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Copyright © 2006 The Biophysical Society. All rights reserved.
Biophysical Journal, Volume 90, Issue 1, 366-380, 1 January 2006

doi:10.1529/biophysj.105.065185

Bioenergetics

A Brownian Dynamics Study of the Interaction of Phormidium Cytochrome f with Various Cyanobacterial Plastocyanins

Elizabeth L. Gross^,   and Irving Rosenberg

Department of Biochemistry, The Ohio State University, Columbus, Ohio

Address reprint requests to Elizabeth L. Gross.

Cytochrome f (cyt f) is a member of the cytochrome b₆f complex 1,2,3,4. It accepts electrons from the Rieske FeS protein and donates them to plastocyanin (PC). PC is a blue copper protein which is a mobile electron carrier located in the lumen of the thylakoid, where it accepts electrons from cyt f and donates them to P700 in Photosystem I 5,6,7,8,9,10,11.

Electrostatic interactions have been shown to be very important for complex formation between cyt f and PC from higher plants using chemical modification 12,13,14, cross-linking 15,16,17, and mutagenesis techniques 18,19,20,21. In contrast, mutagenesis studies of cyt f from the green alga Chlamydomonas demonstrated that electrostatic interactions were not important in Chlamydomonas in vivo 22, although they were observed in vitro 20.

Higher plant cyt fs have a positively-charged electrostatic field 23 due to a series of highly conserved positively charged residues (K58, K65, K66, K187, and R209 in turnip cyt f) 24,25,26, which interact with the negatively-charged electrostatic field on higher plant PCs 27 caused by two clusters of anionic residues 7,8 on PC. In cyanobacterial cyt fs, such as that of Phormidium laminosum, the cationic residues are replaced by anionic residues 1,28 and the anionic patches on PC are replaced by cationic or neutral residues (Fig. 1) 29,30,31,32,33,34,35. The net charge on cyanobacterial PCs varies over a wide range. Prochlorothrix hollandica and Nostoc sp. PCC7119 (formerly Anabaena variabilis) PCs have a net charge of 1.1 and 1.0 at pH 7.0, respectively, as calculated using the program MacroDox 36. Positively-charged residues on these PC molecules, including R93 (consensus sequence; see Appendix, K11, and K35 surround the H92 ligand to the copper atom resulting in a positively-charged electrostatic field over the top of the molecule (Figure 1A). In contrast, Phormidium PC has a net charge of −2.3 at pH 7.0 and shows a much reduced positive patch surrounding H92 (Figure 1A). The PCs from Synechocystis sp. PCC6803 and Synechococcus sp. PCC7922, with a net charge of −1.8 and −4.5, respectively, have a negative electrostatic field except in the vicinity of H92 and R93 (Figure 1B).

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Figure 1

Cyanobacterial plastocyanins. (A) (Top row) View of cyanobacterial PCs looking down on the H92 (consensus sequence) view of three cyanobacterial plastocyanins (Prochlorothrix, Nostoc, and Phormidium) showing charged residues. (H92, black; arginine, dark blue; lysine, light blue; glutamate, red; and aspartate, magenta.) (Bottom row) Electrostatic fields at 1kT/e⁻ (blue) and −1kT/e⁻ (red) for the five plastocyanins. (B) Synechocystis and Synechococcus PC. Other conditions are the same as for Figure 1A.

The role of the electrostatic interactions in complex formation between Phormidium cyt f and both Phormidium PC 37 and Prochlorothrix PC 38 has been studied using NMR spectroscopy. Complex formation between Prochlorothrix PC and Phormidium cyt f was dependent on the salt concentration indicating the presence of electrostatic interactions whereas the interaction of Phormidium PC, also with Phormidium cyt f, showed no salt dependence—suggesting that, in this case, electrostatic interactions do not play an important role in complex formation. However, Schlarb-Ridley et al. 34 observed that mutation of charged residues on Phormidium PC did affect the rate of electron transfer from Phormidium cyt f to Phormidium PC, suggesting that electrostatic interactions do play a role.

In this article, we will use Brownian dynamics (BD) simulations 35,36,39 to examine the relationship between the net charge on five PC molecules from five different species of cyanobacteria (Prochlorothrix hollandica, Nostoc sp. PCC7119, Phormidium laminosum, Synechocystis sp. PCC6803, and Synechococcus sp. PCC7942) and their ability to form complexes with Phormidium laminosum cyt f. We show that electrostatic interactions between cyt f and PC depend on two factors: 1) the net charge on the PC molecule; and 2), the distribution of charged residues surrounding H92 on the surface of the PC molecule, which will, in turn, allow us to show that cyanobacterial PCs possess a common binding site for Phormidium cyt f.

