Brownian dynamics study of cytochrome f interactions with cytochrome c6 and plastocyanin in Chlamydomonas reinhardtii plastocyanin, and cytochrome c6 mutants

Using Brownian dynamics simulations, all of the charged residues in Chlamydomonas reinhardtii cytochrome c(6) (cyt c(6)) and plastocyanin (PC) were mutated to alanine and their interactions with cytochrome f (cyt f) were modeled. Systematic mutation of charged residues on both PC and cyt c(6) confirmed that electrostatic interactions (at least in vitro) play an important role in bringing these proteins sufficiently close to cyt f to allow hydrophobic and van der Waals interactions to form the final electron transfer-active complex. The charged residue mutants on PC and cyt c(6) displayed similar inhibition classes. Our results indicate a difference between the two acidic clusters on PC. Mutations D44A and E43A of the lower cluster showed greater inhibition than do any of the mutations of the upper cluster residues. Replacement of acidic residues on cyt c(6) that correspond to the PC's lower cluster, particularly E70 and E69, was observed to be more inhibitory than those corresponding to the upper cluster. In PC residues D42, E43, D44, D53, D59, D61, and E85, and in cyt c(6) residues D2, E54, K57, D65, R66, E70, E71, and the heme had significant electrostatic contacts with cyt f charged residues. PC and cyt c(6) showed different binding sites and orientations on cyt f. As there are no experimental cyt c(6) mutation data available for algae, our results could serve as a good guide for future experimental work on this protein. The comparison between computational values and the available experimental data (for PC-cyt f interactions) showed overall good agreement, which supports the predictive power of Brownian dynamics simulations in mutagenesis studies.     

Brownian dynamics study of the interaction between plastocyanin and cytochrome f.

The electrostatic interaction between plastocyanin (PC) and cytochrome f (cyt f), electron transfer partners in photosynthesis was studied using Brownian dynamics (BD) simulations. By using the software package MacroDox, which implements the BD algorithm of Northrup et al. (Northrup, S. H., J. O. Boles, and J. C. L. Reynolds. 1987. J. Phys. Chem. 91:5991-5998), we have modeled the interaction of the two proteins based on crystal structures of poplar PC and turnip cyt f at pH 7 and a variety of ionic strengths. We find that the electrostatic attraction between positively charged residues (K58, K65, K187, and R209, among others) on cyt f and negatively charged residues (E43, D44, E59, and E60, among others) on PC steers PC into a single dominant orientation with respect to cyt f, and furthermore, that the single dominant orientation that we observe is one that we had predicted in our previous work (Pearson, D. C., E. L. Gross, and E. S. David. 1996. Biophys. J. 71:64-76). This dominant orientation permits the formation of hydrophobic interactions, which are not implemented in the MacroDox algorithm. This proposed complex between PC and cyt f implicates H87, a copper ligand on PC, as the residue that accepts electrons from the heme on cyt f (and possibly through Y1 as we proposed previously). We argue for the existence of this single dominant complex on the basis of observations that the most favorable orientations of the interaction between PC and cyt f, as determined by grouping successful BD trajectories on the basis of closest contacts of charged residues, tend to overlap one another and have very close distances between the metal centers on the two proteins (copper on PC, iron on cyt f). We use this knowledge to develop a model for PC/cyt f interaction that places a reaction between the two proteins occurring when the copper-to-iron distance is between 16 and 17 A. This reaction distance gives a good estimate of the experimentally observed rate constant for PC-cyt f interaction. Analysis of BD results as a function of ionic strength predicts an interaction that happens less frequently and becomes less specific as ionic strength increases.     

A Brownian dynamics study of the effects of cytochrome f structure and deletion of its small domain in interactions with cytochrome c6 and plastocyanin in Chlamydomonas reinhardtii

The availability of seven different structures of cytochrome f (cyt f) from Chlamydomonas reinhardtii allowed us, using Brownian dynamics simulations, to model interactions between these molecules and their redox partners, plastocyanin (PC) and cytochrome c6 (cyt c6) in the same species to study the effect of cyt f structure on its function. Our results showed that different cyt f structures, which are very similar, produced different reaction rates in interactions with PC and cyt c6. We were able to attribute this to structural differences among these molecules, particularly to a small flexible loop between A-184 and G-191 (which has some of the highest crystallographic temperature factors in all of the cyt f structures) on the cyt f small domain. We also showed that deletion of the cyt f small domain affected cyt c6 more than PC, due to their different binding positions on cyt f. One function of the small domain in cyt f may be to guide PC or cyt c6 to a uniform dock with cyt f, especially due to electrostatic interactions with K-188 and K-189 on this domain. Our results could serve as a good guide for future experimental work on these proteins to understand better the electron transfer process between them. Also, these results demonstrated the sensitivity and the power of the Brownian dynamics simulations in the study of molecular interactions.     

