Tuning Heme Redox Potentials in the Cytochrome c Subunit of Photosynthetic Reaction Centers
2003; Elsevier BV; Volume: 278; Issue: 52 Linguagem: Inglês
10.1074/jbc.m307560200
ISSN1083-351X
AutoresPhilipp Voigt, Ernst‐Walter Knapp,
Tópico(s)Porphyrin and Phthalocyanine Chemistry
ResumoThe photosynthetic reaction center (RC) from Rhodopseudomonas viridis contains four cytochrome c hemes. They establish the initial part of the electron transfer (ET) chain through the RC. Despite their chemical identity, their midpoint potentials cover an interval of 440 mV. The individual heme midpoint potentials determine the ET kinetics and are therefore tuned by specific interactions with the protein environment. Here, we use an electrostatic approach based on the solution of the linearized Poisson-Boltzmann equation to evaluate the determinants of individual heme redox potentials. Our calculated redox potentials agree within 25 meV with the experimentally measured values. The heme redox potentials are mainly governed by solvent accessibility of the hemes and propionic acids, by neutralization of the negative charges at the propionates through either protonation or formation of salt bridges, by interactions with other hemes, and to a lesser extent, with other titratable protein side chains. In contrast to earlier computations on this system, we used quantum chemically derived atomic charges, considered an equilibrium-distributed protonation pattern, and accounted for interdependencies of site-site interactions. We provide values for the working potentials of all hemes as a function of the solution redox potential, which are crucial for calculations of ET rates. We identify residues whose site-directed mutation might significantly influence ET processes in the cytochrome c part of the RC. Redox potentials measured on a previously generated mutant could be reproduced by calculations based on a model structure of the mutant generated from the wild type RC. The photosynthetic reaction center (RC) from Rhodopseudomonas viridis contains four cytochrome c hemes. They establish the initial part of the electron transfer (ET) chain through the RC. Despite their chemical identity, their midpoint potentials cover an interval of 440 mV. The individual heme midpoint potentials determine the ET kinetics and are therefore tuned by specific interactions with the protein environment. Here, we use an electrostatic approach based on the solution of the linearized Poisson-Boltzmann equation to evaluate the determinants of individual heme redox potentials. Our calculated redox potentials agree within 25 meV with the experimentally measured values. The heme redox potentials are mainly governed by solvent accessibility of the hemes and propionic acids, by neutralization of the negative charges at the propionates through either protonation or formation of salt bridges, by interactions with other hemes, and to a lesser extent, with other titratable protein side chains. In contrast to earlier computations on this system, we used quantum chemically derived atomic charges, considered an equilibrium-distributed protonation pattern, and accounted for interdependencies of site-site interactions. We provide values for the working potentials of all hemes as a function of the solution redox potential, which are crucial for calculations of ET rates. We identify residues whose site-directed mutation might significantly influence ET processes in the cytochrome c part of the RC. Redox potentials measured on a previously generated mutant could be reproduced by calculations based on a model structure of the mutant generated from the wild type RC. The photosynthetic reaction center (RC) 1The abbreviations used are: RCphotosynthetic reaction centercytcytochromeETelectron