BD simulations have been used to study the interaction of turnip cyt f with poplar 40 and spinach PC 41,42; Chlamydomonas cyt f interacting with Chlamydomonas PC 43,44; and Phormidium cyt f interacting with Phormidium PC 35. Brownian dynamics simulations of the interaction between Phormidium PC and Phormidium cyt f35 showed that fewer complexes were formed than for the green alga Chlamydomonas reinhardtii PC interacting with Chlamydomonas cyt f, unless the Zn²⁺ ion found in the crystal structure of Phormidium PC 31 was included in the simulations. However, even in the absence of the Zn²⁺ ion, mutation of charged residues on Phormidium PC and cyt f affected the rate of complex formation in BD simulations.

The protein structures were obtained from the Protein Data Bank (PDB) (http://www.rcsb.org/pdb/45). Phormidium laminosum cyt f (structure 1CI3) was taken from Carrell et al. 28. The Phormidium laminosum PC used was structure A (1BAW) from Bond et al. 31; the Prochlorothrix hollandica PC used was the minimized average NMR structure (1B3I) of Babu et al. 30; the Nostoc sp. PCC7119 (formerly Anabaena variabilis) PC used was structure 3 of 1NIN from Badsburg et al. 29; the Synechocystis PCC6803 PC structure was the minimized average structure (1J5D) taken from Bertini et al. 32, and the Synechococcus sp. PCC7922 PC structure (1BXU) was taken from Inoue et al. 33. The structure of C. reinhardtii cyt f used (1CFM) was structure B from Chi et al. 46 and that of Chlamydomonas PC (2PLT) was that of Redinbo et al. 47.

Structures for mutant molecules were generated using the MacroDox program 36,48,49. All mutant residues were kept in the same orientation as their wild-type counterparts (i.e., no energy minimization was performed on the mutants). Mutants were divided into different classes depending on their relative effects (See Table 1,Table 2).

All molecular representations were made using the program GRASP 50. Electrostatic fields for the molecular representation only were also calculated using GRASP. The internal and external dielectric constants of the proteins were 4 and 78, respectively. The ionic strength was 10mM and the pH was 7.0.

BD simulations were carried out using the program MacroDox v. 3.2.1 (http://gemini.tntech.edu/∼s;/index.html), as described 35,40,43,51. In MacroDox simulations, target molecule (Molecule I, in our case, cyt f) is placed with its center of mass at the center of a sphere 87Å in diameter (87Å was chosen so that the initial electrostatic fields would be very small). Molecule II (in our case, PC) is placed randomly on the surface of the sphere. Molecule II is allowed to move in response to both electrostatic and random Brownian forces. After Molecule II has moved an incremental distance, the forces are recalculated. The steps form a trajectory which ends when Molecule II leaves a sphere of 200Å in diameter, with its center at the center-of-mass of the target molecule.

MacroDox determines the closest approach of the two molecules for each trajectory based on a preselected reaction criterion. Closest metal-to-metal distance was chosen as the reaction criterion to select for electron-transfer-active complexes 52,53. The point of closest approach (smallest Cu-Fe distance) was recorded for each trajectory, permitting the calculation of the number of complexes formed as a function of minimal Cu-Fe distance (Fig. 2). Second-order rate constants for complex formation were calculated from the fraction of complexes observed at distances less than or equal to a preselected reaction criterion using equations derived by Northrup et al. 36,48 from the equations of Smoluchowski. If the reaction is diffusion-limited, as was suggested by Hart et al. 54, the rate of complex formation (k₂) should be equal to the rate constant for electron transfer (k_et) However, this may not be true in this case 55 (see Discussion). The number of complexes with a Cu-Fe distances of ≤20Å was used to calculate the rate constants; 20Å was sufficient to include essentially all of the electrostatic complexes formed while excluding those formed solely by random Brownian motion (Fig. 2). MacroDox provides the following information for each trajectory: The structure of the complex at minimum Cu-Fe distance, the 15 closest pairs of charged residues, and the electrostatic interaction energy.

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Figure 2

The number of complexes formed in BD simulations as a function of Cu-Fe distance for Phormidium cyt f interacting with PCs from different species of cyanobacteria. (A) Comparison of Prochlorothrix, Nostoc, and Phormidium PC interacting with Phormidium cyt f with Chlamydomonas PC interacting with Chlamydomonas cyt f (Structure B from Chi et al. 46). Five sets of 5000 trajectories were carried out for Phormidium PC. (B) The effect of Y12G and Y12G+P14L mutations on the number of complexes formed for Prochlorothrix PC interacting with Phormidium cyt f. (C) A comparison of the number of complexes formed for Phormidium PC, Phormidium PC with the electrostatic field turned off; Synechocystis PC, and Synechococcus PC interacting with Phormidium cyt f. Five sets of 10,000 trajectories were carried out for Synechocystis and Synechococcus PC and for all PCs studied in the absence of the electrostatic field. (D) A comparison of the number of complexes formed for Phormidium PC, Synechocystis PC, and Synechococcus PC interacting with Phormidium cyt f after subtractions of the number of complexes formed in the absence of the electrostatic field for that species. Conditions were the same as for Figure 2C.

