Prediction of Protein-Protein Interaction Sites Using Electrostatic Desolvation Profiles

Protein-protein complex formation involves removal of water from the interface region. Surface regions with a small free energy penalty for water removal or desolvation may correspond to preferred interaction sites. A method to calculate the electrostatic free energy of placing a neutral low-dielectric probe at various protein surface positions has been designed and applied to characterize putative interaction sites. Based on solutions of the finite-difference Poisson equation, this method also includes long-range electrostatic contributions and the protein solvent boundary shape in contrast to accessible-surface-area-based solvation energies. Calculations on a large set of proteins indicate that in many cases (>90%), the known binding site overlaps with one of the six regions of lowest electrostatic desolvation penalty (overlap with the lowest desolvation region for 48% of proteins). Since the onset of electrostatic desolvation occurs even before direct protein-protein contact formation, it may help guide proteins toward the binding region in the final stage of complex formation. It is interesting that the probe desolvation properties associated with residue types were found to depend to some degree on whether the residue was outside of or part of a binding site. The probe desolvation penalty was on average smaller if the residue was part of a binding site compared to other surface locations. Applications to several antigen-antibody complexes demonstrated that the approach might be useful not only to predict protein interaction sites in general but to map potential antigenic epitopes on protein surfaces.     

静电和疏水效应对胰岛素二聚体稳定性的影响

从猪胰岛素二聚体的结构出发,着重研究了胰岛素二聚体单体之间的静电和疏水相互作用,用连续介质模型的有限差分方法计算得到胰岛素二聚体的静电势,用溶剂可接近表面（ASA）模型分析了分子表面积及疏水性,还考察了不同pH值对胰岛素二聚体静电和疏水相互作用的影响。结果分析表明,当pH值处于弱酸弱碱范围内时（4．6－8．5）,静电相 互作用能和疏水自由能都呈现出较小的值,当pH为6．2时,疏水性出现一个明显的峰值,这与胰岛素二聚体结晶的实验条件相吻合。     

Calculation of weak protein-protein interactions: the pH dependence of the second virial coefficient

Interactions between proteins are often sufficiently weak that their study through the use of conventional structural techniques becomes problematic. Of the few techniques capable of providing experimental measures of weak protein-protein interactions, perhaps the most useful is the second virial coefficient, B(22), which quantifies a protein solution's deviations from ideal behavior. It has long been known that B(22) can in principle be computed, but only very recently has it been demonstrated that such calculations can be performed using protein models of true atomic detail (Biophys. J. 1998, 75:2469-2477). The work reported here extends these previous efforts in an attempt to develop a transferable energetic model capable of reproducing the experimental trends obtained for two different proteins over a range of pH and ionic strengths. We describe protein-protein interaction energies by a combination of three separate terms: (i) an electrostatic interaction term based on the use of effective charges, (ii) a term describing the electrostatic desolvation that occurs when charged groups are buried by an approaching protein partner, and (iii) a solvent-accessible surface area term that is used to describe contributions from van der Waals and hydrophobic interactions. The magnitude of the third term is governed by an adjustable, empirical parameter, gamma, that is altered to optimize agreement between calculated and experimental values of B(22). The model is applied separately to the proteins lysozyme and chymotrypsinogen, yielding optimal values of gamma that are almost identical. There are, however, clear difficulties in reproducing B(22) values at the extremes of pH. Explicit calculation of the protonation states of ionizable amino acids in the 200 most energetically favorable protein-protein structures suggest that these difficulties are due to a neglect of the protonation state changes that can accompany complexation. Proper reproduction of the pH dependence of B(22) will, therefore, almost certainly require that account be taken of these protonation state changes. Despite this problem, the fact that almost identical gamma values are obtained from two different proteins suggests that the basic energetic formulation used here, which can be evaluated very rapidly, might find use in dynamical simulations of weak protein-protein interactions at intermediate pH values.     