transferMCMonte CarloPRpropionic acid(s).1The abbreviations used are: RCphotosynthetic reaction centercytcytochromeETelectron transferMCMonte CarloPRpropionic acid(s). from the purple bacterium Rhodopseudomonas viridis (with recently proposed taxonomic name Blastochloris viridis) serves as a model system for proton-coupled electron transfer (ET) processes across the membrane. It comprises two membrane-spanning L and M subunits, a cytoplasmic H subunit, and the periplasmic tetraheme cytochrome (cyt) c subunit, which is tightly bound to the RC (Fig. 1). The structure of the RC is known in atomic detail from crystallographic studies (1Deisenhofer J. Epp O. Miki K. Huber H. Michel H. Nature. 1985; 318: 618-624Crossref PubMed Scopus (2566) Google Scholar, 2Deisenhofer J. Epp O. Sinning I. Michel H. J. Mol. Biol. 1995; 246: 429-457Crossref PubMed Scopus (559) Google Scholar). The 14 cofactors bound to the RC subunits are involved in light-driven proton-coupled ET through the membrane protein complex, leading to reduction and protonation of the membrane-soluble quinone (3Lancaster C.R. Michel H. Messerschmidt A. Huber R. Poulos T. Wieghardt K. Handbook of Metalloproteins. John Wiley & Sons, Ltd., Chichester, United Kingdom2001: 119-135Google Scholar). Quinone oxidation taking place at the cyt bc1 membrane protein complex establishes a proton gradient across the membrane, which is converted to chemical energy at the ATP synthase complex. The electrons are returned back to the RC by the periplasmic soluble electron carrier cyt c2 that is supposed to bind to the C chain of the RC, probably close to the outermost heme group to reduce the oxidized hemes (4Osyczka A. Nagashima K.V.P. Sogabe S. Miki K. Yoshida M. Shimada K. Matsuura K. Biochemistry. 1998; 37: 11732-11744Crossref PubMed Scopus (30) Google Scholar). photosynthetic reaction center cytochrome electron transfer Monte Carlo propionic acid(s). photosynthetic reaction center cytochrome electron transfer Monte Carlo propionic acid(s). In the cyt c complex of the R. viridis RC, electrons are transferred through a linear chain of low-high-low-high potential cyt c hemes (heme number 4-3—2-1) to the special pair chlorophyll dimer where photo-oxidation takes place (5Nitschke W. Rutherford A.W. Biochemistry. 1989; 28: 3161-3168Crossref Scopus (63) Google Scholar, 6Dracheva S.M. Drachev L.A. Konstantinov A.A. Semenov A.Y. Skulachev V.P. Arutjunjan A.M. Shuvalov V.A. Zaberezhnaya S.M. Eur. J. Biochem. 1988; 171: 253-264Crossref PubMed Scopus (148) Google Scholar). The redox potentials of the four heme groups were determined by various experimental approaches (5Nitschke W. Rutherford A.W. Biochemistry. 1989; 28: 3161-3168Crossref Scopus (63) Google Scholar, 6Dracheva S.M. Drachev L.A. Konstantinov A.A. Semenov A.Y. Skulachev V.P. Arutjunjan A.M. Shuvalov V.A. Zaberezhnaya S.M. Eur. J. Biochem. 1988; 171: 253-264Crossref PubMed Scopus (148) Google Scholar, 7Fritzsch G. Buchanan S. Michel H. Biochim. Biophys. Acta. 1989; 977: 157-162Crossref Scopus (49) Google Scholar, 8Alegria G. Dutton P.L. Biochim. Biophys. Acta. 1991; 1057: 258-272Crossref PubMed Scopus (46) Google Scholar). Accordingly, the midpoint potentials of hemes 1 to 4 are at 370, 20, 300, and -60 mV, respectively (7Fritzsch G. Buchanan S. Michel H. Biochim. Biophys. Acta. 1989; 977: 157-162Crossref Scopus (49) Google Scholar). All midpoint values are considerably shifted to higher potentials compared with the values obtained for equivalently coordinated heme model systems in aqueous solution (-220 mV for bis-histidine ligated hemes as heme 2, -70 mV for methionine-histidine ligated hemes as hemes 1, 3, and 4; see Ref. 9Wilson G.S. Bioelectrochem. Bioenerg. 