Reduction of cobalticytochrome c by dithionite.

The kinetics of reduction of cobalticytochrome c (““Cyt c+) by dithionite has been measured spectrophotometrically using an excess of the reducing agent. The reaction is biphasic. The observed first order rate constant of the rapid phase is temperature-dependent and is attributed to reduction by the monomeric SOa; whereas the slower process is that of the dimeric SzOda-. From the temperature dependent dissociation constants and concentration of dithionite, the second order rate constants for cOCyt c+ + SOa: (AZ) and for ‘%yt c+ + SSO~%(ka) were obtained. The effect of ionic strength @ = 0.0726 to 2.01 M) on Rs has been determined; the dependence gives an estimate for the effective active site charge of +1.7 for %yt c+. Measurements made from pH 6 to 11 showed both ks and Rs have maximum values at pH 9.3 f 0.1; the dissociation equilibrium of dithionite is pH-independent from 4 to 12. This pH effect is believed to be related to the reported pK = 9.3 transition for ferricytochrome c (“Cyt c+). Reactions were studied from 20”-36°C. The observed kl has an activation energy of 16.6 f 0.5 kcalomol-‘. After the contribution from the activation energy for the dissociation of dithionite is subtracted, the activation energy for ks is about 6 kcal l mol-‘. These results and those for the native cytochrome c, “Cyt c+ + SOa; (k’z) and ‘Tyt c+ + L&O? (k’s) were compared with the theory of vibronically coupled electron tunneling using the same two vibronic coupling parameters previously applied to some twenty other electron transfer reactions involving biological molecules in solution. Good agreements were found between theory and experiment except for R’s. The experimental rate constants all in M-’ 8-l (25”C, pH 8 to 9.3, p 0.2) are: b = 6.6 x lo’, ks = 2.6, k’, = 3.9 x 107, k’a = 1.6 x 10’; the theoretical values are ks = 2.9 x lOa, ka = 6.6, k’z * 4.4 x lo’, and A’3 = 3.2 X 10’. For the SO2; reduction of cOCyt c+, the experimental activation parameters are AH+ = 6 kcal*mol-‘, AS+ = -22 e.u. to be compared with theoretical values of AH* = 6.7 kcal*mol-’ and ASS = -24 e.u.

A theory of electron transfer via vibronicahy coupled tunneling has been formulated by Hopfield (1) and Jortner (2) to interpret the results of light-induced oxidation of cytochrome in the photosynthetic bacterium Cizromatium (3,4). Detailed studies (5,6) showed that the rate of electron transfer from * This investigation was partly supported by Research Grant HL-14270 from the National Institutes of Health and the Materials Research Laboratory of the University of Massachusetts. The costs of publication of this article were defrayed in part by the payment of page charges. This article must therefore be hereby marked "advertisement" in accordance with 18 U.S.C. Section 1734 solely to indicate this fact.
*To whom correspondence and reprint requests should be addressed.
4.5 to 100 K is constant at 3 x 10' s-'; above that temperature the rate constant increases to 3 X ld s-' at 300 K with an apparent activation energy of about 3.3 kcal.mol-'. These results were quantitatively reproduced by theories with some judicious choice of parameters to be detailed below. We have been interested in extending the theories to electron transfer of biological molecuIes in solution. The rate constants for the 'Cyt c" oxidation of '"Cyt c (7), the oxidations of '"Cyt c by oxygen and by Fe(EDTA-), and the reduction of methemoglobin by ""Cyt c catalyzed by mediators (8) have been determined. The observed rate constants and enthalpies and entropies of activation agree well with theoretical values using known midpoint oxidation-reduction potentials, distances of closest approach from x-ray structures or molecular models, and a reasonable and consistent set of vibronic parameters. Similar agreements were also found (9)  of oxidized cytochrome oxidase by its natural substrate FeCyt c+ (23-25) and the reaction of reduced cytochrome oxidase with oxygen (26,27). The purpose of this work is to add to this extensive list of comparison between theory and experiment the reduction of '"Cyt c" by dithionite.
Sodium dithionite is the most versatile, powerful, and widely used reducing agent available to biochemists.