Formal charges were assigned to ionizable groups such as amino, carboxyl, guanido, and imidazole groups. Partial charges were not assigned to polarizable atoms such as oxygen and nitrogen since the inclusion of partial charges had a negligible effect on the number of complexes formed in the interaction of Chlamydomonas cyt f with Chlamydomonas PC 43.

When using formal charges, noninteger values of the charge on PC and cyt f result from the ionization of histidine residues at pH 7. H25 on cyt f and H39 and H92 (see Appendix on PC have a zero net charge because they are ligands to the metal centers. The sulfur atom of the Cys-89 ligand to the Cu on PC was given a net charge of −1 27, and the Cu atom was given a charge of +2. For cyt f, the charges on the heme were as follows: Fe (+2), two ring nitrogen atoms (−1 each), and two propionic acid side chains (−1 each). The pK values were calculated using a modified Tanford-Kirkwood pK algorithm 56.

Electrostatic calculations were carried out using the Warwicker/Watson finite difference method 57 for solving the linearized Poisson-Boltzmann equation. This algorithm is slightly different from that used in GRASP. The center-of-mass of each protein was placed at the center of a 61×61×61 grid. The electrostatic field was first iterated over a 3.6Å grid followed by iteration over a smaller 1.2Å grid for better accuracy. The choice of grid size has a small (<20%) effect on the rates, but no effect on the structure of the complexes formed 43. Most importantly, the relative rates of electron transfer were not affected.

Forces were calculated as described by Northrup et al. 36. Molecule I (cyt f, the target molecule) was given a low internal dielectric constant of 4.0. However, because of computational complexities, Molecule II (PC) was treated as a set of point charges embedded in a medium of the same dielectric 48,58,59 (S. Northrup, personal communication, 2002). Also, mutual desolvation effects 59,60 were neglected. These effects may cause an overestimation of the reaction rates by as much as 25%. However, desolvation effects are not significant in these simulations 35. By neglecting these, neither the relative effects of the mutations nor the structures of the complexes formed should be affected 48 (S. Northrup, personal communication, 2002). Also, hydrodynamic effects can be neglected due to the compact nature of the molecules 39. Torques were calculated using dipoles for the moving protein as described by Northrup et al. 61.

Hydrophobic interaction free energies were determined as described by Gross and Pearson 43. The residues at the complex interfaces were determined by selecting those residues on Phormidium cyt f within 8Å of any residues on PC (10Å for Phormidium PC), using an in-house program. Those residues on PC within 8Å (10Å for Phormidium PC) of any residue on cyt f were chosen using the same method. Ten representative complexes, with Cu-Fe distances less than or equal to those at maximum complex formation, were chosen for study (17Å for Nostoc and Prochlorothrix Y12G PC, 18Å for WT Prochlorothrix PC and 21Å for Phormidium PC). A residue was considered to be part of the interface if it was observed in at least eight of the 10 complexes chosen (seven out of 10 complexes for Phormidium PC). The calculated interaction area is an underestimate, particularly in the case of Phormidium PC, because the two molecules are not as close as they will be in the final electron transfer active dock. The surface areas of the hydrophobic atoms of these residues on both PC and cyt f were calculated using the Richards 62,63 algorithm, which is part of the MacroDox software package. The total hydrophobic surface area was considered to be twice the smaller of the PC or cyt f hydrophobic surface area.

Reported values for hydrophobic interaction energies vary between −25 and −47cal/Ų64,65,66. Because of the wide variation, both −25 and −47cal/Ų were used for our calculations.

Electrostatic interactions were taken from the .rec files of the MacroDox output. In each case, all complexes formed with Cu-Fe values less than the values of maximal complex formation (see above) were included. Five sets of 1000 trajectories for Prochlorothrix and Nostoc and 5000 trajectories for Phormidium PC were averaged and included between 150 and 400 complexes per set.

In these studies (Fig. 2), the number of complexes formed was determined as a function of minimum Cu-Fe distance for cyt f interacting with PCs from several cyanobacteria at 10mM ionic strength and pH 7.0. In all of these plots, the point at 17Å shows the number of complexes in which the minimum distance between the Cu on PC and the Fe on cyt f was between 16 and 17Å.

