J . Phys. Chem. 1986, 90, 3795-3800 provided allows the results to be assigned to a unique value of the parameters (e.g., X = - A G O ) . Conversely, knowledge of the free energy dependence of the rate at a single temperature also provides data that can be contained by the theory. It is only when the temperature dependence of the reaction is known over a fairly substantial free energy range that the weakness of the simple model is revealed. This is largely because of the number of parameters in the theory which allow it to “fit anything” unless constrained by measurements that vary several experimental parameters. Again, it is evident that the data presented here can be fit by the inclusion of more and not unreasonable theoretical variables, but again it will require the measurement of the rate with the modification of additional experimental variables to confirm or disprove the many facets of electron-transfer theories.
Note Added in Proof. Clayton (Biochim. Biophys. Acta 1978, 255, 255-264) has shown that the rate of electron transfer from
3795
QA- to (BChl)*+ in dehydrated reaction center protein films is essentially independent of temperature between 300 and 80 K and that this is similar in rate to that exhibited by hydrated reaction center protein at cryogenic temperatures. Thus, water molecules may play a role in modulating electron-transfer rates in reaction center protein, and modification of this interaction with temperature may be the source of the observed temperature dependence of the rate.
Acknowledgment. We gratefully acknowledge valuable discussions with John R. Miller and Don DeVault regarding theory, and the technical guidance of Russell L. LoBrutto. We are happy to acknowledge collaborators Roger C. Prince (quinone electrochemistry), J. Malcolm Bruce and Paul Lloyd-William (synthesis and purification of quinones), and Barry S. Braun (protein isolation and purification and HPLC). This work was supported by NSF PCM 82-09292 and by DOE DE-ACO2-80-ER 10590.
Coupling of Protein Modes to Electron Transfer in Bacterial Photosynthesis Mordechai Bixon and Joshua Jortner* School of Chemistry, Tel Aviv University, 69978 Tel Aviv, Israel (Received: January 21, 1986; In Final Form: April 9. 1986)
This paper explores the contribution of the protein medium phonon modes to the Franck-Condon nuclear overlap factors, which determine the rates of electron-transfer (ET) reactions in the reaction centers of photosynthetic bacteria. From the analysis of the temperature dependence and some free energy relationships for the quinone reduction reaction and for the back recombination between the quinone and the primary donor, it is concluded that the average vibrational frequency involved in these two activationless ET processes is hw = 100 cm-’, whereupon the dominant contribution to the electron-phonon coupling originates from the exterior protein modes while the contribution of intramolecular vibrations of the prosthetic groups is minor. It is proposed that the unique temperature dependence of the Chance-DeVault cytochrome oxidation reaction in Chromatium is not due to a transition from low-temperature nuclear tunneling to a high-temperature activated ET, but rather originates from two parallel ET processes from two distinct low-potential cytochromes to the dimer cation. These involve a slow activationless process, which dominates at low temperatures ( T 5 120 K) and an activated process, which is practically exclusive at high temperatures. This conjecture provides plausible nuclear and electronic coupling terms for the two cytochrome oxidation reactions, which are in full accord with the quantitative features of other ET processes in the reaction center.
