,= achieved at a scan rate of 20 mV s-l for 150 ,uM 2[4Fe-4Sl ferredoxin at an EPG electrode with a geometric area of 0.2 cm* is 2.1 PA. It should be noted that Z,, differs slightly for various cations under the experimental conditions mentioned above. While several factors may be responsible for this observation, the different peak separations AE, observed for different cations (see Table 1) at a concentration where they are fully promoting seems to be the most important. Various factors may be responsible for the relatively large AE, values observed in our case. We shall refer to this problem later (see below). The values of [PM] at the fully promoted level (i.e. when Z,,,, = 2.1 PA) differ considerably from cation to cation. No proportionality is observed between [PM] and I,,. This indicates that PM is not electro-active. However, a surface equilibrium of the type E+PMKt-
EPM
(6)
317
is possible, where EPM, the PM species adsorbed on the electrode surface E, can be the electro-active species. In eqn. (61, K$ is the equilibrium constant for a particular ion M, Since the cyclic voltammograms obtained for various negatively charged proteins in the presence of various cations do not show any features characteristic of strong adsorption, i.e. no post-wave or pre-wave (ref. 34, Ch. 12) is observed, neither the oxidized species nor the reduced species is strongly adsorbed on the electrode surface. It should be mentioned that if the adsorption of the oxidized or the reduced species is very weak, then near-nernstian behaviour is observed; however, in that case Z,,JZpa is no longer equal to unity and the ratio changes with u [391. We postulate that in our case the adsorption of the electroactive species is so weak and reversible that it does not affect the diffusion-controlled behaviour of the electron transfer. Before we go on to discuss our own work it is imperative to show that our voltammograms do represent a case of electron transfer of an adsorbed electroactive species. Normally, if a species adsorbed on a homogeneous electrode surface undergoes electron transfer, voltammograms do not retain the features of those obtained under diffusion-controlled mass transport since Fick’s diffusion law is no longer valid. For a reversible case symmetrical peaks with A E, = 0 are obtained. A diagnostic feature is the proportionality between the peak current and scan rate. However, as the process moves away from reversibility, AE, increases and the voltammograms become asymmetric. The phenomenon is rather complicated and, as a number of parameters are involved, its mathematical treatment is quite difficult [38]. Mathematical solutions are available only for some idealized situations [30]. The complexity of the situation increases when surface-modified electrodes are involved because of various additional factors [38]. As discussed in the Introduction the surface of our EPG electrode can be assumed to be modified by various C-O functions. There are examples [41-443 where an electro-active species attached to an electrode surface shows all the characteristics of electron transfer following Fick’s diffusion law. The cyclic voltammograms show the characteristics of a diffusion-controlled process with Zpc proportional to ul/’ and consequently various workers [41,42] have used the Randles-Seveik equation (though AE, was found to be greater than 60 mV, presumably to simplify the situation) for this apparent fickian behaviour. In such cases it is argued that the rate of electron transfer is so slow that no non-fickian effects can be observed, which is a limiting situation of the electron-transfer behaviour of an adsorbed electro-active species. Various mechanisms have been suggested to account for the slow nature of the electron transfer between the electrode and the electro-active centres. A point relevant to our purpose is that in such apparent fickian responses A E, is generally found to be greater than 60 mV. We assume that our case represents such a limiting situation and we then try to develop a simple model to explain our various experimental observations. It should be mentioned that the existence of such an equilibrium in our case has been assumed in an earlier work [6]. Since equilibrium (6) occurs at the electrode surface, we can safely assume that this does not affect the bulk equilibrium (eqn. (4)). Thus the two equilibria (eqns.
318
(4) and (6)) can be treated separately. In our model only EPM is electro-active. From eqn. (61, the total active surface area of the electrode is [El + [EPM] where [EPM] indicates the fractional coverage of the electrode surface by PM and [El the fraction of the electrode surface which remains uncovered. In our case the total surface area of the electrode can be related to I_, which is 2.1 PA for 2[4Fe-4Sl ferredoxin (see above). As mentioned earlier, we have assumed that the responses occur under linear diffusion so that an equation like eqn. (5) is valid. We assume that the very weak and reversible adsorption postulated does not affect the situation. Hence the ratio of [EPMI to [El can be expressed in terms of the magnitude of the cathodic peak current Zpcobserved at a given concentration of a promoter and we can evaluate KG using the expression K; = [EPM]/[E][PM]
= ~,/(2.i-
z,)[PM]
(7)
For calculating the Gibbs energy change due to process (6) (or in other words to estimate KG), we have considered several well-known adsorption isotherms. Our calculations show that the adsorption pattern can be described quite satisfactorily by the Frumkin isotherm. Results obtained for 24Fe-4Sl ferredoxin in the presence of various cations are presented here. The Frumkin isotherm (ref. 35, Ch. 9, which, unlike the Langmuir isotherm, includes lateral interactions between the adsorbate molecules in the form of a fitting parameter g, assumes that the Gibbs energy of adsorption increases linearly with increasing surface coverage 8, i.e. AGads= AGO,&+ g0
(8)
giving rise to the isotherm ln[e/(l
- e)C] = -gB/RT-
AG”,,,/RT
(9)
where C is the bulk concentration of the adsorbate. Since in this model 0 is obtained by dividing Zpcby I,,,,, for ferredoxin under the experimental conditions given in Table 1 a plot of ln(ZJ(2.1 - Z,XPM]) versus Zpcshould be a straight line whose intercept gives the standard Gibbs energy of adsorption AGO,, and whose slope gives the value of g: ln(ZrJ(2.1 - Z,)[PM]] = -gZp/2.1RT
- AG”,,/RT
(10)
The results of the calculations are given in Table 1. A typical plot is shown in Fig.
4. It can be seen from the magnitudes of the various AG”,,, values, which lie between - 13.4 and - 22.2 kJ M-‘, that only physical adsorption is implicated (ref. 35, Ch. 51, as proposed in an earlier section. To elucidate the dependence of AGO,& on the nature of a cation, we have also calculated this quantity for 2[4Fe-4S] ferredoxin in the presence of two monovalent cations (Na+ and Cs’) (Table 1). A satisfactory linear dependence is observed between AGoah and z’/r, where t is the charge on the cation and r its ionic radius (ref. 17, Table l-l; ref. 18) (Table 1 and Fig. 5). The adsorption becomes weaker with increasing z’/r,
319
x
Fig. 4. Plot of x = InIl, /(2.1- I,XPM]) vs. Iv for 2[4Fe-4S] ferredoxin in the presence of Ba*+ (see Table 1). Correlation coefficient, 0.991.
The value of the lateral interaction parameter g in eqn. (8) is found to be uniformly negative in all cases which means that the interactions are repulsive in nature. However, for cations of like charge, the larger the size of a cation, the less
Fig. 5. Variation of the standard Gibbs energy of adsorption AC”,, of 2[4Fe-4S] ferredoxin on an EPG surface at pH 8 with the charge z and radius r of a cation. Correlation coefficient, 0.950.
