On the Electron Transfer Reaction between Ferricytochrome c and Ferrohexacyanide in the pH Range 5 to 7*

SUMMARY The electron transfer kinetics between horse heart ferricytochrome c and ferrohexacyanide in the pH range 5 to 7 is essentially the same as the corresponding kinetics for the pH range 7 to 10. The equilibrium constant, computed from the ratio of rate constants is slightly under 300 for the range investigated. Spectrophotometrically (5 to 20 min after mixing), a somewhat different result emerged. The value of the equilibrium constant (with ferrohexacyanide in the numerator) increased about 2 times for a pH decrease from 7.0 to 5.0. A small minimum is indicated at pH 6.5. There is some similarity between this equilibrium behavior and the one found for the range above pH 7. If one accepts the previously established apparent pKH of 6.0 for ferricytochrome c, one arrives at a protonic dissociation for ferrocytochrome c of about 5.4. However, both of them should be considered upper limits. Lower limits are 5.0 for ferricytochrome c and 4 (or less) for ferrocytochrome c. The enthalpy change of the fast electron transfer process is in the range of 14 Cal per mole and shows practically no pH dependence. The differences between the kinetic and the spectrophotometric equilibrium constants are probably


ROSE MARIE ZABINSKI, I~ATHLEEN TATTI, AND GEORGE H. CZERLINSKI
Frm the Northwestern University Medical School, Chicago, Illinois 60611 SUMMARY The electron transfer kinetics between horse heart ferricytochrome c and ferrohexacyanide in the pH range 5 to 7 is essentially the same as the corresponding kinetics for the pH range 7 to 10. The equilibrium constant, computed from the ratio of rate constants is slightly under 300 for the range investigated.
Spectrophotometrically (5 to 20 min after mixing), a somewhat different result emerged. The value of the equilibrium constant (with ferrohexacyanide in the numerator) increased about 2 times for a pH decrease from 7.0 to 5.0. A small minimum is indicated at pH 6.5. There is some similarity between this equilibrium behavior and the one found for the range above pH 7. If one accepts the previously established apparent pKH of 6.0 for ferricytochrome c, one arrives at a protonic dissociation for ferrocytochrome c of about 5.4. However, both of them should be considered upper limits. Lower limits are 5.0 for ferricytochrome c and 4 (or less) for ferrocytochrome c. The enthalpy change of the fast electron transfer process is in the range of 14 Cal per mole and shows practically no pH dependence. The differences between the kinetic and the spectrophotometric equilibrium constants are probably due to the fact that slow structural rearrangements are coupled to the electron transfer.
Such steps also may be the reason for the fact that the measured rate constants are practically independent of pH. Various control experiments were conducted, to establish the constancy of the spectral characteristics of reduced and oxidized cytochrome c between pH 5 and 7 and in the wavelength range 520 to 555 nm. apparatus were branched so that they were fed into a Tektronix 549 storage oscilloscope and also into a Biomation 802 transient recorder.
The data from the Biomation 802 were subsequently transferred onto paper tape. This paper tape was submitted onto the disk of a CDC 6400 computer for further evaluation, using a nonlinear least squares program.
Parallel to the temperature jump experiments, the spectrum of the reaction mixture was taken on the Cary 14 recording spectrophotometer, using a cell of lo-mm path length, thermostatted at 28". Experimental points were taken at wavelengths 550 and 541 nm. The equilibrium data were evaluated, as described earlier (5).

RESULTS
The composition of the five solutions, used at pH 7, are summarized in Table I, which also contains the observed difference extinctions and relaxation time constants.
Similar experiments were carried out at pH 6.5, 6.0, 5.5, and 5.0. Fig. 1 shows the quotient of the inverse observed relaxation time over the analytical ferrohexacyanide concentration versus the quotient of the sum of the determined equilibrium concentrations of ferrocytochrome c and of ferrihexacyanide over the analytical concentration of ferrohexacyanide. The presentation becomes thereby directly comparable with the presentation of earlier data for the pH range above 7.0 ( Fig. 1 of Ref. 5). Only data for two pH values are shown; data for other pH values coincide with those for pH 6.5. The intercepts and slopes lead directly to the two bimolecular rate constants defined by: The symbols Fe", FerIr, and C" refer to ferro-and ferrihexacyanide and ferrocytochrome c; brackets around symbols denote equilibrium concentrations. If Fea" and CO"' represent the analytical concentrations of ferrohexacyanide and ferricytochrome c, originally mixed together, it is As under all experimental conditions: cIII c< Fe11 0 0 the original expression for the inverse relaxation time, may be simplified to give:
Calibration runs were conducted on ferrohexacyanide solutions, to determine the amount of ferrihexacyanide spectrophotometrically at 420 nm; although these calibration runs were extended over 5 hours, chemical relaxation experiments on specific solutions were always completed within 2 hours after mixing.
