Modelling the spectroscopy and dynamics of plastocyanin

David Robinson and Nicholas A. Besley*

Received 27th January 2010, Accepted 26th April 2010

DOI: 10.1039/c001805h

The electronic absorption, electronic circular dichroism and X-ray absorption spectroscopy of the

blue copper protein plastocyanin is studied with density functional theory, time-dependent density

functional theory and multireference configuration interaction in conjunction with classical

molecular dynamics simulations. A strong correlation is observed between the excitation energy of

the intense ligand to metal charge transfer band and the copper–cysteine sulfur bond length. The

results suggest that the copper–cysteine sulfur bond length in the crystal structure of plastocyanin

is too short and should be closer to the corresponding bond lengths in related blue copper

proteins. Averaging over many structural conformations is required to reproduce the major

features of the experimental circular dichroism spectra. A correlation between the rotational

strength of the ligand to metal charge transfer band and the distortion of the copper atom from

the plane of the cysteine sulfur and histidine nitrogen atoms is found. X-ray absorption

calculations show a smaller sulfur p orbital character in the singly occupied molecular

orbital of cucumber basic protein compared to plastocyanin.

I. Introduction

Blue or type I copper proteins play a central role in a numberof important biological processes such as photosynthesis andnitrogen fixation.1 This prominent role has led to a considerableresearch e!ort to study the structure and dynamics of thesesystems with the aim of understanding their function.2–9

Spectroscopic methods have played an important role in thiswork. A variety of spectroscopic techniques have been appliedto study these proteins, predominantly by Solomon andco-workers.10–13 Also of interest are model systems, such asCuCl2!4 , which have been used to inform the interpretation ofthe protein spectra.7 In the ultraviolet (UV) and visible regionsof the spectrum, ligand field and charge transfer excitationsoccur, arising from d ’ d and d ’ ligand excitations,respectively. At much higher energies in the X-ray region ared ’ core excitations, which can be measured at the metalK and L-edges and the ligand K-edge.10–12,14 A useful featureof spectroscopic investigations into these systems is that thedi!erent types of excitation yield complementary information.For example, ligand field excited states are sensitive to theligand field at the metal and can probe the active site geometry,while charge transfer states can probe the nature of the ligand-metal bond. In addition, core excitations can provide informationon the oxidation state, coordination number and nature of theground state wavefunction of the metal centre.7

Plastocyanin represents a classic example of a blue copperprotein. The active site of plastocyanin is shown in Fig. 1, andcomprises a cysteine, a methionine and two histidine ligands.The oxidised form of the protein has a singly occupiedmolecular orbital (SOMO). The absorption spectrum of plasto-cyanin shows peaks at 16 700 cm!1 and a weaker band atabout 12 800 cm!1,15 which are assigned to a Cu ’ S(cys)

ligand to metal charge transfer (LMCT) and d’ d ligand fieldexcitations, respectively. A further weak feature at 21400 cm!1 isalso observed.15 Closely related blue copper sites, such ascucumber basic protein, pseudoazurin and nitrite reductase,have a slightly distorted active site, with a lengthening ofthe Cu–Scys bond and a shortening of the Cu–Smeth bondcompared to plastocyanin, but exhibit di!erent spectral features.The optical absorption spectra of these proteins show a largeincrease in intensity of the feature near 21 400 cm!1 coupledwith a decrease in the intensity of the LMCT band at 16700 cm!1,with the combined intensities of the two bands remainingapproximately constant.16 This indicates a close relationshipbetween the spectroscopy and the underlying structure of theactive site.The electronic circular dichroism (CD) spectra of some blue

copper proteins have also been reported.17,18 More bands areevident in the CD spectra compared to the optical absorptionspectra. For plastocyanin, a small positive band at 10800 cm!1

and larger negative band at about 13 000 cm!1 are observed.The LMCT transition leads to an intense band at 16 700 cm!1

and at higher energy there is a small negative band at21 000 cm!1 followed by a further positive band at about24 000 cm!1.17 For the perturbed blue copper proteins,cucumber basic protein and nitrite reductase, the pattern ofthe bands is similar, but their relative intensities change. Inparticular, the intensity of the band arising from the LMCTexcitation is reduced relative to the ligand field bands.17,18

Theoretical studies of the absorption spectrum of theseproteins have also highlighted the sensitivity of the spectralfeatures to the structure of the active site. Using the Xa

scattered wave method, Solomon and co-workers found theSOMO of plastocyanin to be an antibonding mixture of theCu 3dx2!y2 and the Scys3pp orbitals.