1983; 1: 172-179Crossref Scopus (36) Google Scholar). Heme proteins can be found in a diverse array of enzyme families. This is because of the ability of the heme system to function as a binding and transport site for small molecules or electrons or as a catalytic principle of an enzyme active site. Hemes are redox active groups that are particularly versatile and challenging in the understanding of function. Their central iron atom can be coordinated by a variety of different axial ligands. Hemes may change their redox and protonation state in a concerted way involving the two covalently attached propionic acids (PR). This widens the scope to tune heme redox potentials in proteins enormously and opens the possibility that heme can play an active part in coupled electron and proton translocation processes. A prominent system where it is likely that heme catalyzes such processes is cyt c oxidase (10Iwata S. Ostermeier C. Ludwig B. Michel H. Nature. 1995; 376: 660-669Crossref PubMed Scopus (1976) Google Scholar, 11Tsukihara T. Aoyama H. Yamashita E. Tomizaki T. Yamaguchi H. Shinzawa-Itoh R. Nakashima R. Yaono R. Yoshikawa S. Science. 1996; 272: 1136-1144Crossref PubMed Scopus (1915) Google Scholar, 12Michel H. Biochemistry. 1999; 38: 15129-15140Crossref PubMed Scopus (241) Google Scholar). Several features of protein architecture give rise to modified redox cofactor properties. Most of them rely on electrostatic interactions. These are investigated intensively by structural analysis and mutational studies, as well as by theoretical approaches based on electrostatic models (13Ullmann G.M. Knapp E.W. Eur. Biophys. J. 1999; 28: 533-551Crossref PubMed Scopus (225) Google Scholar, 14Honig B. Nicholls A. Science. 1995; 268: 1144-1149Crossref PubMed Scopus (2519) Google Scholar). Theoretical work on heme proteins was performed before by several groups (see for example Refs. 15Gunner M.R. Honig B. Proc. Natl. Acad. Sci. U. S. A. 1991; 88: 9151-9155Crossref PubMed Scopus (175) Google Scholar, 16Popović D.M. Zarić S.D. Rabenstein B. Knapp E.W. J. Am. Chem. Soc. 2001; 123: 6040-6053Crossref PubMed Scopus (47) Google Scholar, 17Ullmann G.M. J. Phys. Chem. B. 2000; 104: 6293-6301Crossref Scopus (52) Google Scholar). Gunner and Honig (15Gunner M.R. Honig B. Proc. Natl. Acad. Sci. U. S. A. 1991; 88: 9151-9155Crossref PubMed Scopus (175) Google Scholar) calculated the redox potentials of the hemes in the R. viridis RC. Using a crude heme charge model and two conversion factors to adjust the redox potentials calculated for model systems in aqueous solution to the respective experimental values, they achieved acceptable agreement with the redox potentials measured for the hemes in the RC (see Table I). Furthermore, they calculated the protonation pattern of the RC protein side chains but did not consider it in the calculation of the heme redox potentials and also neglected the influence of the solution redox potential. Ullmann (17Ullmann G.M. J. Phys. Chem. B. 2000; 104: 6293-6301Crossref Scopus (52) Google Scholar) used a heme charge model based on density functional calculations and pointed out the importance of coupling between the protonation and redox pattern in his work on cyt c3.Table IRedox potentials of the four cyt c hemes in the R. viridis RC See text for a description of the coordinate sets used. The special pair was kept in the reduced state.Heme 1Heme 2Heme 3Heme 4mVComputed values 1prc-H-titratedaCalculated at pH 7344–15297–52 2prc-H-titratedaCalculated at pH 7291–66207–139 2prc-H-annealedaCalculated at pH 7339–35265–110 Gunner & Honig (15Gunner M.R. Honig B. Proc. Natl. Acad. Sci. U. S. A. 1991; 88: 9151-9155Crossref PubMed Scopus (175) Google Scholar)bNo pH value given346–65241–76Experimental data Fritsch et al. (7Fritzsch G. Buchanan S. Michel H. Biochim. Biophys. Acta. 1989; 977: 157-162Crossref Scopus (49) Google Scholar)cMeasured at pH 637010300–60 Dracheva et al. (6Dracheva S.M. Drachev L.A. Konstantinov A.A. Semenov A.Y. Skulachev V.P. Arutjunjan A.M. Shuvalov V.A. Zaberezhnaya S.M. Eur. J. Biochem. 