Figure 2A compares the results for Nostoc, Prochlorothrix, and Phormidium PC interacting with Phormidium cyt f, with those previously obtained for Chlamydomonas PC interacting with Chlamydomonas cyt f43. In the case of Nostoc PC, maximum complex formation occurred at a Cu-Fe distance of 17Å compared to 15Å for the Chlamydomonas system. However, for Prochlorothrix PC, the peak is shifted to 18Å as a result of the presence of a tyrosine at position #12 in Prochlorothrix PC instead of the glycine found in PCs from all other species 8. When Y12 is replaced by a glycine (Figure 2B), the peak is shifted back to 17Å. The double mutant (Y12G+P14L) described by Crowley et al. 38 showed nearly identical results to the single Y12G mutant. Both Nostoc and Prochlorothrix PC showed a greater number of complexes formed when interacting with Phormidium cyt f than did Chlamydomonas PC interacting with Chlamydomonas cyt f (Figure 2A).

When Phormidium PC interacted with Phormidium cyt f, peak complex formation was shifted to 20Å (Figure 2D). Also, the number of complexes formed was only 20.4±0.5 complexes/1000 trajectories compared to 341.2±4.7 for Prochlorothrix PC under the same conditions. However, in the absence of the electrostatic field, the number of complexes formed were 2.0±0.2 35 and 1.8±0.8 (Table 1) for Phormidium and Prochlorothrix PC, respectively, indicating that the differences in complex formation reflect the differences in charge on the two PC proteins. Maximum complex formation was observed at a Cu-Fe distance of 22Å (with a value of 33.7±0.6 complexes/1000 trajectories) for Synechocystis PC (Figure 2D).

Interestingly, in the case of Synechococcus PC, fewer complexes were formed in the presence of the electrostatic field than in its absence (Figure 2CD), indicating charge repulsion between Synechococcus PC and Phormidium cyt f. This is not surprising, since the net charge on Synechococcus PC is −4.5 compared to a net charge −14.0 Phormidium cyt f. This raises the questions as to whether Synechococcus PC would show greater complex formation when interacting with Synechococcus cyt f than with Phormidium cyt f. For this reason, Synechococcus cyt f was built by homology-modeling with SWISS MODEL (67http://swiss-model.expasy.org), using turnip and Phormidium cyt f as templates. When Synechococcus PC interacted with Synechococcus cyt f, 17.1±0.1 complexes with Cu-Fe distances ≤20Å were formed per 1000 trajectories compared to 18.0±0.1 for Phormidium cyt f under the same conditions. The rates of interaction were 4.9±1.3 and 5.3±1.0×10⁷M⁻¹s⁻¹, respectively. These results are not surprising since the net charge on the Synechococcus cyt f molecule is −18.7 as calculated by MacroDox compared to −14.0 for Phormidium cyt f. Therefore, the poor performance of Synechococcus PC can not be attributed to using the “wrong” cyt f.

One reason for the difference in the number of complexes formed for PCs from different species of cyanobacteria may be the difference in net charge on the various PC molecules. To test this hypothesis, two types of simulations were performed (Fig. 3). In the first experiment, indicated by the numbers 1–9 next to the data points in Fig. 3, the net charge on Prochlorothrix PC was varied between −2.0 and +3.0 by mutating charged residues to alanine. The results show that the number of complexes formed was a linear function of the net charge at values more positive than −1.0. The results for mutants of Phormidium PC also fall on the same line 68. In the second set of simulations, the five cyanobacterial PCs shown in Figure 1 and Figure 2 were compared. These are indicated by letters A–D and the number 5 on Fig. 3. It can be seen that few, if any, complexes were formed, due to electrostatic interactions alone, if the net charge on the PC molecule was more negative than −2, but that the data point for Nostoc PC falls on the same line as for the Prochlorothrix mutants. Thus, the number of complexes formed is a linear function of the net charge on the PC molecule for a net charge greater than −2. Note that, in both sets of experiments, hydrophobic interactions were not included in the simulations. If they had been, the number of complexes formed would have been greater and significant complex formation would have been observed for Synechocystis, Synechococcus, and Phormidium PC.

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Figure 3

The dependence of BD complex formation on the net charge on the PC molecule. All complexes with Cu-Fe distance <20Å were counted. The ionic strength was 10mM and the pH was 7.0. Other conditions were as described for Fig. 2. Experiment 1: Phormidium cyt f interacting with Prochlorothrix PC mutants. (1) K35A+K11E (net charge=−2); (2) K35A+K11A (net charge=−1); (3) K35A (net charge=0); (4) K11A (net charge=0); (5) WT (net charge=+1.0); (6) D10A (net charge=+2.0); (7) D44A (net charge=+2.0); (8) D10K (net charge=+3.0); and (9) D44K (net charge=+3.0). Experiment 2: PC molecules from different species of cyanobacteria interacting with Phormidium cyt f. (A) Synechococcus PC (net charge=−4.5). (B) Phormidium PC (net charge=−2.3). (C) Synechocystis PC (net charge=−1.8). (D) Nostoc PC (net charge=+1.1). Net charges were calculated using MacroDox.