15,19 The four lowest energyexcitations were assigned to copper ligand field transitions,and the intense band was attributed to excitation from thebonding Cu 3d-Scys3pp orbital to the singly occupied orbital,

School of Chemistry, University of Nottingham, University Park,Nottingham, NG7 2RD, UK. E-mail: nick.besley@nottingham.ac.uk

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and computed to lie at 16 940 cm!1. Higher energy bands wereassigned to charge transfer excitations from the imidazole psystem to copper. Larsson et al. have reported semiempiricalCNDO/S calculations of the active site of azurin.20 An intenseband was predicted to lie at 13 800 cm!1, and in agreementwith Solomon was assigned to excitations from the bondingCu 3d-Scys3pp orbital. Contrary to the earlier work, ligandfield excitations were found at higher energy.

Roos and co-workers performed complete active spaceself-consistent field (CASSCF) with multi-configurationalsecond-order perturbation theory (CASPT2) calculations onplastocyanin.21 Consistent with the earlier theoretical studies,the SOMO was found to be an antibonding combination ofthe Cu 3dx2!y2 and Scys3pp orbitals which is delocalised overthe Cu–Scys bond. Calculations were performed on a variety ofmodels of the active site with the experimental and optimizedstructures, and further calculations were performed with theremainder of the protein and solvent described by pointcharges. Overall, good agreement with the experiment wasobtained, with the excitation energies of the six lowest excitationspredicted within 2000 cm!1 of their experimental values. Theintense spectral band was assigned to excitation from thebonding Cu 3d-Scys3pp orbital to the SOMO, and the fourligand field excitations were found to lie at lower energy. Themost intense of these bands corresponded to excitation fromthe Cu 3dyz orbital. This study highlighted the sensitivity of thespectral properties on the structure of the active site, inparticular, the length of the Cu–Scys bond was a crucial factor.This work was extended to the related blue copper proteinspseudoazurin, cucumber basic protein and nitrite reductase.22

Consistent with experiment, the calculations predicted anincrease in intensity around 22 000 cm!1, which was associatedwith an excitation from a bonding Cu 3d-Scyss orbitalorbital to the singly occupied orbital. Furthermore, trigonal

structures resulted in spectra with a low intensity at 22000 cm!1,while tetragonal structures had an increased intensity at22000 cm!1 relative to the intensity of the band at 17000 cm!1.More recently, the multistate CASPT2 approach was used tostudy plastocyanin in conjunction with large basis sets.23 Thefocus of this work was the calculation of the g tensor, but amore detailed analysis of the e!ects of the extended proteinenvironment on the excitation energies was included. Theligand field states were found to be the most sensitive to theextended protein environment, with a decrease in excitationenergy as large as 2000–2500 cm!1. The e!ect on the chargetransfer states was more modest, with a lowering in excitationenergy of about 1000 cm!1 for the LMCT band. This wasconsistent with the earlier work of Sinnecker and Neese whostudied plastocyanin with a quantum mechanics/molecularmechanics (QM/MM) approach with density functional theory(DFT).24 In this study, an absorption spectra was computedusing time-dependent density functional (TDDFT) with theB3LYP exchange–correlation functional. The calculatedexcitation energies were too high, although analysis showedthe ligand field excitations to be more sensitive to the proteinenvironment with shifts larger than 1000 cm!1. QM/MMoptimization of the structure of the active site and itssurroundings using the BP86 functional and split-valenceSV(P) basis set found bond lengths of 2.22 A for Cu–Scysand 2.77 A for Cu–Smeth. Furthermore, values of 2.02 and1.99 A were predicted for the two Cu–Nhis bond lengths.Theoretical calculations of the reduction potential of plasto-

cyanin have shown that configurational sampling can beimportant in modelling the properties of these systems.25

The molecular dynamics of plastocyanin was studied withinthe classical CHARMM force field by Voth and co-workers.4