320
is the magnitude of g. Thus the lateral interactions between the adsorbed protein molecules seem to depend on the nature of the cation inducing the adsorption. EXPERIMENTAL CONSEQUENCES
The more negative the value of the AGO,,, for a particular cation M and a given protein P, the larger is the value of the equilibrium constant KG and the amount of EPM generated, where EPM is the species adsorbed on the electrode surface. Since in our model only EPM is electrochemically active, it is understandable that the smaller the amount of PM adsorbed on the electrode surface, the smaller is the peak current observed. Thus our model predicts that the smaller the value of KG for a particular cation and a given protein, the greater is the promotion concentration. In the case of 2[4Fe-4Sl ferredoxin the order of KG for the divalent cations studied is found to be as follows: Mg2+ < Ba*+ < Fe(o-phen)z+ . The order of the corresponding promotion concentrations is expected to be the exact opposite, which is found experimentally. In the case of Z4Fe-4S] ferredoxin the value of the standard Gibbs energy change of adsorption is found to be the most negative for Fe(o-phen)i+ among all the cations considered (Table l), which means that the adsorption is strongest when ferredoxin is associated with this cation. This is found to be true experimentally. An EPG electrode, when dipped in a solution of ferredoxin and Fe(o-phen)i+ , adsorbs the protein. An electrode modified in this way gives a non-persistent voltammogram characteristic of ferredoxin in a plain buffer solution [33]. This behaviour is not observed for any other cation listed in Table 1. We have recently shown [45] that plastocyanin, which bears an overall negative charge in the pH range S-10, is adsorbed on a gold electrode modified by a divalent cation and that it is possible to observe an electrochemical response of the adsorbed protein. Thus the type of adsorption under discussion exists in practice. THE NATURE OF THE ADSORPTION
We now consider the nature of the adsorption in some detail. A freshly polished edge-oriented pyrolytic graphite surface is known to consist of about 25% oxygen and 75% carbon atoms [5]. The distances between two carbon atoms in th: hexagonal arrangement found in a graphite crystal layer are known to be 1.42 A (nearest) and 2.46 and 2.84 A (diagonal) (ref. 17, Ch. 11). The average distance between two cationic binding sites, i.e. the oxygen atoms, on a polished EPG surface is 4 A. It can be shown that, if a protein molecule is approximated by a cube of dimensions 20 A, nearly 25 negatively charged sites are buried under the protein molecule in a square of side 20 A. A molecule of 2[4Fe-4S] ferredoxin can probably be enclosed in a cube of dimensions between 20 and 60 A. Actually, a protein molecule can be said to have an oval shape [3]. Consequently, the effective contact area between a protein-promoter complex and the electrode will be much smaller than the square face of a cube. In any case there are enough cation binding
321
sites on the electrode surface for all the protein-promoter complex molecules which diffuse to the electrode surface to be readily held to the electrode. Fe(o-phen):+ , the largest of all the cationic promoters listed in Table 1, has a diameter of 14 A. Thus the largest of the PM molecules is still much smaller than the electrode. In an earlier section we have mentioned that the rolling of a smaller species on the surface of a larger one is common in all examples. Similar rolling of the PM species over the electrode surface may take place. In order to understand the Frumkin repulsion in the electrochemistry of ferredoxin it is important to remember that the protein molecules themselves repel one another electrostatically because of their negative charge. The PM species are not adsorbed uniformly, not only because of a statistical requirement but also because of the heterogeneity of a polished EPG surface. The absolute values of the parameter g are found to be smaller for the comparatively larger cations. With complexes can behave as larger cations such as Fe(o-phen)i+ , protein-cation dipoles. A dipole-dipole interaction through a favourable orientation of the PM-PM or MP-MP type can partially compensate the native repulsion between the protein molecules. A small cation like Mg2+ is buried, so that the P-P repulsion is the dominant interaction between two adsorbed molecules. It should be noted that the size of the protein-cation complex causes it to project over the outer Helmholtz plane into the diffuse layer when adsorbed on the electrode surface.
CONCLUDING REMARKS
Small redox proteins with various negative charges form 1: 1 complexes with cations. Such complexes are adsorbed weakly on an EPG surface at pH 8 and the adsorbed species undergoes electron transfer. It can be stated that the role of the cation is essentially to induce reversible adsorption of a negatively charged protein suitable for electron transfer at a negatively charged EPG surface. In the case of a given protein and cations of same charge, less negative values of the standard Gibbs energy of adsorption result in a higher promotion concentration of the cation. This has been exemplified by detailed calculations for 24Fe-4S] ferredoxin using a very simple model.
ACKNOWLEDGEMENTS
Part of the work was performed when DD and HN were in &ford. DD gratefully acknowledges the financial assistance received from the Indian National Science Academy, New Delhi, and the Royal Society, London. I-IN thanks the Kagawa Nutrition College, Japan, and the Japan Private School Promotion Foundation for support through an outside studies programme.
322
APPENDIX A CALCULATION OF EFFECTIVE THE PROTEINS
CHARGE AT THE CATION-ANION
BINDING SITES OF
Equation (2) applies when the ionic strength I is zero. However, using eqn. (3) we can develop the equation log Kc,, = IO.477 - 1.018[ Z1/2/( 1 + 11’2) - 0.31])2,2,
+ 0.105
(Al)
which will apply for any given strength I. The data for various association constants shown in Table 4 were obtained [26] at Z = 0.10 M (except for the cytochrome c-Fe(CN)i+ complex). At Z = 0.10 M, eqn. (Al) becomes log Z&0.10) = 0.263~~~~ + 0.105
(A2)
Equation (A2) can be used to derive the total charge product for a protein-ion complex from the corresponding experimental association constant (Table 4) at Z = 0.10 M and then, knowing the charge on the inorganic ion, the effective charge at the binding site of the protein can be calculated. The version of eqn. (Al) at Z = 0.18 M is used to calculate the total charge product for the cytochrome c-Fe(CN)zcomplex. REFERENCES 1 F.A. Armstrong, A.M. Bond, H.A.O. Hill, B.N. Oliver and I.S.M. Psalti, J. Am. Chem. Sot., 111 (1989) 9185. 2 H.A.O. Hill, Pure Appl. Chem., 62 (1990) 1047. 3 J.E. Frew and H.A.O. Hill, Eur. J. Biochem., 172 (1988) 261. 4 F.A. Armstrong, H.A.O. Hill and N.J. Walton, Act. Chem. Res., 21(1988) 407; Q. Rev. Biophys., 18 (1986) 261. 5 H.A.O. Hill, Pure Appl. Chem., 59 (1987) 743. 6 F.A. Armstrong, P.A. Cox, H.A.O. Hill, V.J. Lowe and B.N. Oliver, J. Electroanal. Chem., 217 (1987) 331. 7 G.N. Kamau, W.S. Willis and J.F. Rusling, Anal. C&em., 57 (1985) 545. 8 R.E. Panzer and P.J. Elving, Electrochim. Acta, 20 (1975) 635. 9 S. Evans and J.M. Thomas, Proc. R. Sot. London, Ser. A, 353 (1977) 103. 10 C.W. Miller, D.H. Kanveik and T. Kuwana, in K. Fuwa (Ed.), Recent Advances in Analytical Spectroscopy, Pergamon Press, New York, 1982, p. 233. 11 R. Schogl and H.P. Boehm, Carbon, 21 (1983) 345. 12 A. Proctor and P.M.A. Sherwood, Carbon, 21(1983153. 13 T. Takahagi and A. Ishitani, Carbon, 22 (1984) 43. 14 R.C. Engstrijm and V.A. Strasser, Anal. Chem., 56 (1984) 136. 15 G.E. Cabaniss, A.A. Diamantis, W.R. Murphy Jr., R.W. Linton and T.J. Meyer, J. Am. Chem. Sot., 107 (19851 1845. 16 F.A. Armstrong, P.A. Cox, H.A.O. Hill, B.N. Oliver and A.A. Williams, J. Chem. Sot. Chem. Commun., (1985) 1236. 17 F.A. Cotton and G. Wilkinson, Advanced Inorganic Chemistry (4th edn) Wiley, New York, 1980. 18 C.A. Koval, M.E. Ketterer and CM. Reidsema, J. Phys. Chem., 90 (1986) 4201. 19 N. Bjerrum, K. Dans. Vid. Sels., 7 (1926) 9. 20 M.T. Beck, Coord. Chem. Rev., 3 (1968) 91. 21 J.T. Denison and J.B. Ramsey, J. Am. Chem. Sot., 77 (1955) 2615.