It is almost invariably employed in the preparation of the reduced state of purified enzymes, electron transfer proteins, hemoglobins, and cofactors. It is largely through the work of Palmer and co-workers (26,29) that the mode of action of dithionite was elucidated. However, their experiments covered rather limited ranges of pH and temperature and did not include the effect of ionic strength. One purpose of our work is to remedy this situation. Finally, the rate constants for the reduction of FeCyt c+ by dithionite have been reported (30). A comparison of the dithiomte reduction of FeCyt c+ and of ""Cyt c+ from both experimental and theoretical standpoints is yet another objective of our present work. Analysis of Kinetic Data-The reaction of c*Cyt c+ with dithionite as it was for "Cyt c+ (30) is clearly biphasic as illustrated by Fig. 1. This is due to the equilibrium (29,33) s204*-2 2 schr (1) Both SZOZ-and SO27 act as reducing agents, the monomer being the stronger of the two (see below).
soz-+ ""Cyt c+ 2 so* + ""Cyt c (2) s*o4*-+ ""Cyt c+ % &on-+ ""Cyt c s*o4-+ c"cyt c+ 2 2so.J + ""Cyt c (4) The concentration of dithionite is 40-to 80-fold excess of c'Cyt c+. The observed rate constants for Reactions 2 and 3 are both first order. The resolution of the kinetic data is usually clean (Fig. 2). The observed pseudo-first order rate constants are related to the true second order rate constants by    The observed first order rate constants are given in columns 2 and 3 of Table I.  The kinetic   results for reactions from pH 6 to 11 are summarized in Table II; the observed rate constants being contained in columns 2 and 3. The effect of ionic strength on the rate of reduction of "'Cyt c* by dithionite is summarized in Table III. In these reactions, the rapid phase is only a small fraction of the total reaction and is not well resolved. As it will be shown below, increase of ionic strength lowers the equilibrium constant for the dissociation of SZO~~-and the monomer concentration.
Dissociation Equilibria of Dithionite-Burlamacchi et al. (33) measured the dissociation constants of &04'-from 25"-60°C. Lambeth and Palmer (29) obtained Kl values which are affected by both pH and ionic strength changes. We have determined separately the effect of pH and ~1 on the dissociation constants. At a given temperature, the EPR spectrum of SO27 is a symmetrical singlet (34-36). The linewidth is 1.8 G at 25°C independent of pH and CL. Increase of ionic strength decreases the dissociation as shown in Table IV. On the other hand, the equilibrium constant is unaffected by pH changes from 4.1 to 14.0 as evidenced by the constant EPR intensity of SOZ' (Table V).

DISCUSSION
Biphasic Kinetics-The kinetics of reduction of ""Cyt c' by dithionite is biphasic. This may be due to the presence of either two protein species or two reducing entities. The former is highly unlikely because other oxidation-reduction reactions of cobalt, cytochrome c are monophasic, i.e. oxidation of '"Cyt c by FeCyt c+ (7), by methemoglobin mediated by phenazine methosulfate (8), by oxygen and by Fe(EDTA-), unless at neutral pH '"Cyt c+ exists in two conformation and %yt c has two conformational states. On the other hand, that SZO~'is in equilibrium with SOZ: is well documented (29, 33-36). The observed dependences of rates of reduction upon pH and p can be readily accounted by their effects on the equilibria. In the above mentioned oxidation reactions of ""Cyt c, the rates are either unaffected by or slightly dependent on ionic strength. As it will be shown below, the relative rates of the f&t and the slow phase are exactly to be expected from the different reduction potentials of SzO4'-and SOZ:. Finally, the biphasic reduction of FeCyt c by dithionite has also been attributed to the presence of two reducing species (29). Dissociation Equilibria of Dithionite-Equilibrium Reaction 1 does not involve proton, and should not be affected by pH as observed over a wide pH range. Dithionite appears to be stable under careful anaerobic conditions even down to pH 4, but decomposes rapidly at pH d 2. It seems that the often mentioned instability of dithionite at acidic pH may be prevented at least down to pH 4 under certain conditions. The significant dependence of [S02T] and K on ionic strength, Figs. 3 and 4, respectively, can be readily understood. The dissociation reaction of S,O,"-should not be significantly affected by p whereas the reverse combination of SOZ; would be. If we designate the rate constants and equilibrium constants at c and 00 ionic strength with the appropriate superscript, then In KI" = In k," -In k?l (7) But according to the Debye-Hiickel treatment (37)   03) and In kj" = In kl" In Equation  The tangent of the curve of In K versus fi (Fig. 4) has the slope given by the quantity in the parenthesis of Equation 10. At fi= 0.5, the tangent gives 2 = -1.05 f 0.1 which is the correct value. The charges obtained at higher ionic strengths are less satisfactory; the values for 2 are -1.2 f 0.1 and -1.3 f 0.1 at fief 1.0 and 1.5, respectively. This is expected since the Debye-Huckel treatment is inappropriate for high ionic strength solutions.
