Photosynthetic Reaction Centers

Transcription

1 JBC Papers in Press. Published on September 15, 2003 as Manuscript M Tuning Heme Redox Potentials in the Cytochrome C Subunit of Photosynthetic Reaction Centers Philipp Voigt and Ernst-Walter Knapp* Institute of Chemistry, Department of Biology, Chemistry, and Pharmacy, Free University of Berlin, Takustraße 6, D Berlin, Germany RUNNING TITLE: Tuning Heme Redox Potentials * Corresponding author: knapp@chemie.fu-berlin.de; fax This work was supported by the Deutsche Forschungsgemeinschaft SFB 498, Project A5, GRK 80/2, GRK 268, GRK 788/1, the Fond der Chemischen Industrie with the BMBF. Abbreviations: cyt, cytochrome; ET, electron transfer; MC, Monte Carlo; MD, molecular dynamics; PR, propionic acid(s); RC, photosynthetic reaction center; RMS, root mean square; Rps., Rhodopseudomonas. Copyright 2003 by The American Society for Biochemistry and Molecular Biology, Inc.

2 SUMMARY 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. 1

3 INTRODUCTION The photosynthetic reaction center (RC) from the purple bacterium Rhodopseudomonas (Rps.) 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 membranespanning 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 (1,2). 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 (3). Quinone-oxidation taking place at the cyt bc 1 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 c 2 that is supposed to bind to the C chain of the RC, probably close to the outermost heme group to reduce the oxidized hemes (4). In the cyt c complex of the Rps. viridis RC, electrons are transferred through a linear chain of low high low high potential cyt c hemes (heme number ) to the special pair chlorophyll dimer where photo-oxidation takes place (5,6). The redox potentials of the four heme groups were determined by various experimental approaches (5-8). Accordingly, the midpoint potentials of hemes 1 to 4 are at 370, 20, 300 and 60 mv, respectively (7). All midpoint values are considerably shifted to higher potentials compared to 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. 9). Heme proteins can be found in a diverse array of enzyme families. This is due to 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 2

4 play an active part in coupled electron and proton translocation processes. A prominent system where it is likely that heme catalyses such processes is cyt c oxidase (10-12). 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 (13,14). Theoretical work on heme proteins was performed before by several groups (see for example Refs. 15,16,17). Gunner and Honig calculated the redox potentials of the hemes in the Rps. viridis RC (15). 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 1). 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 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 c 3 (17). 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 RESP procedure (18,19) to generate charge sets for the hemes, which harmonize with the charges of the CHARMM22 force field (20,21) 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 (13,14,22,23) and by applying a Monte Carlo (MC) titration method to generate the equilibrium protonation and redox pattern (24). 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 3

5 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 (25) and reproduced the measured redox potentials to further validate our approach. METHODS Coordinates. For most calculations, the crystal structure of the Rps. viridis RC at 2.3 Å resolution was used as reported by Deisenhofer et al. (1,2; PDB entry 1prc). In that crystal structure the Q B 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 sulphate 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 (26) routine of CHARMM22 (20,21). 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 otherwise noted. For reasons of comparison the crystal structure reported by Lancaster et al. (27; PDB entry 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 Q B 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. In order to use the 2prc structure in a more sensible way, a restrained simulated annealing molecular dynamics (MD) simulation was performed to optimize the positions of the crystallographically 4

6 undefined side chain atoms within and close to the C chain in the 2prc structure (see the Supplemental Material for details). The structure of the RC mutant C264-RK (25) 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 while 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 ( 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 (21); non-standard charge states for some titratable groups (Arg, Cys, Lys, Tyr, C-ter, N-ter) not available there were used as calculated before (16). 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. (28). These were treated as non-titratable (charge invariant) groups during the electrostatic calculations, since 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 (29). 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 methylester groups. For the special pair, charges derived from Mulliken population analysis (30) 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 5

7 Glu side chain from the CHARMM22 force field. The wave functions of the hemes and their axial ligands were calculated with the program JAGUAR (31), 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 (18,19) 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, while 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, while 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 Table S1 of the Supplemental Material. Theoretical framework for the computation of protonation and redox patterns. Since the derivation of the formalism is equivalent for protonation and redox reactions, the respective terms for redox reactions are given in parentheses. The probability x µ 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 2 N different states (charge patterns) (13) according to N 2 1 (n) (n) x G / RT), with Z = exp( G / RT), (1) (n) µ = xµ exp( Z n= 1 N 2 n= 1 where T is the absolute temperature and R the universal gas constant. In the charge pattern (n), the individual charge state of the titratable (redox active) group µ is denoted by the integer, 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 (n) x µ over self-energies int µ sol G (ph,e ) and pair interactions Wµν 6

