J. Phys. Chem. 1995, 99, 4860-4865
4860
Connection between Structure, Electronic Spectrum, and Electron-Transfer Properties of Blue Copper Proteins Sven Larsson* and Anders Broo Department of Physical Chemistry, Chalmers University of Technology and Goteborg University, S-412 96 Goteborg, Sweden
Lennart SjiSlin Department of Inorganic Chemistry, Chalmers University of Technology and Goteborg Universiry, S-412 96 Goteborg, Sweden Received: October 13, 1994; In Final Form: January 13, 1995@
The connections between site structure, electronic structure and spectra, and electron-transfer properties of type 1 or blue copper proteins are investigated. The theoretical model includes the nearest neighbors of the Cu ion and the residues to which these neighbors are attached. The electronic structure is calculated using an extended CNDO/S method adapted to spin doublet states. The calculated spectra agree reasonably well with the experimental ones as well as with the calculations of Solomon et al. The strong absorption at about 16 000 cm-' is due to a n n* transition, where the n and n* orbitals are extended in the trigonal plane with Cu 3&, S 3pn, and, to a lesser extent, N 2p0 character. Strong absorption at other energies is due to n* transition because of symmetry lowering ligand field transitions which borrow intensity from the n from C2". Comments, based on calculations, are offered on copper-zinc superoxide dismutase mutants, whose spectral properties to some extent resemble those of the blue proteins.
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1. Introduction Blue or type 1 copper proteins which have a strong absorption (2000 < c '8000) in the region 595-630 nm (15 800-16 800 cm-I) belong to the structurally and spectroscopically best characterized metalloenzymes.'-8 The crystallographic structure has been determined for several of the single copper site proteins: p l a s t o c y a n i n ~azurins , ~ ~ ~ ~ (Pseudomonas aeruginosa' and Alcaligenes denitr$cans2, and others.I3 By site-directed mutagenesis it has been possible to modify the ligand structure around the copper atom in a number of azurinI4 and plastocyanin mutant^.^.'^ The crystallographic structure of some of the mutants has also been determined, and it is consequently of a great interest to understand how this structure correlates with spectroscopic and other properties. In the present paper we have calculated the electronic structure of some natural blue proteins and their mutants in order to get insight into the relationship between structure and spectra. A common feature of all blue proteins is the geometry around the Cu(I1) center which is a distorted trigonal plane where the closest ligands are a cysteine sulfur atom and two imidazole nitrogen atoms (Figures 1 and 2). In azurin the latter ligands belong to the His-46 and His-1 17 residues and the former one to Cys-112. In addition there are two axial ligands; in azurin the sulfur atom of Met-121 and an the oxygen atom of Gly-45. The Cu-Cys S bond distance is unusually short, 2.10-2.15 A, whereas the Cu-N distances are the normal ones for Cu-N complexes (1.9-2.1 A). The axial S and 0 ligands are at quite large a distance, about 3 A. One therefore expects that the covalent ligand bonding in the Cu2+case is in the trigonal plane and that the half-occupied, antibonding molecular orbital (MO) is extended in this plane. Site directed mutagenesis has also been applied to the zinccopper site in superoxide d i ~ m u t a s e . ' ~The ' ' ~ tetrahedral zinc site has been modified to a site with one Cys and two His ligands.I6 If zinc is replaced by copper, absorption occurs in @
Abstract published in Advance ACS Abstracts, March 1, 1995.
