Definition of the Interaction Domain for Cytochrome con Cytochrome c Oxidase

The electron transfer complex between bovine cytochrome c oxidase and horse cytochrome c has been predicted with the docking program DOT, which performs a complete, systematic search over all six rotational and translational degrees of freedom. Energies for over 36 billion configurations were calculated, providing a free-energy landscape showing guidance of positively charged cytochrome c to the negative region on the cytochrome c oxidase surface formed by subunit II. In a representative configuration, the solvent-exposed cytochromec heme edge is within 4 Å of the indole ring of subunit II residue Trp104, indicating a likely electron transfer path. These two groups are surrounded by a small, hydrophobic contact region, which is surrounded by electrostatically complementary hydrophilic interactions. Cytochrome c/cytochrome c oxidase interactions of Lys13 with Asp119 and Lys72 with Gln103 and Asp158 are the most critical polar interactions due to their proximity to the hydrophobic region and exclusion from bulk solvent. The predicted complex matches previous mutagenesis, binding, and time-resolved kinetics studies that implicate Trp104 in electron transfer and show the importance of specific charged residues to protein affinity. Electrostatic forces not only enhance long range protein/protein association; they also predominate in short range alignment, creating the transient interaction needed for rapid turnover.

The determination of structures of bacterial and mitochondrial cytochrome c oxidases (CcO) 1 by x-ray crystallography (1)(2)(3)(4)(5) has opened the door to understanding the structural basis for its function in respiratory chain activity. One step of the respiratory chain involves the transfer of electrons from cytochrome bc 1 complex to CcO, both membrane-bound complexes, via the water-soluble protein cytochrome c (Cc). Efficient electron transfer requires both rapid complex formation and rapid product dissociation. Determination of the structure of the complex formed between CcO and Cc would reveal the interactions promoting this transient interaction as well as possible paths for intermolecular electron transfer. The complex structure, however, has yet to be determined, in part due to the difficulties in crystallizing membrane-bound proteins and possibly also due to the transient nature of the interaction. On the other hand, this redox system may be particularly amenable to computational search methods based on static crystallographic structures because of the fast kinetics of these interactions, which suggest that large conformational changes do not occur upon complex formation. In addition, computational techniques may shed light on long range electrostatic guidance between the two partners and on the dynamic nature of the interaction.
The docking program DOT (6) provides a complete search of all orientations between two rigid molecules by systematically rotating and translating one molecule about the other, a procedure considered computationally unfeasible just a few years ago (7). At that time, the extent of the search was limited to, at most, energy calculations for a few million configurations, as in the programs TURNIP (8) and DOCK (9). Alternately, the representation of the moving molecule was greatly simplified to a few point charges (10,11). DOT systematically samples configurations for two rigid molecules over all space and expresses the interaction energies as correlation functions, which are rapidly computed using fast Fourier transforms. The electrostatic potentials used by DOT are calculated by Poisson-Boltzmann methods (12)(13)(14), which take both solvent and ionic strength effects into account. Because DOT performs a complete search, both long range and short range interactions can be examined.
Here, we describe the application of DOT to the interaction of bovine CcO with horse Cc. The calculated complex identifies the CcO Trp 104 (Trp 143 ) 2 side chain as the point of electron entry into CcO and implicates specific charged side chains in protein-protein association, in agreement with mutagenesis, binding, and time-resolved kinetics studies (15)(16)(17). Properties of the calculated interface resemble those found in the crystallographic structure of the electron transfer complex of yeast cytochrome c peroxidase (CcP) with yeast Cc (18), suggesting a general structural motif for transient protein-protein interactions.

EXPERIMENTAL PROCEDURES
Coordinate Preparation-Coordinates for bovine CcO (1OCC) and horse Cc (1HRC) were obtained from the Protein Data Bank (19). Rhodobacter sphaeroides cytochrome c 2 was also investigated because its interactions with CcO have been examined (16,17). Polar hydrogen atoms were added with the computer graphics program Insight (MSI Inc., San Diego). Partial atomic charges for protein atoms and heme groups were based on the AMBER library that includes polar hydrogen atoms only (20). Histidine residues were neutral with a single proton on N-⑀ unless metal ligation or salt-bridge formation indicated otherwise. For horse Cc, the C terminus was negatively charged, the N terminus was neutral because of acetylation, and the heme group had an overall charge of Ϫ2, resulting in a total charge of ϩ6. Of the three available coordinate sets for R. sphaeroides cytochrome c 2 (1CXA, 2CXB, and 1CXC), 1CXC was used because it is the most complete and determined at the highest resolution (1.6 Å). Missing atoms for residues 10,32,33,35,74,78,85,89,95,97,105, and 106 were added with Insight while using other two structures as guides. Both termini were charged, and both His 75 and His 111 were doubly protonated to satisfy intramolecular salt bridges, giving a total charge of 0. An overall charge of Ϫ2 was previously used (21), possibly because all His residues were left neutral.