8 N N (n) (n) int (n) (n) = µ µ + µ ν µ= 1 ν > µ= 1 µν G x G x x W, (2) where for a titratable group µ ( int exp int model µ = a,µ + a,µ a,µ G (ph) RT ln10 ph ( pk pk pk ) ) (3) or for a redox active group µ ( int exp int model µ sol bias = sol + bias µ + µ µ G (E, E ) F E E (E E E ) ), (4) exp pk a,µ with solution ph, solution redox potential E sol, bias potential E bias and Faraday constant F. The selfenergy terms account for the experimental value (redox potential ) of group µ and the exp E µ model µ difference of the computed pka (E µ ) in the model system pk (E ) and the intrinsic int E µ ( ) in a specific molecular environment. The intrinsic (E ) 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) while all model a,µ int pk a,µ int µ int pk a,µ int µ int pk a,µ other groups are in the reference charge state. The intrinsic (E ) values are formal expressions and do not correspond to measurable quantities. They provide the pk a (E µ ) 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 Eq. (1) involving the energy function G (n) that includes also the pair interactions W µν leads to meaningful charge states. The int a,µ int E µ procedure to compute the intrinsic pk and values and the pair interactions Wµν is discussed in more detail elsewhere (13). A simple method to obtain an estimate of pk aµ values (redox potentials E µ ) of a particular variably charged group µ is to consider the midpoint values pk 1/2 (E 1/2 ), which are defined as the solution ph value (solution redox potential E sol ), where group µ is with probability 0.5 protonated (oxidized), i.e. x µ = 0.5. Note that this definition of pk 1/2 and E 1/2 is formally different from that of pk and E m. One can also probe the redox potential of redox active groups individually while keeping all other 7

9 redox active groups exposed to the solution redox potential. To enforce this non-equilibrium situation a bias potential E bias is used in Eq. (4) and the E 1/2 of that particular redox active group is obtained as E 1/2 = E bias + E sol, while x µ = 0.5. Computation of protonation and redox patterns. The electrostatic energies represented by the int int intrinsic pk a,µ (E µ ) values and the Wµν interaction energies were calculated from the solution of the Poisson-Boltzmann equation using the program MULTIFLEX (22,23). The respective experimental pk a values of the model compounds in aqueous solution were used as reported before (16). 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 (E m = -220 mv in water, Ref. 9) and the histidinyl-methionyl heme model compound (E m = -70 mv in water, Ref. 9) 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, since 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, 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 ε P = 4. The solvent was modeled as a medium with a dielectric constant of ε S = 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, since the cyt c unit is entirely in the aqueous phase where it should experience little influences form the membrane, as has been shown before (15,28). 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 highest resolution were placed at the center of the considered molecular groups. Since the large number of 282 titratable groups prohibits a direct evaluation, the Boltzmann averaged sums (Eq. 1) were calculated using a Monte Carlo (MC) titration method with Metropolis 8

10 sampling. The program KARLSBERG was used for this task (28), which is freely available under the GNU public license ( Oxidation probabilities were evaluated at ph 7 by varying the solution redox potential E sol (Eq. 4) yielding the respective E 1/2 potential. To turn off specific coupling between oxidized heme redox states (inter-heme redox coupling), all hemes were kept at a solution redox potential of 200 mv while the heme of interest was subject to an additional bias potential E bias. In this way, all hemes were kept fully reduced except the heme of interest, which was MC titrated by varying the additional bias potential. To probe the dependency of the E 1/2 value on E sol the midpoint redox potentials were determined with a bias potential applied to the individual hemes (17). Details on the procedure used for the MC titration are given in the Supplemental Material. RESULTS AND DISCUSSION Protonation pattern. We calculated the protonation pattern of all titratable groups in the RC and the redox potentials of the four cyt c hemes using three different structures, i.e. the 1prc (1prc-Htitrated) and 2prc (2prc-H-titrated) crystal structures and an annealed version (2prc-H-annealed) of the latter one. These three structures show the same protonation pattern at ph 7, except for a few differences: The 1prc and 2prc crystal structures differ by a total of 3.1 protons affecting 24 residues with the 1prc structure showing the higher overall protonation. Throughout the protein, these differences are almost exclusively located at solvent-exposed residues. A closer inspection of the crystallographic data revealed that the coordinates of these residues or of other residues in their vicinity are only partially resolved, i.e. the side chain ends have zero occupancy. Allowing some of these partially undefined residues to relax in an MD simulation based on the 2prc structure produced the 2prc-H-annealed structure. Figure S1 shows an example of the structural differences within these three structures. The close contact between the terminal side chain nitrogens of Arg-C199 and Lys- C198 in the 2prc structure (N-N distance 2.8 Å) leads to a partial deprotonation of Lys-C198, which is fully protonated in the 1prc and the 2prc-H-annealed structure. In the latter structure, Lys-C198 forms a salt bridge with Asp-C197, which is fully deprotonated in all considered structures. While the crystal structure 1prc exhibits a sensible placing of undefined side chain atoms, these atom positions may not be fully optimized in the crystal structure 2prc. The difference in total protonation 9