A Brownian dynamics study of the interaction of Phormidium laminosum plastocyanin with Phormidium laminosum cytochrome f

The interaction of Phormidium laminosum plastocyanin (PC) with P. laminosum cytochrome f (cyt f) was studied using Brownian dynamics (BD) simulations. Few complexes and a low rate of electron transfer were observed for wild-type PC. Increasing the positive electrostatic field on PC by the addition of a Zn(2+) ion in the neighborhood of D44 and D45 on PC (as found in crystal structure of plastocyanin) increased the number of complexes formed and the calculated rates of electron transfer as did PC mutations D44A, D45A, E54A, and E57A. Mutations of charged residues on Phormidium PC and Phormidium cyt f were used to map binding sites on both proteins. In both the presence and absence of the Zn(2+) ion, the following residues on PC interact with cyt f: D44, D45, K6, D79, R93, and K100 that lie in a patch just below H92 and Y88 and D10, E17, and E70 located on the upper portion of the PC molecule. In the absence of the Zn(2+) ion, K6 and K35 on the top of the PC molecule also interact with cyt f. Cyt f residues involved in binding PC, in the absence of the Zn(2+) ion, include E165, D187, and D188 that are located on the small domain of cyt f. The orientation of PC in the complexes was quite random in accordance with NMR results. In the presence of the Zn(2+) ion, K53 and E54 in the lower patch of the PC molecule also interact with cyt f and PC interacts with E86, E95, and E123 on the large domain of cyt f. Also, the orientation of PC in the complexes was much more uniform than in the absence of the Zn(2+) ion. The difference may be due to both the larger electrostatic field and the greater asymmetry of the charge distribution on PC observed in the presence of the Zn(2+) ion. Hydrophobic interactions were also observed suggesting a model of cyt f-PC interactions in which electrostatic forces bring the two molecules together but hydrophobic interactions participate in stabilizing the final electron-transfer-active dock.     

A Brownian dynamics computational study of the interaction of spinach plastocyanin with turnip cytochrome f: the importance of plastocyanin conformational changes

Brownian Dynamics (BD) computer simulations were used to study electrostatic interactions between turnip cytochrome f (cyt f) and spinach plastocyanin (PC). Three different spinach PC structures were studied: The X-ray crystal structure of Xue and coworkers [(1998) Protein Sci 7:2099–2105] and the NMR structure of Musiani et al. [(2005) J Biol Chem 280:18833–18841] and Ubbink and co-workers [(1998) Structure 6:323–335]. Significant differences exist in the backbone conformation between the PC taken from Ubbink and coworkers and the other two PC structures particularly the regions surrounding G10, E59–E60, and D51. Complexes formed in BD simulations using the PC of Ubbink and colleagues had a smaller Cu–Fe distance than the other two. These results suggest that different PC conformations may exist in solution with different capabilities of forming electron-transfer-active docks. All three types of complexes show electrostatic contacts between D42, E43, and D44 on PC and K187 on cyt f as well as between E59 on PC and K58 on cyt f. However, the PC of Ubbink and coworkers reveals additional contacts between D51 and cyt f as a result of the difference in backbone configuration. A second minor complex component was observed for the PC of Ubbink and co-workers and Xue and co-workers which had contacts between K187 on cyt f and E59 and E60 on PC rather than between K187 on cyt f and D42-D44 on PC as observed for the major components. This second type of complex may represent an earlier complex which rearranges to form a final complex capable of electron transfer. Professor Elizabeth L. Gross, Professor Emeritus of Biochemistry, The Ohio State University, passed away on June 27, 2007.     

Electrostatic analysis and Brownian dynamics simulation of the association of plastocyanin and cytochrome f.