CcO presents a challenging computational problem because of its large size (ϳ204,000 kDa). Since Cc interacts with CcO in the mitochondrial intermembrane space, only this region of CcO was used in the calculation. The bovine CcO complex was cut by a plane placed below the ring of positively charged residues that presumably lie at the inner mitochondrial membrane surface (See Fig. 1C). All residues with any atom above this plane were retained. The selected coordinates included all of subunit II, except the transmembrane helical segment, and parts of subunits I, IV, VIa, VIb, VIc, VIIb, VIIc, and VIII. The heme groups and the other bound metal ions lie in the membrane-bound portion of the molecule and were not included. Polypeptide termini resulting from cutting out the membrane-bound region were kept neutral, while standard N termini and C termini were charged. Each copper atom of the dicopper site Cu A in subunit II was assigned a charge of ϩ1.5, giving the metal cluster a total charge of ϩ3 (22). The total charge on the selected bovine CcO coordinates was Ϫ7.
Electrostatic Potentials-Electrostatic potentials were calculated with the program UHBD (13), which uses finite difference methods to solve the Poisson-Boltzmann equations for electrostatic potential. Potentials were calculated on a grid of the same size and spacing used in the DOT calculation: 128 Å on a side with 1-Å spacing. A dielectric of 3 for the protein, a dielectric of 80 for the surrounding environment, an ion exclusion radius of 1.4 Å, and an ionic strength of 50 mM were used.
Molecular Descriptions Used in the DOT Calculation-In the DOT calculation, Cc was assigned as the moving molecule and CcO as the stationary molecule. The shape distribution of Cc was represented by a value of 1 at each atomic position. Note that with this description, the volume of the moving molecule is represented by its atomic coordinates rather than by its full van der Waals volume. The charge distribution of Cc was represented by partial charges at the atomic positions of all nonhydrogen and polar hydrogen atoms, with charges taken from the AMBER library.
The selected coordinates of CcO were centered in the x and y directions on a cubical grid 128 Å on a side with 1-Å grid spacing (about 2.1 million total grid points). The coordinates were moved in the z direction to position the approximate plane of the membrane near the bottom of the box, increasing the region representing the surrounding intermembrane space that Cc can occupy. The shape of CcO was represented by an excluded van der Waals volume surrounded by a 3.0 Å layer of favorable potential. To map the shape potential of CcO onto the grid, grid points within 4.5 Å of all nonhydrogen atoms were assigned a value of Ϫ1, and then grid points within 1.5 Å of all nonhydrogen atoms were assigned a highly unfavorable value of 1000. All other grid points were assigned a value of 0.
Since the electrostatic potential is calculated only once for the stationary molecule, sophisticated, computationally expensive methods can be used. The Poisson-Boltzmann electrostatic potential for CcO was calculated with UHBD. It was assumed that an aqueous environment surrounded the selected CcO coordinates; the low dielectric of the membrane was not taken into account. Since the stationary molecule is represented by its van der Waals volume but the moving molecule is represented by its atomic centers, some atoms of the moving molecule can approach within 1.5 Å of the stationary molecule atom centers. This accommodates small conformational changes induced upon complex formation. Unfortunately, too close an approach can also result in an artificially large electrostatic contribution when a moving molecule atom lies between the molecular and the solvent-accessible surfaces of the stationary molecule. Large changes in magnitude and distribution of electrostatic potential occur in the region between the two surfaces. The most intense potential on the molecular surface is concentrated on protuberances (termini of Lys, Arg, Asp, and Glu side chains), whereas the potential on the solvent-accessible surface is more delocalized, with the most intense potential generally concentrated in concave regions of the protein (see Fig. 1, A, B, and D). To alleviate this problem, the electrostatic potential grid values of CcO were clamped based on the extreme potentials found at the solvent-accessible surface, which represents the closest approach of the center of a water molecule (ϳ2.9 Å between atomic centers). For CcO, the upper limit was ϩ4 kcal/mol/e and the lower limit was Ϫ6.0 kcal/mol/e. We initially used limits of Ϯ 15 kcal/mol/e, the extremes found on protein molecular surfaces, but these limits gave a much larger number of favorable-energy false positives in DOT calculations.
Energy Computation by Correlation Functions-All energies computed by DOT are derived by placing the moving molecule in a potential field generated by the fixed molecule. The total energy for each configuration of the two molecules is the sum of the electrostatic and van der Waals energy terms, each of which can be described as a correlation function. Given a potential field S(r) describing the stationary molecule and a probe function M(r) describing the moving molecule, the energy is given by the following.
If the moving molecule is rotated by an angle and displaced from the origin by a vector r 0 , the energy of the system is given by the following.