11 between 1prc and 2prc-H-annealed is confined to 17 as compared to 24 residues, but its value is slightly enlarged (from 3.1 to 3.6 protons, compared to the 1prc-2prc difference) due to a higher degree of deprotonation at acidic residues. The most drastic changes in protonation probability between 2prc and the 2prc-H-annealed structure are located on Glu-C48, Glu-C149, Lys-C198 and Glu-C299, ranging from 0.15 to 0.58 protons. An annealing-based optimization considering all undefined atom positions is likely to further reduce these differences but would be beyond the scope of this study. All further stated results refer to the 1prc structure unless otherwise noted. For this structure, all but 15 of the 282 titratable amino acid residues show standard protonation at ph 7. According to their acidic nature, the heme PR are deprotonated, except for those bound to heme 3. At ph 7, they appear both to be protonated in the crystal structure 1prc. This unusual protonation state is due to the crowded conformation of the heme 3 PR, whose shortest oxygen-oxygen distance is 2.5 Å only. However, in the 2prc and 2prc-H-annealed structures, where the shortest oxygenoxygen distance between the acidic PR is expanded to 3.0 Å, only PR D was calculated to be protonated. Since the protonation state of a protein is not known a priori, the optimization of the crystallographically undefined hydrogen atom positions has to be performed without a profound knowledge about hydrogen bonding schemes allowed by the actual protonation state, which can be computed only after defining the molecular system completely. We therefore minimized the hydrogen positions again, using the obtained protonation scheme. This led to small structural changes most relevant around the protonated heme 3 PR. In the corrected structure (1prc-H-titrated), the polar hydrogens of the Tyr-C89 and Tyr-C102 hydroxyl groups and of the Arg-C293 guanidinium group moved away from the protonated PR oxygens by up to 0.25 Å. The protonation pattern computed at ph 7 from this corrected structure was significantly different only at some residues showing unusual protonation with mean changes in protonation of about 3% and maximum changes of up to 20% (Glu-C327) relative to the initial structure (1prc-H). Additionally, these structural changes gave rise to different redox potentials for heme 3. Using the initial structure (1prc-H), a redox potential of 241 mv was computed as compared to the value of 297 mv obtained for the optimized structure. For the other three heme groups these values differed only by up to 3 10

12 mv. Further details on the protonation pattern and the redox behavior of heme 3 in the considered structures are given in the Supplemental Material. Heme redox potentials. The experimental determination of the heme redox potentials is performed by varying the solution redox potential and monitoring the heme redox states by UV-VIS spectroscopy (6,7). In doing so, the special pair remains continuously in the reduced state due to its high redox potential of 500 mv (3) and the lack of strong illumination at a wavelength suitable for an effective photo-oxidation. Hence, our computations are based on models where the special pair charges refer to its reduced state. If we instead used the charges of a oxidized special pair, the calculated redox potential of heme 1, which is closest to the special pair, was increased by 15 mv, while the influence on the other hemes was negligible. This result was independent of the structure used for the computations. The calculated redox potentials of the four hemes are summarized in Table 1 together with experimental data and previous theoretical results. The 430 mv span of the midpoint potentials as well as their inter-heme differences are well reproduced in all our calculations regardless of the considered structure. Figure 2 shows the calculated oxidation probabilities of the heme groups as a function of the solution redox potential. All four hemes show an almost ideal Nernst-like titration curve as experimentally measured (5). The calculated absolute values of heme midpoint potentials obtained with the crystal structure 1prc agree with experimental data with an accuracy of 25 mv (5-7), while the quality of agreement obtained with the 2prc structure was less good. The main reason for these differences seems to be the above described improper placement of several side chain atoms, which leads to a different protonation scheme and therefore a different electrostatic environment of the hemes within the RC structures. This is clarified by the significant improvement achieved with the use of the 2prc-H-annealed structure: Its protonation pattern more closely resembles that of the 1prc structure, and the calculated heme midpoint potentials agree within 50 mv with the experimental values, which we consider to be still a reasonable agreement. Static influence of the protonation pattern on the heme redox potentials. The results presented here were obtained with an approach that considers protonation and redox equilibria simultaneously. Thereby, coupling between changes in protonation and redox states is taken into account. 11

13 Additionally, fluctuations in protonation and reduction/oxidation are accounted for by using an MC titration. The influence of such fluctuations was thoroughly investigated and termed occupational entropy by Baptista et al. in their study on cyt c 3 from Desulfovibrio vulgaris (32). In the equivalent treatment used here, a faithful representation of the system is achieved. In previous calculations on the RC by Gunner and Honig (15), such coupling influences were only partially accounted for by using a static protonation pattern. To directly assess the differences between a dynamic and a static treatment of the protonation pattern in determining the heme redox potentials, results obtained with the approach used here were compared to redox potentials obtained with a fixed protonation pattern (Table 2). All protein side chains were constrained to their standard protonation state, which is an approximate but reasonable treatment considering the low number of protein side chains in unusual protonation states. The PR were either left unconstrained or constrained to be ionized on all hemes. Heme 3 was also considered with both of its PR constrained to be protonated, since that is the equilibrium protonation state found in the complete MC titration. The order of the heme redox potentials was still computed correctly for most of these static models, but the absolute values differed. Nevertheless, accounting for the coupling between protonation and redox states leads to a significant improvement. Changes between the dynamic and static treatments are mostly due to interruption of the coupling between the heme redox centers and nearby titratable residues, as for example Arg-C264 at heme 1, PR D of heme 4 and most importantly PR D of heme 3 (see below and Fig. S2 of the Supplemental Material). Mutual redox coupling of hemes. Having the available experimental data concerning the redox behavior of the cyt c heme cofactors of the Rps. viridis RC faithfully reproduced, we set out to analyze by which means the protein environment determines the individual midpoint potentials of the heme cofactors. The cyt c hemes establish the upper part of an ET chain through the Rps. viridis RC (Fig. 1). As can be expected from their function and spatial proximity, their redox behavior is strongly coupled. Figure 3 shows the dependence of each midpoint potential on the solution redox potential, which governs the degree of oxidation of each redox active group and is an experimentally accessible parameter. Experimentally, this dependence can not be measured easily, since 12