1988; 171: 253-264Crossref PubMed Scopus (148) Google Scholar)dMeasured at pH 7 and pH 838020310–60a Calculated at pH 7b No pH value givenc Measured at pH 6d Measured at pH 7 and pH 8 Open table in a new tab Here, we also used a charge model derived from quantum chemical calculations but calculated the wave functions in the Hartree-Fock approximation and used the restrained electrostatic potential procedure (18Bayly C.I. Cieplak P. Cornell W.D. Kollman P.A. J. Phys. Chem. 1993; 97: 10269-10280Crossref Scopus (5540) Google Scholar, 19Cornell W.D. Cieplak P. Bayly C.I. Kollman P.A. J. Am. Chem. Soc. 1993; 115: 9620-9631Crossref Scopus (1087) Google Scholar) to generate charge sets for the hemes, which harmonize with the charges of the CHARMM22 force field (20Brooks B.R. Bruccoleri R.E. Olafson B.D. States D.J. Swaminathan S. Karplus M. J. Comput. Chem. 1983; 4: 187-217Crossref Scopus (13880) Google Scholar, 21MacKerell Jr., A.D. Bashford D. Bellott R.L. Dunbrack Jr., R.L. Evanseck J.D. Field M.J. Fischer S. Gao J. Guo H. Ha S. Joseph-McCarthy D. Kuchnir L. Kuczera K. Lau F.T.K. Mattos C. Michnick S. Ngo T. Nguyen D.T. Prodhom B. Reiher III, W.E. Roux B. Schlenkrich M. Smith J.C. Stote R. Straub J. Watanabe M. Wiórkiewicz-Kuczera J. Yin D. Karplus M. J. Phys. Chem. B. 1998; 102: 3586-3616Crossref PubMed Scopus (11611) Google Scholar) that we used as the main body of atomic charges. We determined the heme redox potentials, as well as the protonation pattern of all titratable residues, by calculating the difference in electrostatic energies between heme model systems in solvent and in protein environment from the solutions of the linearized Poisson-Boltzmann equation (13Ullmann G.M. Knapp E.W. Eur. Biophys. J. 1999; 28: 533-551Crossref PubMed Scopus (225) Google Scholar, 14Honig B. Nicholls A. Science. 1995; 268: 1144-1149Crossref PubMed Scopus (2519) Google Scholar, 22Bashford D. Karplus M. J. Phys. Chem. 1991; 95: 9557-9561Crossref Scopus (251) Google Scholar, 23Bashford D. Gerwert K.J. J. Mol. Biol. 1992; 224: 473-486Crossref PubMed Scopus (514) Google Scholar) and by applying a Monte Carlo (MC) titration method to generate the equilibrium protonation and redox pattern (24Rabenstein B. Ullmann G.M. Knapp E.W. Eur. Biophys. J. 1998; 27: 628-637Crossref Scopus (73) Google Scholar). In this paper, we first present our computational results concerning the heme redox potentials and the protonation pattern of the titratable groups and discuss differences in the results obtained with different crystallographic structures of the RC. In the second part, we focused on the interactions between heme groups, giving values for the so-called working potentials (i.e. the actual midpoint potential at a given solution redox potential) of the hemes as a function of the solution redox potential. Next, we investigated general factors of the protein environment that influence the heme redox potentials, followed by a detailed analysis of the interactions of specific charged protein side chains with the porphyrin ring system and the heme PR groups. Thus, the outstanding role of the PR in these interactions was revealed. Finally, we generated a model structure of a mutant RC (25Chen I.-P. Mathis P. Koepke J. Michel H. Biochemistry. 