Barstar is electrostatically optimized for tight binding to barnase

We used a novel charge optimization technique to study the small ribonuclease barnase and to analyze its interaction with a natural tight binding inhibitor, the protein barstar. The approach uses a continuum model to explicitly determine the charge distributions that lead to the most favorable electrostatic contribution to binding when competing desolvation and interaction effects are included. Given its backbone fold, barstar is electrostatically optimized for tight binding to barnase when compared with mutants where residues have been substituted with one of the 20 common amino acids. Natural proteins thus appear to use optimization of electrostatic interactions as one strategy for achieving tight binding.     

MCCE analysis of the pKas of introduced buried acids and bases in staphylococcal nuclease

The pK(a)s of 96 acids and bases introduced into buried sites in the staphylococcal nuclease protein (SNase) were calculated using the multiconformation continuum electrostatics (MCCE) program and the results compared with experimental values. The pK(a)s are obtained by Monte Carlo sampling of coupled side chain protonation and position as a function of pH. The dependence of the results on the protein dielectric constant (ε(prot)) in the continuum electrostatics analysis and on the Lennard-Jones non-electrostatics parameters was evaluated. The pK(a)s of the introduced residues have a clear dependence on ε(prot,) whereas native ionizable residues do not. The native residues have electrostatic interactions with other residues in the protein favoring ionization, which are larger than the desolvation penalty favoring the neutral state. Increasing ε(prot) scales both terms, which for these residues leads to small changes in pK(a). The introduced residues have a larger desolvation penalty and negligible interactions with residues in the protein. For these residues, changing ε(prot) has a large influence on the calculated pK(a). An ε(prot) of 8-10 and a Lennard-Jones scaling of 0.25 is best here. The X-ray crystal structures of the mutated proteins are found to provide somewhat better results than calculations carried out on mutations made in silico. Initial relaxation of the in silico mutations by Gromacs and extensive side chain rotamer sampling within MCCE can significantly improve the match with experiment.     

Continuum electrostatic model for the binding of cytochrome c2 to the photosynthetic reaction center from Rhodobacter sphaeroides

Electrostatic interactions are important for protein-protein association. In this study, we examined the electrostatic interactions between two proteins, cytochrome c(2) (cyt c(2)) and the reaction center (RC) from the photosynthetic bacterium Rhodobacter sphaeroides, that function in intermolecular electron transfer in photosynthesis. Electrostatic contributions to the binding energy for the cyt c(2)-RC complex were calculated using continuum electrostatic methods based on the recent cocrystal structure [Axelrod, H. L., et al. (2002) J. Mol. Biol. 319, 501-515]. Calculated changes in binding energy due to mutations of charged interface residues agreed with experimental results for a protein dielectric constant epsilon(in) of 10. However, the electrostatic contribution to the binding energy for the complex was close to zero due to unfavorable desolvation energies that compensate for the favorable Coulomb attraction. The electrostatic energy calculated as a function of displacement of the cyt c(2) from the bound position showed a shallow minimum at a position near but displaced from the cocrystal configuration. These results show that although electrostatic steering is present, other short-range interactions must be present to contribute to the binding energy and to determine the structure of the complex. Calculations made to model the experimental data on association rates indicate a solvent-separated transition state for binding in which the cyt c(2) is displaced approximately 8 A above its position in the bound complex. These results are consistent with a two-step model for protein association: electrostatic docking of the cyt c(2) followed by desolvation to form short-range van der Waals contacts for rapid electron transfer.     

BiGGER: a new (soft) docking algorithm for predicting protein interactions

A new computationally efficient and automated "soft docking" algorithm is described to assist the prediction of the mode of binding between two proteins, using the three-dimensional structures of the unbound molecules. The method is implemented in a software package called BiGGER (Bimolecular Complex Generation with Global Evaluation and Ranking) and works in two sequential steps: first, the complete 6-dimensional binding spaces of both molecules is systematically searched. A population of candidate protein-protein docked geometries is thus generated and selected on the basis of the geometric complementarity and amino acid pairwise affinities between the two molecular surfaces. Most of the conformational changes observed during protein association are treated in an implicit way and test results are equally satisfactory, regardless of starting from the bound or the unbound forms of known structures of the interacting proteins. In contrast to other methods, the entire molecular surfaces are searched during the simulation, using absolutely no additional information regarding the binding sites. In a second step, an interaction scoring function is used to rank the putative docked structures. The function incorporates interaction terms that are thought to be relevant to the stabilization of protein complexes. These include: geometric complementarity of the surfaces, explicit electrostatic interactions, desolvation energy, and pairwise propensities of the amino acid side chains to contact across the molecular interface. The relative functional contribution of each of these interaction terms to the global scoring function has been empirically adjusted through a neural network optimizer using a learning set of 25 protein-protein complexes of known crystallographic structures. In 22 out of 25 protein-protein complexes tested, near-native docked geometries were found with C(alpha) RMS deviations < or =4.0 A from the experimental structures, of which 14 were found within the 20 top ranking solutions. The program works on widely available personal computers and takes 2 to 8 hours of CPU time to run any of the docking tests herein presented. Finally, the value and limitations of the method for the study of macromolecular interactions, not yet revealed by experimental techniques, are discussed.     