323 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45
R.M. Fuoss, J. Am. Chem. Sot., 80 (1958) 5059; Proc. Natl. Acad. Sci. USA, 75 (1978) 16. S.C. Tam and R.J.P. Williams, Struct. Bonding, 63 (1985) 103. E. Hiigfeldt, Stability Constants of Metal-Ion Complexes, Pergamon Press, &ford, 1982, Part A. C.J. Nyman and R.A. Plane, J. Am. Chem. Sot., 82 (1960) 5787. S.K. Chapman, J.D. Sinclair-Day, A.G. Sykes, S.C. Tam and R.J.P. Williams, J. Chem. Sot. Chem. Commun., (1983) 1152. S.C. Tam, D. Phil. Thesis, University of Oxford, 1984. E.A. Guggenheim, Philos. Mag., 19 (1935) 588. K.T. Yasunobu and M. Tanaka, in W. Lovenberg (Ed.), Iron-Sulfur Proteins, Vol. 2, Academic Press, New York, 1973, Ch. 2. C.S.G. Eley, E. Ragg and G.R. Moore, J. Inorg. B&hem., 21 (1984) 295. P.C. Driscoll, H.A.O. Hill and C. Redfield, Eur. J. B&hem., 170 (1878) 279. G.L. McLendon and H.A.O. Hill, private communication. B.N. Oliver, D. Phil. Thesis, University of Oxford, 1985. A.J. Bard and L.R. Faulkner, Electrochemical Methods, Wiley, New York, 1980. R. Greef, R. Peat, M. Peter, D. Pletcher and J. Robinson, Instrumental Methods in Electrochemistry, Ellis Horwood, Chicester, 1985. R.S. Nicholson and I. Shain, Anal. Chem., 36 (1964) 706. J.E.B. Randles, Trans. Faraday Sot., 44 (1948) 327. A. Sew%, Collect. Czech. Chem. Commun., 13 (1948) 349. R.H. Wopschall and I. Shain, Anal. Chem., 39 (1967) 1515. E. Laviron, in A.J. Bard (Ed.), Electroanalytical Chemistry, Vol. 12, Marcel Dekker, New York, 1982, p. 53. R.J. Nowak, F.A. Schultz, M. Umana, R. Lam and R.W. Murray, Anal. Chem., 52 (1980) 315. P. Daum, J.R. Lenhard, D. Rolison and R.W. Murray, J. Am. Chem. Sot., 101 (1979) 3442. P.J. Peerce and A.J. Bard, J. Electroanal. Chem., 114 (1980) 377. C.P. Andrieux and J.M. Saveant, J. Electroanal. Chem., lll(1980) 377. D. Datta, H.A.O. Hill and H. Nakayama, J. Electroanal. Chem., 297 (1991) 309.
J. Electroanal. Chem., 324 (1992) 307-323 Elsevier Sequoia S.A., Lausanne
JEC 01877
Promotion of the electrochemical response of some negatively charged proteins at an edge-plane graphite electrode by various redox inert cations: an electrochemical manifestation of Frumkin adsorption Dipankar Datta
l
Department of Inorganic Chemistry, Indinn Association for the Cultivation of Science, Calcutta 700 032 (India)
H. Allen 0. Hill Inorganic Chemistry Laboratory, University of Oxford, South Parks Road, Oxford OX1 3QR (UK)
Hiroaki Nakayama Laboratory of Chemistry, Kagawa Nutrition College, Sakado, Saitama 350-02 (Japan) (Received 30 April 1991; in revised form 25 June 1991)
Promotion of the cyclic voltammetric response of several small negatively charged metalloproteins P at an edge-plane graphite (EPG) electrode E by various inorganic cations M at pH 8 has been interpreted in terms of hvo equilibria: P+MK-PM E+PM -
KC4
EPM
The first equilibrium, where a 1: 1 protein-cation complex PM is formed, occurs in the bulk, while the second takes place at the electrode surface. The value of the equilibrium constant K depends on the cation charge and the charge on the cation binding site of the protein. A simple mode1 for understanding the interactions in the inorganic ion pairs in an aqueous medium has been developed. The mode1 is extended to compare the association of the inorganic ions with various proteins in an aqueous medium and is used to estimate K. The adsorption of the protein-metal ion complex on the electrode surface (the second equilibrium) is assumed to be weak (i.e. the equilibrium constant K& is small) and reversible. It is found that only EPM, the PM species adsorbed on the electrode surface, is electro-
l
To whom correspondence
0022-0728/92/$05.00
should be addressed.
0 1992 - Elsevier Sequoia S.A. All rights reserved
active. The experimental consequences of the two equilibria are discussed. The adsorption pattern is found to obey the Frumkin isotherm. The standard Gibbs energies of adsorption AC&,, have been calculated specifically for U4Fe-4S] ferredoxin in the presence of various cations. The magnitude of the AG$, values, which are found to lie within the range - 13.4 to 22.2 kJ mol- * for 2/4Fe-As] ferredoxin, suggests physical adsorption of the protein. The AC& values for the various cations are found to vary linearly with .z2/r where z is the charge on the cation and r is its ionic radius. It is concluded that the role of the cation is to induce a reversible weak adsorption of a negatively charged protein suitable for electron transfer on an EPG surface at pH 8. Speculations are made on the nature of the adsorption.