I. Introduction The Marcus theory of electron transfer (ET) advanced in 19561-5constitutes the first quantitative microscopic description of a chemical reaction in solution. At about the same time, Kubo and Toyozawa6 advanced a quantum mechanical theory of nonadiabatic multiphonon processes, which is applicable for the description of a broad spectrum of intermolecular reactions in condensed phases, e.g., thermal ionization in semiconductors,6 electron-hole recombination in crystalline and amorphous solids,’,* small polaron motion? and intermolecular electronic energy transfer between molecules and ions in solids and glasses.lOJ1 The Marcus, R. A. J. Chem. Phys. 1956, 24, 966. Marcus, R. A. J. Chem. Phys. 1957, 26, 867. Marcus, R. A. Discuss. Faraday SOC.1960, 29, 31. Marcus, R. A. J. Chem. Phys. 1%5,43, 679. ( 5 ) Marcus, R. A. Annu. Rev. Phys. Chem. 1964, 15, 155. (6) Kubo, R.; Toyozawa, Y . Prog. Theor. Phys. 1966, 13, 160. (7) Henry, C. H.; Lang, D. V. Phys. Rev. B Solid State 1977,15,989. ( 8 ) Mott, N. F.; Davis, E. A.; Street, R. A. Philos. Mag. 1975, 32, 961. (9) Holstein, T. Ann. Phys. (Leipzig) 1959, 8, 343. (10) Forster, T. Natunvissenschaften 1946, 33, 166. (11) Dexter, D. L. J. Chem. Phys. 1953, 21, 836. (1) (2) (3) (4)
0022-3654/86/2090-3795$01 S O I O
nonadiabatic version of the Marcus ET theory’-5 corresponds to the high-temperature limit of a multiphonon process,6 where electron-phonon coupling involves the low-frequency optical phonon modes of the dielectric medium. The connection between the classical description of E T in solution and the nonadiabatic multiphonon theory was established by Levich and Dogonadze.IZ Subsequent extensions of the ET theory during the 1970~’~-’’ focused on the contribution of high-frequency molecular modes to the electron-phonon coupling, which is amenable to a quantum mechanical treatment. From the point of view of general methodology, the description of ET processes in solution, glasses, and solids constitutes the extension of a particular corner of the radiationless transitions theory. The ET process corresponds to a radiationless transition in a “supermolecule” consisting of the (12) Levich, V. G. Physical Chemistry: An Advanced Treatise; Eyring, H., Henderson, D., Jost, W., Eds.; Academic: New York, 1970; Vol. 9B. (13) Kestner, N. R.; Logan, J.; Jortner, J. J . Phys. Chem. 1974, 78, 2148. (14) Dogonadze, R. R.; Kuznetsov, A. M.; Vorotyntsev, M. A. Phys. Status Solidi B 1972, 54, 125; 1972, 54, 425. (15) Van Duyne, R.; Fischer, S. Chem. Phys. 1974, 5 , 183. (16) Efrima, S.; Bixon, M. Chem. Phys. Lett. 1974, 25, 34. Chem. Phys.
1976, 13, 447. (17) Ulstrup, J.; Jortner, J. J . Chem. Phys. 1975, 63, 4358.
0 1986 American Chemical Societv
3796 The Journal of Physical Chemistry, Vol. 90, No. 16, 1986 donor-acceptor pair together with the entire medium.18 ET in biological systems is of considerable interest, as both photosynthesis and oxidative phosphorilation involve a sequence of ET reactions. The quantitative understanding of these processes is central to the establishment of a conceptual framework for this important aspect of efficient bioenergetics. In bacterial photosynthesis, the processes involved in charge separation are’9-22
hv
antenna (BChl), (BChl),*(BChl)(Bph)Q (BChl)2+(BChl)( Bph)-Q ferrocytochrome c
antenna*
antenna’
(1.1)
(BChl)2*
(BChl),+(BChl)(Bph)-Q
(1.3)
(BChl) 2’( BChl)( Bph)Q-
(1.4)
+ (BChl)2+
ferricytochrome c
+ (BChl),
(1.5)
In addition, the back charge recombination p r o c e ~ s ~ ~ - ~ ’ (BChl)2+(BChl)( Bph)Q-
---+
(BChl)2( BChl) (Bph)Q
(1.6)