0022-365419512099-4860$09.00/0
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two bands, in one at about the same wavelength as in the blue copper proteins. If on the other hand one of the four His residues in the type 2 copper site is replaced by Cys, the new site absorbs strongly at 375 nm, thus at a much higher energy than the blue type 1 copper p r o t e i n ~ . ' The ~ latter absorption will be discussed below in light of our results. A detailed calculation of blue copper centers has previously been carried out by Solomon et al. using the multiple scattering X a method (MSXa).18,19The strong absorption was found to be a charge-transfer transition, Sn Cun, where both MOs are extended in the plane of the trigonal complex. The orbital mixing has been probed by X-ray absorption studies of the L-edge and it was found that the upper, half-occupied MO has 38% S character.*O The term "charge-transfer" is in fact less appropriate as a label in the case of blue proteins since very little charge is transferred in a transition when the mixing ratio is close to unity. The intensity of the transition depends on the charge transfer and is at its maximum for the case of equal mixing. The unusually large ligand admixture in the metal orbitals is consistent with photoelectron spectra. If an electron is ejected from an inner 2p shell of Cu2+ in a normal non-sulfur complex, the charge donation to the copper atom increases strongly.21x22 This gives rise to satellites in the photoelectron spectrum at 4-5 eV lower kinetic energy than the 2~312or 2~112main lines. In a Cu+ complex the 3d subshell is filled and no charge transfer involving this subshell is possible, and consequently there are no Cu 2p satellites.21 However, even in the case of Cu2+ complexes with S ligands, the satellites often disappear, and this hints to a strong bias of the charge toward Cu already before i o n i z a t i ~ n . ~ ' In - ~other ~ words the Cu2+ ion is partly reduced to Cu+ (and S partly oxidized) so that a large charge transfer toward Cu at ionization is prevented. In such a case, if sulfur instead is ionized, the charge may be transferred back to this atom at ionization so that a satellite appears close to the S 2p line. Such a satellite has been found in small blue copper proteins.24
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0 1995 American Chemical Society
J. Phys. Chem., Vol. 99, No. 13, 1995 4861
Properties of Blue Copper Proteins
Figure 1. Stereoview of the blue site in azurin Pseudomonas aeruginosa showing the atoms included in the calculation. The filled circle is the Cu- atom. S 1 is Cys and S2 Met sulfur.
Y \ \
i 1 I
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X
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Figure 2. Model of a blue center with the definition of the coordinate system.
The electronic structure and spectrum calculated by Solomon et al. explains many experimental results such as the large oscillator strength of the absorption at about 16 000 cm-' and ESR ~ p e c t r a . ' ~ .A ' ~ calculation using an extended CNDO/S method for azurin also gives a good agreement with the experiments with the same interpretation of the strong transition in the absorption spectrum.25 The latter approach permits studies of large systems, and the electronic coupling for an electron transfer has also been ~ a l c u l a t e d . In ~ ~the present paper we have applied the extended CNDO/S method to a number of blue copper centers in particular of azurin mutants of known ~tructure.'~ On the basis of these results we are able to explain the strong absorption at about 16 000 cm-I and other strong absorptions in the visible or near IR spectrum.
2. CNDO/S Method The CNDO/S method is a well-tested method for organic n-systems and has produced results in good agreement with the experimental spectra.26 The method was originally parametrized only for molecules containing H, C, N, and 0 atoms, but we have extended it to allow arbitrary atoms.27 The MOs are expressed as linear combinations of atomic orbitals (LCAO). An SCF calculation is first carried out for the ground state. Subsequently singly substituted Slater determinants are constructed by replacing an occupied spin orbital by an unoccupied one. Linear combinations of spin doublet projected Slater determinants are formed and the electronic states calculated in an eigenvalue problem.