The concentration of ferrocytochrome c is determined spectrophotometrically, as described under "Experimental Procedure." The "kinetic" equilibrium constant is given by: The "spectrophotometric" equilibrium constant is defined by: The concentration of ferricytochrome c is determined as a differ- 1. Evaluation of data from temperature jump experiments. Only the results associated with two pH values are shown. The data for pH 5.5, 6.0, and 7.0 practically coincide with those at pH 6.5. The expression used for the independent variable in this figure contains the concentration of ferrihexacyanide separately from that of ferrocytochrome c. This separation is due to the fact that small amounts of ferrihexacyanide are produced in our system through the (indirect?) action of molecular oxygen upon ferrohexacyanide at these pH values. Successive experiments on the temperature jump apparatus with various solutions took time and made it necessary to correct for the additional amount of ferrihexacyanide which can no longer be neglected at low concentrations of initial cytochrome c concentrations.  The data are derived from intercepts and slopes of plots of the type shown in Fig. 1 for two pH values.  Table II. The kinetic results are presented in Table III with ADbsO representing the difference extinction at 550 nm, Feorx the total ferrohexacyanide concentration (8 mM), Co"' the total cytochrome c concentration, A~550 the derived difference extinction coefficient, and K, the derived equilibrium constant. Fig. 2 shows a plot of the left side of Equation 10 versus Co"'/ ADSSO. The intercept with the ordinate gives Ae550/K,, the intercept with the abscissa l/AebsO and the slope (At&2/K,. One obtains by several calculations Acr,50 = 2.07 X lo* M-~ cm-l, which is independent of pH, as may also be derived from the values in Table II. While K1.2 is essentially constant, K, changes distinctly with pH, as is best seen in Fig. 3. The value for K, reaches a mini- As mentioned earlier, the experimental data are evaluated by a program, using a nonlinear least squares subroutine and returning values for three parameters: the exponential decay time constant r (or ri), the factor ASi in front of the exponential term, and a constant A&.
Values of AS0 and AS, carry the unit millivolt and represent equilibrium signal changes observed at the output of the temperature jump apparatus.
The parameter values ASi may be algebraically connected to the cnthalpy change AH of the electron transfer step, utilizing dl nK 3H __=-(11) dT RT2 A variety of specific cases for evaluating cl In K = A 111 K = AK/K were discussed in a monograph (11). ,4 more condensed relation may be obtained by applying DeDonder's "extent of a reaction," as introduced by Eigen and DeMaeyer (12) and used for specific reactions by Thusius (13).
In zero approximation, one may consider the following relation between AS, and A 111 Kl,z: with the definitions : An = x qi with qi = aS/ac. (13)  1   (14) In the last two equations it is ci the equilibrium concentration of the ith component; pi becomes then the photometric conversion constant for the ith component.
In the system under consideration, summation proceeds from 1 to 4. Equation 14 becomes then for the system under consideration: As this is not the case in the presented experiments, vi becomes dependent upon concentration and one has to employ: 10 is the signal for 100% transmission, eZ is the extinction coefficient for the ith component; for simplicity ci = [C"] and c2 = [C"'] with e3 = e4 = 0 for 520 nm 5 X 2 555 nm. One obtains from the last equation for S = I: one obtains The AH values varied between 15.3 Cal per mole (at pH 6) and 11.0 Cal per mole (at pH 5) with standard errors varying between 10% (at pH 6) and 40% (at pI1 6.5). Although the average is 12.45 Cal per mole, this average considers equal weighting of the individual A1I values. If the error limits are properly considered, one arrives at a weighted average of 14.0 Cal per mole.

DISCUSSIOS
While the kinetic results from the chemical relaxation esperiments were anticipated, the associated equilibrium results from spectrophotometry were not. If we assume in very crude approximation that K,, changes with pH like a sigmoidal curve, one could get along with two apparent protonic dissociation constants, one each on the side of reduced and oxidized cytochrome c. The associated schematic is shown in Fig. 4A. The various protonated forms of cytochrome c are labeled, as introduced previously (7). The schematic leads directly to an expression for the pH-dependent equilibrium constant: -r ~2 1 + c= /K" with K& = H III [Fe " ' 1 [HC;'] The protonic concentration in this equation is written 2, which refers to buffered proton concentrations.