A second question is whether the location of the charged residues on the surface of the PC molecule affects complex formation. If so, it should be possible to use mutations to map the binding site on PC for cyt f and to determine whether the binding site for cyt f on PC is the same for the various cyanobacterial PCs studied. Fig. 4 depicts the effect of mutation of all of the conserved residues on Prochlorothrix, Nostoc, and Phormidium PC plus the K11A mutation for Prochlorothrix and Nostoc PC (Residue #11 is a serine rather than a lysine on Phormidium PC) on the ability of PC to form complexes with Phormidium cyt f. A similar pattern was observed for all three cyanobacterial plastocyanins shown as well as for Synechocystis PC (not shown). In all cases, the D10A, E17A, and D44A mutations increased the number of complexes formed. In contrast, the K11A, K35A, and R93A mutants decreased complex formation. All of these residues are located on the top face of the cyanobacterial PCs surrounding H92 (which corresponds to H87 in higher plant and algal PCs; see Appendix , and Figure 1 and Figure 5). Note that all of the conserved charged residues are located on the top face of the PC molecule.

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Figure 4

The effect of mutations of conserved charged residues on the number of complexes formed for Prochlorothrix, Nostoc, and Phormidium PC interacting with Phormidium cyt. ■ WT; △ WT=off; ( D44A; ( D10A; ♦ E17A; □ K35A; ( R86A; ( K11A.

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Figure 5

Location of charged amino acid residues involved in complex formation for Prochlorothrix, Nostoc, and Phormidium PC. (Top) Residues involved in complex formation as shown by mutational studies. Prochlorothrix PC: Residues found in Classes I, II, and V of Table 1+K45. Nostoc PC: Residues found in Classes I, II, and V of Table 2. Phormidium PC: Residues found in Classes I and V from Table 2 from Gross 35. (Black, H92; blue, cationic residues; and red, anionic residues.) (Bottom) Residues on PC than make >0.5 electrostatic contacts with Phormidium cyt f. (Cationic residues, green; and anionic residues, yellow.)

Table 1,Table 2 summarize the effects of mutating all of the charged residues on Prochlorothrix and Nostoc PC on their ability to form complexes Phormidium cyt f. In each case, the number of complexes formed with Cu-Fe distances ≤20Å was determined. A 20Å reaction criterion was chosen under the assumption that once the metal centers of the two molecules approach to within that distance, hydrophobic interactions come into play. For comparison, the PC and cyt f touch each other at a Cu-Fe distance of 15Å for Nostoc PC and 16Å for Prochlorothrix and Phormidium PC. Changing the reaction criterion to 18Å changes the number of complexes included but not the relative effects of the mutations 35.

For both Prochlorothrix and Nostoc PC, the mutants were divided into five classes:

D44A, D10A, and E17A also showed maximal stimulation of the interaction of Phormidium PC with Phormidium cyt f35, and D10A and E17A also showed significant stimulation for Synechocystis PC (not shown) interacting with Phormidium cyt f. K6A, K35A, K46A, K100A, and R93A also showed severe inhibition for Phormidium PC interacting with Phormidium cyt f35 as did mutants K6A, K35A, and R93A (consensus sequence) for Synechocystis PC (not shown). Thus, the same residues (especially D10, E17, D44, K35, R93, and possibly K6) are involved in complex formation in all four cyanobacterial PCs studied. K11 is also important for Prochlorothrix and Nostoc PC. S11K mutants of Phormidium and Synechocystis PC (not shown) stimulated complex formation to the same extent as the neighboring D10A mutants, indicating that a lysine at position 11, when present, also assists in complex formation. The locations of these important (Classes I, IV, and V) residues on the surface of Prochlorothrix, Nostoc, and Phormidium PC are shown in Fig. 5. Note that they all surround H93 (H87 in higher plant and algal PCs) on the top face of the PC molecule. Also, note the significant role of conserved charged residues in complex formation. Moreover, the location of these charged residues controls the location of binding site on PC for cyt f but the net charge on the PC molecule controls the strength of the electrostatic portion of the interaction.

The output of the MacroDox program provides a list of the 15 closest electrostatic contacts for all complexes with reaction coordinate distances less than or equal to a preset value. For our studies of cyanobacterial PCs interacting with Phormidium cyt f, we chose a Cu-Fe distance less than or equal to that which gave the peak value for complex formation. This value was 20Å for Phormidium PC, 17Å for Nostoc PC, and 18Å for Prochlorothrix PC, respectively. The results are presented in Table 3. A given residue was listed if it appeared as one of the 15 closest contacts in at least 50% of the complexes formed.