We include 100 CI configurations. A calculation using 300 configurations did not change the energy levels to any significant extent. For this type of system there is a large mixing between the atomic orbitals from metal ion and ligand atoms and also a strong mixing between CI configurations. For this reason we have constructed a transition density matrix, expressed in atomic orbitals. The result may then be easily interpreted and appears to be consistent with the results from the MSXa m ~ d e l . ~ * * ~ ~ The method has also been tested on some simple Cu2+ complexes with good results. The x axis (Figure 2) is chosen to be along the Cu-Cys S bond. The y axis is in the trigonal plane and the z axis pointing approximately toward Met S . In this way the singly occupied orbital (n*) is an antibonding mixing of Cu 3d, and S 3py atomic orbitals, with some N 2pa character. It is very similar to the corresponding orbital calculated by the MSXa m e t h ~ d . ' ~ . ' ~ In the coordinate system of the latter work, however, a rotation of 45" around the z axis in comparison to ours, is made. In this way the half occupied orbital has Cu 3dx2-y2 rather than Cu 3d, character. Ab initio methods may be applied nowadays to rather large systems, for example, of the size that was studied by Solomon et The application to a blue copper site is difficult because of the strong tendency toward exaggerated localization in the Hartree-Fock method. In a blue copper site the halfoccupied MO tends to localize to either Cu or S but not half on each.28 Although the CNDO/S method is also based on HartreeFock theory, the electron repulsion is screened26in order to make the fit to spectra of organic n systems possible. A corresponding screening is introduced in our extension27in such a way that the method is consistent with local exchange methods. The result is that the CNDO/S method as well as the MSXa or other local exchange methods predict ionization energies and electron affinities well. Of these two methods, only CNDO/S has the CI procedure, which makes it possible to calculate spectra of organic n-systems. al.1s919
3. Structural Models Normally in transition metal complexes, the dipole-allowed transitions are from a bonding MO (Q)L), mainly localized to the ligands, to an antibonding MO (Q)M), mainly localized in the metal d subshell, or possibly from the metal levels to the unoccupied ligand levels. It is thus appropriate to use the term "charge-transfer transitions" for the transition Q)L Q)M. Energetically the latter are most often in the W region and stand out because of their high intensity relative to the dipole forbidden ligand field transitions at a lower energy. In the series
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4862 J. Phys. Chem., Vol. 99, No. 13, 1995
Fe2+, Co2+, Ni2+, Cu2+ the orbital energy of the 3d orbital decreases relative to the ligand orbitals, which leads to an increased metal-ligand mixing.29 Moreover ligands of the third period (Cl- or S2-) have less strongly bound p orbitals than ligands of the second period (F- and 02-).Thus if the metal ion is Cu2+ and one ligand a thiolate group, the energies are about the same and the mixing ratio close to unity. Tetrahedral zinc complexes occur frequently in protein systems, one example being the so-called zinc finger proteins, another the superoxide dismutase mentioned The corresponding Cu+ complexes are isoelectronic but probably less stable due to the smaller charge on the metal ion. Soft ligands such as sulfur or n-accepting ligands such as CN- or imidazole increase the stability of a Cu+ complex. When Cu+ is oxidized, a “hole” is created in the complete 3d shell structure among antibonding MOs. The metal-ligand bonding is thus increased, and the geometrical structure is expected to be rather dramatically changed. Cu2+has a preference for a square-planar structure (D4h). One may arrive from a Cut tetrahedral conformation to the square-planar conformation by rotating two ligands relative to the other two. The half empty MO (the hole state) has c u 3d,2-,.2 character in the D4h case, a antibonding to all four ligands. The blue copper site, on the other hand, may be formed by simply displacing the Cu2+ ion from the center of the tetrahedron, away from the Met residue down to a trigonal plane formed by the Cys sulfur and two His nitrogens. The bonding to the latter imidazole nitrogens is still of u type. The S 3p, orbital is in the trigonal plane and has to play the role of the two u orbitals from the two missing ligands opposite to the nitrogens. The hole state is an MO with Cu 3d, character which is antibonding to the N 2pa’s and n-antibonding to S 3py. All covalent bonding is in the trigonal plane. Even if the trigonal Cu2+ site may be less stable than a tetragonal one, it has the advantage of a structure which is close to the tetrahedral Cu+ site. The change of structure at reduction of Cu2+ may be expected to be small, providing an excellent reaction path for fast electron transfer. Before the MSXa calculations were carried out,I9 it was believed that the Sa-Nn antibonding MO is the hole state. This is an obvious possibility since indeed the mixing is larger between the Cu and S orbitals than between the Cu and N orbitals. One would expect the hole to be a a hole, Le., an antibonding S 3p,-Cu 3d,2-)2 combination. However, if there are only two other ligands in a trigonal plane, the antibonding to these ligands would be of n type. The MSXa result^'^,'^ suggest that Cu2+prefers to bind in a bonds to N and that the hole state thus is antibonding with N a and S n. Our calculations give the same result.25 The antibonding S 3pxCu 3d,2-,.2 n*,as expected, forms the first excited state, only about 0.6 eV higher than the ground state. If there are three ligands in addition to the S ligand, the hole state should be of Cu 3da-S 3pa type. We believe that the His Cys mutation at the type 2 copper site of superoxide dismutase17 creates such a structure. In our calculation of an idealized square planar structure the hole state is a antibonding between S and Cu. Not surprisingly the strongly allowed transition from its bonding counterpart is somewhat higher in energy than the corresponding n n* transition in the blue copper proteins.