Kinetics of Dithionite Reduction of "Cyt c'-The rate constants for the rapid phase are temperature-dependent whereas those for the slow phase are not (Table I). Fig. 5 is the Arrhenius plot of the first order rate constant kzDh, the slope gives an apparent activation energy of 16.6 +-0.5 kcal.mol-'. Since the rapid phase is the reduction of c'Cyt c+ by the monomeric SO*:, then according to Equation 5, AEzeh" = AZ& + +AHi where AH1 is the enthalpy change for the dissociation of dithionite and LL!& is the activation energy for Reaction 2. The values of AHI is found to be (33) 21.3 f 0.4 kcal . mol-'. Therefore, AEx is about 6 kcal . mol-'. The values of rate constants k2 were calculated with Equation 5 and given in column 5 of Table I. Column 6 of the table  lists values of ka calculated with Equation 6. The Arrhenius plot for kz ( Fig. 6) gives an activation energy Es of 6 rt 1 kcal.mol-', in agreement with the above estimate.
The results of experiments in Table II to show the effect of pH on the rate of dithionite reduction of ""Cyt c+ were obtained with various buffers given in the experimental section. These buffers have different ionic strengths. To calculate kp from the observed rate constants of the rapid phase, the ,.,U 3 value of K1 for a particular ionic strength was obtained from the data in Fig. 4. The variation of kz and ka with pH are shown in Fig. 7. Both reactions have maximum rates at about pH 9.3 + 0.1 which are about 2 to 3 times faster than the rates at neutral pH. The self-exchange reaction rate of native cytochrome c is fastest at about pH 9.8 which is about 4 times greater than the rates at neutral pH (13). In this case, the pH effect was attributed to the isoelectric point for FeCyt c which is at about pH 10. It is said that the protein molecules are electrically neutral, whereas at other pH values the like charged molecules repel each other. This interpretation is inapplicable to the dithionite reduction of ""Cyt c+ where the reacting molecules are oppositely charged. Also, reactions involving the reduced state of cobalt cytochrome c have maximum rates at about pH 7.0. This includes the autoxidation of ""Cyt c2 and the mediated reduction of methemoglobin by c*Cyt c (8). It seems, therefore, the pH effect on k2 and ka may be related to some ionizable group in the oxidized molecule.
Optical spectroscopic titrations of FeCyt c+ (39), particularly in the 695 nm region, have shown a heme-linked protonic ionization with a pK of about 9.3. There are also changes in the thermodynamic properties at this pH (40,41). On the other hand, NMR experiments have shown that the contactshifted proton resonance of the methyl group of Met-80 disappears with a pK of about 9 (42) or as the azide '%yt c+ complex is formed (43). Finally, the EPR g values of '%yt c+ change with increasing pH, again with a pK of about 9, and the EPR spectrum of the major species at alkaline pH is consistent with methionine having been replaced by an -NH2 function (44). This ligand change does not alter the spin multiplicity of FeCyt c+ according to EPR and optical criteria.
It has been postulated (28,42) that the major species of FeCyt c+ formed in the pK 9.3 transition is coordinated in the camino group of Lys-79.