which occurs in the absence of both cytochrome c and a secondary quinone, is of considerable mechanistic interest. Here, (BChl)2 is the chlorophyl dimer, (BChl) is the auxiliary bacteriochlorophyl, (Bph) is the bacteriophenophytin, and Q is a quinone. The reaction center (RC) of photosynthetic bacteria constitutes a remarkable microscopic.electronic device, as the sequence of the ET processes 1.3-1.5 results in electron-hole charge separation of about 30 A at the opposite sides of the membrane, which provides a driving force for useful biological chemistry. In this paper we shall focus on some aspects of the interrelationship between structure and ET dynamics in photosynthetic bacteria. The recent structural data for the RC of Rps Viridis28resulted in extensive information regarding the relative spectral and orientational arrangement of the pigments, which are involved in the primary charge separation events, reactions 1.2-1.5, in the RC. The “intermolecular engineering” of the prosthetic groups provides a central structural principle for the control of the highly efficient ET within the RC. A supplementary environmental control p r i n ~ i p l e * ~of. ~the ~ function of the R C involves the protein medium, which affects the ET dynamics by (at least) two mechanisms: (1) electrostatic stabilization of ion-pair states and (2) electron-phonon coupling with the medium modes. Mechanism 1 is of considerable importance to ensure the gross unidirectionality of charge separation across a single branch in the RC.29,30This paper is devoted to mechanism (2), exploring the role and implications of the coupling of the prosthetic groups and their ions with the polar modes of the protein medium. The contributions of the exterior protein modes to the nuclear Franck-Condon factors, which determine (18) Bixon, M.; Jortner, J. Discuss. Faraday SOC.1982, 74, 17. (19) Okamura, M. Y.; Feher, G.; Nelson, N . In Photosynthesis Energy Conversion by Plants and Bacteria: Govindjee, Ed.; Academic: New York, 1982; VOI. I, p 195. (20) Parson, W. W.; Ke, B. In Photosynthesis Energy Conversion by Plants and Bacteria; Govindjee, Ed.; Academic: New York, 1982; Vol. 1, p 331. (21) Hoff, A. J. In Light Reaction Path of Photosynthesis; Fong, F. K., Ed.; Springer-Verlag: Berlin, 1982; p 80. (22) Antennas and Reaction Centres of Photosynthetic Bacteria; Michel-Beyerle, M. E.,Ed.; Springer-Verlag: Berlin, 1985; in press. (23) Parson, W. W. Biochim. Biophys. Acta 1967, 153, 248. (24) Loach, R. A,; Kung, M.; Hales, B. J. Ann. N.Y. Acad. Sci. 1975,244, 291. (25) Mar, T.; Vadeboncoeur, C.; Gingras, G. Biochim. Biophys. Acta. 1983, 724, 317. (26) Debus, R. J.; Feher, G.; Okamura, M. Y. Biochemistry 1985, 24, 2488. (27) Feher, G.; Okamura, M. Y.; Kleinfeld, D. In Proceedings of Philadelphia Conference on Protein Structure; in press. (28) Deisenhofer, J.; Epp, 0.:Miki, K.; Huber, R.; Michel, R. J. Mol. Biol. 1984, 180, 385. (29) Bixon, M.; Jortner, J.; Michel-Beyerle, M. E.; Fischer, S . , to be published. (30) Jortner, J.; Bixon, M. In Comments in Cellular Biophysics; in press.
Bixon and Jortner the ET rates of reactions 1.3-1.6, bear a close conceptual analogy to the optical phonon modes of a polar medium, which play a dominant role in the Marcus theory of ET between ions in solution. 11. Electron Transfer in the Reaction Center
The nonadiabatic multiphonon ET rate constant, k , can be expressed in the well-known
k = (27r/h) l v 2 F
(11.1)