2000; 39: 3592-3602Crossref PubMed Scopus (38) Google Scholar) and reproduced the measured redox potentials to further validate our approach. Coordinates—For most calculations, the crystal structure of the R. viridis RC at 2.3-Å resolution was used as reported by Deisenhofer et al. (1, 2; Protein Data Bank number 1prc). In that crystal structure the QB binding pocket, which lies within the lower part of the L chain, does show a low occupancy, but that was considered to be uncritical in our application, which focuses on features confined to the cyt c part of the RC. All water molecules and sulfate ions were removed from the structure. The four missing C-terminal amino acids of chain C (Ala-Ala-Ala-Lys) were added. Hydrogens were placed using the HBUILD (26Brünger A.T. Karplus M. Proteins. 1988; 4: 148-156Crossref PubMed Scopus (502) Google Scholar) routine of CHARMM22 (20Brooks B.R. Bruccoleri R.E. Olafson B.D. States D.J. Swaminathan S. Karplus M. J. Comput. Chem. 1983; 4: 187-217Crossref Scopus (13880) Google Scholar, 21MacKerell Jr., A.D. Bashford D. Bellott R.L. Dunbrack Jr., R.L. Evanseck J.D. Field M.J. Fischer S. Gao J. Guo H. Ha S. Joseph-McCarthy D. Kuchnir L. Kuczera K. Lau F.T.K. Mattos C. Michnick S. Ngo T. Nguyen D.T. Prodhom B. Reiher III, W.E. Roux B. Schlenkrich M. Smith J.C. Stote R. Straub J. Watanabe M. Wiórkiewicz-Kuczera J. Yin D. Karplus M. J. Phys. Chem. B. 1998; 102: 3586-3616Crossref PubMed Scopus (11611) Google Scholar). The resulting structure was energetically minimized keeping all atoms that are defined by the crystal structure in fixed positions. After a first titration procedure, the energy minimization was repeated considering the actual average protonation pattern by using fractional degrees of protonation and the resulting net charges for the titratable groups where necessary. The resulting structure (termed 1prc-H-titrated) was used for all further calculations unless noted otherwise. For reasons of comparison the crystal structure reported by Lancaster et al. (27Lancaster C.R. Michel H. Structure. 1997; 5: 1339-1359Abstract Full Text Full Text PDF PubMed Google Scholar; Protein Data Bank number 2prc) was also used and subjected to the same procedure as described for the 1prc structure. This crystal structure was solved at 2.45-Å resolution but shows a markedly higher occupancy within the QB binding pocket. Atom positions within the cyt c part are nearly identical in both structures, except for a few solvent-exposed side chain atoms. These have zero occupancy in both structures and have been placed in the model building process to complete the respective side chains. Inspection of these side chains in the 2prc structure showed some geometrically unfavorable peculiarities (see "Results and Discussion"). Therefore, we decided to use the 1prc structure for the main body of our study. To use the 2prc structure in a more sensible way, a restrained simulated annealing molecular dynamics simulation was performed to optimize the positions of the crystallographically undefined side chain atoms within and close to the C chain in the 2prc structure (see Supplemental Material for details). The structure of the RC mutant C264-RK (25Chen I.-P. Mathis P. Koepke J. Michel H. Biochemistry. 2000; 39: 3592-3602Crossref PubMed Scopus (38) Google Scholar) was modeled by replacing the arginine side chain at position 264 of the C chain with that of lysine in the 1prc structure. The positions of the Lys-C264 side chain atoms and all hydrogens within 5 Å of these atoms were energetically optimized whereas all other atom positions were kept fixed. The atomic coordinates (including hydrogens) of all structures used for our computations can be found on our web server (agknapp.chemie.fu-berlin.de) as 1prc-H, 1prc-H-titrated, 2prc-H, 2prc-H-titrated, 2prc-H-annealed, and 1prc-C264-RK-H. Atomic Partial Charges—Amino acid partial charges were taken from the CHARMM22 parameter set (21MacKerell Jr., A.D. Bashford D. Bellott R.L. Dunbrack Jr., R.L. Evanseck J.D. Field