Conserved positively-charged cationic residues, K35 and R93, showed at least one contact with a residue on cyt f for Prochlorothrix, Nostoc, and Phormidium PC as well as for Synechocystis PC (not shown). Also, K11 showed more than one contract for Prochlorothrix and Nostoc PC that have this residue. Close contacts for nonconserved cationic residues include K19 and K59[63] for Prochlorothrix PC, K62 for Nostoc PC, and K46 for Phormidium PC. Close contacts for anionic residues include D10, which is observed for Prochlorothrix and Phormidium PC. E90 is also prominent in Nostoc PC and D44 and E70 are involved in charge repulsion in Phormidium PC. All of these residues (cationic and anionic) lie in a circle surrounding H92 (consensus sequence; see Appendix ) (Fig. 5).

The most prevalent electrostatic contacts for residues on Phormidium cyt f are listed in Table 4. A residue is listed if it showed at least an average of 0.5 contacts/complex for at least one of the PC species represented. The following residues show at least 0.9 contacts/complex for all three PCs: D63, E123, R157, E165, D188, and the heme. All of these residues surround the heme as shown in Fig. 6. E165 and D188 are located on the small domain whereas all of the other residues are located on the large domain of cyt f.

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Figure 6

Location of residues on Phormidium cyt f that show >0.9 electrostatic contacts per complex formed for all three plastocyanins (Prochlorothrix, Phormidium, and Anabaena PC). The conditions are described for Table 4 and in Methods.

The heterogeneity of the complexes formed is compared in Fig. 7 for complexes formed between Phormidium cyt f and PCs from Nostoc, Phormidium, and both WT and the Y12G mutant of Prochlorothrix. In each case, five complexes were chosen at random from those in which the Cu-Fe distance was less than the Cu-Fe distance at which the greatest number of complexes was observed. Considerable heterogeneity in the structure of the complexes was observed in all cases, except for the Y12G mutant of Prochlorothrix PC. There is less conformational heterogeneity than Crowley et al. 38 found for the double mutant Y12G-P14L, based on their NMR studies. Thus, these complexes are different from those previously observed between Chlamydomonas cyt f and Chlamydomonas PC 43, which showed considerable homogeneity in complex formation.

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Figure 7

Homogeneity of complex formation for Phormidium cyt f interacting with various cyanobacterial PCs. Five complexes were selected at random from the 5000 (5×1000) trajectories per experiment for Nostoc and Prochlorothrix PC and from the 25,000 trajectories run for Phormidium PC. The only criterion used was that the Cu-Fe distance be less than the mean of the peaks shown in Fig. 2.

Typical complexes are shown in Fig. 8 for Phormidium cyt f interacting with Prochlorothrix Y12G-PC. The mutant was chosen because the complexes were the most uniform of those studied and, thus, the structure represents that of a typical complex. The left-hand set of views is perpendicular to the long axis of cyt f and the right-hand view is looking down the long axis from the viewpoint of the small domain. As in the case of the Phormidium cyt f-Phormidium PC NMR complexes reported previously 37, the PC sits vertically on cyt f in contrast with both the BD simulations for Chlamydomonas PC interacting with Chlamydomonas cyt f43 and the NMR results for spinach PC interacting with turnip cyt f69 in which PC is slanted toward the small domain of cyt f. However, the view looking down the length of cyt f shows that the PC binding site is located toward the front side of cyt f where the heme and Y1 are located.

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Figure 8

Typical BD complex between Phormidium cyt f and Prochlorothrix PC mutant Y12G. The complex shown is one of those chosen for Fig. 7. (PC residues are labeled in black; cyt f residues are labeled in red. Heme, black; cyt f-Y1, yellow; PC-H92, green; lysine, light blue; arginine, dark blue; aspartate, magenta; and glutamate, red.)

Residues K11, K35, and R93 interact with cyt f in agreement with the results of the mutant and electrostatic contact studies. D10 and E17 also lie close to the surface of cyt f where they cause electrostatic repulsion leading to a decrease in complex formation and the associated reaction rates. D63, E123, E165, and D188 on Phormidium cyt f interact with cationic residues on PC.

MacroDox is a very useful program for studying electrostatic interactions between proteins. In particular, it can predict the effects of mutations and determine the structure of the complexes formed, which, in turn, provides the basis for further experiments. It requires relatively little computational time per simulation so that a large number of conditions (mutations, different ionic strengths, etc.) can be studied in a brief time. Steric effects can also be examined since both molecules have irregular geometrical shapes taken from the PDB files. For example, MacroDox was able to distinguish between wild-type and the Y12G mutant of Prochlorothrix PC interacting with Phormidium cyt f (Figure 2B). However, there are some serious limitations which are discussed in detail in Gross and Pearson 43 and Gross 35. The most serious considerations are:

The question arises as to how well the BD results agree with experiments both with respect to rates of electron transfer, and the structure of the complexes formed.