V is the two-center, one-electron e ~ c h a n g e ’ ~ -(or ~ ’ superex-~~ ~ h a n g e ~electronic ~ - ~ ~ ) interaction term, which manifests the implications of “intermolecular engineering”, i.e., the spatial spacing and orientation of the donor and acceptor centers. F is the thermally averaged Franck-Condon nuclear overlap factor. This nuclear contribution arises from the modification of the nuclear vibrational states of the “supermolecule”, involving the donoracceptor pair together with the medium by the change in the electronic states. These (1) The changes in the equilibrium configurations Aq, and frequencies (w,’ and w”, in the initial and final states, respectively) of the exterior medium modes, which are characterized by the coordinates q,,,. These are specified by the medium reorganization energy E,, which is given by (11.2) where rn, is the mass of the particular medium mode. (2) The changes in the intramolecular vibrational equilibrium configurations Aqc and the frequencies ( u l and u/ for the initial and final states, respectively) are specified by the coordinates q, of the donor and acceptor centers. These are specified in terms of the intramolecular rearrangement energy, E,, which for the simple case of equal frequency (u: = u:‘) is given by (11.3)
where m, is the mass of particular intramolecular modes. The total nuclear reorganization, E,, energy is E, = E,
+ E,
(11.4)
For the case of ET between ions in solution524and between organic molecules held by rigid the dominating contribution to the nuclear term F originates from the coupling to medium modes, Le., E,/Ec > 1, although both the E, and E, terms have to be incorporated for a quantitative description of the ET dynamic~.~~ What are the relative contributions of the medium and the intramolecular reorganization energies in the ET rates in the RC? Very little is known concerning the coupling of the electronic states of the prosthetic groups and their ions to the low-frequency polar modes of the protein medium. The Chance-DeVault cytochrome oxidation, reaction was analyzed31~32~44-46 in terms of a Hopfield, J. J. Proc. Natl. Acad. Sci. U.S.A.1974, 71, 3840. Jortner, J. J. Chem. Phys. 1976, 64, 4860. Jortner, J. J. Am. Chem. SOC.1980, 102, 6676. Marcus, R. A.; Sutin, N . Biochim. Biophys. Acta 1985, 811, 265. Jortner, J.; Bixon, M . In Proceedings of the Philadelphia Conference on Protein Structure; in press. (36) McConnell, H. M. J . Chem. Phys. 1961, 35, 508. (37) Heitele, H.; Michel-Beyerle, M. E. J . Am. Chem. SOC.1985, 107, 8286. (38) Miller, J. R.;Calcaterra, L. T.; Closs, G. J . Am. Chem. SOC.1984, 106, 3047. (39) Wasielewski, M. R.; Niemczyk, M. P.; Pewitt, E. P. J. Am. Chem. SOC. 1985.107. 1080. (40) Joran, A. D.; Leland, B. A.; Geller, G. G.; Hopfield, J. J . J . Am. Chem. SOC.1984, 106,6090. (41) DeVault, D.; Chance, B. Biophys. J . 1966, 6, 825. (42) Dutton, P. L.; Kihara, T.; McCray, J.; Thornber, J. P. Biochim. Biophys. Acta 1971, 226, 81. (43) Hales, B. J. Biophys. J . 1976, 16, 471.
The Journal of Physical Chemistry, Vol. 90, No. 16, 1986 3797
Coupling of Protein Modes to Electron Transfer transition from low-temperature nuclear tunneling to a hightemperature activated process, resulting in the characteristic nuclear frequency of w = 400-500 cm-'. This high frequency implies that the dominating nuclear coupling involves the intramolecular vibrational mode(s) of the porphyrin rings of the cytochrome characterized by a huge configurational change, Le., Aqc = 0.7 8, in four modes, and a very large intramolecular reorganization energy46of E, = 18 500 cm-I. A cursory examination of these results may lead to the conclusion that E J E , >> 1 for this E T process. This conclusion is in contrast with the available structural information concerning very small intramolecular configurational changes accompanying cytochrome oxidation,47which result in E, = 350 c ~ - I . ~ * A reexamination of the dynamics of cytochrome oxidation, reaction 1.5, is obviously required. To extract information regarding the role of the coupling of the ET with the protein modes, we shall analyze the temperature