M.J. Fischer S. Gao J. Guo H. Ha S. Joseph-McCarthy D. Kuchnir L. Kuczera K. Lau F.T.K. Mattos C. Michnick S. Ngo T. Nguyen D.T. Prodhom B. Reiher III, W.E. Roux B. Schlenkrich M. Smith J.C. Stote R. Straub J. Watanabe M. Wiórkiewicz-Kuczera J. Yin D. Karplus M. J. Phys. Chem. B. 1998; 102: 3586-3616Crossref PubMed Scopus (11611) Google Scholar); non-standard charge states for some titratable groups (Arg, Cys, Lys, Tyr, C-ter, N-ter) not available there were used as calculated before (16Popović D.M. Zarić S.D. Rabenstein B. Knapp E.W. J. Am. Chem. Soc. 2001; 123: 6040-6053Crossref PubMed Scopus (47) Google Scholar). Fractional degrees of protonation needed for the optimization of hydrogen positions after a first titration procedure were accounted for by using atomic partial charges that were obtained by linear interpolation between the charges for the fully protonated and fully deprotonated state of the corresponding molecular groups. Redox active cofactors of the RC, which are positioned downstream of the special pair (i.e. accessory bacteriochlorophylls, pheophytins, quinones, and non-heme iron center) were only accounted for by using the neutral (reduced) charge set as calculated by Rabenstein et al. (28Rabenstein B. Ullmann G.M. Knapp E.W. Biochemistry. 1998; 37: 2488-2495Crossref PubMed Scopus (98) Google Scholar). These were treated as non-titratable (charge invariant) groups during the electrostatic calculations, because they are located too far away from the hemes to influence their redox behavior significantly. Charges for the special pair bacteriochlorophyll dimer in its oxidized and reduced state were calculated using the program GAUSSIAN98 (29Frisch M.J. Trucks G.W. Schlegel H.B. Scuseria G.E. Robb M.A. Cheeseman J.R. Zakrzewski V.G. Montgomery Jr., J.A. Stratmann R.E. Burant J.C. Dapprich S. Millam J.M. Daniels A.D. Kudin K.N. Strain M.C. Farkas O. Tomasi J. Barone V. Cossi M. Cammi R. Mennucci B. Pomelli C. Adamo C. Clifford S. Ochterski J. Petersson G.A. Ayala P.Y. Cui Q. Morokuma K. Malick D.K. Rabuck A.D. Raghavachari K. Foresman J.B. Cioslowski J. Ortiz J.V. Baboul A.G. Stefanov B.B. Liu G. Liashenko A. Piskorz P. Komaromi I. Gomperts R. Martin R.L. Fox D.J. Keith T. Al-Laham M.A. Peng C.Y. Nanayakkara A. Gonzalez C. Challacombe M. Gill P.M.W. Johnson B. Chen W. Wong M.W. Andres J.L. Gonzalez C. Head-Gordon M. Replogle E.S. Pople J.A. Gaussian 98 Revision A.7. Gaussian, Inc., Pittsburgh, PA1998Google Scholar). The quantum chemical calculations were performed in Hartree-Fock approximation with an STO-3G basis set for all atoms, considering the isoprene tails only as methyl ester groups. For the special pair, charges derived from Mulliken population analysis (30Mulliken R.S. J. Chem. Phys. 1955; 23: 1833-1840Crossref Scopus (9678) Google Scholar) were used, except for isoprene tail atoms, which were assigned to have zero atomic partial charge each. A detailed protocol for the derivation of the heme charges can be found in the Supplemental Material. In brief, the PR were treated as separate titratable groups that interact only electrostatically with the heme pyrrole ring system. Charges for the PR were assigned using the partial charges of the Glu side chain from the CHARMM22 force field. The wave functions of the hemes and their axial ligands were calculated with the program JAGUAR (31Jaguar 4.2. Schrodinger, Inc., Portland, OR2000Google Scholar), using the Hartree-Fock method and a 6-31G* basis set for all atoms except iron, whose transition metal identity was taken into account by using the LAVCP basis set. The program RESP (18Bayly C.I. Cieplak P. Cornell W.D. Kollman P.A. J. Phys. Chem. 1993; 97: 10269-10280Crossref Scopus (5540) Google Scholar, 19Cornell W.D. Cieplak P. Bayly C.I. Kollman