INTRODUCTION
The electron transfer behaviour of various negatively charged proteins at an edge-plane graphite (EPG) electrode has been extensively studied by Hill and coworkers using dc cyclic voltammetry [l-6]. The nature of the electrochemical response obtained under various experimental conditions can be explained by invoking radial diffusion (microscopic model for the electrode) or linear diffusion (macroscopic model for the electrode) [l]. A number of studies [7-161 have shown the existence of C-OH functions at the polished surface of an EPG electrode. The electrode surface is believed [3] to be negatively charged at pH > 5.6. For cytochrome c, which is positively charged at pH 8, direct electron transfer is achieved at an EPG electrode at pH 8, but no such electrochemistry is observed for plastocyanin, rubredoxin, 2Fe-2s ferredoxin or 2[4Fe-4S] ferredoxin, presumably because of the negative charge on them at pH 8. Thus electrostatic effects seem to play an important role in bringing about a suitable interaction between the electrode surface and the proteins for electron transfer to occur. However, it was possible to achieve electrochemical responses for the various negatively charged proteins in the presence of some cations (inorganic or organic) which are redox inert in the potential range of interest [6]. These cations are believed to reduce the electrostatic repulsions between the electrode surface and the proteins, and they are termed “promoters”. The ability of a cation to promote an electrochemical response seems to depend on its charge and size. The degree of effectiveness of promotion is measured by the concentration of a cation needed to give rise to the same magnitude of peak current in a cyclic voltammetric experiment at the same scan rate for a given concentration of a protein solution. The amount required for obtaining the maximum peak current is called the “promotion concentration”. For a particular protein, the general order of the promotion concentration for various inorganic cations is found to be as follows [6]: Li+> Na+> K+> Cs+> Mg2+> Ca2+> Ba2+> Fe(o-phen):+ > Cr(NH&+ > Pt(NH&+. Some selected data [6] are given in Table 1 for 2[4Fe-4S] ferredoxin (from Clostridium pasteurianum), which is the most extensively studied system. In this paper we try to understand the role of various inorganic cations in promoting the electrochemical responses of various negatively charged proteins. Before we do so, it is necessary to understand the interactions between these ions and the various proteins.
309 TABLE 1 Variation of the cathodic peak current Ipc and peak separation AE, in the first cycle voltammetric scan of 2[4Fe-4S] ferredoxin at an EPG electrode with concentration chl of various inorganic cations at 25°C and pH 8.0; standard Gibbs energy of adsorption and lateral interaction parameter g of a4Fe-4Sl ferredoxin on an EPG surface in presence of various cations together with their ionic radii ra Cation M Mg*+
Ba2+
Fe(o-phen):+
crwH&+
Crien):’
Naf
Cs+
g/RT
r/A
- 13.2 (0.963 d,
- 6.97
0.65 ’
- 16.5 (0.991 d)
- 5.50
1.35 =
- 22.2 (0.941 d)
- 3.30
6.9 g
- 16.4 (0.993 d)
-5.42
3.4 g
- 18.0 (0.972 d,
- 4.54
4.2 g
0.082 0.093 0.103
- 19.5 (1.000 d)
- 2.86
0.95 c
0.082 0.093 0.103
- 20.4 (0.947 d)
- 2.69
1.69 =
I,/
A&/
[PM1b/
‘=“a,, /
PA
mV
mM
kJ mol-’
9 11 13 15 17 20 21 28 e
1.4 1.4 1.7 1.6 1.7 1.8 2.0 2.2
178 132 115 106 106 107 93 86
0.079 0.082 0.082 0.085 0.088 0.090 0.092 _f
4 5 6 7 9 13 e
1.4 1.7 1.8 1.8 1.9 2.4
183 145 115 108 83 80
0.065 0.070 0.072 0.075 0.079 _f
0.50 1.00 1.50 2.00 2.50 =
1.1 1.2 1.6 1.8 1.9
150 150 140 103 92
0.021 0.033 0.043 0.050 0.055
0.26 0.29 0.33 0.35 0.38 0.42 0.46 =
1.3 1.3 1.7 1.8 1.9 1.9 2.1
133 120 93 85 80 80 73
0.074 0.078 0.083 0.085 0.089 0.092 _f
0.20 0.30 0.40 0.50 0.70 =
1.5 1.6 1.8 1.8 1.9
100 73 70 68 65
0.065 0.079 0.091 0.096 0.103
200 300 400
0.8 1.0 1.2
200 193 130
200 300 400
1.2 1.4 1.5
175 130 98
cM/mM
For footnotes see over.
01
1 2
I
I
1
6
IO
I&
1951
Fig. 1. Relation between log K and I z1z2I for inorganic ion pairs (Table 2) in aqueous medium at ionic strength I = 0. Correlation coefficient, 0.985.
ASSOCIATION
IN INORGANIC ION PAIRS AND OF PROTEINS WITH INORGANIC IONS
For inorganic ion pairs, Bjerrum’s equation [19,201 K = O.O0047rN( I zlz2 I e2/~kT)3/py-4 y = I zlz2 I e2/crkT
exp( y) dy
(1)
b = I zlz2 I e2/eakT
relates the association constant K to the charges zi and zz on the ions in a medium of dielectric constant E. In eqn. (11, The closest distance of approach a is an adjustable empirical parameter which may not always have real physical significance. Though several later modifications of this theory have been made [21,22] the essence remains the same. Simply stated, the interactions in inorganic ion pairs are largely electrostatic. However, it is possible to develop a model
Notes to Table 1: Scan rate, 20 mV s-l; geometric surface area of EPG, 0.20 cm’; [ferredoxinl= 150 PM in 5 mM Tricine + 1 mM NaCl. a For definitions of the symbols see text. The peak current and the peak separation data are taken from ref. 6. b For divalent cations, see Fig. 2; for trivalent cations, see Fig. 3; for monovalent cations eqn. (41 is used with the logarithm of association constant equal to 1.586 (eqn. (2); see text). ’ Pauling’s ionic radius (ref. 17, Table l-1). d Correlation coefficient for the plot of In{& /(2.1- I,XPMjl vs. I,. e Promotion concentration. f Not used in the plot of In{& /(2.1- IJPMI) vs. iW since IW > 2.1 ALA. 8 Estimated from space-filling models [181.
311
O-05
Fig. 2. Variation in the population of U4Fe-4S] ferredoxin associated with an ion [PM] with the addition of a 1: 2 electrolyte to a 150 PM solution of a4Fe-4S] ferredoxin in 5 mM Tricine + 1 mM NaCl.
without any explicit reference to the nature of the interactions. Figure 1 shows that the linear equation log K = 0.477 I zlz* I + 0.015 incorporating only I zlz2 I, the modulus of the product of the charges on the two ions, can be used to describe the association of inorganic ion pairs in an aqueous medium at ionic strength Z = 0 (Table 2). The examples used in Fig. 1 are essentially the same as those of Tam and Williams [23], in which pure outer-sphere interactions are believed to be involved, i.e. the examples deliberately exclude the possibility of any specific interactions between the two members of an ion pair. In Fig. 1 we have introduced some additional data [24] (Table 2) to give equal
0.10
:
2
e
0.05
:r -
Fig. 3. Variation in the population of 2[4Fe-4S] ferredoxin associated with an ion [PM] with the addition of a 1:3 electrolyte to a 150 PM solution of 2[4Fe-4S] ferredoxin in 5 mM Tricine + 1 mM NaCI.