The oxidation of cytochrome f by the soluble cupredoxin plastocyanin is a central reaction in the photosynthetic electron transfer chain of all oxygenic organisms. Here, two different computational approaches are used to gain new insights into the role of molecular recognition and protein-protein association processes in this redox reaction. First, a comparative analysis of the computed molecular electrostatic potentials of seven single and multiple point mutants of spinach plastocyanin (D42N, E43K, E43N, E43Q/D44N, E59K/E60Q, E59K/E60Q/E43N, Q88E) and the wt protein was carried out. The experimentally determined relative rates (k(2)) for the set of plastocyanin mutants are found to correlate well (r(2) = 0.90 - 0.97) with the computed measure of the similarity of the plastocyanin electrostatic potentials. Second, the effects on the plastocyanin/cytochrome f association rate of these mutations in the plastocyanin "eastern site" were evaluated by simulating the association of the wild type and mutant plastocyanins with cytochrome f by Brownian dynamics. Good agreement between the computed and experimental relative rates (k(2)) (r(2) = 0.89 - 0.92) was achieved for the plastocyanin mutants. The results obtained by applying both computational techniques provide support for the fundamental role of the acidic residues at the plastocyanin eastern site in the association with cytochrome f and in the overall electron-transfer process.     

On the interaction between cytochrome f and plastocyanin

The interaction between cytochrome f and its electron acceptor plastocyanin (PC) was studied. To address the question of which specific regions and which of the positively charged residues of cytochrome f are important for the interaction with the negatively charged residues of PC we have used two different experimental approaches. Cytochrome f was proteolytically cleaved and fragments that could bind to a PC-affinity column were isolated. The smallest of these fragments was analysed to give information on the minimum structural requirement for binding to PC. By this procedure, we identified a peptide of approx. 11 kDa, containing the heme binding site, and having an N-terminal sequence identical to that of the mature cytochrome f. This finding suggests that the first 90 amino acids of cytochrome f contain at least some of the residues interacting with PC. The second approach involved modification of Arg residues of cytochrome f with the specific chemical modifier, hydroxyphenylglyoxal (HPG). Cytochrome f modification was performed in the absence of PC to enable identification of residues that are protected from modification when PC is bound to cytochrome f. Two peptides containing Arg residues which are modified in the absence of PC, but are not modified when PC is present, were isolated. Sequence analysis of these two peptides revealed that Arg residues no. 88 and 154 of cytochrome f are the residues that are protected from modification when cytochrome f is bound to PC, suggesting a role for these residues in the binding of cytochrome f to PC.     

A Brownian dynamics study of the interactions of the luminal domains of the cytochrome b6f complex with plastocyanin and cytochrome c6: the effects of the Rieske FeS protein on the interactions

The availability of the structures of the cytochrome b6f complex (cyt b6f), plastocyanin (PC), and cytochrome c6 (cyt c6) from Chlamydomonas reinhardtii allowed us, for the first time, to model electron transfer interactions between the luminal domains of this complex (including cyt f and the Rieske FeS protein) and its redox partners in the same species. We also generated a model structure in which the FeS center of the Rieske protein was positioned closer to the heme of cyt f than observed in the crystal structure and studied its interactions with both PC and cyt c6. Our data showed that the Rieske protein in both the original crystal structure and in our modeled structure of the cyt b6f complex did not physically interfere with binding position or orientation of PC or cyt c6 on cyt f. PC docked on cyt f with the same orientation in the presence or the absence of the Rieske protein, which matched well with the previously reported NMR structures of complexes between cyt f and PC. When the FeS center of the Rieske protein was moved close to the heme of cyt f, it even enhanced the interaction rates. Studies using a cyt f modified in the 184-191 loop showed that the cyt f structure is a more important factor in determining the rate of complex formations than is the presence or the absence of the Rieske protein or its position with respect to cyt f.     

A Brownian dynamics study of the interaction of Phormidium cytochrome f with various cyanobacterial plastocyanins