In contrast of "Cyt c*, the stable species of both FeCyt c and "Cyt c has Met-80 as the sixth ligand in the pH range of 4 to 12. Neither the optical absorption spectrum (39,45) nor the contact-shiid methyl proton resonance of Met-80 (42) is sensitive to pH values less than 12. In the case of ""Cyt c, EPR spectra (32,46) showed that between pH 4 and 11, '"Cyt c has Met-80 and His-18 as the axial ligands. Above pH 11, '%yt c is five-coordinated having only His-18 as the axial ligand; below pH 4, '"Cyt c is also five-coordinated but has Met-80 as the axial ligand. Lambeth et al. (28) proposed that below pH 9, reduction of FeCyt c+ occurs by This species cannot be reduced by either ascorbate (47,48) or ferrocyanide (49). Once reduced, further substitution occurs with Met-80 replacing Lys-79. If this interpretation is accepted for the reduction of &Cyt c, then our results show that the species with coordinated Lys-79 is more easily reduced than that having coordinated Met-80. The fact that increase of pH from 6 to 9.3 increases kz and ks by only 2-to 3-fold was somewhat surprising. According to Equations 11 and 12, the midpoint potential at pH 9.3 should be 0.39 V more negative than that at pH 6. The main driving force in the theory of vibronically coupled electron tunneling is the potential difference between the electron donor and acceptor molecules (see below). It is estimated that dithionite reduction of %Cyt c' should be faster at pH 9.2 by some 30fold over that at pH 6.0 based on the difference in the oxidation-reduction potential of dithionite at these pH values. The oxidation-reduction potential of native cytochrome c is insensitive to pH (50) and the same may be assumed for cobalt cytochrome c. A possible explanation is that the rate-determining step is Reactions 2 and 3, and that the subsequent reactions of SO2 and SrO, with OH-are rapid.
The effect of ionic strength on the rate of Reaction 3 is shown as a plot of kz versus G (Fig. 8). The plot is markedly curved. To calculate the effective active site charge for '"Cyt c+, Equation 8 has to be rewritten to take into account that the reacting molecules are not the same. The expression is: 1 (a&) (16) where subscript 1 (2) refers to dithionite ("Cyt c'). If one takes the slope at t/F = 0.3 ra112 of Fig. 8, i.e. low ionic strength at which Equation 16 is more apt to be valid, and using & = -2, RI = 5 A, and RZ = 17 A (51), a value of 22 = +1.7 is obtained for the protein molecule.
That the effective active site charge of a protein molecule is a small fraction of its full charge which in the case of 'Y?yt c' would be +7.5 from the sequence data (51) is often noted.  Table III. The effective active site charge for native cytochrome c is +1.7 for the reduction of '"Cyt c+ with Fe(EDTA)2-(15); it is +1.3 for the self-exchange reaction of FeCyt c/"Cyt c+ (11). The effective active site charge for cobalt cytochromes c is more variable depending upon the reaction. The charge for the molecule is about zero for its oxidation by "Cyt c+ (7), +0.45 for its oxidation by Fe(EDTA)-, and +1.2 for its reduction of methemoglobin catalyzed by phenaxine methosulfate (8). Based on the charge for o'Cyt c' of +1.7 in dithionite reduction, one may conclude that dithionite approaches cobalticytochrome c at a portion of the protein surface similar to that involved in the oxidation-reduction reactions of the native cytochrome c.
Comparison of the Dithionite Reductions of "Cyt c" and '"Cyt c' with Theory-The rates of dithionite reduction of FeCyt c+ are much faster than the corresponding reactions with "Cyt c. The rate constants at pH 8.0 for 32yt c+ + so27 J.+cyt c + so* and F'Cyt c+ + s,o,2-3 *Y?yt c + s*o,- are k'2 = 3.88 X 10' M-' s-l and k's = 1.5 X 10' M-' s-l (29). At comparable pH and CL, k2 -5.55 X 10' M-' 8-l and ks = 1.77 M-' s-l. Therefore, for either reaction of SOZ: or S2012-, the rate is about 7.5 x 10' faster for the native protein. We will now compare these results with theory. Hopfield formulated the theory of vibronica.Uy coupled electron tunneling based on parallelism to the theory of resonance energy transfer (52-54). The electron is initially around site a; the final state will have the electron localized around site b. The rate of electron transfer from a to b is where Tcrb is the tunneling matrix element or the electron exchange matrix element which is a fimction of the distance R separating a and b, and D, (E) and D'b (E) are the electron removal spectral distribution and electron insertion spectrum, respectively, both being Gaussian line shape functions. When the electron is localixed at site a(b), the nuclear coordinate is q. (qa) with k, (kb) as the curvature for the wave function.