Mathematically, this is the correlation of the potential field S(r) and the rotated function M(r). For the electrostatic energy term, S(r) is the electrostatic potential field of CcO and M(r) is the set of partial charges for Cc. For the van der Waals term, S(r) is the shape potential for CcO described above. Each Cc atom within the favorable layer surrounding CcO contributes Ϫ0.1 kcal/mol to the interaction energy. A Cc atom lying within the van der Waals volume of CcO contributes a large unfavorable value to the interaction energy. To allow for side chain rearrangement induced upon complex formation, a user-specified number of moving molecule atoms can penetrate the volume of the stationary molecule without incurring an energy penalty, but no penetrations were allowed in these runs. This method for computing overlap is similar to that previously described (23,24) except that here S(r) has been constructed to return a composite number containing both a count of collisions and a count of favorable interactions.
Correlations can be calculated very efficiently through the use of the Convolution Theorem. The electrostatic and nonbonded energy functions are described on a grid of N points (128 3 ). Evaluating the correlation directly requires N ϫ N multiplications, in our case 128 6 . Evaluating the correlation using fast Fourier transforms costs three fast Fourier transforms, each proportional to NlogN, and N multiplications, so the computational cost is proportional to N(3logN ϩ 1), in our case 128 3 ϫ 20, or a savings of about 10 5 .
Results from DOT: The Minimum-energy and Free-energy Grids-In the systematic search performed by DOT, Cc is centered at all grid points and then rotated, and the calculation is repeated. The full search performed here uses a grid of 128 3 points and 17,354 distinct rotational orientations, resulting in ϳ36 billion configurations between Cc and CcO. DOT maintains two 128 3 interaction grids. In the minimumenergy grid, the rotational orientation with the most favorable energy at each grid point is kept. The second grid, the free-energy grid, represents a free-energy landscape of intermolecular energies. To obtain the free-energy grid, the Boltzmann-weighted sum of the energies over all orientations at each grid point is calculated to give the partition sum as follows, where j is a grid point, R is the number of angles through which the moving molecule is rotated, T is the temperature in degrees Kelvin, and k B is the Boltzmann constant. Q j is then converted to the Helmholtz free energy as follows.

RESULTS
Calculation of Electrostatic Potentials-Electrostatic potentials for CcO and Cc were derived by integration of the Poisson-Boltzmann equation, which accurately takes into account the ionic strength of the surrounding medium and the dielectric boundaries between protein and solvent. Accurate representation of electrostatic forces is particularly important for electron transfer systems because of the role of electrostatics in both short range orientation and long range guidance, as suggested by the strong dependence of the reactions on ionic strength. Electrostatic potentials were calculated at a low ionic strength (50 mM), where Cc and CcO show strong binding (17).
Electrostatic Potentials of Horse Cc and R. sphaeroides Cytochrome c 2 -R. sphaeroides cytochrome c 2 has a slower electron transfer rate with R. sphaeroides CcO than does horse Cc (17). To investigate the source of this difference, we calculated the electrostatic potential for both molecules, as has been done previously (21). In horse Cc, the Lys residues surrounding the exposed heme edge create patches of strong positive potential (Fig. 1A). The opposite face of Cc is generally neutral, creating a dipole (21). The sequence of R. sphaeroides cytochrome c 2 is very different from that of horse Cc, including the loss of lysine at positions 13 and 72, resulting in a very different distribution of positive potential on the face of the molecule surrounding the exposed heme edge (Fig. 1B).
Electrostatic Potential of Bovine CcO-Since Cc and CcO interact in the intermembrane space, only that region of CcO along with the adjacent membrane-embedded portion (Fig. 1C) was used (see "Experimental Procedures"). The selected coordinates include the subunit II dicopper Cu A site, the initial site of electron transfer from Cc (25)(26)(27). The most significant electrostatic feature is a large patch of negative potential formed by a concentration of Asp and Glu side chains in subunit II (Fig.  1D). The greatest concentration of negative potential lies in a shallow pocket between Asp 119 (Glu 157 ) and Glu 109 (Glu 148 ). Within this negative patch is a hydrophobic surface loop that lies over the Cu A site and consists of subunit II residues His 102 (Tyr 141 ), Gly 103 (Gly 142 ), Trp 104 (Trp 143 ), and Tyr 105 (Tyr 144 ). The rest of the CcO surface is generally neutral with small regions of positive and negative potential.
DOT: Calculation of Intermolecular Energies-DOT centers each rotational orientation of one molecule, the moving molecule, at each position on a grid that surrounds a second molecule, the stationary molecule. For each configuration of the two molecules, the intermolecular energy, a sum of electrostatic and van der Waals terms, is calculated (see "Experimental Procedures"). The time required for the calculation is independent of the number of atoms in either molecule and instead depends on the size of the grid and the number of rotational orientations of the moving molecule. The mathematics of the DOT calculation requires periodic boundary conditions; the grid is repeated in all directions over all space. Therefore, the grid must be large enough that the stationary molecule potentials are close to zero at the grid boundary. In addition, at least one diameter of the moving molecule about the stationary molecule must fit within the grid. We have found that a grid spacing of 1 Å provides a sufficiently accurate description of the stationary molecule and a reasonable fineness for the translation search. A cubical grid of 128 Å on each side fulfilled the size requirements for the interaction of the CcO fragment with Cc.