Optimization of binding electrostatics: charge complementarity in the barnase-barstar protein complex

Theoretical and experimental studies have shown that the large desolvation penalty required for polar and charged groups frequently precludes their involvement in electrostatic interactions that contribute strongly to net stability in the folding or binding of proteins in aqueous solution near room temperature. We have previously developed a theoretical framework for computing optimized electrostatic interactions and illustrated use of the algorithm with simplified geometries. Given a receptor and model assumptions, the method computes the ligand-charge distribution that provides the most favorable balance of desolvation and interaction effects on binding. In this paper the method has been extended to treat complexes using actual molecular shapes. The barnase-barstar protein complex was investigated with barnase treated as a target receptor. The atomic point charges of barstar were varied to optimize the electrostatic binding free energy. Barnase and natural barstar form a tight complex (K(d) approximately 10(-14) M) with many charged and polar groups near the interface that make this a particularly relevant system for investigating the role of electrostatic effects on binding. The results show that sets of barstar charges (resulting from optimization with different constraints) can be found that give rise to relatively large predicted improvements in electrostatic binding free energy. Principles for enhancing the effect of electrostatic interactions in molecular binding in aqueous environments are discussed in light of the optima. Our findings suggest that, in general, the enhancements in electrostatic binding free energy resulting from modification of polar and charged groups can be substantial. Moreover, a recently proposed definition of electrostatic complementarity is shown to be a useful tool for examining binding interfaces. Finally, calculational results suggest that wild-type barstar is closer to being affinity optimized than is barnase for their mutual binding, consistent with the known roles of these proteins.     

Electrostatic calculations of the pKa values of ionizable groups in bacteriorhodopsin.

The effects of solvation and charge-charge interactions on the pKa of ionizable groups in bacteriorhodopsin have been studied using a macroscopic dielectric model with atom-level detail. The calculations are based on the atomic model for bacteriorhodopsin recently proposed by Henderson et al. Even if the structural data are not resolved at the atomic level, such calculations can indicate the quality of the model, outline some general aspects of electrostatic interactions in membrane proteins, and predict some features. The effects of structural uncertainties on the calculations have been investigated by conformational sampling. The results are in reasonable agreement with experimental measurements of several unusually large pKa shifts (e.g. the experimental findings that Asp96 and Asp115 are protonated in the ground state over a wide pH range). In general, we find that the large unfavorable desolvation energies of forming charges in the protein interior must be compensated by strong favorable charge-charge interactions, with the result that the titrations of many ionizable groups are strongly coupled to each other. We find several instances of complex titration behavior due to strong electrostatic interactions between titrating sites, and suggest that such behavior may be common in proton transfer systems. We also propose that they can help to resolve structural ambiguities in the currently available density map. In particular, we find better agreement between theory and experiment when a structural ambiguity in the position of the Arg82 side-chain is resolved in favor of a position near the Schiff base.     

Study of protein-protein interaction using conformational space annealing

We apply conformational space annealing (CSA), an efficient global optimization method, to the study of protein-protein interaction. The CSA is incorporated into the Tinker molecular modeling package along with a B-spline method for CAPRI Round 5 experiments. We have used an energy function for the protein-protein interaction that consists of electrostatic interaction, van der Waals interaction, and solvation energy terms represented by the occupancy desolvation method. The parameters of the AMBER94 all-atom empirical force field are used. Each energy term is calculated by precalculated grid potentials and B-spline method approximation. The ligand protein is placed inside a sphere of 50 A radius centered at an appropriate location, and the CSA rigid docking studies are carried out to find stable complexes. Up to 10 complexes are selected using the K-mean clustering method and biological information when available. These complexes are energy-minimized for further refinement by considering the flexibility of interacting proteins. The results show that the CSA method has a potential for the study of protein-protein interaction.     