312
TABLE 2 Representative association constants for some inorganic ion pairs in an aqueous medium at 25°C and ionic strength I = 0 a Cation
Anion
IZtZrl
log(K/M-‘1
[CoWQOH,13+
[Fe(CN1614[Fe(CN),14-
12 12
5.70 5.95
m31:[Fe(CN),13-
12 9 9
5.74 3.70
KdNH3),PY13+
[!?+m3)613+ KowH3),L13+ L = 4-phenylpyridine L = 4-phenylpyridine Ca2+ Ca2+ [Co(NL$),13+ ;$L-L3)613+ [GANH3)sN0212+
[Fe(CN),L’13L’ = 4,4’-bipyridine L’ = 1,2-bis(4-pyridylethane) [Fe(CN),14[Fe(CN),13so;wo,2SO;SO;-
$~3),13+ 2+ Koten)313 + KJoW313 +
so;Clclao;
34 3 3
2.23 1.85 b 1.90 b 1.15
E;2.t Ba2+
so;NO; NO;
2 2
0.85 0.68 0.84
8 6 6 64
4.80 4.64 3.63 2.63 3.56 2.19 2.59
4
2.69
a 1zl.z21is the modulus of the product of the charges on the cation and the anion in an ion pair. The log K data are taken from ref. 24 unless otherwise specified. b From ref. 23.
statistical weight to each type of charge product (except for I zlzz I = 8). Equation (2) gives rise to a standard error of f 0.370 in the estimation of log K at I = 0. In Table 3 we show that, for a number of ion pairs [24,25], the error remains almost the same, i.e. f0.402. Using this linear model for association in inorganic ion pairs in aqueous medium (Bjerrum’s model is non-linear), we can now go on to examine the association of various proteins with various inorganic ions in an aqueous medium. Basically, we re-examine the work of Chapman et al. [26] on mapping the surfaces of various proteins by using different inorganic ions as the probes. The local charges at the binding sites of the proteins listed in Table 4 have been calculated using our model (see Appendix) and match the results reported previously [261 quite well. A notable difference is that, when the total charge product is less than 15, our values are consistently lower than those obtained by Chapman et al. [26] (Table 4) using Bjerrum’s model. This is probably because in eqn. (0, with a = 6 A (the value used by Chapman et al. [26] in their calculations), the association constants for I z1.z2 I < 15 are underestimated. Such problems with Bjerrum’s equation are well known [27]. However, our present results, in conjunction with those of Chapman et al. [26], show that the association of inorganic ions with
313 TABLE 3 Deviation of the association constants for various inorganic ion pairs in an aqueous medium at 25°C and ionic strength Z = 0 from eqn. (2) a
I ZlZZ I
Theoretical b log(K/M-‘1
Cation
Anion
Experimental log (K/M-‘)
A(log K) ’
9
4.398
Ells+ Lu’f Als+
fFetCN),13[Fe(CN)ipKo(CN),13-
3.65 3.69 4.30
- 0.748 - 0.708 - 0.098
8
3.921
[Pt(en),14+
so:-
3.52 d
- 0.401
6
2.967
Ko(en1313 + Kofpn),l’+ (D-form) bW313 +
so;so;-
2.974 3.084
0.007 0.117
soi-
2.884
- 0.083
ziEm) Ga3+ In3+ Las+ Eu3+ Lus+ Ca2+
so4’ so:so4’ so;so:so;p,o; -
3.01 2.77 3.04 3.50 3.54 3.49 3.40
0.043 - 0.197 0.073 0.533 0.573 0.523 0.433
Be’+ Mn2+ Ni2+ cur+ Zn2+ Cd’+ Mnzf Cos+ Ni2+ Naf
so:so;so;so;so;so;SeO,ZSeOaSe0,2p40;‘,-
2.16 2.20 2.27 2.40 2.23 2.55 2.43 2.70 2.67 2.12
0.147 0.187 0.257 0.387 0.317 0.537 0.417 0.687 0.657 0.107
MNH,),l”
ICr(en),13 + W$NH,),13+
c10; ClO, c10; NO;
1.2 1.0 1.34 1.74
- 0.336 - 0.536 - 0.196 0.204
Mg2+ Ca2+ Zn2+ Sr2+ cur+ Zn2+
B(GH); B(Gf-0; SCNNO; NO; NO;
1.23 1.23 1.33 0.77 0.54 0.42
0.171 0.171 0.271 - 0.289 - 0.519 - 0.639
4
3
2
2.013
1.536
1.059
a 1z1z2 1 is the modulus of the product of the charges on the cation and the anion in an ion pair. The experimental log K data are taken from ref. 24 unless otherwise specified. b Calculated using eqn. (2). ’ A0og K) = experimental log K - theoretical log K; standard deviation, f 0.402. d From ref. 25.
314 TABLE 4 Formation constants for association of inorganic ions with various proteins (in reduced state) at 25°C ionic strength I = 0.10 M (NaCi) and pH 7.5, and the local effective charges on the binding sites of the proteins Protein
Inorganic ion
Io~(K/M-‘)~
Local effective charge b
Charge at binding site a from structure
PCU’ c
]~~*‘]s+ d rPtwH,>alq+ KdNH,),l’+ [Cdo-phen),]” + [Cr(o-phenj313+
4.204 4.342 2.763 2.223 2.246
-3.12(-3.0) - 4.03( - 4.0) - 3.37( - 3.8) - 2.68( - 2.8) - 2.71( - 2.8)
-4
[2Fe-2S] ’
w”15’ d ]Pt(NH 316I [Cow-L,),;:+
-3.28(-3.0) - 4.01( - 4.0) - 3.67( - 4.0) -3.25x-3.5) -3.38(-3.8) -4.15(-4.5)
-3
[Cr(en),13 + [CdNH,),c11*+
4.422 4.322 2.999 2.666 2.771 2.288
2[4Fe-4S]’
PtwH3)J4+ rd~3M3+ DwH3),13+
3.398 2.649 2.326
-3.13(-3.0) - 3.23 -3.0) - 2.81( - 3.0)
ca. -3
Cytochrome b, g
[CO~~*]~’ e
-3.13(-3.0) - 3.W - 4.0) - 3.39(- 3.8) - 3.02(- 3.3)
-3/-4
;zey$$3+
4.220 4.170 2.778 2.490
[Fe(CN),13 - i
2.653
~cdNH3),13+
[PWH3)14’ 3
Cytochrome c h
f
3.71 ka. 4.0)
3/4
’ From ref. 26. b Calculated using eqn. (2) (see Appendix); values obtained by Chapman et al. [26] are given in parentheses. ’ Parsley. d [C$r]5+ -[tNH,),CoNH,Co(NH,),]‘+. e Clo&diwn pasteurimum. f At pH 6.8. 8 Calves’ liver. h Horse heart in oxidized form. ‘1=0.18 M.