However, the buffering is weak enough so that addition of strong base or strong acid could produce a stepwisc pH change. Let us temporarily assume that the inflection point of a sigmoidal curve is reached at pH 5.0. The sigmoidal change then should flatten out near pH 4.0 with K,, increasing 3-fold over the value at $1 6.5. If one assumes K', = 300, ~K'rrr = 6.0, as derived earlier (7), one obtains for pK"rrr a value of 5.4. However, it is obvious from the experimental data that pK'rII < 6.0. Furthermore, the data show no evidence for sigmoidal shape, meaning pK"rrr < 5.4 (and most likely pK"rrr < 5.0). Aside from the upper limit for pK'rII (being 6.0), a lower limit could be derived from the data. The lower limit is directly obtained from the data under the assumption that pK"rrr 5 4.0. It is then pK'rII = 5.0. Further details could only be obtained, if the experiments would be extended to at least p1-I 4.0. Tlowever, earlier experiments on the absorption changes at 695 nm indicated (7) that the system starts to become unstable below pH 5.0. was decided to initiate an investigation of this deviation in a separate study (varying other independent parameters of the system).
With reference to the kinetic experiments, the scheme of Fig.  4A would have to be extended to the symmetric scheme of Fig.  4B, where another type of subscripting is indicated for the various forms of cytochrome c, to the extent of ignoring any explicit indication of protonation. Different subscripting is necessary, as the quantit,ative connection to the schematic of Fig. 4A can only be partially established.
Reasonably firm is only one relation, namely (7) : Similarly, one may write p";,, = p"; + ~(1 + k;/k;' Furthermore, the two cycles allow the relations: These relations are equilibrium relations and should be fulfilled for the condition of the photometrically determined equilibrium constant. If one assumes constant electron transfer, we may assume K', = K"o. The pH dependence of the over-all equilibrium then is given by pK'H (with PK"~ not effective in the experimental range of pH 5 to 7). The data require K"'. >> K",,. However, as pK'H cannot be determined from the experiments, it is not appropriate to compute [c~ "'] and correct the total ferricytochrome c concentration.
It is most likely that PK'~ < 6.7 as most likely pK'rrr < 6.0. Using flow calorimetry, Watt and Sturtevant (14) determined the enthalpy change accompanying the oxidation of ferrocytochrome c by ferrihexacyanide in the pH range 6 to 11 at 25". They obtained about 14 Cal per mole at pH 6 and converged toward 28 Cal per mole at pH 11. Their sigmoidal pH curve is associated with an inflection point at 9.3. They ascribe the additional enthalpy change at high pH to a conformational rearrangement.
It is quite interesting that we obtained the same constant enthalpy change of 14 Cal per mole meaning that the structural and protonic dissociations do not contribute any essential amount to the enthalpy change (their individual enthalpy changes may compensate each other).
The opening of the heme crevice of ferricytochrome c (as revealed by the disappearance of the 695~nm band) was recently investigated in the presence of the denaturants methanol, isopropyl alcohol and urea (at comparatively high concentrations) (15). Of particular interest is the pH dependence of the enthalpy change at around 25", derived from an extrapolation to zero inhibitor concentration.
A minimum of 7.5 Cal per mole is obtained at pH 6 with 16 Cal per mole at pH 5, 32 Cal per mole at pH 7 and 42 Cal per mole at pH 8. Although only four pH values were investigated, a minimum in the enthalpy change was observed at the pH value where our spectrophotometric equilibrium constant showed a maximum.
The rate of reduction of ferricytochrome c by Chromium(I1) ion was investigated in the pH range 1 to 7, revealing a maximum rate (k = 115 x lo3 M-l s-i) at pH 3.7 (16). Two pKH values are considered to be involved, one at (or below) 3.4, the other one at (or above) 4.0. Protonation (or replacement) of the ordinary ligands of the heme iron are presumed to be involved with these pKH values. In connection with the discussion of the scheme of Fig. 4A it is unlikely that the described constants pK'rIl and pK"rrr relate in any way to these results.
We have to assume an additional protonic dissociation in the measurements of a reduction with Chromium(I1) ion. In this connection it may be pointed out that the rate constant kz shows a significant increase at pH 5.0, compared to the values at higher pH. This rate constant may be expected to increase further until pH 4, although the values are expected to be different from those in the presence of chloride ion.
As far as the earlier experiments of Brandt et al. (5) are concerned, we obtained essentially the same rate constants for the electron transfer.
However, it became necessary to conduct experiments much more closely spaced along the pH scale than done by Brandt et al. This need derives from the fact that the coupling-in of protonic dissociations and monomolecular structural interconversions is more complex for the pH range 5 to 7 than for the pH range 7 to 10. As one would expect, the previously measured slow structural rearrangements (7) do not show up in the electron transfer kinetics, but are presumably contained in the spectrophotometric equilibrium constant K,,, determined a few minutes after mixing of the solutions.