With respect to the rates, three questions need to be answered:

With respect to the first question, Schlarb-Ridley et al. 55 studied the effect of viscosity and temperature on electron transfer rates for Phormidium cyt f interacting with Phormidium PC. They concluded that the reaction is not diffusion-limited, but instead involves a rearrangement of the initial diffusion-controlled complex to bring PC to a position in which it can rapidly receive an electron from cyt f. Thus, the overall reaction is at least partially activation-limited.

The second question concerns whether the MacroDox complexes observed in our simulations are the result of diffusion or activation-limited processes. This depends on the reaction criterion used. If the reaction criterion used is best electrostatic interactions, then the complexes observed will be entirely electrostatically driven and diffusion-limited. On the other hand, the use of minimum Cu-Fe distance as the reaction criterion yields complexes as they would appear after a rearrangement with a small Cu-Fe distance allowing rapid electron transfer.

In the case of cyt f and PC, hydrophobic residues on both proteins would be brought together. Thus, although hydrophobic forces do not provide a driving force for complex formation, they are evident in the final complexes. However, the MacroDox complexes do not represent the final electron-transfer-active dock because many of them stop short of the final docked position (because of the random forces and the lack of an explicit inclusion of hydrophobic forces). This is the reason that hydrophobic interaction energies are underestimated.

With respect to question three, the magnitude of the rate constants determined by MacroDox simulations are always greater than the corresponding experimental values.

There are at least three reasons for the larger rate constants in MacroDox simulations. First, the rate constants for the simulations are overestimated due to the absence of a low internal dielectric constant for PC and the desolvation effects mentioned above. Second, no attempt was made to correct the BD reaction rates for attenuation due to the distance between the metal centers, which would decrease the measured electron transfer reaction rates 52,53. Third, the calculated rates are a function of the reaction coordinate cutoff distance. For these simulations, a 20Å cutoff distance was chosen to include all possible complexes in which the Cu on PC might come close enough via electrostatic or hydrophobic interactions to receive an electron from cyt f. The 20Å cutoff distance resulted in a calculated reaction rate (k_a) of 360×10 ⁶M⁻¹s⁻¹35. Decreasing Cu-Fe reaction criterion distance to 18Å 35 decreased the calculated rate to 80×10 ⁶M⁻¹s⁻¹, which is comparable to the experimental value of 47×10 ⁶M⁻¹s⁻¹34.

The most important point, however, is that the relative effects of the mutations are independent of the reaction coordinate cutoff distance and are in general agreement with experiments, not only for mutations of Phormidium PC 34 but also for Chlamydomonas PC 44 when compared to experimental mutations of higher plant PCs 19,21. Thus, MacroDox simulations can be used to predict the effects of PC mutations in systems for which there are no experimental data.

Overall, the structures of the BD complexes formed also agree with those determined by NMR. For example, the complex formed between Chlamydomonas PC and Chlamydomonas cyt f is very similar to that of spinach 69, poplar 71, and parsley 72 PC. In all of these cases, H87 (H92 in the cyanobacteria) faces the heme on cyt f and the PC molecule is tilted toward the small subunit with the two acidic clusters on PC interacting with the cationic residues on cyt f.

In contrast, in the complexes formed between Phormidium cyt f and Phormidium PC 35, Prochlorothrix PC (Figure 7 and Figure 8), and Nostoc PC (Fig. 7) PC, the PC molecules sits vertically on top of the cyt f with its long axis perpendicular to the long axis of cyt f. These results agree with the NMR results of Crowley et al. 37,38 for complexes formed between Phormidium cyt f and Phormidium and Prochlorothrix PC, respectively.

Electrostatic interactions between Phormidium cyt f and various cyanobacterial PCs depend on two factors: 1), the net charge on the PC molecule; and 2), the charge configuration around H92.

The results depicted in Fig. 3 show that the number of complexes formed in MacroDox simulations is a linear function of the net charge on the PC molecule whether the net charge on the PC molecule is altered by mutation or by using PCs from different species of cyanobacteria. Those species of cyanobacteria for which the net charge on PC at pH 7.0 is <−1.0, such as Synechococcus, Synechocystis, and Phormidium, show few if any complexes due to weaker electrostatic interactions in the Brownian dynamics (BD) simulations (note that there may still be complex formation due to hydrophobic interactions). These results agree with the NMR studies of complex formation between Phormidium cyt f and Phormidium PC 37, in which there was no effect of ionic strength on complex formation to indicate a paucity of electrostatic interactions. In contrast, cyanobacterial PCs having net charges more positive than −1.0, including WT Nostoc PC (net charge=+1.1) and Prochlorothrix PC (net charge=+1.0), showed a linear relationship between the number of complexes formed and the net charge on the PC molecule. This is true both for the Prochlorothrix mutants shown here and the Phormidium mutants described by Gross 68. Also, NMR studies of complex formation between Phormidium cyt f and Prochlorothrix PC 38 showed an ionic strength-dependence of complex formation indicating significant electrostatic interactions in agreement with the BD results described above. Note that a linear dependence of electron transfer rate on net charge was also observed for higher plants 19.