The larger molecule, CcO, was assigned as the stationary molecule, and the smaller Cc was assigned as the moving molecule. This assignment provided two advantages. First, it allowed use of a finer spacing for the 128 ϫ 128 ϫ 128 grid, since the minimum dimension of the grid must be at least 2M ϩ S, where M and S represent the diameters of the moving and stationary molecules. Second, a smaller molecule will be sampled more finely over its surface for a given set of rotations. Our set of 17,354 rotational orientations provides ϳ9°sampling, which corresponds to about a 2-Å spacing on the Cc surface.
Storage requirements make it impractical to retain the energies and positions of all 36 billion configurations (128 3 ϫ 17,354) calculated. Instead, two types of interaction summary grids are maintained (see "Experimental Procedures"). The minimum-energy grid contains the energy, position, and orientation for the configuration (out of a possible 17,354) with the most favorable energy at each grid point. The free-energy grid provides a free-energy landscape combining information from all energy calculations. This grid displays a smoother change in energy across the grid than the minimum-energy grid, but rotational information is not retained. Both grids can be calculated simultaneously in about 7 h using 20 Sun Ultra-1 workstations running in parallel.
Application of DOT to CcO-A preliminary test with a single proton as the moving molecule demonstrated that the CcO shape and electrostatic potentials were properly aligned on the grid. A complete rotational search with 17,354 rotational orientations was then performed with DOT. Although our description of CcO allows Cc to move into the region of the grid that should be occupied by the membrane and membrane-bound portions of CcO, this area was electrostatically neutral, making favorable-energy interactions here unlikely. The top 2000 so-  is the largest tight cluster of solutions with five (black and yellow) particularly close in both spatial and rotational orientation and two outliers (blue). From these seven solutions, the yellow one, which is in the middle of the cluster, showed the shortest distance from heme edge to CcO and was selected for investigating specific interactions in the interface. C, the free-energy landscape of the interactions between bovine CcO and horse Cc. Each point represents an energy-weighted sum over all 17,354 rotations centered at that grid point. The green sphere is the center of the Cc solution selected to represent the complex; its C-␣ trace (yellow) is also shown. The brown surface, which represents the free-energy grid points with the 2000 most favorable energies, consists of two connected lobes. One lobe is centered over the selected Cc coordinates. The second lobe is above the first, farther from the membrane, and may indicate a second Cc-binding site. D, the heme rings of the top 30 solutions from the fine rotational search. The selected Cc configuration from the full DOT search (yellow) almost superposes the best-energy configuration from the fine search (red). The most exposed atom (CBC, orange) of the heme is well clustered, showing the tight spatial and rotational alignment among these solutions.
The top 30 configurations of the minimum-energy grid show a more localized spatial distribution and had interaction energies ranging from Ϫ27.2 to Ϫ24.5 kcal/mol. Of these 30 solutions, 29 lie over the patch of negative potential on the CcO surface, with 25 having their exposed heme edge generally oriented toward the CcO molecule (Fig. 2B). Within the top 30 configurations, there is a single, tight cluster consisting of five solutions with two nearby outliers (Fig. 2B) having energies ranging from Ϫ26.5 to Ϫ24.9 kcal/mol. Among the closest five, rotations vary by 8 -30°, and root mean square (r.m.s.) deviations for all nonhydrogen atoms range from 2.8 to 5.5 Å (average r.m.s. deviation ϭ 4.1 Å). The two outliers have an r.m.s. deviation of less than 6 Å with at least one of the other five solutions. The r.m.s. deviations of the heme atoms are generally smaller, ranging from 1.8 to 5.5 Å (average r.m.s. deviation ϭ 3.4 Å) for the closest five solutions, with the two outliers having an r.m.s. deviation of less than 4.5 Å with one of the five. The tighter clustering of the heme rings relative to the whole molecule indicates that the fit is best at the interface. All seven Cc solutions in this cluster have their exposed heme edge near the indole ring of CcO residue Trp 104 (Trp 143 ).
In the free-energy grid, Cc solutions having the most favorable energies (Fig. 2C) are concentrated over the negative patch of CcO, forming a two-lobed grouping. One lobe is centered about the best-energy cluster found in the top 30 configurations of the minimum-energy grid, and the other lobe is further from the membrane. This second lobe may indicate a weaker binding site for Cc. In both the free-energy and minimum-energy grids, favorable interactions extend from the large surface patch of negative potential on CcO out into solution, showing the effect of long range electrostatic guidance.