14 conventional methods to determine midpoint potentials are limited to conditions near equilibrium where the solution redox potential is close to the midpoint potential of the cofactor in focus. Nevertheless, this information is crucial to the understanding of kinetic data on ET processes that generally correspond to a non-equilibrium situation of the participating redox active groups (33). Theoretical computations enabled us to describe the midpoint potential of a redox active group under varying influences from other redox centers in the system, thereby allowing for a description of interactions between multiple redox active groups. Hemes, whose redox state has switched from reduced to oxidized, shift the midpoint potentials of nearby hemes to higher values. These shifts describe a redox titration pattern that is similar to a Nernst titration curve (Fig. 3). As expected, the inter-heme redox coupling plays a significant role in the determination of the high-potential heme redox potentials. Under conditions where all four hemes are reduced, the high-potential hemes possess midpoint potentials which are 70 mv (heme 1), respectively 85 mv (heme 3), lower than under equilibrium conditions used to experimentally assess these midpoint values. The heme redox potentials at low solution redox potential, where all hemes are reduced, are applicable to ET processes along the linear chain of hemes that are (approximately) adiabatic with respect to the protonation pattern. Compared to the 70 mv midpoint potential of a methionine-histidine ligated heme group in aqueous solution (9), the reduced states of hemes 1 and 3 are stabilized by 414 mev, respectively 367 mev, within the RC. Nearly one sixth, respectively one quarter of this stabilization energy is due to interactions with the oxidized low-potential hemes. Notably, these interactions are confined to pairs of one low and one high potential heme: Oxidation of heme 3 has no further influence on the midpoint potential of heme 1, probably due to the separating distance. On the other hand, heme 4 is markedly influenced by oxidation of heme 3, which leads to an increase in midpoint potential of 35 mv. Surprisingly, the low-potential heme 2 shows no dependence on the redox state of the highpotential hemes, although it exerts a strong influence on these hemes (Fig. 3). This apparent asymmetry of inter-heme redox coupling is in contrast to assumptions made in preceding work (15). Factors determining heme redox potentials. Generally, midpoint potentials of redox active cofactors in proteins depend strongly on the electrostatic interactions provided by the protein 13

15 environment. Here, we tried to separate different influences of this environment and to describe their relevance in tuning the heme midpoint potentials. In contrast to the strong electrostatic shielding in water due to its high dielectric constant of ε S = 80, electrostatic interactions in proteins are much more pronounced. Inside proteins, the value of the dielectric constant is estimated to be as low as ε P = 4, although this value is still a matter of debate and differs depending on the type of application and model description used (14,24,34). Therefore, a basic factor in midpoint potential tuning is the transfer of a cofactor group from aqueous solution to its position in the protein. We modeled this by placing each heme alone at its corresponding position inside the protein volume devoid of all atomic charges and surrounded by aqueous solution. With the attached PR protonated (i.e. in neutral charge state), the midpoint potentials were shifted to higher values according to the degree of solvent-exposure (Table 3). Heme 1 as the most buried group is shifted by 223 mv, heme 4 as the most solvent-exposed by only 144 mv. A prerequisite for this stabilization of the uncharged reduced state of the heme porphyrin ring system are protonated (neutral) PR. Constraining the two PR to be deprotonated leads to a different situation, where the corresponding heme redox potentials are shifted even below the respective values in aqueous solution due to the amplified influence of the negative charges at the PR, which destabilize the heme reduced state. However, leaving the PR protonation state unconstrained in these computations, protonated PR are obtained with the exception of heme 2. The heme 2 PR are largely solventexposed such that they have a preference to be partially ionized in this state of modeling. Heme 2, with its PR A and PR D being 25%, respectively 75%, protonated, has a redox potential of -125 mv. For the other hemes, the repulsive interactions of the largely unshielded negative charges of ionized PR force them to be fully protonated. As the peptide backbone is an integral part of a protein, it may not offer a distinct way to tune midpoint potentials. Nevertheless, its influence has to be taken into account for all further steps considering protein side chains as a mean to tune the values of cofactor redox potentials. To measure the backbone influence on the heme redox potentials independent of influences on the PR protonation, the PR were constrained to bear charges as they do in the complete model (i.e. deprotonated for hemes 1, 2, 4, protonated for heme 3). In comparison with the respective values 14