Interpreting trends in the binding of cyclic ureas to HIV-1 protease

The design of new HIV protease inhibitors requires an improved understanding of the physical basis of inhibitor/protein binding. Here, the binding affinities of seven aliphatic cyclic ureas to HIV-1 protease are calculated using a predominant states method and an implicit solvent model based upon finite difference solutions of the Poisson-Boltzmann equation. The calculations are able to reproduce the observed U-shaped trend of binding free energy as a function of aliphatic chain length. Interestingly, the decrease in affinity for the longest chains is attributable primarily to the energy cost of partly desolvating charged aspartic and arginine groups at the mouths of the active site. Even aliphatic chains too short to contact these charged groups directly are subject to considerable desolvation penalties. We are not aware of other systems where binding affinity trends have been attributed to long-ranged electrostatic desolvation of ionized groups. A generalized Born/surface area solvation model yields a much smaller change in desolvation energy with chain length and, therefore, does not reproduce the experimental binding affinity trends. This result suggests that the generalized Born model should be used with caution for complex, partly desolvated systems like protein binding sites. We also find that changing the assumed protonation state of the active site aspartyl dyad significantly affects the computed binding affinity trends. The protonation state of the aspartyl dyad in the presence of cyclic ureas is discussed in light of the observation that the monoprotonated state reproduces the experimental results best.     

What determines the van der Waals coefficient beta in the LIE (linear interaction energy) method to estimate binding free energies using molecular dynamics simulations?

Recently a semiempirical method has been proposed by Aqvist et al. to calculate absolute and relative binding free energies. In this method, the absolute binding free energy of a ligand is estimated as deltaGbind = alpha + beta, where Vel(bound) and Vvdw(bound) are the electrostatic and van der Waals interaction energies between the ligand and the solvated protein from an molecular dynamics (MD) trajectory with ligand bound to protein and Vel(free) and Vel(free) and Vvdw(free) are the electrostatic and van der Waals interaction energies between the ligand and the water from an MD trajectory with the ligand in water. A set of values, alpha = 0.5 and beta = 0.16, was found to give results in good agreement with experimental data. Later, however, different optimal values of beta were found in studies of compounds binding to P450cam and avidin. The present work investigates how the optimal value of beta depends on the nature of binding sites for different protein-ligand interactions. By examining seven ligands interacting with five proteins, we have discovered a linear correlation between the value of beta and the weighted non-polar desolvation ratio (WNDR), with a correlation coefficient of 0.96. We have also examined the ability of this correlation to predict optimal values of beta for different ligands binding to a single protein. We studied twelve neutral compounds bound to avidin. In this case, the WNDR approach gave a better estimate of the absolute binding free energies than results obtained using the fixed value of beta found for biotin-avidin. In terms of reproducing the relative binding free energy to biotin, the fixed-beta value gave better results for compounds similar to biotin, but for compounds less similar to biotin, the WNDR approach led to better relative binding free energies.     

Free energy landscapes of encounter complexes in protein-protein association

We report the computer generation of a high-density map of the thermodynamic properties of the diffusion-accessible encounter conformations of four receptor-ligand protein pairs, and use it to study the electrostatic and desolvation components of the free energy of association. Encounter complex conformations are generated by sampling the translational/rotational space of the ligand around the receptor, both at 5-A and zero surface-to-surface separations. We find that partial desolvation is always an important effect, and it becomes dominant for complexes in which one of the reactants is neutral or weakly charged. The interaction provides a slowly varying attractive force over a small but significant region of the molecular surface. In complexes with no strong charge complementarity this region surrounds the binding site, and the orientation of the ligand in the encounter conformation with the lowest desolvation free energy is similar to the one observed in the fully formed complex. Complexes with strong opposite charges exhibit two types of behavior. In the first group, represented by barnase/barstar, electrostatics exerts strong orientational steering toward the binding site, and desolvation provides some added adhesion within the local region of low electrostatic energy. In the second group, represented by the complex of kallikrein and pancreatic trypsin inhibitor, the overall stability results from the rather nonspecific electrostatic attraction, whereas the affinity toward the binding region is determined by desolvation interactions.     