dependence and free energy relations of some other ET reactions within the R C and in closely related model systems in an attempt to estimate the characteristic frequency of the nuclear modes, which are involved in these processes. Intramolecular modes are expected to be identified by their characteristic frequencies w, I 400 cm-I, involving in-plane stretching of the porphyrin ring, while intermolecular protein modes are expected to be specified by frequencies in the range om= 0-150 cm-I, which correspond to the frequency spectrum of typical proteins.49 The magnitude of the characteristic frequency, which will emerge from the temperature dependence of the E T rates, will provide a diagnostic criterion for the identification of the nature of the relevant nuclear modes which dominate the E T dynamics. The sequence of the primary ET process in the RC, eq 1.3-1.6, can conveniently be subdivided into two sets of processes, that is, (1) early ET proceeding on a time scale of 10 ps, which involves reaction 1.3 and (2) later ET corresponding to the time scale exceeding 10 ps, which involves reactions 1.4-1.6. The early ET process is so fast that it may occur in a system which does not achieve thermal equilibrium and where the electronic process competes with medium-induced vibrational relaxation. Accordingly, it is still an open question whether the conventional multiphonon theory, eq 11.2, which rests on the separation of time scales for the (fast) vibrational relaxation and for the (slow) electronic process, is applicable for the description of early ET. The later E T processes occur on a sufficiently long time scale to ensure the applicability of conventional ET. The relevant features of these processes will now be discussed. 111. Later Electron-Transfer Processes The first experimental picosecond studies of electron transfer (ET) in the RC50*51 established that the fast quinone reduction process, reaction 1.4, is characterized by a rate of 1OIo s-l at room temperature and exhibits a weak temperature dependence over the broad temperature range 4-300 K. This unique temperature dependence has been attributed52to an activationless ET, which involves the crossing of the potential energy surfaces at the minimum of the initial donoracceptor state, which is characterized by the following f e a t ~ r e s : ~( 1 ~) The . ~ ~ rate constant is temperature-independent over the range kT C ohw, where w is the relevant characteristic frequency and 9 = 0.2-0.3. (2) At higher temperatures the rate is proportional to ( T)-'l2, exhibiting a small apparent negative activation energy. These expectations were borne out by the recent work of Parson et aLs3on the temperature
-
(44) Kuznetsov, A. M.; Serndergard, N. C.; Ulstrup, J. Chem. Phys. 1978, 29, 383. (45) Sarai, A. Eiochim. Biophys. Acta 1980, 589, 71. (46) Buhks, E.; Bixon, M.; Jortner, J. Chem. Phys. 1981, 55, 41. (47) Takano, T.; Dickerson, R. E.J . Mol. Eiol. 1981, 153, 95. (48) Churg, A. K.; Weiss, R. M.; Warshel, A.; Takeno, T. J. Phys. Chem. 1983, 87, 1683. (49) GO,N.; Noguti, T.; Nishikawa, T. Proc. Natl. Acad. Sci. U.S.A. 1983, 80, 3696. (50) Kaufman, K. J.; Dutton, P. L.; Netzel, T. A.; Leigh, J. S.; Rentzepis, P.Science (Washington, D.C.) 1975, 188, 1301. (51) Rockley, M. G.; Winsdor, M.W.; Cogdell, R. J.; Parson, W. W. Proc. Natl. Acad. Sci. U.S.A. 1975, 72, 2251. (52) Jortner, J. Eiochim. Eiophys. Acta 1980, 594, 193.
2t7 100 200 TEMPERATURE ( O K )
0
300
Figure 1. Temperature dependence of the rate of the quinone reduction reaction, eq 1.4. The points are experimental data from ref 53. The solid line represents the fit to an activationless ET reaction eq 111.2, with k(T = 0) = 1.1 X 1Olo s-] and hw = 100 cm-I.