proteins essentially
A very important result which emerges from this exercise is that eqn. (2) can be used to describe the interactions of various ions with the proteins, and the association constant is determined mainly by the product of the charge on the inorganic ion and the local effective charge on the binding sites of the proteins. The model based on eqn. (2) is worked out explicitly for a4Fe-G] ferredoxin obtained from Chtridium pasteutinum as an example to elucidate the variation
315
in the population of the 1: 1 protein-cation complex in a given aqueous solution at a given pH. The logarithm of the association constants K of 2[4Fe-4S] ferredoxin with a divalent cation and a trivalent cation at ionic strength Z = 0 are calculated from eqn. (2) as 2.967 M-’ and 4.398 M-i respectively, assuming the local charge at the binding site to be -3 (Table 4). The dependence of log K on the ionic strength [28] is given by log K, = log Kc,,,,, - 1.018 I .zlz* I {[V/(
1 + Z1’2)] - 0.31)
(3)
Thus we can calculate the equilibrium concentration [PM] of the protein P associated with a metal-ion complex M for any equilibrium concentration [PI of the protein and [Ml of the ion: P+M-
K
PM
(4) Figures 2 and 3 show the variations of [PM] when 1:2 and 1:3 electrolytes respectively are added to a 150 PM solution of 24Fe-4S] ferredoxin in 5 mM Tricine (pK = 8.1) at pH 8.0 in the presence of 1 mM NaCl. The contribution of the protein to the ionic strength of the solution is calculated by considering the net charge on the protein at pH 8.0 (- 10 in the case of a4Fe-4S] ferredoxin [29]) to be made up of discrete charges 1301. The curves (Figs. 2 and 3) show that, as expected, the concentration of PM is higher for an M3+ ion than that for an M2+ ion when the same amount of the two ions is considered. However, there is an important difference between the inorganic ion pairs and the protein-inorganic ion complexes. An inorganic ion, which is much smaller in size than a protein molecule, probably rolls around on the surface of a protein molecule as revealed from NMR studies of the binding of Cr(NH,)i+ to plastocyanin [31]. This phenomenon is similar to the rolling of a substrate molecule on an enzyme molecule [32]. ADSORPTION
As stated in the Introduction, in a cyclic voltammetric experiment the various negatively charged proteins do not show any electrochemical response at pH 8 at a polished EPG electrode unless a “promoter” is added to the solution. At concentrations much lower than the “promotion concentration” radial diffusion takes place [1,61, giving rise to sigmoidal voltammograms. For our purpose we have chosen those concentrations of promoters where linear diffusion predominates. In the region of linear diffusion, voltammograms show two important features [6,33]: up to a scan rate u of 200 mV s-i the cathodic peak current Zpc is proportional to u112, i.e. the plot of Z, versus u112 is a straight line which passes through the origin, and the anodic peak current Z,, is almost equal to ZW, i.e. Zpc/Zpa= 1. If we assume that only the 1: 1 protein-cation complex PM is electro-active, the situation represents a chemical reaction C, preceding the electron transfer E,, i.e. a C,E, mechanism operates here. Depending on its nature, this chemical reaction can affect the nemstian behaviour of the electron transfer process in various ways
316
(ref. 34, Ch. 11; ref. 35, Ch. 6). In cyclic voltammetry, two diagnostic features of a C,E, mechanism are as follows: (i) Z& ‘1’ decreases as u increases, and (ii) Z,,JZpa increases with u and is always greater than or equal to unity. In our case, since Zpc is proportional to z#/* and Z&Z,, = 1 for scan rates up to 200 mV s-l, it is clear that the preceding reaction has little effect on the nernstian behaviour of the electron transfer process. In fact it is well known that, when the equilibrium constant of the preceding reaction (in our case, reaction (4)) is greater than or equal to 20 M-‘, the electrochemical response appears as an unperturbed nemstian behaviour (ref. 34, Chll; ref. 36). In our case the minimum value of K (for the association of monovalent cations with 4[4Fe-4S] ferredoxin) is 38.5 M-i. Thus the equilibrium (4) lies so far to the right that we expect an unvitiated electron transfer behaviour of PM alone to be reflected in the cyclic voltammograms. For a planar electrode in the experimental conditions chosen here, we can expect the cyclic voltammetric data to obey the Randles-Sevcik equation [37,381 ZPC = 2 *69 x 105D~‘2~,Av1’2
(5)
where Zpc is in amperes, u is in V s -I, the area A of the electrode is in cm*, the bulk concentration c,, of the oxidized species is in mol cmm3 and the diffusion coefficient D, of the oxidized species is in cm s -l. Actually this equation is meant for a reversible electron transfer process. As revealed by the AE, values given in Table 1, our process can be said to be only quasi-reversible. However, as mentioned earlier we have observed a proportionality between Zpc and ul/* up to v=200 mV s- ‘. Thus we can say that an equation like eqn. (51, where the numerical constant is different, is applicable in our case (ref. 35, Ch. 6). From the above discussion it follows that, in our case, the C,E, mechanism leads to the fact that the observed Zpc should be directly proportional to the bulk equilibrium concentration [PM], of the 1: 1 protein-cation complex for a particular scan rate at a given EPG electrode (neglecting the small variations in the diffusion coefficient of PM for a particular protein P with Ml. From the IF data given in Table 1 we find that when the response is fully promoted, the average of the maximum cathodic peak current I,,,= achieved at a scan rate of 20 mV s-l for 150 ,uM 2[4Fe-4Sl ferredoxin at an EPG electrode with a geometric area of 0.2 cm* is 2.1 PA. It should be noted that Z,, differs slightly for various cations under the experimental conditions mentioned above. While several factors may be responsible for this observation, the different peak separations AE, observed for different cations (see Table 1) at a concentration where they are fully promoting seems to be the most important. Various factors may be responsible for the relatively large AE, values observed in our case. We shall refer to this problem later (see below). The values of [PM] at the fully promoted level (i.e. when Z,,,, = 2.1 PA) differ considerably from cation to cation. No proportionality is observed between [PM] and I,,. This indicates that PM is not electro-active. However, a surface equilibrium of the type E+PMKt-
EPM
(6)
317
is possible, where EPM, the PM species adsorbed on the electrode surface E, can be the electro-active species. In eqn. (61, K$ is the equilibrium constant for a particular ion M, Since the cyclic voltammograms obtained for various negatively charged proteins in the presence of various cations do not show any features characteristic of strong adsorption, i.e. no post-wave or pre-wave (ref. 34, Ch. 12) is observed, neither the oxidized species nor the reduced species is strongly adsorbed on the electrode surface. It should be mentioned that if the adsorption of the oxidized or the reduced species is very weak, then near-nernstian behaviour is observed; however, in that case Z,,JZpa is no longer equal to unity and the ratio changes with u [391. We postulate that in our case the adsorption of the electroactive species is so weak and reversible that it does not affect the diffusion-controlled behaviour of the electron transfer. Before we go on to discuss our own work it is imperative to show that our voltammograms do represent a case of electron transfer of an adsorbed electroactive species. Normally, if a species adsorbed on a homogeneous electrode surface undergoes electron transfer, voltammograms do not retain the features of those obtained under diffusion-controlled mass transport since Fick’s diffusion law is no longer valid. For a reversible case symmetrical peaks with A E, = 0 are obtained. A diagnostic feature is the proportionality between the peak current and scan rate. However, as the process moves away from reversibility, AE, increases and the voltammograms become asymmetric. The phenomenon is rather complicated and, as a number of parameters are involved, its mathematical treatment is quite difficult [38]. Mathematical solutions are available only for some idealized situations [30]. The complexity of the situation increases when surface-modified electrodes are involved because of various additional factors [38]. As discussed in the Introduction the surface of our EPG electrode can be assumed to be modified by various C-O functions. There are examples [41-443 where an electro-active species attached to an electrode surface shows all the characteristics of electron transfer following Fick’s diffusion law. The cyclic voltammograms show the characteristics of a diffusion-controlled process with Zpc proportional to ul/’ and consequently various workers [41,42] have used the Randles-Seveik equation (though AE, was found to be greater than 60 mV, presumably to simplify the situation) for this apparent fickian behaviour. In such cases it is argued that the rate of electron transfer is so slow that no non-fickian effects can be observed, which is a limiting situation of the electron-transfer behaviour of an adsorbed electro-active species. Various mechanisms have been suggested to account for the slow nature of the electron transfer between the electrode and the electro-active centres. A point relevant to our purpose is that in such apparent fickian responses A E, is generally found to be greater than 60 mV. We assume that our case represents such a limiting situation and we then try to develop a simple model to explain our various experimental observations. It should be mentioned that the existence of such an equilibrium in our case has been assumed in an earlier work [6]. Since equilibrium (6) occurs at the electrode surface, we can safely assume that this does not affect the bulk equilibrium (eqn. (4)). Thus the two equilibria (eqns.