Brownian dynamics simulations were used to study the role of electrostatic forces in the interactions of cytochrome f from the cyanobacterium Phormidium laminosum with various cyanobacterial plastocyanins. Both the net charge on the plastocyanin molecule and the charge configuration around H92 (H87 in higher plants) are important in determining the interactions. Those plastocyanins (PCs) with a net charge more negative than -2.0, including those from Synechococcus sp. PCC7942, Synechocystis sp. 6803, and P. laminosum showed very little complex formation. On the other hand, complex formation for those with a net charge more positive than -2.0 (including Nostoc sp. PCC7119 and Prochlorothrix hollandica) as well as Nostoc plastocyanin mutants showed a linear dependence of complex formation upon the net charge on the plastocyanin molecule. Mutation of charged residues on the surface of the PC molecules also affected complex formation. Simulations involving plastocyanin mutants K35A, R93A, and K11A (when present) showed inhibition of complex formation. In contrast, D10A and E17A mutants showed an increase in complex formation. All of these residues surround the H92 (H87 in higher plant plastocyanins) ligand to the copper. An examination of the closest electrostatic contacts shows that these residues interact with D63, E123, R157, D188, and the heme on Phormidium cytochrome f. In the complexes formed, the long axis of the PC molecule lies perpendicular to the long axis of cytochrome f. There is considerable heterogeneity in the orientation of plastocyanin in the complexes formed.     

Different modes of interaction in cyanobacterial complexes of plastocyanin and cytochrome f

The highly efficient electron-transfer chain in photosynthesis demonstrates a remarkable variation among organisms in the type of interactions between the soluble electron-transfer protein plastocyanin and it partner cytochrome f. The complex from the cyanobacterium Nostoc sp. PCC 7119 was studied using nuclear magnetic resonance spectroscopy and compared to that of the cyanobacterium Phormidium laminosum. In both systems, the main site of interaction on plastocyanin is the hydrophobic patch. However, the interaction in the Nostoc complex is highly dependent on electrostatics, contrary to that of Phormidium, resulting in a binding constant that is an order of magnitude larger at low ionic strength for the Nostoc complex. Studies of the mixed complexes show that these differences in interactions are mainly attributable to the surface properties of the plastocyanins.     

Regulation by copper of the expression of plastocyanin and cytochrome c552 in Chlamydomonas reinhardi.

Plastocyanin and cytochrome c552 are interchangeable electron carriers in the photosynthetic electron transfer chains of some cyanobacteria and green algae (P. M. Wood, Eur. J. Biochem. 87:9-19, 1978; G. Sandmann et al., Arch. Microbiol. 134:23-27, 1983). Chlamydomonas reinhardi cells respond to the availability of copper in the medium and accordingly accumulate either plastocyanin (if copper is available) or cytochrome c552 (if copper is not available). The response occurs in both heterotrophically and phototrophically grown cells. We have studied the molecular level at which this response occurs. No immunoreactive polypeptide is detectable under conditions where the mature protein is not spectroscopically detectable. Both plastocyanin and cytochrome c552 appear to be translated (in vitro) from polyadenylated mRNA as precursors of higher molecular weight. RNA was isolated from cells grown either under conditions favorable for the accumulation of plastocyanin (medium with Cu2+) or for the accumulation of cytochrome c552 (without Cu2+ added to the medium). Translatable mRNA for preapoplastocyanin was detected in both RNA preparations, although mature plastocyanin was detected in C. reinhardi cells only when copper was added to the culture. Translatable mRNA for preapocytochrome, on the other hand, was detected only in cells grown under conditions where cytochrome c552 accumulates (i.e., in the absence of copper). We conclude that copper-mediated regulation of plastocyanin and cytochrome c552 accumulation is effected at different levels, the former at the level of stable protein and the latter at the level of stable mRNA.     

Computer simulation of plastocyanin interaction with cytochrome f and photosystem I in cyanobacterium Phormidium laminosum

The paper is devoted to computer simulation of complex formation of protein plastocyanin with transmembrane pigment-protein complex photosystem I and subunit f of cytochrome b ₆ f complex in the cyanobacterium Phormidium laminosum. The computer algorithm considers diffusion and electrostatic interactions of protein molecules. The computer models have shown that electrostatic interactions in the cyanobacterium play a less important role than in higher plants because of different electrostatic potentials created by charged amino acid residues on the protein surfaces.     