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4. Calculations on Simplified Models We have carried out exploratory calculations on a simplified complex consisting of a Cu ion and two nitrogen and two sulfur ligands. Cysll2 is represented by SH- where the H atom replaces Cp, Met121 by SH2, and the two imidazoles by two
Figure 3. Schematic MO diagram showing the Cu character of the highest occupied MO’s: (a) blue, trigonal site with two imidazole ligands; (b) proposed ordering for a tetragonal site with three imidazole ligands. Arrows show the strong transitions. * or - denote antibonding MO. Unmarked MO are antibonding. Calculations on different sites show a great variation in the MO energies.
NH3 molecules. The coordinates, taken from azurin from Pseudomonas a e r ~ g i n o s awere , ~ ~ symmetrized to C, symmetry with the xz plane as a symmetry plane. The calculated spectrum agrees well with that of the blue copper proteins. Due to charge donation in the bonding MOs, Cu2+ has effectively 9.6-9.7 3d electrons, in good agreement with the discussion above and ref 22. The strong transition appears at 16 400 cm-’ using 100 CI configurations. The dipole forbidden d dv transitions range from 6000-20 000 cm-’. These transitions are allowed in C, and CzVsymmetry if there is metal-ligand mixing. The energy order of the Cu 3d orbitals (Figure 3a) is determined by how strongly they are antibonding to the ligands of the protein. The antibonding S 3p,-Cu 3d, (n*) is the highest and the antibonding S 3p,-Cu 3dx2-y2 (a*)the second highest MO of this type, since they are antibonding in the trigonal plane. The MO with Cu 3d,2 character is also antibonding in this plane and is third. The MO’s with Cu 3dx, and 3dyzcharacter are at 19 000 and 20 000 cm-’, respectively. The reason is that SH2, representing Metl21, are very distant, causing little antibonding on the Cu orbitals extended along the z axis. In C2v symmetry the Cu 3d orbitals are a1 (z2,x2 - y2), a2 bz), bl (xz), and b2 (xy). In C, symmetry z2, x2 - y 2 , and xz are a’, whereas yz and xy are a”. The allowed transition is x-polarized as we have seen. If there are distortions of the symmetry, for example from the axial ligands, the b2 orbitals may pick up al, q , and bl character and vice versa. This means that the ligand field transitions “borrow” intensity from the strong transition and this intensity borrowing increases the larger the approach by the axial ligands or the larger the N-asymmetry. The borrowed intensity is x-polarized as the strong transition and different from the polarization of the much weaker Czv ligand field transitions, for which al b:! is y and a2 bz z polarized whereas bl b2 is forbidden. In the simulations of the azurin wild-type spectrum the lowest transition, involving Cu 3d+y2 always has a low intensity in agreement with the n* ligand field experimental spectra. The xz and yz transitions are at a rather high energy, about 20000 cm-I, whereas z2 n* has about the same energy as the strong transition. Particularly transitions with the same energy may have a large intensity borrowing. If the SH2 group, representing Met, approaches Cu rather small changes take place in the spectrum at first. If the SH2 is moved down as much as 1 A, the y z n* absorption is increased in energy to 23 400 cm-I and also increased in intensity. A similar result is obtained if Cu is moved out of +
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J. Phys. Chem., Vol. 99, No. IS, 1995 4863