16 obtained if only a single heme is considered, the peptide backbone invokes a stabilization of the reduced state for hemes 1 and 4, while destabilizing it for hemes 2 and 3. Different degrees of PR neutralization through hydrogen bonds with backbone atoms could explain this result. The acidic PR of hemes 1 and 4 establish several hydrogen bonds with backbone NH groups while the PR of hemes 2 and 3 do not or only weakly, respectively. Already on this level of description one can observe the two different populations of high and low potential hemes (Table 3). Placement of atomic charges from all side chains (titratable and non-titratable) in a neutral charge state into the low-dielectric protein volume leads to slight reductions in redox potentials for hemes 1, 3 and 4, while the reduced state of heme 2 is stabilized by 165 mev. Establishment of hydrogen bonds of heme 2 PR with the side chains of Gln-C263 and Thr-C128 could explain this difference, since the other heme PR sparsely establish hydrogen bonds with side chains. Taken together, the atomic charges from backbone and side chains in neutral charge state stabilize the reduced state of the hemes by up to 140 mev. Heme 3 is an exception, in that it experiences a destabilization of its reduced state by 80 mev, presumably since it is the only heme whose PR are protonated. If the PR protonation is left unconstrained in the latter charge model, the two heme populations become more distinct. Two high-potential hemes (1 and 3) with midpoint potentials around 150 mv are distinguished from two low-potential hemes (2 and 4) with a redox potential around 70 mv. This is at least partially due to the fact that heme 3 has both of its PR protonated and that heme 1 is bearing 1.5 protons on its PR, while heme 4 and heme 2 only show 0.5 and 0.07 protons, respectively, on their PR at their midpoint values. The midpoint values obtained on this model are comparable to those of the single hemes with neutralized PR (with the exception of heme 4, see Table 3). Here, charge neutralization is achieved to a substantial extent by direct PR protonation. In the complete model, basic side chains compensate the negative PR charges and also raise the heme redox potentials further on through electrostatic interactions. Influences of individual charged residues. The placement of acidic and basic side chains, which can carry a unit negative or positive charge, respectively, is a major tool to specifically tune the redox potential of a nearby cofactor. This can influence electrostatic interactions through the medium and, more importantly, through the establishment of bond-like structures in terms of 15

17 hydrogen bonds and salt bridges. The C chain contains 38 basic and 28 acidic residues including the 8 PR, thus leading to an overall positive electrostatic potential in this part of the RC. The shifts in the heme redox potentials brought about by including charged groups into the RC protein model are for this reason generally positive. Cyt c type hemes can establish hydrogen bonds or salt bridges only through their PR and, to much lesser extent, through their axial ligands. Taking a closer look on the environment of the hemes, some charged residues with direct involvement in PR hydrogen bonding and salt bridge networks or just spatial proximity to the hemes can be identified. We examined the influence of these residues with respect to their charged nature by forcing them to stay in their uncharged state (Table 4). Residues closer than 5 Å to any atom of the hemes as well as residues involved in salt bridges with such residues were considered. Figure S3 displays the arrangement of the considered residues around each heme. Notably, such charged residues are found mostly at the heme edge where the PR are attached and are involved in salt bridges with the PR. As mentioned above, neutralization of the PR charges is prerequisite for the hemes to have a midpoint potential that lies significantly above the value assumed in aqueous solution. The basic residues Arg-C202 and Arg-C272 are more or less directly neutralizing PR A and PR D of heme 1, respectively. Arg-C264 is involved in a strong salt bridge (N-O distance 4 Å) with PR A. Under conditions where Arg-C264 is neutral, PR A of heme 1 is 60% protonated at a solution redox potential where heme 1 is half way oxidized. The absence of the positive charge of Arg-C264 forces the otherwise fully deprotonated PR A into a partially protonated state. Arg-C264 is by far the most significant single residue influencing a heme redox potential in the RC. Gunner and Honig (15) stated an influence of Arg-C264 on the redox potential of heme 1 of more than twice the magnitude gained from our calculations. However, they omitted the influence of this residue on the PR, an interaction that is crucial for the determination of the heme 1 redox potential. Complex interactions also account for the results obtained on the two acidic residues in the salt bridge network around the heme 1 PR. Despite their negative charge, Glu-C254 and Asp-M314 exert a stabilizing influence on the reduced state of heme 1, since the buried positive charge of Arg-C264 is stabilized by interactions with these two acidic residues. Absence of this stabilizing effect would lead to a decrease in protonation probability of Arg-C264, which occurs if Glu-C254 or Asp-M314 16