Solvation energy density occlusion approximation for evaluation of desolvation penalties in biomolecular interactions

In calculations involving many displacements of an interacting pair of biomolecules, such as brownian dynamics, the docking of a substrate/ligand to an enzyme/receptor, or the screening of a large number of ligands as prospective inhibitors for a particular receptor site, there is a need for rapid evaluation of the desolvation penalties of the interacting pair. Although continuum electrostatic treatments with distinct dielectric constants for solute and solvent provide an account of the electrostatics of solvation and desolvation, it is necessary to re-solve the Poisson equation, at considerable computational cost, for each displacement of the interacting pair. We present a new method that uses a formulation of continuum electrostatic solvation in terms of the solvation energy density and approximates desolvation in terms of the occlusion of this density. We call it the SEDO approximation. It avoids the need to re-solve the Poisson equation, as desolvation is now estimated by an integral over the occluded volume. Test calculations are presented for some simple model systems and for some real systems that have previously been studied using the Poisson equation approach: MHC class I protein-peptide complexes and a congeneric series of human immunodeficiency virus type 1 (HIV-1) protease--ligand complexes. For most of the systems considered, the trends and magnitudes of the desolvation component of interaction energies obtained using the SEDO approximation are in reasonable correlation with those obtained by re-solving the Poisson equation. In most cases, the error introduced by the SEDO approximation is much less than that of the often-used test-charge approximation for the charge-charge components of intermolecular interactions. Proteins 2001;43:12-27.     

Protein stabilization by salt bridges: concepts, experimental approaches and clarification of some misunderstandings

Salt bridges in proteins are bonds between oppositely charged residues that are sufficiently close to each other to experience electrostatic attraction. They contribute to protein structure and to the specificity of interaction of proteins with other biomolecules, but in doing so they need not necessarily increase a protein's free energy of unfolding. The net electrostatic free energy of a salt bridge can be partitioned into three components: charge-charge interactions, interactions of charges with permanent dipoles, and desolvation of charges. Energetically favorable Coulombic charge-charge interaction is opposed by often unfavorable desolvation of interacting charges. As a consequence, salt bridges may destabilize the structure of the folded protein. There are two ways to estimate the free energy contribution of salt bridges by experiment: the pK(a) approach and the mutation approach. In the pK(a) approach, the contribution of charges to the free energy of unfolding of a protein is obtained from the change of pK(a) of ionizable groups caused by altered electrostatic interactions upon folding of the protein. The pK(a) approach provides the relative free energy gained or lost when ionizable groups are being charged. In the mutation approach, the coupling free energy between interacting charges is obtained from a double mutant cycle. The coupling free energy is an indirect and approximate measure of the free energy of charge-charge interaction. Neither the pK(a) approach nor the mutation approach can provide the net free energy of a salt bridge. Currently, this is obtained only by computational methods which, however, are often prone to large uncertainties due to simplifying assumptions and insufficient structural information on which calculations are based. This state of affairs makes the precise thermodynamic quantification of salt bridge energies very difficult. This review is focused on concepts and on the assessment of experimental methods and does not cover the vast literature.     

Electrostatic potentials and electrostatic interaction energies of rat cytochrome b5 and a simulated anion-exchange adsorbent surface.