dependence of reaction 1.4 (reproduced in Figure l), which exhibits a temperature-independent rate, k, at very low temperatures, Le., T C 50 K,while at higher temperatures k decreases slowly with increasing temperature, decreasing by a numerical factor of -2.5 in the range 50-300 K (Figure 1). One can readily utilize a simple but transparent version of the multiphonon ET theory to account for these observations. In the single mode approximation eq 11.1 reduces to33 k =
-(
2alVl2 0 + 1
PP
7 )exp[-S(2~+ 1)]1,[2S(~(~+ 1 ) ) 1 / 2 ]
h2o
(111.1) where w is the (average) effectively coupled vibrational frequency, ij = [exp(hw/kT) - 11-I is the thermal population of that mode, and S = E,/hw is the nuclear organization, eq 11.4, in the frequency units. Finally, p = A E / h w , where AE is the energy gap of the reaction, Le., the free energy of the ET process. For an activationless process p = S and eq 111.1 for the strong coupling limit, Le., S >> 1, reduces to
where k(0) =
2 4 v12 hw(2ap)'/2
(111.3)
is the low-temperature (kT > h w ) . temperature-independent rate in the range 4-50 K, which subsequently decreases with increasing temperature in the temperature IV. Mechanism of Cytochrome Oxidation range 50-300 K. Previous attempts to account for the experiFrom the foregoing discussion, we conclude that the temperature mental data in terms of an activationless p r o c e s used ~ ~ ~the ~~~ dependence of two activationless processes in the RC, Le., reactions characteristic frequency h w = 400 cm-’, which results in a gross 1.4 and 1.6, can well be accounted for in terms of a low relevant overestimate of the E T rate at high temperatures. It has been phonon frequency h w = 100 cm-I, providing novel evidence for suggested that thermal expansion effects have to be invoked to the effective coupling of the intermolecular medium protein modes account for this discrepancy. However, the thermal expansion with these ET processes. This conclusion appears to be in variance coefficient resulting from such an analysis is larger by about 1 with the traditional analysis31~32~44-46 of the unique temperature order of magnitude than that determined for a protein.27 We find dependence of the Chance-DeVault cytochrome oxidation in the that the experimental data for the temperature dependence of photosynthetic bacterium C h r ~ m a t i u m , ~which I - ~ ~ resulted in the reaction 1.6 can be well fit by an activationless reaction rate, eq (presumably intramolecular) vibrational frequency of h w = 111.4, with the low phonon frequency hw = 100 cm-I, which is 400-500 cm-I for the electron-phonon coupling. Although the identical with the value of h w utilized to account for the temqualitative i n t e r p r e t a t i ~ nof ~ ~the . ~ temperature ~ dependence of perature dependence of reaction 1.3 (Figure 1) and which correaction 1.6 is very plausible and appealing, the quantitative responds to the protein medium mode(s). As is apparent from physical parameters, which emerge from such an analysis, raise Figure 2, the rate reaction 1.6 can be well fit by eq 111.4 over the serious conceptual difficulties. In particular, we note the following: temperature range 4-200 K. The discrepancy between the cal(1) The huge intramolecular reorganization energy E, = 18 500 culated and the experimental rates in the temperature range cm-I in Chromatium& implies an unphysically large intramolecular 200-300 K presumably originates from thermal expansion efconfigurational change, which has already been alluded to in f e c t ~ ,whose ~ ~ , contribution ~~ is now much smaller than previously section 11. This reorganization energy, which corresponds to the a s s ~ m e d The . ~ ~low-temperature ~~~ rate k(0) = 58 s-I used for “normal region” of ET, is unique, as one cannot fit experimental the fit of the temperature dependence of reaction 1.6 (Figure 2), data in the “inverted region” with such a high frequency of 400 together with AE = 4200 cm-’ and E, = A E = 4200 cm-I, results, cm-I. according to eq 111.2, in the small electronic coupling IVl = 3 X (2) A large electronic coupling46 V 90 cm-’ is required to 10-4 cm-’ being consistent with the large separation between fit the data for Chromatium. Such a large interaction can only (BChl)2 and Q, which is characterized by the center-to-center arise from a close contact between cytochrome c and (BChl)2, distance of 28 A in Rps Viridk2* which contradicts all the available structural information. The In an attempt to test the applicability of conventional ET ESR data in Chromatiums4 and crystallographic data for Rps theories to the RC, Feher et al.27have explored the applicability Viridis indicate that the separation between these prosthetic groups of the free energy relationships, which are implied by eq 111.1, is 23 A. At such distances one expects that Vis lower than by substituting quinones with different redox potentials for the 1 cm-’. native ubiquinone. Figure 3 shows the experimental data for the ( 3 ) A close e ~ a m i n a t i o nof~ the ~ fit of the experimental data rates of reaction 1.6 at 77 K in a RC modified by the substitution for C h r ~ m a t i u m ~tol - the ~ ~ multiphonon ET theory clearly inof another quinone2’ and plotted against the redox potentials of dicates the inadequacy of the theory around the “transition” at the quinone^.^' The parabolic free energy relationship can reaabout 120 K. The experimental data fit a sharp break rather than sonably be accounted for in terms of eq 111.3 with the low-frea smooth change. quency h w = 100 cm-’ and with E, = 4200 cm-I. The agreement between theory and experiment, as shown in Figure 3, is as good as expected, providing further support for the coupling of the (54) Tredi, D. M.; Leigh, J. S.; Dutton, P.L. Biochim. Biophys. Acra 1978, low-frequency protein medium mode with the ET process in the 503,524.