18 are neutralized by protonation, yielding a protonation probability of Arg-C264 that is reduced from 0.75 to 0.41 or 0.33, respectively. Since Arg-C264 is much closer to heme 1, the decrease of positive charge on Arg-C264 overcompensates for the loss of negative charge at Glu-C254 or Asp-M314 brought about by protonation of these residues. This interaction scheme is also not taken into account in the calculations of Gunner and Honig (15). Since the heme 1 PR are essentially buried in the RC, their charges need to be neutralized by basic residues. This is unnecessary for the heme 2 PR, which are essentially solvent-exposed, and thus their charges are strongly shielded. Therefore, no direct involvement of salt bridges is needed here. The heme 2 PR are close to the basic residue Lys-C314, which however is involved in a salt bridge with Glu-C21. Accordingly, these charged residues, albeit close to heme 2, have comparatively little influence on its redox potential. The same is true for the salt-bridged pair Asp-C304 Arg-C306 that has no net influence on the redox potential of heme 2, since the positive and negative charges cancel. For the salt bridge Arg-C137 Asp-C35 an overall stabilizing influence on the reduced state of heme 2 can be observed. The action of Asp-C35 on Arg-C137 is similar to that of Asp-M314 on Arg-C264. Under conditions where Asp-C35 is neutral, Arg-C137 is still 20% protonated, whereas it assumes a fully protonated state when Asp-C35 is ionized. If one constrains both of these residues to have zero net charge by protonating Asp-C35 and deprotonating Arg-C137, it turns out that the ion pair contributes a positive electrostatic potential at the site of heme 2, shifting the redox potential by +42 mv. Arg-C272 acts on the redox potential of heme 2 despite their relatively large distances and significantly stabilizes the reduced state of this heme. Since the PR at heme 3 are protonated, its electrostatic environment is markedly different from all other hemes. PR A is fully protonated under all conditions considered in our computations and PR D is partially deprotonating as heme 3 is changing to its oxidized state (Fig. S2). Therefore, no need arises to compensate the negative charge of the PR through basic side chains. Nevertheless, the closely located Arg-C293 would be able to establish a salt bridge to PR A, provided that PR A is deprotonated. The 2prc structure shows a more relaxed conformation of the heme 3 PR, leading to a protonation of PR D only. There, PR A is able to establish a salt bridge with Arg-C293. Forcing Arg-C293 to be deprotonated in the 2prc-H-annealed structure, the redox potential of heme 3 is 17

19 lowered by 50 mv compared to the unconstrained situation. This is consistent with an influence of the positively charged Arg-C293 that can compensate negative charge at PR A. The salt bridge Arg- C137 Asp-C35 invokes an up-shift of the heme 3 redox potential by 26 mv, as obtained by neutralizing the side chains of both residues, i.e. deprotonating Arg and protonating Asp. Since Arg- C137 is much closer to heme 3 as is Asp-C35, the influence of the positive charge of the basic group is not completely counterbalanced by the negative charge of the acidic group. Heme 4 is least buried in the protein volume of the RC. Its PR A is involved in a salt bridge with Arg-C108, which is also interacting with Glu-C99. Although neutralizing Arg-C108 is accompanied with a 25% increase in protonation of PR A, a significant decrease in the heme 4 redox potential is observed. Also here, a single residue plays a crucial role in the determination of a heme redox potential. Mutant C264-RK. Chen et al. (25) recently reported the generation of a mutant Rps. viridis RC where arginine was replaced by lysine on position 264 of the C chain. The redox potential of heme 1 decreases to 270 mv due to this mutation (25). We modeled the C264-RK structure based on the 1prc coordinates and calculated the heme redox potentials. The measured and calculated redox potentials of hemes 2 4 are essentially the same for the mutant and wild type structure. The redox potential of heme 1 was calculated to be 162 mv. This is significantly lower than the experimentally measured value. The titration behavior of heme 1 is strongly coupled to Lys-C264. At a solution redox potential of 170 mv (heme 1 is half way oxidized), Lys-C264 has a protonation probability of 0.53, compared to 0.89 at a solution redox potential of 0 mv. In the wild type structure, Arg-C264 is not as strongly coupled to heme 1, showing a decrease of protonation probability from 1 to This higher degree of coupling in our model of the mutant structure could be due to an overestimation of the cavity generated by the loss of the guanidinium group. Constraining Lys-C264 to titrate similarly as Arg-C264 in the wild type structure, i.e. to carry atomic charges corresponding to 0.75 protons at a solution redox potential of 260 mv (heme 1 is half way oxidized), yields a redox potential of 239 mv for heme 1. With this correction for the overestimated coupling, the calculated value compares well with the experimental value. Even if one considers a slightly stronger coupling with the Lys-C264 protonation reduced to 0.6, the calculated value of 195 mv is still reasonable 18

20 considering the uncertainties of the model with respect to the coordinates. Additionally, changes in the electronic structure of the porphyrin ring system indicated by the spectral shift of the heme 1 absorption band accompanying the mutation (25) were not taken into account in this solely electrostatic treatment of interactions. CONCLUSION In this study, we calculated the redox potentials of the cyt c hemes in the RC from Rps. viridis. Our results agree with measured data within experimental uncertainty. This is considerably better than previous computations on the same system. Possible reasons for the better quality of our data are the use of quantum chemically derived atomic charges for the hemes, consideration of the actual protonation pattern of the RC as well as of the coupling between the redox and protonation pattern in the computation of the heme redox potentials, a more accurate treatment of the surrounding solvent by accounting for the influence of the solution redox potential and an accurate connection with experimental redox potentials of suitable model systems without the involvement of correction factors. Our calculations performed on two different crystal structures of the RC showed that a crystal or NMR structure of high quality is a prerequisite to obtain reliable results in the computation of electrostatic properties. Correcting structural artifacts in one of the considered crystal structures that are likely due to incomplete structural optimization improved the agreement achieved with this structure. Another crucial point for the success of the present study was to correct the coordinates of the hydrogen atoms after a preliminary computation of the protonation pattern and to repeat the computation of the protonation pattern with the new hydrogen coordinates, similarly emphasizing the importance of well-defined coordinates. The procedure used to obtain atomic partial charges for the hemes was successful for the present applications, and will probably be also useful for similar calculations on other systems containing cyt c type hemes. The usage of Hartree-Fock based quantum chemical calculations was sufficient to obtain sensible charges and no improvement could be achieved with charges based on density functional calculations (unpublished results), consistent with previous observations made by other groups (35). 19