The CcO⅐Cc Interface-The five configurations in the single, large cluster (Fig. 2B) are energetically equivalent (within 1.0 kcal/mol in energy). From this group, the Cc configuration with the shortest distance from its exposed heme edge to CcO (ranked 19th in energy) was examined for specific intermolecular interactions. Distances are approximate, since rigid structures from individually determined structures were used and complex formation will cause some local rearrangement. The interface shows a central, relatively hydrophobic region surrounded by polar interactions. The exposed Cc heme edge is within 4 Å of the indole ring of CcO residue Trp 104 (Trp 143 ) ( Table I, Fig. 3A), supporting the role of Trp 104 (Trp 143 ) as the site of electron entry (15)(16)(17). The hydrophobic region of Cc consists of the exposed heme edge, the adjacent Gln 16 and Cys 17 side chains, and residues 81-83, which form a ␤-strand paralleling one heme face (Fig. 1A). This region contacts a corresponding hydrophobic region of CcO (Fig. 3, A and B) consisting of residues 102-105 (R. sphaeroides residues 141-144), which form a loop over the Cu A site, the adjacent residues Tyr 121 (Tyr 159 ) and Asn 203 (Ser 259 ), and backbone atoms of CcO Glu 157 (Ala 213 ) and Asp 158 (Asp 214 ) (Table II).
Asp 158 (Asp 214 ) is central to the interface (Fig. 3B), lying adjacent to the backbone of the hydrophobic loop. Unlike all other CcO acidic residues in the interface, the Asp 158 (Asp 214 ) side chain does not extend out into solvent. Instead it forms two intramolecular hydrogen bonds, one with Cu A ligand His 161 (His 217 ) and a second with the backbone amide nitrogen atom of Gln 103 (Gln 142 ) (Fig. 3C), indicating that Asp 158 (Asp 214 ) is unlikely to undergo conformational rearrangement upon complex formation. The closest positively charged Cc residue, Lys 72 , could interact directly with Asp 158 (Asp 214 ) by undergoing substantial conformational change. Intermolecular distances, however, suggest that Lys 72 forms a hydrogen bond with the conserved CcO Gln 103 (Gln 142 ) side chain (Table I) and has a more delocalized electrostatic interaction with CcO Asp 158 (Asp 214 ). One of the Asp 158 (Asp 214 ) carboxylate atoms is close enough to the backbone nitrogen atom of Cc Ala 83 to form a hydrogen bond without side chain rearrangement (Table I, Fig. 3C).
Immediately adjacent to the hydrophobic region of the interface is CcO residue Asp 119 (Glu 157 ) with its carboxylate group very close to Cc Lys 13 (Table I, (Table I). At the edge of the interface, Asp 139 (Asp 195 ) and subunit I residue Asp 221 (Gln 265 ) probably contribute to local orientation, perhaps through water-mediated interactions with Cc (Table I). The five bovine subunit II acidic side chains that contribute to the interface with Cc correspond to acidic side chains in R. sphaeroides CcO, except for Glu 157 (Ala 213 ).
A Fine Rotational Search about the Best-energy Cluster-The tight cluster of seven configurations in the 30 best-energy solutions was the basis of a finer rotational search. For each configuration, 1000 rotational orientations were generated within 30°. This provided a set of 7000 rotations with better than a 3°spacing, which corresponds to a distance of less than 0.6 Å on the Cc surface. Because of the DOT methodology, each rotation of Cc must still undergo a full translational search. The top 30 minimum-energy grid solutions from this fine rotational search were close in both position and rotational orientation (Fig. 2D). The best-energy solution from this search closely overlays the solution selected from the full search used to determine specific interface interactions (Fig. 2D), with an r.m.s. deviation for all nonhydrogen atoms of 1.4 Å. The fit between these two solutions is best at the interface, with distances between corresponding atoms of Lys 13 , Lys 72 , and Phe 82 ranging from 0.4 to 0.7 Å. Both solutions display the same interactions with CcO, validating the choice of the selected configuration from the full search. DISCUSSION Given the difficulties in determining crystallographic structures of electron transfer protein complexes, computational techniques may provide the best method for predicting these transient interactions and, moreover, may suggest pathways of approach. Recent applications of computational docking to pro-  3. The interface for the transient electron transfer interaction. A, stereo pair of the CcO⅐Cc interface. The hydrophobic patch of horse Cc (right, yellow C-␣ backbone and selected side chains (black labels), with blue Lys side chains and green heme) consisting of the exposed heme tein systems (28,29) demonstrate that these methods are now sufficiently developed to successfully predict intermolecular interactions. A major problem with computational docking is distinguishing correct solutions from false positives (9), which are favorable-energy incorrect solutions. This problem is exacerbated when coordinates from individually determined proteins rather than from crystallographic complexes are used. Visual inspection of hundreds of possible solutions along with use of biochemical knowledge has been necessary to separate correct answers from false positives (28), but this is a timeconsuming and subjective task.