P.A. J. Am. Chem. Soc. 1993; 115: 9620-9631Crossref Scopus (1087) Google Scholar) was used to derive atomic partial charges that reproduce the electrostatic potential obtained from the quantum chemical wave functions on grid points in the neighborhood of the considered molecular group. The general properties of the cyt c heme system were considered for each heme in an equivalent way by using appropriate constraints in the RESP computation. The total charge of the reduced state of heme was zero, whereas the oxidized heme charge set had a total charge of one positive charge unit. Of that charge difference, 0.23 charge units were confined to the heme iron, whereas the remainder was allowed to be delocalized within the ring system and the axial ligands. The quantum chemical and RESP calculations were performed for each heme individually, using the heme coordinates of the 1prc structure. The atomic partial charges that we used for the four heme groups are given in Supplemental Table S1 of the Supplemental Material. Theoretical Framework for the Computation of Protonation and Redox Patterns—Because the derivation of the formalism is equivalent for protonation and redox reactions, the respective terms for redox reactions are given in parentheses. The probability 〈xμ〉 that a specific titratable (redox active) group say μ is protonated (oxidized) in a molecular system with a total of N variably charged molecular groups where each one can adopt two different charge states is given by a thermodynamic average over all 2N different states (charge patterns) (13Ullmann G.M. Knapp E.W. Eur. Biophys. J. 1999; 28: 533-551Crossref PubMed Scopus (225) Google Scholar) according to Equation 1, shown below, where T is the absolute temperature and R the universal gas constant.〈xμ〉=1Z∑n=12Nxμ(n)exp(-G(n)/RT),withZ=∑n=12Nexp(-G(n)/RT)(Eq. 1) In the charge pattern (n), the individual charge state of the titratable (redox active) group μ is denoted by the integer x(n)μ, which adopts the value 0 for unprotonated (reduced) state and 1 for protonated (oxidized) state. The total free energy G(n) of the charge pattern (n) of the considered molecular system is expressed as sum over self-energies Gintμ and pair interactions Wμν, shown in Equation 2G(n)=∑μ=1Nxμ(n)Gμint+∑v>μ=1Nxμ(n)xv(n)Wμv(Eq. 2) where for a titratable group μGμint(pH)=RTln10(pH-(pKa,μexp+pKa,μint-pKa,μmodel))(Eq. 3) or for a redox active group μGμint(Esol,Ebias)=F(Esol+Ebias-(Eμexp+Eμint-Eμmodel))(Eq. 4) with solution pH, solution redox potential Esol, bias potential Ebias, and Faraday constant F. The self-energy terms account for the experimental pKa,μexp value (redox potential Eμexp) of group μ and the difference of the computed pKa (Eμ) in the model system pKa,μmodel (Eμmodel) and the intrinsic pKa,μint (Eμint) in a specific molecular environment. The intrinsic pKa,μint (Eμint) of group μ refers to the reference charge state in a specific molecular environment. This charge state corresponds to the charge pattern where all variably charged groups are deprotonated (reduced). The pair interaction Wμν contributes only if both variably charged groups (μ and ν) are protonated (oxidized) whereas all other groups are in the reference charge state. The intrinsic pKa,μint (Eμint) values are formal expressions and do not correspond to measurable quantities. They provide the pKa (Eμ) of the variably charged group μ in the fictitious reference charge state, which differs significantly from a realistic charge state, whereas the ensemble average obtained from Equation 1 involving the energy function G(n) that includes also the pair interactions Wμν leads to meaningful charge states. The procedure to compute the intrinsic pKa,μint, and (Eμint) values and the pair interactions Wμν is discussed in more detail elsewhere (13Ullmann G.M. Knapp E.W. Eur. Biophys. J. 1999; 28: 533-551Crossref PubMed Scopus (225) Google Scholar). A simple method to obtain an estimate of pKa,μ values (redox potentials Eμ) of a particular variably charged group μ is to consider the midpoint values pK½ (E½), which are defined as the solution pH value (solution redox potential Esol), where group μ is with probability 0.5 protonated (oxidized), i.e.