318
(4) and (6)) can be treated separately. In our model only EPM is electro-active. From eqn. (61, the total active surface area of the electrode is [El + [EPM] where [EPM] indicates the fractional coverage of the electrode surface by PM and [El the fraction of the electrode surface which remains uncovered. In our case the total surface area of the electrode can be related to I_, which is 2.1 PA for 2[4Fe-4Sl ferredoxin (see above). As mentioned earlier, we have assumed that the responses occur under linear diffusion so that an equation like eqn. (5) is valid. We assume that the very weak and reversible adsorption postulated does not affect the situation. Hence the ratio of [EPMI to [El can be expressed in terms of the magnitude of the cathodic peak current Zpcobserved at a given concentration of a promoter and we can evaluate KG using the expression K; = [EPM]/[E][PM]
= ~,/(2.i-
z,)[PM]
(7)
For calculating the Gibbs energy change due to process (6) (or in other words to estimate KG), we have considered several well-known adsorption isotherms. Our calculations show that the adsorption pattern can be described quite satisfactorily by the Frumkin isotherm. Results obtained for 24Fe-4Sl ferredoxin in the presence of various cations are presented here. The Frumkin isotherm (ref. 35, Ch. 9, which, unlike the Langmuir isotherm, includes lateral interactions between the adsorbate molecules in the form of a fitting parameter g, assumes that the Gibbs energy of adsorption increases linearly with increasing surface coverage 8, i.e. AGads= AGO,&+ g0
(8)
giving rise to the isotherm ln[e/(l
- e)C] = -gB/RT-
AG”,,,/RT
(9)
where C is the bulk concentration of the adsorbate. Since in this model 0 is obtained by dividing Zpcby I,,,,, for ferredoxin under the experimental conditions given in Table 1 a plot of ln(ZJ(2.1 - Z,XPM]) versus Zpcshould be a straight line whose intercept gives the standard Gibbs energy of adsorption AGO,, and whose slope gives the value of g: ln(ZrJ(2.1 - Z,)[PM]] = -gZp/2.1RT
- AG”,,/RT
(10)
The results of the calculations are given in Table 1. A typical plot is shown in Fig.
4. It can be seen from the magnitudes of the various AG”,,, values, which lie between - 13.4 and - 22.2 kJ M-‘, that only physical adsorption is implicated (ref. 35, Ch. 51, as proposed in an earlier section. To elucidate the dependence of AGO,& on the nature of a cation, we have also calculated this quantity for 2[4Fe-4S] ferredoxin in the presence of two monovalent cations (Na+ and Cs’) (Table 1). A satisfactory linear dependence is observed between AGoah and z’/r, where t is the charge on the cation and r its ionic radius (ref. 17, Table l-l; ref. 18) (Table 1 and Fig. 5). The adsorption becomes weaker with increasing z’/r,
319
x
Fig. 4. Plot of x = InIl, /(2.1- I,XPM]) vs. Iv for 2[4Fe-4S] ferredoxin in the presence of Ba*+ (see Table 1). Correlation coefficient, 0.991.
The value of the lateral interaction parameter g in eqn. (8) is found to be uniformly negative in all cases which means that the interactions are repulsive in nature. However, for cations of like charge, the larger the size of a cation, the less
Fig. 5. Variation of the standard Gibbs energy of adsorption AC”,, of 2[4Fe-4S] ferredoxin on an EPG surface at pH 8 with the charge z and radius r of a cation. Correlation coefficient, 0.950.