The efficient, systematic search generated by DOT allows us to investigate new techniques for distinguishing correct solutions from false positives. We have tested DOT on systems for which complex and individual structures are available, including dimer interfaces, strongly bound protein-protein complexes, and electron transfer partners. 3 DOT partially allows for induced fit by letting atomic centers of the moving molecule approach to within one atomic radius of the atomic centers of the stationary molecule. Unfortunately, this can result in a few artificially large electrostatic energy terms that may dominate the interaction energy. To solve this problem, the electrostatic potential of the stationary molecule was clamped to the maximum values found on its solvent-accessible surface. This has greatly reduced the number of false positives and allowed the same relative weighting of electrostatics and van der Waals terms for all systems we have examined. Because DOT retains the most favorable energy configuration at every grid point (the minimum-energy grid), adjacent configurations can be examined and compared. We expect that correct solutions should have nearby configurations with closely related rotational orientations and similarly favorable energetics.
Both the minimum-energy and the free-energy grids generated by DOT showed one distinct, energetically favored region for the interaction of Cc with CcO. This region predominates in the top 2000 and in the top 30 solutions in the minimum-energy grid (Fig. 2, A and B). Only one of the top 30 solutions lies far from this localized region (Fig. 2B) and was immediately distinguishable as a false positive because of the lack of surrounding, favorable-energy solutions. Calculation of r.m.s. deviations among the top 30 configurations revealed a single, tight cluster of seven solutions. Just these seven Cc positions were examined in detail by computer graphics. All positioned their exposed heme edge near CcO residue Trp 104 (Trp 143 ). We selected the Cc configuration with its heme edge closest to CcO as representative of the docked complex for examining specific intermolecular contacts. This selection was further justified by its very close alignment with the best-energy solution from a finer rotational search (Fig. 2D). Thus, data from the DOT calculation itself were sufficient to predict a docked complex; no screening using biochemical data was required. The consistency of the predicted CcO⅐Cc complex to concurrent mutagenesis, binding, and kinetics studies (15)(16)(17)30) shows that DOT can be a successful predictive tool.
Structural Similarity of Bovine and R. sphaeroides CcO-The principal peptide chain of CcO involved in the interaction with Cc, subunit II, has high sequence similarity in the bovine and R. sphaeroides enzymes (Fig. 3E). Sequence identity is highest surrounding the Cu A site and on the Cc-binding surface, with only one conservative difference in the hydrophobic loop overlaying the Cu A site, residues 101-105 (R.  be applicable to the bovine enzyme. Differential Activity for Horse Cc and R. sphaeroides Cytochrome c 2 -In contrast, horse Cc and R. sphaeroides cytochrome c 2, the two cytochrome c molecules examined in experimental studies on R. sphaeroides CcO (16,17), have significantly different sequences, structures, and electrostatic environments (Fig. 1, A and B). Both have a small, solventexposed hydrophobic region surrounding the exposed heme edge that includes the Cys residue bound to the heme and a ␤-strand running parallel to the heme edge with a Phe (position 82 in horse Cc) side chain packed against the heme. The distribution of positive electrostatic potential around the hydrophobic patch appears to be critical for alignment of cytochrome c with electron transfer partners (21). This distribution is very different in the two cytochrome c molecules (Fig. 1, A and B), explaining their different activities and differential sensitivity to specific mutations in R. sphaeroides CcO (17). Thus, even though R. sphaeroides cytochrome c 2 and horse Cc share some Lys side chains, it is unlikely that they have the same intermolecular contacts with CcO. In a related system, crystallographic structures of yeast cytochrome c peroxidase show different orientations for bound yeast and horse Cc (18), despite their Ͼ60% sequence identity and similar structures.
Trp 104 (Trp 143 ) and Its Hydrophobic Loop: The Electron Entry Site into CcO-Our calculated complex of horse Cc with bovine CcO indicates specific intermolecular contacts that are consistent with mutagenesis data on both Cc and CcO and suggests new interactions to be tested. In the tightly oriented, favorable-energy cluster of Cc solutions, the exposed heme edge is close to Trp 104 (Trp 143 ) (Fig. 2B), strongly implicating this side chain in electron transfer. In the calculated complex, the Trp 104 (Trp 143 ) indole ring has two contacts under 4 Å with the exposed heme edge (Table I), which is remarkable given the coarseness of the search (1-Å translation and 9°rotation) and the use of rigid, uncomplexed protein structures. The hydrophobic loop of CcO, residues 102-105 (R. sphaeroides residues 141-144), is packed against the ␤-strand paralleling the Cc heme (Fig. 3A, Table II). These hydrophobic contacts may facilitate rapid electron transfer across the interface, explaining their conserved structures in both CcO and Cc. The position of Trp 104 (Trp 143 ) in the interface explains the severe drop in intrinsic electron transfer rate upon mutation to Phe or Ala (16). Mutation of residues 102 (141) and 105 (144), whose side chains contribute to the hydrophobic patch, should also decrease the electron transfer rate if the overall hydrophobic environment is an important factor in intrinsic electron transfer rates. Although mutation of Tyr 105 (Tyr 144 ) has little effect on the turnover rate (30), 4 the effect of this mutation on the rate of intrinsic electron transfer has not yet been examined.