Properties of Blue Copper Proteins the trigonal plane. The change in energy is rather unpredictable since many orbital transitions are involved, confusing the picture. If the S-H group, representing Cys, is rotated around the x-axis 90" to the trigonal plane, the singly occupied MO changes character to a mixture of Cu z2, Cu xz, and S 3p,. The reason is that 3p, is the lone-pair orbital of S in the new conformation and this orbital determines the hole state. The strong transition remains but with a lower intensity and with much smaller Cu-N antibonding components. Another experiment is made by representing Cys by SH2 instead of SH-. This complex, according to our calculations, has no absorption in the visible, since all d d transitions appear below 11 000 cm-' and the first allowed transition appears in the ultraviolet. This shows clearly that the Cys is essential for a blue protein. Only in Cys the sulfur 3p orbitals are sufficiently destabilized to put the allowed transition in the visible spectrum. Site-directed mutagenesis where Cysll2 is replaced by Asp gives a protein which is not blue,3' consistent with our result. Summarizing we find that the trigonal plane around Cu2+, where one sulfur ligand is of -S- type with a high energy lonepair orbital, is necessary for the formation of a blue copper center. It is of great interest that Lu et al. have been able to prepare such a center by a His Cys mutation in a tetrahedral Zn center.I6 The appearance of a second absorption at about 20 000 cm- is probably due to a y z n* transition since the yz orbital mixes with xy, as discussed above. The reason for the second strong absorption may be that the structure is closer to tetrahedral than a normal blue copper center, with a fourth ligand close to the trigonal plane. In contrast in the His Cys modified copper site of superoxide dismutase" there remain three His residues in the site in an approximately planar configuration. It is likely that the Cys sulfur atom binds in the fourth square-planar ligand position. We carried out a calculation on a planar model of such a site, replacing imidazole by NH3 and Cys by SH-. The following result was obtained (Figure 3b). The half filled orbital is Cu 3d,~-~2-s 3p,, u antibonding to the three nitrogens and the Cys sulfur atom in the normal way. The highest completely filled MO is x*,resembling the half-occupied MO in the blue proteins. The strongly allowed transition has to be of u .-+ u* type, with a higher energy since S u and Cu u interact more strongly than their n counterparts.
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5. Calculations Including the Liganding Peptides In the calculation of azurin from wild-type Pseudomonas aeruginosa the coordinates of ref 30 were used. Five peptides, Gly-45, His-46, Cys-112, His-117, and Met-121, and the N atom of the next peptide in the chain were included in the calculation. These peptides have each one atom within ligating distance to the Cu ion. Hydrogen atoms were added to the crystallographic atoms and in particular to the nitrogen end atoms of the peptide chain to avoid dangling bonds. The calculated singly occupied orbital is distributed 50% on S, 32% on Cu, 4% on each of the N's, and the remaining 10% on other atoms with more than 1% only on the C/3 atom of Cys-112. This MO is thus mainly localized in the trigonal plane. The strong transition was calculated at 13 800 cm-' (Table 1). This may be regarded as a good result for a coarse method like the CNDO/S method. In addition the crystallographic coordinates may be slightly different from the actual equilibrium geometry. We have not tried to energy optimize the structure. There is a second strong line at about 2000 cm-' higher wave number which is mainly a z2 n* ligand field transition with borrowed intensity (20% of main line) as mentioned above. The xz x* and y z x* ligand field transitions appear at 18 000-