21 Redox potentials of cofactors in proteins containing multiple redox active centers, which must experimentally be determined under equilibrium conditions, often differ from the potentials adopted by these groups under physiological or non-equilibrium conditions used for kinetic studies on ET processes. This difference is due to coupling interactions between the redox active centers. We calculated the coupling influences between the hemes in the RC and plotted the working potentials of the heme groups as a function of the solution redox potential, showing that these interactions strongly depend on the redox state of the protein and providing data for the interpretation of ET kinetics. The redox potentials of the individual hemes are established by the action of several influences. The reduced state of a heme group is stabilized by the hydrophobic environment of the protein proportionally to the degree of solvent inaccessibility, provided that the bound PR are neutralized. A deprotonation of the PR turns this stabilization into a destabilization. Heme is a unique redox system, fundamentally different from most others, since it is covalently connected to the charge variable PR, which are most important heme redox potential determinants. Therefore, also the solvent accessibility of the PR is of importance for the heme redox potential. The aqueous solvent shields the PR charges and thus promotes their deprotonation, which is observed for heme 2. Filling the protein dielectric medium with atomic point charges from the backbone and neutral side chain atoms leads generally to a stabilization of the heme reduced state independent of the PR protonation. However, neutralization of PR charges is a prerequisite to obtain heme redox potentials that are above the values assumed by the heme model systems in the solvent. This can occur by salt bridges formed between the PR and basic residues. The action of positive charges of basic residues is most pronounced on heme 1. The presence of negatively charged groups nearby stabilize the positive charges on the basic residues to allow for their full protonation. For example, Arg-C272 and Arg- C202 are fully protonated over the whole ph range from 0 to 14, due to their interactions with Glu- C254, Asp-M314 and the heme 1 PR. Around heme 3, the neutralization of the PR is achieved by a direct protonation brought about by steric constraints. Further increases of the heme redox potentials are also possible through residues that are not interacting directly with the heme PR. These are obviously not as important as those engaged in salt bridges with the PR (Table 4). 20

22 Generally, influences of single residues can be of a very complex nature as they influence the protonation scheme of the whole protein, leading to charge compensations whose net impact on the redox active group can be either to increase or decrease its redox potential. The redox potentials calculated in this study by replacing single charged residues with neutral ones to probe their influences consider all direct and indirect actions. Some of those mutations considered here should be relevant for kinetic measurements on ET processes, as they change the order of heme redox potentials. For instance, replacing Arg-C137 with a neutral residue should place the redox potential of heme 2 below that of heme 4. Mutations of Arg at position C264 should be particularly interesting, since that residue shifts the heme 1 redox potential so enormously (Table 4). One mutant of this type was generated by Chen et al. (25) changing Arg to Lys. In our calculations, the impact of this mutation on the heme redox potentials was reproduced. Our results show the general feasibility of a combination of force field and electrostatic computations in the prediction of changes in titration and redox behavior brought about by site-directed mutagenesis. The investigation of side chain influences covers the most important residues involved in the redox potential tuning. However, the impact of subtle changes between the 2prc and the corresponding 2prc-H-annealed structure, which are seemingly unrelated to the hemes, demonstrates that numerous but comparatively small conformational changes can have a perceptible effect on redox potentials, if these changes alter the protonation pattern of the protein significantly. It becomes clear from the work presented here that one should be cautious to calculate redox potentials by a simple summation of independent influences from individual charged residues because of the complexity stemming from a large number of interacting groups and more importantly of the fact that the interaction patterns of some charged residues have a complex nature by themselves. Nevertheless, important residues can be identified and their influences on cofactor redox potentials can be understood as we have shown in this study. We demonstrated that it is possible to gain a thorough understanding of protein redox cofactor tuning from calculations based on electrostatic models and to make predictions about possible mutations that can significantly change redox properties of those cofactors. The heme redox system is different from most other redox cofactors due to the variably charged PR. Since heme proteins 21