320
is the magnitude of g. Thus the lateral interactions between the adsorbed protein molecules seem to depend on the nature of the cation inducing the adsorption. EXPERIMENTAL CONSEQUENCES
The more negative the value of the AGO,,, for a particular cation M and a given protein P, the larger is the value of the equilibrium constant KG and the amount of EPM generated, where EPM is the species adsorbed on the electrode surface. Since in our model only EPM is electrochemically active, it is understandable that the smaller the amount of PM adsorbed on the electrode surface, the smaller is the peak current observed. Thus our model predicts that the smaller the value of KG for a particular cation and a given protein, the greater is the promotion concentration. In the case of 2[4Fe-4Sl ferredoxin the order of KG for the divalent cations studied is found to be as follows: Mg2+ < Ba*+ < Fe(o-phen)z+ . The order of the corresponding promotion concentrations is expected to be the exact opposite, which is found experimentally. In the case of Z4Fe-4S] ferredoxin the value of the standard Gibbs energy change of adsorption is found to be the most negative for Fe(o-phen)i+ among all the cations considered (Table l), which means that the adsorption is strongest when ferredoxin is associated with this cation. This is found to be true experimentally. An EPG electrode, when dipped in a solution of ferredoxin and Fe(o-phen)i+ , adsorbs the protein. An electrode modified in this way gives a non-persistent voltammogram characteristic of ferredoxin in a plain buffer solution [33]. This behaviour is not observed for any other cation listed in Table 1. We have recently shown [45] that plastocyanin, which bears an overall negative charge in the pH range S-10, is adsorbed on a gold electrode modified by a divalent cation and that it is possible to observe an electrochemical response of the adsorbed protein. Thus the type of adsorption under discussion exists in practice. THE NATURE OF THE ADSORPTION
We now consider the nature of the adsorption in some detail. A freshly polished edge-oriented pyrolytic graphite surface is known to consist of about 25% oxygen and 75% carbon atoms [5]. The distances between two carbon atoms in th: hexagonal arrangement found in a graphite crystal layer are known to be 1.42 A (nearest) and 2.46 and 2.84 A (diagonal) (ref. 17, Ch. 11). The average distance between two cationic binding sites, i.e. the oxygen atoms, on a polished EPG surface is 4 A. It can be shown that, if a protein molecule is approximated by a cube of dimensions 20 A, nearly 25 negatively charged sites are buried under the protein molecule in a square of side 20 A. A molecule of 2[4Fe-4S] ferredoxin can probably be enclosed in a cube of dimensions between 20 and 60 A. Actually, a protein molecule can be said to have an oval shape [3]. Consequently, the effective contact area between a protein-promoter complex and the electrode will be much smaller than the square face of a cube. In any case there are enough cation binding
321
sites on the electrode surface for all the protein-promoter complex molecules which diffuse to the electrode surface to be readily held to the electrode. Fe(o-phen):+ , the largest of all the cationic promoters listed in Table 1, has a diameter of 14 A. Thus the largest of the PM molecules is still much smaller than the electrode. In an earlier section we have mentioned that the rolling of a smaller species on the surface of a larger one is common in all examples. Similar rolling of the PM species over the electrode surface may take place. In order to understand the Frumkin repulsion in the electrochemistry of ferredoxin it is important to remember that the protein molecules themselves repel one another electrostatically because of their negative charge. The PM species are not adsorbed uniformly, not only because of a statistical requirement but also because of the heterogeneity of a polished EPG surface. The absolute values of the parameter g are found to be smaller for the comparatively larger cations. With complexes can behave as larger cations such as Fe(o-phen)i+ , protein-cation dipoles. A dipole-dipole interaction through a favourable orientation of the PM-PM or MP-MP type can partially compensate the native repulsion between the protein molecules. A small cation like Mg2+ is buried, so that the P-P repulsion is the dominant interaction between two adsorbed molecules. It should be noted that the size of the protein-cation complex causes it to project over the outer Helmholtz plane into the diffuse layer when adsorbed on the electrode surface.
CONCLUDING REMARKS
Small redox proteins with various negative charges form 1: 1 complexes with cations. Such complexes are adsorbed weakly on an EPG surface at pH 8 and the adsorbed species undergoes electron transfer. It can be stated that the role of the cation is essentially to induce reversible adsorption of a negatively charged protein suitable for electron transfer at a negatively charged EPG surface. In the case of a given protein and cations of same charge, less negative values of the standard Gibbs energy of adsorption result in a higher promotion concentration of the cation. This has been exemplified by detailed calculations for 24Fe-4S] ferredoxin using a very simple model.
ACKNOWLEDGEMENTS
Part of the work was performed when DD and HN were in &ford. DD gratefully acknowledges the financial assistance received from the Indian National Science Academy, New Delhi, and the Royal Society, London. I-IN thanks the Kagawa Nutrition College, Japan, and the Japan Private School Promotion Foundation for support through an outside studies programme.
322
APPENDIX A CALCULATION OF EFFECTIVE THE PROTEINS
CHARGE AT THE CATION-ANION
BINDING SITES OF
Equation (2) applies when the ionic strength I is zero. However, using eqn. (3) we can develop the equation log Kc,, = IO.477 - 1.018[ Z1/2/( 1 + 11’2) - 0.31])2,2,
+ 0.105
(Al)
which will apply for any given strength I. The data for various association constants shown in Table 4 were obtained [26] at Z = 0.10 M (except for the cytochrome c-Fe(CN)i+ complex). At Z = 0.10 M, eqn. (Al) becomes log Z&0.10) = 0.263~~~~ + 0.105
(A2)
Equation (A2) can be used to derive the total charge product for a protein-ion complex from the corresponding experimental association constant (Table 4) at Z = 0.10 M and then, knowing the charge on the inorganic ion, the effective charge at the binding site of the protein can be calculated. The version of eqn. (Al) at Z = 0.18 M is used to calculate the total charge product for the cytochrome c-Fe(CN)zcomplex. REFERENCES 1 F.A. Armstrong, A.M. Bond, H.A.O. Hill, B.N. Oliver and I.S.M. Psalti, J. Am. Chem. Sot., 111 (1989) 9185. 2 H.A.O. Hill, Pure Appl. Chem., 62 (1990) 1047. 3 J.E. Frew and H.A.O. Hill, Eur. J. Biochem., 172 (1988) 261. 4 F.A. Armstrong, H.A.O. Hill and N.J. Walton, Act. Chem. Res., 21(1988) 407; Q. Rev. Biophys., 18 (1986) 261. 5 H.A.O. Hill, Pure Appl. Chem., 59 (1987) 743. 6 F.A. Armstrong, P.A. Cox, H.A.O. Hill, V.J. Lowe and B.N. Oliver, J. Electroanal. Chem., 217 (1987) 331. 7 G.N. Kamau, W.S. Willis and J.F. Rusling, Anal. C&em., 57 (1985) 545. 8 R.E. Panzer and P.J. Elving, Electrochim. Acta, 20 (1975) 635. 9 S. Evans and J.M. Thomas, Proc. R. Sot. London, Ser. A, 353 (1977) 103. 10 C.W. Miller, D.H. Kanveik and T. Kuwana, in K. Fuwa (Ed.), Recent Advances in Analytical Spectroscopy, Pergamon Press, New York, 1982, p. 233. 11 R. Schogl and H.P. Boehm, Carbon, 21 (1983) 345. 12 A. Proctor and P.M.A. Sherwood, Carbon, 21(1983153. 13 T. Takahagi and A. Ishitani, Carbon, 22 (1984) 43. 14 R.C. Engstrijm and V.A. Strasser, Anal. Chem., 56 (1984) 136. 15 G.E. Cabaniss, A.A. Diamantis, W.R. Murphy Jr., R.W. Linton and T.J. Meyer, J. Am. Chem. Sot., 107 (19851 1845. 16 F.A. Armstrong, P.A. Cox, H.A.O. Hill, B.N. Oliver and A.A. Williams, J. Chem. Sot. Chem. Commun., (1985) 1236. 17 F.A. Cotton and G. Wilkinson, Advanced Inorganic Chemistry (4th edn) Wiley, New York, 1980. 18 C.A. Koval, M.E. Ketterer and CM. Reidsema, J. Phys. Chem., 90 (1986) 4201. 19 N. Bjerrum, K. Dans. Vid. Sels., 7 (1926) 9. 20 M.T. Beck, Coord. Chem. Rev., 3 (1968) 91. 21 J.T. Denison and J.B. Ramsey, J. Am. Chem. Sot., 77 (1955) 2615.
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