-
Coupling of Protein Modes to Electron Transfer (4) Some information which has accumulated regarding analogous E T processes in other bacterial system^^^*^^ reveals that the temperature dependence of reaction 1.5 in Chromatium is by no means universal, as other systems reveal a broad spectrum of behavior from a fast (1 O6 s-I) temperature-independent rates5 to a very weak temperature dependence in the range 80-300 K.56 This information provides compelling evidence that it is highly improbable that a tunneling process prevails at temperatures around 100 K for the ET between cytochrome c and the primary donor. We assert that cytochrome oxidation in Chromatium does not exhibit the transition from low-temperature nuclear tunneling to a high-temperature activated process, which involves E T from a single cytochrome c to the dimer cation. Rather, we propose that the unique temperature dependence for this reaction originates from the combination of several parallel E T reactions with different activation energies, each of them occurring from a different cytochrome molecule. At least for three photosynthetic bacteria it is known that the RC includes four cytochrome molecule^.^^^^^^^^ Some evidence for parallel E T reactions is available for Chromatium at room temperature, where the E T rate from the lowpotential cytochrome and the high-potential cytochrome are (1 ps)-I and (2 ps)-I, r e s p e ~ t i v e l y ,while ~ ~ at low temperatures oxidation by the high-potential cytochrome is tenfold slower than that by the low-potential c y t ~ c h r o m e .We ~ ~ propose that both low-potential cytochromes in Chromatium can be operative in ET and that (at least) two ET processes occur: (I) a moderately slow activationless process and (11) an activated process. At high temperatures, reaction I1 is much faster, while at low temperatures reaction I predominates. The low-temperature nuclear tunneling contribution from reaction I1 is negligible. The difference between the dynamics of reactions I and I1 originates from different medium reorganization energies, Le., E, = E,,, of the protein low-frequency modes, which are due to two causes: (a) different protein configurations, which involve the local structures of polar groups around the two cytochromes, and (b) different donoracceptor distances, which provide an electrostatic contribution to We now proceed to the analysis of the temperature dependence of reactions I and I1 in terms of eq 111.1. Regarding nuclear reorganization energy, we assert that on the basis of structural data4' the dominant contribution to E,, eq 11.4, originates from the protein medium reorganization, and we choose again the low characteristic frequency hw = 100 cm-', which has emerged from the analysis of reactions 1.4 and 1.6 (section 111). The energy gap ' I is attributed for both reactions is AE = 3480 ~ m - ' . ~Reaction to an activationless process, Le., E,(') = A E = 3480 cm-I. The low-temperature data for the Chance-DeVault reaction can be well fit by eq 111.2 with k l ( T = 0) = 500 s-' and h w = 100 cm-' (Figure 4). The value of kl(T = 0) results in the low value of electronic coupling, VI = 8 X IO4 cm-l. Reaction I1 is an activated process for which eq 111.1 reduces in the high-temperature limit to the well-known form k=
2 4 v1'
(AE - E,)'
h( 4 ~ E , k T ) l / ~
which is isomorphous to the Marcus ET rate The high-temperature ( T > 120 K) data (Figure 4) were fit by relation IV.1 in the empirical form kII = 2.2 X 108T1/2exp(-EJkT) s-', with E, = 1230 cm-I. From the Marcus relation, E, = (AE E,)2/4E,, together with A E = 3480 cm-', we estimate the reasonable value = 1125 cm-l for reaction 11, while the preexponential factor in kll results in a moderately large electronic coupling, lVlll = 0.55 cm-I. The low-temperature tunneling limit of reaction I1 corresponds, according to eq 111.1, to the rate kII(T = 0) = 15 s-I, which is negligible relative to the experimental low-temperature rate (500 s-l). The fit of the experimental data in terms of reactions I and I1 (Figure 4) is as good as can be (55) Chamorovsky, S . K.; Kononenko, A. A,; Remennikov, S.M.; Rubin, A. B . Biochim. Biophys. Acta 1980, 589, 151. (56) Kihura, T.; McCray, J. A. Biochim. Biophys. Acta 1973, 292, 247.