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TABLE 1: Calculated Electronic Transitions and Their Predominant Character for Azurin of Pseudomonas aeruginosa (Wild-Typey energy kK (lo00 cm-I) osc str x lo3 character 5.1 13.8 15.9 18.0 19.4 22.7 23.1 25.5
3.0 186 38 3.0 3.2 0.0 0.0 2.0
U-X*
----
n-n* 22 n* xz n* yz n* Iml n Iml n* Im2 n Im2 n* Iml n n*
x* is the singly occupied MO with antibonding S 3p, and Cu 3d,, character (see also Figure 3). TABLE 2: Calculated Electronic Transitions and Their Predominant Character for Mutation MetlZlGlu" energy kK (1000 cm-I) osc str x lo3 character 6.3 16.6 17.0 18.6 21.7 22.5 23.1 27.6
1.6
53 106 53 0.0 0.0 25.3
0.8
-- --- -- -
0-n* n n*, 2 2 n* n n*, XZ n* n n*, Z2,XZ n* Iml n Iml n* Im2 n Im2 n* yz JC* Iml n, Imz JC n*
n* is the singly occupied MO with antibonding S 3p, and Cu 3d,, character (see also Figure 3). (I
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19 000 cm-' and the x2 - y2 x* transition at 5000 cm-' all about 2% of the main line. At the high-wavenumber end of the visible spectrum there are n n* transitions involving the imidazole groups of the His residues. The results are in a reasonable agreement with experimental results.32 For the mutation Metl21Glu the calculation gives a rather strong line at 23 100 cm-' (24% of main line) which agrees with the one observed at the same energy (Table 2). The latter state is mainly a y z n* transition. As mentioned above this type of transition borrows intensity when the trigonal plane is not a reflection plane and the axial ligand is able to penetrate deeper into the cavity. There is an even larger intensity borrowing in z2 n* and xz n*,but these transitions have about the same energy and contribute to the strong absorption. At a pH = 5 the spectrum of Metl21Glu is b1ea~hed.I~ To simulate the deprotonation which very likely occurs on the carboxyl group of Glu, we have removed a proton from this group, keeping the same number of electrons and the same coordinates as for Metl21Glu at a low pH. Our calculations suggest a reason for the bleaching. When the proton is removed the n MO of the carboxyl group is destabilized. This orbital is in a position to interact with the Cu z2 MO. The latter orbital, in an antibonding combination with COO--n, is strongly mixed into the Cu x y - S 3p, MO. Most of the Cu x y - S 3py character appears in a completely filled MO. The possible transitions are then mainly of ligand field type with a low intensity. The redox potential should correlate linearly with the negative of the energy of the singly occupied MO (SOMO). It turns out that SOMO for WT is more strongly bound than SOMO for Met12 lGlu mutation, consistent with the lower reduction potential for the latter protein. The closeness in energy of the x2 - y 2 (o*) xy (n*)state (< 1 eV) explains the deviation from C2"symmetry that is seen in all blue copper centers, as a second order Jahn-Teller effect.33 If we assume that there is C2" symmetry, the doubly occupied u* level, containing Cu 3d,2->2 character, has symmetry al whereas the singly occupied n* level, containing Cu d3, character, has the symmetry b2. The group theoretical product al x b2 = b2 and this means that a distortion of type B2 may easily occur if al b2 is sufficiently low in energy.33
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Summarizing, since the sites are lacking symmetry elements, deviations from CzVin the trigonal plane usually lead to intensity borrowing in the z2 n* and xz n* ligand field transitions, which are close to the strong transition in energy. If the axial n* borrows intensity and this ligands approach Cu, yz transition is usually in the region 20 000-25 000 cm-I.