〈xμ〉 = 0.5. Note that this definition of pK½ and E½ is formally different from that of pK and Em. One can also probe the redox potential of redox active groups individually while keeping all other redox active groups exposed to the solution redox potential. To enforce this non-equilibrium situation a bias potential Ebias is used in Equation 4, and the E½ of that particular redox active group is obtained as E½ = Ebias + Esol, whereas 〈xμ〉 = 0.5. Computation of Protonation and Redox Patterns—The electrostatic energies represented by the intrinsic pKa,μint, and (Eμint) values and the Wμν interaction energies were calculated from the solution of the Poisson-Boltzmann equation using the program MULTIFLEX (22Bashford D. Karplus M. J. Phys. Chem. 1991; 95: 9557-9561Crossref Scopus (251) Google Scholar, 23Bashford D. Gerwert K.J. J. Mol. Biol. 1992; 224: 473-486Crossref PubMed Scopus (514) Google Scholar). The respective experimental pKa values of the model compounds in aqueous solution were used as reported before (16Popović D.M. Zarić S.D. Rabenstein B. Knapp E.W. J. Am. Chem. Soc. 2001; 123: 6040-6053Crossref PubMed Scopus (47) Google Scholar). The only redox active groups treated as such were the hemes considered together with their axial and cysteine ligands but without the PR, which were treated separately as independent titratable groups. The bis-histidinyl heme model compound (Em = -220 mV in water; see Ref. 9Wilson G.S. Bioelectrochem. Bioenerg. 1983; 1: 172-179Crossref Scopus (36) Google Scholar) and the histidinyl-methionyl heme model compound (Em = -70 mV in water; see Ref. 9Wilson G.S. Bioelectrochem. Bioenerg. 1983; 1: 172-179Crossref Scopus (36) Google Scholar) were used as reference model systems. All other redox active groups were kept in their reduced state. To compute heme redox potentials that can be compared with the experimental values, the special pair was fixed in the reduced state. Heme redox potentials relevant for ET processes are calculated with the special pair fixed in the oxidized state, because that is the state it adopts under conditions of ET from the cyt c complex to the special pair. All residues of the types Arg, Asp, Glu, Lys, Tyr, Cys, and His (except for residues coordinating cofactors), all N and C termini (except for the formylated H chain N terminus), and the PR were considered titratable. The interior of the protein was assigned a dielectric constant of ϵP = 4. The solvent was modeled as a medium with a dielectric constant of ϵS = 80 and an ionic strength of 100 mm. An ion exclusion layer of 2 Å and a solvent probe radius of 1.4 Å were used to define the volume of the protein. The membrane embedding of the M and L chain was not taken into account, because the cyt c unit is entirely in the aqueous phase where it should experience little influences form the membrane, as has been shown before (15Gunner M.R. Honig B. Proc. Natl. Acad. Sci. U. S. A. 1991; 88: 9151-9155Crossref PubMed Scopus (175) Google Scholar, 28Rabenstein B. Ullmann G.M. Knapp E.W. Biochemistry. 1998; 37: 2488-2495Crossref PubMed Scopus (98) Google Scholar). Because of the large dimensions of the protein, the electrostatic potential was calculated by a three step focusing procedure using a grid spacing of 2.5, 1, and 0.25 Å, respectively. The grids with the
Referência(s)