The Journal of Physical Chemistry, Vol. 90, No. 16, 1986 3799
T E M P E R AT U R E (" K )
Figure 4. Temperature dependence of the rate for the Chance-DeVault cytochrome oxidation reaction, eq 1.6, in Chromatium. The points represent the experimental data from the following sources: (0)ref 41; (A) ref 42; (0)ref 43. The solid and the dashed curve represent the rates of two parallel ET reactions. The dashed curve corresponds to an activationless process, eq 111.2, with k ( T = 0) = 500 s-' and hw = 100 cm-I. The solid curve corresponds to a high-temperature activated process, eq IV.1, with AE = 3480 cm-I, E , = 1125 cm-I, and = 0.55 cm-I.
expected. The validity of our new mechanistic description of cytochrome oxidation does not solely rest on this excellent fit of the experimental data, as this research area has previously been fraught with very convincing fits between theory and experiment for cytochrome oxidation, which has resulted in unreasonable physical parameters. Rather, the validity of our physical description should be judged on the basis of the plausible physical parameters emerging from our analysis. In particular, we note the following: (1) The nuclear reorganization energies E,(1)= 3480 cm-' and E,(") = 1125 cm-I for the two parallel ET processes are reasonable. These are attributed to the medium reorganization energy, being rather close to the corresponding values of E, derived in section I11 for the E T processes 1.4 and 1.6. (2) The electronic coupling terms for reactions I and I1 are 1.5 X This result implies widely different, Le., IVI/VIII a large separation between the two distinct low-potential cytochromes involved in the low-temperature and in the high-temperature ET process. The low-temperature activationless ET occurs from a distant cytochrome, while the high-temperature activated ET proceeds from a cytochrome closer to the dimer. Invoking the primitive relation for the distance scale ( R ) of the electronic c ~ u p l i n gV, a~ exp(-aR) ~ ~ ~ ~ ~with ~ ~a N 0.6 we obtain a rough estimate of RI - RI1 11 %, for the differences in the distances of the two low-potential cytochromes from the special pair. This distance is consistent with information derived from ESR data,54which implies that the separation between the two low-potential cytochromes in Chromatium exceeds 10 A, while crystallographic data for Rps Viridis yield the center-to-center distance of 14 %, between two cytochromes.28
-
-
V. Concluding Remarks From the analysis of the temperature dependence of the three later ET reactions 1.4-1.6 in the RC, we conclude that the major electron-phonon coupling mechanism for these nonadiabatic and multiphonon processes involves the coupling of the prosthetic groups and their ions with the exterior polar modes of the protein medium. On the other hand, the contribution of the coupling of these ET processes with the intramolecular vibrational modes of the donor and acceptor molecules is small. Stated in alternative terms, the intramolecular configuration changes of the prosthetic groups accompanying their oxidation or reduction are small, which is in accord with crystallographic data,47 and the major contri-
J. Phys. Chem. 1986, 90, 3800-3804
3800
bution to the Franck-Condon factor F, which determines the E T rate, eq 11.1, originates from the protein modes. These polar medium modes essentially involve dislocation and rotation of polar groups of the protein. These modes differ from the optical modes of a polar liquid, which are prominent in the Marcus theory of ET1-Sand which involve rotations of solvent molecules. Our admittedly simplified treatment of ET, which rests on a single mode approximation, eq 111.1, provides only an average, coarsegrained description of the nature of the nuclear modes relevant for the ET dynamics. The magnitude of the average nuclear frequency ho = 100 cm-I emerging from our analysis of three ET processes implies that the dominating contribution to electron-phonon coupling originates from the medium modes, Le., E J E ,