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6. Electron Transfer Suitable redox potentials and high reaction rates are important in biological ET processes. The ET rate may be expressed as34
In the Marcus model for ET the Franck-Condon factor FC is approximately proportional to exp( -E,/kBT) where Ea is the activation energy. Ea is determined by the reorganization energy 1 and the free energy of the reaction,
:(9;
E =-I-a
Metal ions which are abundant in nature, such as Fe and Cu, have at least two stable oxidation states and suitable redox potentials, but the changes in the metal-ligand bond lengths in the redox process are often large for all bonds, implying 1 >> E. The activation energy is then also large and the rate of the ET reaction slow. This is often the case in proteins where in addition to the internal bond reorganization there is reorganization due to the change of polarization of the protein and the surrounding water. To keep the solvent at a distance, evolutional pressure has probably led to the selection of bulky organic ligands. The reason for the large change in structure at oxidation of a metal site is that the attraction of the ligands increases due to ionic forces. The metal-ligand bond distance is also decreased due to a decrease of the number of electrons in the antibonding orbitals. Evolution may have selected multi-metal sites where the added antibonding electron is affecting each bond less. The crystallographic structure of the copper center in Alcaligenes denitrificans has been obtained in both oxidation states35 and for the a p ~ p r o t e i n .The ~ ~ Cu-S bond distance change at reduction is quite large or 0.12 8,35whereas the Cu-N bond length changes are less. The trigonal structure around the Cu2+ center is apparently acceptable also as a Cu+ center and even if the metal ion is removed.36 One may suspect that the protein contributes to the stability of the trigonal structure for Cu2+ and prevents a possible collapse into a square-planar geometry. Whether the geometry of the Cu+ site is induced by the protein or “natural” for a Cu+ site is not known at the present, although the results of ref 10 suggest that the best site may be a trigonal one with two sulfurs and one nitrogen. The idea of a protein induced geometry has been referred to as the rack mechanism.37 In the square-planar geometry, a larger structural change must occur in the redox reduction, implying a much larger 1. Since the structural changes are moderate in ET reactions, one may assume a quadratic behavior of the energy as the system moves away from the equilibrium geometry: (3) The summation runs over all bond lengths and bond angles. 6Ri is the change at reduction or oxidation in this bond length or bond angle. The force constants Ki may be obtained from the vibrational mode. The Cu-S stretching frequency has been determined to 400 ~ m - ’ , ~and * we then calculate the force constant as 0.578 au. The distance change has been determined
for azurin by Shepard et al.,35who found 6 R = 0.11 8, for the Cu-S(Cys) bond which by eq 3 gives 1 = 0.34 eV. The N-Cu bond lengths both change by 0.05 A. If we assume the same force constant for N-Cu as for S-Cu we obtain a contribution to 1 from these bonds equal to 0.14 eV. The Met-S-Cu purely ionic bond should have a small force constant and therefore a small 1. Other contributions, including the solvent contribution, may be ignored. We obtain 1 = 0.5 eV for the oxidation of this Cu+ center. In the redox process one reduction and one oxidation takes place at the same time and their A’s should be added. This means that our calculated 1 is a lower limit. Experimentally a value of 0.42 eV has been found for 1 for plastocyanin bound to PSI.39 Although others have obtained values of about 0.8 eV,4O the value estimated here on the basis of bond-length differences appears too large, probably due to uncertainties in the crystallographic bond lengths. For azurin Pseudomonas aeruginosa, Nar has obtained a much smaller Cu-S bond-length change which leads to 1 = 0.21 eV.30 A considerably larger 1 = 0.81 eV is obtained for plastocyanin if the crystallographic coordinates at pH 7.8 of the reduced form are compared to the corresponding coordinates at pH 6.0 of the oxidized form.10 If E = 0 the Arrhenius factor for 1 = 0.5 is exp(-1/4k~T) = (for T = 300 K). As a comparison if we assume a 8x bond length change of 0.11 8, in four bonds, as would apply to a square planar Cu2+ center and no other contributions to 1,we obtain A = 4 x 0.34 = 1.36 eV, which leads to exp(-1/4k~T) =2 x at T = 300 K. This crude estimation suggests to a faster rate by a factor of 4000 for a blue copper center as compared to a normal copper center. Since 1 is quadratic in dR, the importance of small distance changes at reduction or oxidation is obvious, as is the importance of few ligands. However, a distribution of the antibonding capacity on many bonds is to be preferred. The delocalization of the hole in a Cu-S center is important in order to minimize the increased electrostatic attraction to the metal ion in the oxidized state. Another advantage with a blue center is the solvent reorganization energy which is decreased because the bulky imidazole ligands makes the Cu ion inaccessible to water. In eq 1 Hda is due to an interaction between donor D and acceptor A which, if D and A are in contact, is roughly proportional to the overlap between their orbital^.