Dynamic interaction of plastocyanin with the cytochrome bf complex

The interaction between plastocyanin and the intact cytochrome bf complex, both from spinach, has been studied by stopped-flow kinetics with mutant plastocyanin to elucidate the site of electron transfer and the docking regions of the molecule. Mutation of Tyr-83 to Arg or Leu provides no evidence for a second electron transfer path via Tyr-83 of plastocyanin, which has been proposed to be the site of electron transfer from cytochrome f. The data found with mutations of acidic residues indicate that both conserved negative patches are essential for the binding of plastocyanin to the intact cytochrome bf complex. Replacing Ala-90 and Gly-10 at the flat hydrophobic surface of plastocyanin by larger residues slowed down and accelerated, respectively, the rate of electron transfer as compared with wild-type plastocyanin. These opposing effects reveal that the hydrophobic region around the electron transfer site at His-87 is divided up into two regions, of which only that with Ala-90 contributes to the attachment to the cytochrome bf complex. These binding sites of plastocyanin are substantially different from those interacting with photosystem I. It appears that each of the two binding regions of plastocyanin is split into halves, which are used in different combinations in the molecular recognition at the two membrane complexes.     

Role of charges on cytochrome f from the cyanobacterium Phormidium laminosum in its interaction with plastocyanin

The role of charge on the surface of cytochrome f from the cyanobacterium Phormidium laminosum in the reaction with plastocyanin was investigated in vitro using site-directed mutagenesis. Charge was neutralized at five acidic residues individually and introduced at a residue close to the interface between the two proteins. The effects on the kinetics of the reaction were measured using stopped-flow spectrophotometry, and the midpoint potentials of the mutant proteins were determined. The dependence of the bimolecular rate constant of reaction, k(2), on ionic strength was determined for the reactions of the cytochrome f mutants with wild-type and mutant forms of plastocyanin. Double mutant cycle analysis was carried out to probe for the presence of specific electrostatic interactions. The effects of mutations on Cyt f were smaller than those seen previously for mutants of plastocyanin [Schlarb-Ridley, B. G. et al. (2002) Biochemistry 41, 3279-3285]. One specific short-range interaction between charged residues of wild-type plastocyanin (Arg93) and wild-type cytochrome f (Asp63) was identified. The kinetic evidence from this study and that of Schlarb-Ridley et al., 2002, appears to conflict with the NMR structure of the P. laminosum complex, which suggests the absence of electrostatic interactions in the final complex [Crowley, P. et al. (2001) J. Am. Chem. Soc. 123, 10444-10453]. The most likely explanation of the apparent paradox is that the overall rate is diffusion controlled and that electrostatics specifically influence the encounter complex and not the reaction complex.     

Role of electrostatics in the interaction between cytochrome f and plastocyanin of the cyanobacterium Phormidium laminosum

The role of charged residues on the surface of plastocyanin from the cyanobacterium Phormidium laminosum in the reaction with soluble cytochrome f in vitro was studied using site-directed mutagenesis. The charge on each of five residues on the eastern face of plastocyanin was neutralized and/or inverted, and the effect of the mutation on midpoint potentials was determined. The dependence of the overall rate constant of reaction, k(2), on ionic strength was investigated using stopped-flow spectrophotometry. Removing negative charges (D44A or D45A) accelerated the reaction and increased the dependence on ionic strength, whereas removing positive charges slowed it down. Two mutations (K46A, K53A) each almost completely abolished any influence of ionic strength on k(2), and three mutations (R93A, R93Q, R93E) each converted electrostatic attraction into repulsion. At low ionic strength, wild type and all mutants showed an inhibition which might be due to changes in the interaction radius as a consequence of ionic strength dependence of the Debye length or to effects on the rate constant of electron transfer, k(et). The study shows that the electrostatics of the interaction between plastocyanin and cytochrome f of P. laminosum in vitro are not optimized for k(2). Whereas electrostatics are the major contributor to k(2) in plants [Kannt, A., et al. (1996) Biochim. Biophys. Acta 1277, 115-126], this role is taken by nonpolar interactions in the cyanobacterium, leading to a remarkably high rate at infinite ionic strength (3.2 x 10(7) M(-1) s(-1)).     

Respiratory cytochrome c oxidase can be efficiently reduced by the photosynthetic redox proteins cytochrome c6 and plastocyanin in cyanobacteria

Plastocyanin and cytochrome c6 are two small soluble electron carriers located in the intrathylacoidal space of cyanobacteria. Although their role as electron shuttle between the cytochrome b6f and photosystem I complexes in the photosynthetic pathway is well established, their participation in the respiratory electron transport chain as donors to the terminal oxidase is still under debate. Here, we present the first time-resolved analysis showing that both cytochrome c6 and plastocyanin can be efficiently oxidized by the aa3 type cytochrome c oxidase in Nostoc sp. PCC 7119. The apparent electron transfer rate constants are ca. 250 and 300 s(-1) for cytochrome c6 and plastocyanin, respectively. These constants are 10 times higher than those obtained for the oxidation of horse cytochrome c by the oxidase, in spite of being a reaction thermodynamically more favourable.     