The Position of Charged Side Chains in the Interface Parallels Their Influence on Binding Affinity-The closer a charged side chain is to the hydrophobic region central to the interface of the calculated complex, the more important it is to binding affinity. Chemical modification of Lys residues of horse Cc showed decreased activities with the order Lys 13 Ͻ Lys 72 Ͻ Lys 87 Ͻ Lys 8 (31,32), which follows their distance from the heme and adjacent ␤-strands (Fig. 1A). Similarly, mutation of the R. sphaeroides CcO side chains Asp 158 (Asp 214 ) or Asp 119 (Glu 157 ), which are close to the hydrophobic loop residues 102-105 (R. sphaeroides 141-144) (Fig. 3B), decreases binding to horse Cc more than mutation of Glu 109 (Glu 148 ) or Asp 139 (Asp 195 ), which are farther from the hydrophobic loop (16).
In the interface, the two most influential horse Cc Lys side chains, Lys 13 and Lys 72 , are paired with the two most influen-tial CcO acidic side chains, Asp 119 (Glu 157 ) and Asp 158 (Asp 214 ) (17). Close contact (Table I) and good orientation (Fig. 3A) of Lys 13 and Asp 119 (Glu 157 ) are consistent with salt bridge formation, which may be important for aligning the hydrophobic patches of the two proteins. This pairing brings together the greatest concentration of positive electrostatic potential on horse Cc (between Lys 13 , Lys 86 , and Lys 87 ; Fig. 1A) and the greatest concentration of negative electrostatic potential on bovine CcO (between Asp 119 (Glu 157 ) and Glu 109 (Glu 148 ); Fig.  1D). Lys 72 lies near Asp 158 (Asp 214 ) (Fig. 3A), but constraints on the Asp 158 geometry (see below) suggest that electrostatic interactions between the two charged side chains are indirect. Lys 72 may, however, form a hydrogen bond with conserved CcO residue Gln 103 (Gln 142 ), explaining the reduced binding upon mutation of Gln 103 (Gln 142 ) (33).
Further from the hydrophobic contact region are interactions across the interface that may be direct or mediated by water molecules (Table I) (16), consistent with their greater distance from the interface. These side chains lie on the Cc-binding face of CcO, and therefore may have a small role in long range guidance.
Neutralization of a single charge in the CcO⅐Cc interface only modestly affects binding affinity (15,17). In contrast, neutralization of a charged side chain in tightly bound protein-protein complexes such as dimer interfaces or antibody-antigen complexes can decrease binding by orders of magnitude. In these stable complexes, pairs of oppositely charged side chains are often buried within a large hydrophobic interface. The surrounding low dielectric and separation from ions and solvent creates a strong, highly directional interaction. In the CcO⅐Cc interface, complementary charge-charge interactions lie outside the small hydrophobic contact region, allowing interaction with bulk solvent and ions and decreasing their contribution to binding affinity.
Despite the weak contribution of each charged side chain to binding affinity, their combined electrostatic interactions appear to dominate the binding interaction, with the total interaction energy of the complex having a greater electrostatic energy term (Ϫ14 kcal/mol) than van der Waals energy term (Ϫ11 kcal/mol). Consistent with the small contribution of van der Waals energy, mutating Trp 104 (Trp 143 ), which is centered in the hydrophobic region, to Phe or Ala has little or no effect on the equilibrium dissociation constant, despite its large effect on intrinsic electron transfer rate (16). In contrast, DOT calculations show that the van der Waals energy term in strongly bound complexes is 3-4-fold greater than the electrostatic energy contribution. 3 The closely oriented, favorable-energy configurations from the restricted, finely sampled rotational search (Fig. 2D) suggest that electrostatic forces align the electron transfer partners but are not sufficiently directional to provide a single, precise "lock-and-key" fit. These computational results fit well with the idea of a pseudospecific docking surface for electron transfer proteins that allows a single protein to recognize multiple partners (34).