^^^^^ In a depends primarily on the distance protein the magnitude O f between D and A, in the following way: (4) where p = 1 k‘and R is the distance between D and A. C depends very much on the character of the contact between D and A and the intervening protein.4’~~~ The consequence of the particular hole localization in a blue copper center for the electron transfer properties is that electrons cannot easily enter via Met121 (C small) but very easily through Cysll2 ( C large).42-45 The path through the protein is also of a great importance. Theoretically an electron prefers a pathway with a high density of atom^.^',^^ The existence of aromatic side groups have not yet been implicated as a favourable factor for fast ET.25 It is more reasonable to believe that aromatic side groups, if the redox potentials can be suitably tuned, act themselves, in some cases as donors and acceptors of electrons. One example is photosystem I1 where phenol side groups of tyrosine seem to act in this way.
7. Conclusion By calculating the electronic structure and spectrum we have clarified which features in the structure are responsible for the
Properties of Blue Copper Proteins strong blue color of the complex. Our results agree with earlier theoretical s t ~ d i e s ' * ~when ' ~ comparisons can be made. In addition to the color, the electronic structure calculated in the various theoretical models explains a number of other properties of blue copper proteins. The color is strong because of the high energy of the Cys sulfur lone pair which has the consequence that the hole state consists of about half of this lone pair and half of the Cu 3d orbital that it interacts with. Since the interaction is of n type, the energy difference between the bonding and antibonding combination is small and shows up as the strongly allowed transition in the visible spectrum. The delocalization toward the Cys sulfur implies that this ligand is the best way into the site for the electron. The imidazole path should be somewhat slower and pathways along the z axis very slow, at least for those proteins which do not have any covalent axial interaction. The geometry of the Cys ligand appears to be important for the color, stability, and the ET properties of the site. The carbon atom bonding to S is away from the trigonal plane thereby assuring that the S 3p, orbitals is the one that is labilized. The axial ligands may prevent distortion of the trigonal structure and tune the reduction potential. Met is useful in this respect whereas, in the Metl21Glu mutation, Glu gets too far into the cavity and starts to interact with the Cu ion at elevated pH. The invariability of the blue color is remarkable. The ligating peptides apparently have some freedom to adjust to a very specific Cu2+ site despite protein strains. In our calculations where crystallographicallydetermined geometries are employed, the variation in absorption maxima is larger than measured experimentally for the same copper proteins. At least the Cu-S bond distance should be determined mainly by covalent bonding. The result is then a site with a small variation in bond distances, in spite of the differences in the protein structures. If a blue copper center is going to be a fast ET protein, E should be close to A (eq 2 ) . Since E should also be small to save energy, this means a small A. A small A is possible only if the site structure is almost unchanged at reduction. A remaining problem for the complete understanding of the blue copper proteins is that it is not well-known which structures are preferred by Cu+. It is important to determine structures for the reduced sites as well as to determine A for as many proteins as possible. If all sites tend to have small A's, the structure equality between the Cu2+ site and its reduced form should be universal and an inherent property of blue copper sites. The function of the rack mechanism3' is then reduced to providing a site with two instead of three or four imidazoles, although protein strains may still be necessary for the fine tuning of the ET and other properties.
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