Electrostatic interaction of cytochrome c with cytochrome c1 and cytochrome oxidase

The reactions of horse heart cytochrome c with succinate-cytochrome c reductase and cytochrome oxidase were studied as a function of ionic strength using both spectrophotometric and oxygen electrode assay techniques. The kinetic parameter Vmax/Km for both reactions decreased very rapidly as the ionic strength was increased, indicating that electrostatic interactions were important to the reactions. A new semiempirical relationship for the electrostatic energy of interaction between cytochrome c and its oxidation-reduction partners was developed, in which specific complementary charge-pair interactions between lysine amino groups on cytochrome c and negatively charged carboxylate groups on the other protein are assumed to dominate the interaction. The contribution of individual cytochrome c lysine amino groups to the electrostatic interaction was estimated from the decrease in reaction rate caused by specific modification of the lysine amino groups by reagents that change the charge to 0 or -1. These estimates range from -0.9 kcal/mol for lysines immediately surrounding the heme crevice of cytochrome c to 0 kcal/mol for lysines well removed from the heme crevice region. The semiempirical relationship for the total electrostatic energy of interaction was in quantitative agreement with the experimental ionic strength dependence of the reaction rates when the parameters were based on the specific lysine modification results. The electrostatic energies of interaction between cytochrome c and its reductase and oxidase were nearly the same, providing additional evidence that the two reactions take place at similar sites on cytochrome c.     

The interaction of nitrotyrosine-83 plastocyanin with cytochromes f and c: pH dependence and the effect of an additional negative charge on plastocyanin.

Spinach plastocyanin was selectively modified using tetranitromethane which incorporates a nitro group ortho to the hydroxyl group of tyrosine 83 (Anderson, G.P., Draheim, J.E. and Gross, E.L. (1985) Biochim. Biophys. Acta 810, 123-131). This tyrosine residue has been postulated to be part of the cytochrome f binding site on plastocyanin. Since the hydroxyl moiety of nitrotyrosine 83 is deprotonated above its pK of 8.3, it provides a useful modification for studying the effect of an extra negative charge on the interaction of plastocyanin with cytochrome f. No effect on cytochrome f oxidation was observed at pH 7 under conditions in which the hydroxyl moiety is protonated. However, the rate of cytochrome f oxidation increased at pH values greater than 8, reaching a maximum at pH 8.6 and decreasing at still higher pH values. The increase was half-maximal at pH 8.3 which is the pK for the hydroxyl moiety on nitrotyrosine 83. In contrast, the rate of cytochrome f oxidation for control plastocyanin was independent of pH from pH 7 to 8.6. These results show that increasing the negative charge on plastocyanin at Tyr-83 increases the ability to react with cytochrome f, supporting the hypothesis that cytochrome f interacts with plastocyanin at this location. In contrast, the reaction of Ntyr-83 plastocyanin with mammalian cytochrome c was independent of pH, suggesting that its mode of interaction with plastocyanin is different from that of cytochrome f. A comparison of the effects of Ntyr-83 modification of plastocyanin with the carboxyl- and amino-group modifications reported previously suggests that plastocyanin binds to cytochrome f in such a way that electrons could be donated to plastocyanin at either of its two binding sites.     

Direct simulation of plastocyanin and cytochrome f interactions in solution

Most biological functions, including photosynthetic activity, are mediated by protein interactions. The proteins plastocyanin and cytochrome f are reaction partners in a photosynthetic electron transport chain. We designed a 3D computer simulation model of diffusion and interaction of spinach plastocyanin and turnip cytochrome f in solution. It is the first step in simulating the electron transfer from cytochrome f to photosystem 1 in the lumen of thylakoid. The model is multiparticle and it can describe the interaction of several hundreds of proteins. In our model the interacting proteins are represented as rigid bodies with spatial fixed charges. Translational and rotational motion of proteins is the result of the effect of stochastic Brownian force and electrostatic force. The Poisson-Boltzmann formalism is used to determine the electrostatic potential field generated around the proteins. Using this model we studied the kinetic characteristics of plastocyanin-cytochrome f complex formation for plastocyanin mutants at pH 7 and a variety of ionic strength values.