CcO Residue Asp 158 (Asp 214 ) Has a Unique Role-Asp 158 (Asp 214 ) is unique among the acidic CcO side chains in the interface for two reasons. First, it lies along the protein surface instead of extending into solution. Second, its mutation to Asn significantly decreases the rate of intrinsic electron transfer (16). Asp 158 (Asp 214 ) is a second-sphere ligand of the Cu A site, forming an Asp-His-copper triad (Fig. 3C). Such triads are common in protein metal sites and may align metal-binding ligands or modulate metal site properties. In the metalloenzyme carbonic anhydrase, mutation of Glu 117 in the Glu-Hiszinc triad to Gln caused a Ͼ1000-fold reduction of catalytic activity and altered the kinetics of metal binding (35). Surprisingly, no discrete structural changes were found in the crystallographic structure of the mutant. Like Asp 158 (Asp 214 ) in CcO, carbonic anhydrase Glu 117 forms hydrogen bonds with both a metal-binding His ligand and a backbone amide nitrogen atom. The Gln mutant maintains these bonds, resulting in the stabilization of the His ligand as an imidazolate anion, thereby causing an electrostatic rather than a structural change (35). Analogously, mutation of CcO Asp 158 (Asp 214 ) to Asn neutralizes residue 158 (214) but may stabilize His 161 (His 217 ) as an imidazolate anion. Given the sensitivity of the electron transfer reaction to charge distribution and the central position of His 161 (His 217 ) between the interface and the Cu A center (Fig.  3C), a shift in charge distribution could have a more profound effect on electron transfer than neutralization of a single charge within the interface. The shift in charge distribution could lock the complex into an unproductive configuration, resulting in the observed decrease in the rate of intrinsic electron transfer at low ionic strength (16).
A Second Binding Site for Cc-Experimental evidence strongly supports a second, weaker Cc-binding site on CcO. This second Cc may also interact directly with Cc bound in the primary binding site (36). The less well oriented group of solutions lying in the upper portion of the CcO negative patch (Fig.  2, A-C) may indicate the second site. Cc binding could be more disordered than the high affinity site or could require a bound Cc at the high affinity site to define its orientation. If the latter is true, then adding our bound Cc molecule to the stationary complex and searching with a second Cc moving molecule would resolve this question.
Comparison of the CcO⅐Cc Interface with That of CcP⅐Cc, a General Motif for Transient Interactions-The similarity of yeast Cc to horse Cc (Ͼ60% sequence identity) prompted us to compare our predicted complex of bovine CcO and horse Cc with the complex of yeast CcP and yeast Cc, which has been determined by x-ray crystallography (18). The crystallographic structure of CcP⅐Cc (2PCC in the Protein Data Bank) shows close contacts between CcP residues Ala 193 and Ala 194 and the exposed Cc heme edge, consistent with mutagenesis experiments indicating that the surface loop containing residues Ala 193 and Ala 194 is the point of electron entry (37,38). The CcP⅐Cc interface is unusual in having a small van der Waals contact region and only one specific hydrogen bond and a single salt bridge, despite the large number of charged side chains in the interface. All other interface interactions are mediated by a layer of water molecules.
To compare the calculated complex of bovine CcO and horse Cc with the yeast CcP⅐Cc complex, the heme rings of the two Cc molecules were superposed. This superposition puts the two electron entry sites, the CcO Trp 104 (Trp 143 ) indole ring and CcP residue Ala 194 , on top of each other (Fig. 3D) despite the very different structures of CcO and CcP. The hydrophobic contact surface of CcP residues Ala 194 -Val 197 overlays the CcO conserved side chains Gln 103 (Gln 142 ) and Trp 104 (Trp 143 ). Differences between the distribution of Lys side chains in yeast and horse Cc correspond to differences between the acidic environments in CcP and CcO (Table III). Horse Cc residue Lys 13 , which interacts with CcO Asp 119 (Glu 157 ), is replaced by the more charge-delocalized Arg 13 in yeast Cc, which interacts with CcP Tyr 39 . Yeast Cc Lys 72 is trimethylated on the terminal amine, preventing hydrogen bond formation. The polar environment in CcO that interacts with Lys 72 (Gln 103 (Gln 142 ) and Asp 158 (Asp 214 )) is replaced by less polar side chains in CcP (Val 197 and Gln 120 ) (Fig. 3D). There are equivalent chargecharge interactions for two Lys residues shared by both Cc molecules: Cc Lys 87 interacts with Glu 109 (Glu 148 ) in CcO and with Glu 32 and Asp 34 in CcP; Cc Lys 73 interacts with subunit I Asp 221 (Gln 265 ) in CcO and Glu 290 in CcP. The similarities of the two interfaces also extend to the energetics. A preliminary DOT calculation of the complex between CcP and Cc 3 shows that the electrostatic energy term dominates, as found for the CcO⅐Cc interaction.
The similarities in the two complexes suggest that an interface consisting of a small hydrophobic region surrounded by a highly charged, electrostatically complementary surface is a general motif for electron transfer partners involved in transient interactions. The delocalized distribution of charge over the surface of the electron transfer partners, rather than the formation of many specific salt bridge or hydrogen bonding interactions, appears to control local orientation while allowing rapid product dissociation. Maximizing the electrostatic complementarity concurrently brings the electron transfer groups into close proximity. Thus, the most energetically favored complex is also optimized for electron transfer. This is consistent with time-resolved kinetics studies showing that the intrinsic electron transfer rate is the same at low and intermediate ionic strengths, indicating that slow product dissociation is responsible for the slow rate of turnover at low ionic strength (16).