23 function at key points of the living cell, a profound knowledge of these systems is of general importance. ACKNOWLEDGMENTS We thank Dr. Donald Bashford and Dr. Martin Karplus for providing the programs MULTIFLEX and CHARMM, respectively. We are grateful to Dr. Dragan Popović, Dr. Björn Rabenstein, Daniel Winkelmann and Giulia Morra for helpful discussions and to Marcel Schmidt am Busch for the help with quantum chemical calculations. SUPPLEMENTAL MATERIAL AVAILABLE The on-line version of this article (available at contains Supplemental Material, which covers extensions to the Methods and Results sections as indicated in the main text, Supplemental Figures S1, S2 and S3 and Supplemental Table S1. The atomic coordinates on which the computations are based are available at REFERENCES 1. Deisenhofer, J., Epp, O., Miki, K., Huber, H., and Michel, H. (1985) Nature 318, Deisenhofer, J., Epp, O., Sinning, I., and Michel, H. (1995) J. Mol. Biol. 246(3), Lancaster, C. R., and Michel, H. (2001) in Handbook of Metalloproteins (Messerschmidt, A., Huber, R., Poulos, T., and Wieghardt, K., eds), pp , John Wiley & Sons, Ltd, Chichester 4. Osyczka, A., Nagashima, K. V. P., Sogabe, S., Miki, K., Yoshida, M., Shimada, K., and Matsuura, K. (1998) Biochemistry 37, Nitschke, W., and Rutherford, A. W. (1989) Biochemistry 28, Dracheva, S. M., Drachev, L. A., Konstantinov, A. A., Semenov, A. Y., Skulachev, V. P., Arutjunjan, A. M., Shuvalov, V. A., and Zaberezhnaya, S. M. (1988) Eur. J. Biochem. 171, Fritzsch, G., Buchanan, S., and Michel, H. (1989) Biochim. Biophys. Acta 977, Alegria, G., and Dutton, P. L. (1991) Biochim. Biophys. Acta 1057,

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26 Table 1. Redox potentials of the four cyt c hemes in the Rps. viridis RC (values in mv) heme 1 heme 2 heme 3 heme 4 computed values 1prc-H-titrated a prc-H-titrated a prc-H-annealed a Gunner & Honig (15) b experimental data Fritsch et al. (7) c Dracheva et al. (6) d See text for a description of the coordinate sets used. The special pair was kept in the reduced state. a calculated at ph 7. b no ph value given. c measured at ph 6. d measured at ph 7 and ph 8. Table 2. Static contributions from side chain and PR protonation in calculating heme redox potentials. Heme redox potentials, given in units of mv, were computed while applying different constraints to the protonation pattern. Constraints on protonation heme 1 heme 2 heme 3 heme 4 No constraints all side chains in standard charge a state, PR unconstrained all side chains in standard charge b state, heme 3 PR protonated all side chains in standard charge c state, all PR ionized a All titratable protein side chains were fixed in their standard charge state at ph 7, i.e. Asp and Glu with negative and Lys and Arg with positive unit charge, while the PR were left unconstrained. b All titratable protein side chains were fixed in their standard charge state at ph 7, while the PR were constrained to be protonated for heme 3 and ionized for heme 1, 2 and 4. c All titratable protein side chains were fixed in their standard charge state at ph 7, while the PR were constrained to be ionized for all hemes. 25

27 Table 3. Basic factors determining the cyt c heme redox potentials. Heme redox potentials, given in units of mv, were computed for different charge models based on the 1prc crystal structure. charge model heme 1 heme 2 heme 3 heme 4 aqueous solution (9) single heme, PR ionized a single heme, PR neutral b all hemes & backbone atoms, c PR constrained all side chains in neutral charge d state, PR constrained all side chains in neutral charge e state, PR unconstrained complete model without f inter-heme redox coupling Complete model with inter-heme redox coupling a All atomic partial charges were set to zero except those of the heme in focus, including its axial ligands and PR in the deprotonated state. b All atomic partial charges were set to zero except those of the heme in focus, including its axial ligands and PR in the protonated state. c All atomic partial charges were set to zero except backbone atoms and all hemes including their axial ligands and PR. The latter were constrained to the most probable charge state obtained from the complete model. To turn off the inter-heme redox coupling, all hemes were kept at a solution redox potential of 200 mv while the heme of interest was subject to an additional bias potential. All results shown below this table entry were obtained with the same method so that inter-heme redox coupling is absent except where noted. d All titratable protein side chains were fixed in their neutral charge state except the PR, which were kept in the charge state obtained from the complete model. e All titratable protein side chains were fixed in their neutral charge state, while the PR were left unconstrained. f All hemes except the heme under consideration is kept in the reduced state of neutral charge. 26

28 Table 4. Influence of individual titratable groups on heme redox potentials (values in mv). Residue in focus heme 1 heme 2 heme 3 heme 4 Arg-C Glu-C Arg-C Arg-C Asp-M Glu-C Lys-C Asp-C Arg-C Arg-C Asp-C Arg-C Arg-C Glu-C Shifts of the redox potentials are computed for each heme by fixing the residue in focus to its neutral charge state that is protonated for acidic and deprotonated for basic residues. The given values are differences E ½ - E neutral, where E ½ represents the redox potential obtained on the full model and E neutral stands for the redox potential obtained with the respective residue set to its neutral charge state. Shifts whose absolute values are larger than 30 mv are displayed in boldface type. Residues are listed according to their order of discussion in the text. 27

29 Figure 1. Crystal structure of the cyt c part (C chain) of the RC from Rps. viridis. The inset shows the whole RC crystal structure (2) with its membrane spanning L and M chains and the cytoplasmic H chain. The C chain is situated at the top of the RC. Hemes and axial ligands are shown in dark gray. Heme 1 is closest to the special pair. The numbering scheme of the hemes used in this study is indicated in the figure. A helical turn is omitted for better visibility of heme 2. The figure was generated using MOLSCRIPT (36) and Raster3D (37). 28