Reduction of %yt c+ by Dithionite
Assuming the k values to be the same for the wave functions with and without the electron, and using the classical probability distribution, Hopfleld derived the rate of electron transfer between two fixed sites as k:b = (2+) 1 Tczdr) 1' (2d-"' exp  where c? ic (k,q,2/2)knT. coth (TJ2T) and A = ks,q,z2/2 + k&/2 In equation 21, kB is the Boltxmann's constant, T is temperature in degree Kelvin, kBT,(kBT& is equal to tiw,(fiwb), the energy separation between the nuclear harmonic oscillator states for site a (b), and A is the vibronic coupling parameter. Jortner (2) formulated a complete quantum mechanical treatment of electron transfer incorporating the effect of both low frequency medium modes (10 to 100 cm-') and high frequency molecular modes (300 to 3000 cm-l). The nonadiabatic multiphonon electron transfer process occurs between the vibronic levels where $ is the electronic wave function and X is the nuclear wave function. The transition probability is given by the perturbation theory to be k!$ = fi-'l Tab( Therefore, the theories of Hopfield and Jortner are equivalent at the high temperature limit with A = Sfi < w > aside from a difference of a factor of l/G Hopfield approximated the tunneling matrix element as The characteristic temperatures T,, and Tb were assumed to be the same (350 K) which is about twice the temperature marking the transition from the temperature-independent to thermally activated electron transfers.
The unimolecular expressions 25 and 27 may be extended to describe bimolecular electron transfers. When the relative location of the donor and acceptor varies with time, the rate of transfer can be calculated by suitably averaging the rate as a function of distance over the probability distribution of geometries. If one neglects naively a particular geometry for electron transfer, then the bimolecular rate can be expressed as k% = 6.023 X 10e4 kL(27rk' r/R,) where h is the characteristic decay constant defined as %(1/0.72) = 0.7 A, and for hemeproteins, r is the distance of closest approach between the carbon atoms on the exposed edge of the hemes of the two protein molecules. The activation parameters can be shown to be AH+ = (E,, -E,, -A)=/4A -3RT/2 AS$=Rln [ 2.3t3;C2 (y) (&)1'21 Td912] -W2 The physical significance of some of the parameters in Equations 19 to 31 is seen with the aid of Fig. 9. Electron transfer occurs from one vibronic state of a to another vibronic state of b indicated by the arrow. The form of the vibrations is assumed to be simply that of a harmonic oscillator. Therefore, %kq2 in Equation 22 is just the vibrational potential energy with k and q being the force constant and displacement from equilibrium nuclear position, respectively. The vibronic parameter A is then the sum of the vibrational potential energies of states u and b.
Although A appears to be a curve-fitting parameter as its value was first estimated by Hopfield (1) and Jortner (2)  The results of calculation using Equations 29 to 31 are summarized in Table VI. In row 2, the vibronic parameters are the same as used in previous applications of the theory (1,(7)(8)(9)55), which is 1 eV for reactions of iron hemoproteins and 1.5 eV for reactions involving cobalt-containing molecules. The component distance of closest approach is 2 A for the cytochrome c since its heme edge is situated by this distance from the surface of the molecule (51); rh is from molecular models. The potentials in row 4 of the table has been corrected to pH 8 and for one-electron processes. N, is the number of n-electrons of the porphyrin system, and Nh are those nonbonded sp hybrid electrons of the reductants. The calculated and experimental rate constants for SOz: reduction (rows 7 and 8, columns 3 and 5) are in excellent agreement. The same can be said for the activation enthalpies and entropies for the SO27 reduction of ""Cyt c+. No experimental activation parameters have been reported for the corresponding reaction for FeCyt c'. The agreement between theory and experiment for the reactions involving Sz04'-is within a factor of 2.6. It is only for the Sz04'-reduction of FeCyt c+, that theory and experimental rate constants are in poor agreement differing by some 20-fold.
The vibronic coupling parameters for oxidation-reduction reactions involving cobalt ions are all significantly greater than those of iron complexes and enzymes. According to the model given above, cobalt complexes probably have larger force constants than iron complexes for the same molecular mode. The infrared spectra band assignments for metal complexes is still a developing field. However, there seems to be supporting evidences for cobalt complexes having higher band fksquencies than the corresponding iron complexes. Experiments to detect charge transfer band of cobalt cytochrome c complexes are underway.
In conclusion, the vibronicahy coupled electron tunneling theory seems to constitute a good model for the description of electron transfers involving biological molecules in solution. Further studies of electron transfer reactions of proteins are continued in our laboratories.