The increase in the number of BD complexes formed as a function of increasing positive charge on the PC molecule parallels the increase in binding constants for Phormidium cyt f-cyanobacterial PC complexes determined by NMR spectroscopy. For example, the binding constant for Phormidium PC complexes was 0.3mM⁻¹ PC 37, 6±2mM⁻¹ for Prochlorothrix PC 38, and 12±1mM⁻¹ for Nostoc PC 73 interacting with Phormidium cyt f. The increase in both the number of BD complexes formed and the magnitude of the binding constants reflect the increase in electrostatic interactions.

There are also specific charge interactions that are superimposed upon the net charge effects and influence the structure of the complexes formed between Phormidium cyt f and cyanobacterial PCs. Mutation of R93 and K35 to alanine inhibits complex formation for Prochlorothrix PC (Table 1), Nostoc PC (Table 2), Phormidium PC (Table 2 from Gross 35), and Synechocystis PC (not shown). Mutant studies also show that K11 is important in Prochlorothrix and Nostoc PC as is K62 in Nostoc PC. K35, R93, and K11 (present only in Prochlorothrix and Nostoc PC) also showed more than one electrostatic contact per complex formed 3. On the other hand, mutation of D10 and E17 stimulated complex formation in all four cyanobacteria. Removal of D44 in Prochlorothrix, Nostoc, and Phormidium PC and E56 in Synechocystis PC also stimulated complex formation. Additional residues that are involved include E90 in Nostoc PC, E70 in Synechocystis PC, and D45, D55, and E70 in Phormidium PC.

R93, K35, D10, E17, and a residue in the vicinity of D44 are highly conserved in cyanobacterial PCs. Moreover, all of these residues surround H92 on the top face of cyanobacterial PC molecules (Fig. 5) implying that this is the face presented to cyt f in agreement with the NMR results for Phormidium37 and Prochlorothrix38 PCs interacting with Phormidium cyt f. These results contrast with those obtained for higher plant and green algal PCs in both NMR 62,64,65 and BD simulations 35,40,43,44, in which the anionic residues surrounding Y88 (Y83 in green plant numbering) provide the electrostatic interactions.

The question arises as to the role of hydrophobic interactions in complex formation. This is particularly important for those PCs such as Synechococcus, Synechocystis, and Phormidium that show poor electrostatic interactions. All PCs including those from higher plants and green algae have a highly conserved hydrophobic patch surrounding H92 (H87 in higher plants and green algae) 8, which includes the following amino acid residues: G8, G12 (Y in Prochlorothrix), L14 (P in Prochlorothrix), F16 (Y in Prochlorothrix), Residue 36 (hydrophobic in cyanobacteria and G in higher plants and algae), P38, L64 (Y in green algae and some higher plant PCs such as parsley), P91, G94, A95, and G96, plus some other residues in individual PCs. Thus, hydrophobic interactions appear to be ubiquitous.

One of the weaknesses of MacroDox is that it does not explicitly include hydrophobic interactions. What this means is that hydrophobic interactions are not included as a driving force for complex formation (i.e., the number of complexes formed and the corresponding reaction rates would be greater upon inclusion of hydrophobic forces. This is particularly important in the case of mutants R93A (Nostoc PC) and R86A (Prochlorothrix PC) as well as wild-type Phormidium, Synechocystis, and Synechococcus PC, which would have shown significant complex formation if hydrophobic interactions had been included.

However, even though it was not possible to include hydrophobic interactions as a driving force for complex formation, it was possible to estimate the hydrophobic interaction energies of the complexes formed. The strength of the hydrophobic interactions was estimated for Prochlorothrix, Nostoc, and Phormidium PC interacting with Phormidium cyt f (Table 5). The procedure involved determining the surface areas of those residues involved in hydrophobic interactions between PC and cyt f. The surface areas of individual residues and atoms thereof for both cyt f and PC were determined using the method of Richards 62,63. Of these, the residues involved in hydrophobic interactions and the sum of their surface areas were determined as described in Methods and in Gross and Pearson 42. Two times the smaller of the two hydrophobic surface areas (PC or cyt f) was taken as the hydrophobic surface area given in Table 5.