Electrostatic potentials were determined for the soluble tryptic core of rat cytochrome b5 (using a structure derived from homology modeling) and a simulated anion-exchange surface through application of the linearized finite-difference Poisson-Boltzmann equation with the simulation code UHBD. Objectives of this work included determination of the contributions of the various charged groups on the protein surface to electrostatic interactions with a simulated anion-exchange surface as a function of orientation, separation distance, and ionic strength, as well as examining the potential existence of a preferred contact orientation. Electrostatic interaction free energies for the complex of the model protein and the simulated surface were computed using the electrostatics section of UHBD employing a 110(3) grid. An initial coarse grid spacing of 2.0 A was required to obtain correct boundary conditions. The boundary conditions of the coarse grid were used in subsequent focusing steps until the electrostatic interaction free energies were relatively independent of grid spacing (at approximately 0.5 A). Explicit error analyses were performed to determine the effects of grid spacing and other model assumptions on the electrostatic interaction free energies. The computational results reveal the presence of a preferred interaction orientation; the interaction energy between these two entities, of opposite net charge, is repulsive over a range of orientations. The electrostatic interaction free energies appear to be the summation of multiple fractional interactions between the protein and the anion-exchange surface. The simulation results are compared with those of ion-exchange adsorption experiments with site-directed mutants of the recombinant protein. Comparisons of the results from the computational and experimental studies should lead to a better understanding of electrostatic interactions of proteins and charged surfaces.     

Charge-charge interactions are key determinants of the pK values of ionizable groups in ribonuclease Sa (pI=3.5) and a basic variant (pI=10.2)

The pK values of the titratable groups in ribonuclease Sa (RNase Sa) (pI=3.5), and a charge-reversed variant with five carboxyl to lysine substitutions, 5K RNase Sa (pI=10.2), have been determined by NMR at 20 degrees C in 0.1M NaCl. In RNase Sa, 18 pK values and in 5K, 11 pK values were measured. The carboxyl group of Asp33, which is buried and forms three intramolecular hydrogen bonds in RNase Sa, has the lowest pK (2.4), whereas Asp79, which is also buried but does not form hydrogen bonds, has the most elevated pK (7.4). These results highlight the importance of desolvation and charge-dipole interactions in perturbing pK values of buried groups. Alkaline titration revealed that the terminal amine of RNase Sa and all eight tyrosine residues have significantly increased pK values relative to model compounds.A primary objective in this study was to investigate the influence of charge-charge interactions on the pK values by comparing results from RNase Sa with those from the 5K variant. The solution structures of the two proteins are very similar as revealed by NMR and other spectroscopic data, with only small changes at the N terminus and in the alpha-helix. Consequently, the ionizable groups will have similar environments in the two variants and desolvation and charge-dipole interactions will have comparable effects on the pK values of both. Their pK differences, therefore, are expected to be chiefly due to the different charge-charge interactions. As anticipated from its higher net charge, all measured pK values in 5K RNase are lowered relative to wild-type RNase Sa, with the largest decrease being 2.2 pH units for Glu14. The pK differences (pK(Sa)-pK(5K)) calculated using a simple model based on Coulomb's Law and a dielectric constant of 45 agree well with the experimental values. This demonstrates that the pK differences between wild-type and 5K RNase Sa are mainly due to changes in the electrostatic interactions between the ionizable groups. pK values calculated using Coulomb's Law also showed a good correlation (R=0.83) with experimental values. The more complex model based on a finite-difference solution to the Poisson-Boltzmann equation, which considers desolvation and charge-dipole interactions in addition to charge-charge interactions, was also used to calculate pK values. Surprisingly, these values are more poorly correlated (R=0.65) with the values from experiment. Taken together, the results are evidence that charge-charge interactions are the chief perturbant of the pK values of ionizable groups on the protein surface, which is where the majority of the ionizable groups are positioned in proteins.     

Modeling of denatured state for calculation of the electrostatic contribution to protein stability

Existing models of the denatured state of proteins consider only one possible spatial distribution of protein charges and therefore are applicable to a limited number of cases. In this article, a more general framework for the modeling of the denatured state is proposed. It is based on the assumption that the titratable groups of an unfolded protein can adopt a quasi-random distribution restricted by the protein sequence. The model was applied for the calculations of electrostatic interactions in two proteins, barnase and N-terminal domain of the ribosomal protein L9. The calculated free energy of denaturation, DeltaG(pH), reproduces the experimental data better than the commonly used null approximation (NA). It was shown that the seemingly good agreement with experimental data obtained by NA originates from the compensatory effect between the pairwise electrostatic interactions and the desolvation energy of the individual sites. It was also found that the ionization properties of denatured proteins are influenced by the protein sequence.     

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.