Force field parameters for the active site of plastocyanin weredeveloped and subsequently used to study the electron transferdynamics. Blue copper proteins have also been studied withligand field molecular mechanics. This approach was shown toreproduce the ground state structures of a variety of type Icenters accurately.9 Recently, conformational sampling hasbeen incorporated into theoretical studies of the excited statesof blue copper proteins.26–28 Ando has studied the ligand tometal charge transfer dynamics in plastocyanin.27 Usingpotential energy functions computed using the multi-configurational self-consistent field method26 in conjunctionwith molecular dynamics simulations of the protein, importantcoupling motions of the transition from the ground state tothe ligand to metal charge transfer state were identified.Non-equilibrium simulations showed that relaxation fromthe ligand to metal charge transfer state occurs via ballisticand coherent potential crossings in 70–80 and 500 fs time-scales, followed by thermally activated random transitions.The optical absorption spectrum of the blue copper proteinazurin has been calculated through a hybrid TDDFT andCar–Parrinello molecular dynamics simulation approach.28

The results were in good agreement with experiment and theCASPT2 calculations, illustrating that TDDFT can provide areasonable description of these systems.In comparison, there has been relatively little theoretical

work reported for the X-ray absorption spectra of these proteins.The Cl K-edge spectra of a series of metal tetrachloride

Fig. 1 Active site of plastocyanin.

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complexes, including CuCl2!4 , has been studied with TDDFT.29

It was found that the relative energies and intensities of thepre-edge features were modelled well by the calculations.A Dself-consistent field (SCF) approach has been used tocalculate the copper and ligand pre-edge features in theX-ray absorption spectra of CuCl2!4 and plastocyanin.30

Errors of 2–6 eV in the computed excitation energies wereobtained when uncontracted basis functions in conjunctionwith relativistic corrections were used. Core excitation energiescomputed with TDDFT with standard exchange–correlationfunctionals are known to significantly underestimateexperiment.31–34 This was addressed recently through the useof a short-range corrected functional.35 When applied to thepre-edge features in the Cu and S K-edge spectra, the excitationenergies were predicted in good agreement with experiment.

In this paper, the UV/vis absorption, electronic CD andX-ray absorption spectra of plastocyanin are studied with acombination of DFT and multireference configurationinteraction (MRCI). To capture the e!ects of the proteindynamics, finite temperature spectra are simulated by averagingover structural snapshots taken from molecular dynamicssimulations. These simulations of the absorption spectra are usedto inform and refine the molecular dynamics force field. Inparticular, we argue that the Cu–Scys bond length of plastocyaninis too short in the crystal structure and should be closer to theCu–Scys bond lengths observed in the crystal structure of otherblue copper proteins. Furthermore, conformational sampling isshown to be essential to obtain CD spectra that reproduce themajor features of the experimental spectra. Using TDDFT,excitation energies for the copper and sulfur K edges arepredicted in good agreement with experiment. The calculatedintensity of the sulfur K edge of the closely related cucumberbasic protein is less than for plastocyanin which suggests asmaller component of sulfur p orbital in the SOMO.

II. Computational details

TDDFT is well established for computing electronic excitedstates.36 While TDDFT has proved successful in many studiesencompassing a wide variety of systems, some problems arewell documented.37,38 Of particular relevance for the excitedstates of blue copper proteins is that charge transfer states arenot described well by standard generalized gradient correctedor hybrid functionals. Currently, the most satisfactory solutionis so called long-range corrected or Coulomb attenuatedexchange–correlation functionals. In recent years, there hasbeen considerable development and optimization of thesefunctionals,39–47 resulting in methods that provide accurateexcitation energies for valence and charge transfer excitedstates.41

Alternatively, excited states can be computed using aDKohn–Sham approach. Recently, a newmethod for convergingKohn–Sham calculations to yield excited states, termed themaximum overlap method (MOM), was reported.48 In thisapproach, the variational collapse to the ground state duringthe SCF procedure is prevented by an overlap criterion.In conventional SCF approaches, the orbitals of lowestenergy are occupied. Within the MOM approach, a di!erentprocedure is adopted, and the new occupied orbitals are

chosen to be those that overlap most with the span of theold occupied orbitals. This allows the SCF calculation toproceed while maintaining the excited state orbital occupations.The new occupied orbitals are identified by defining an orbitaloverlap matrix between the old and new molecular orbitals

O = (Cold)wSCnew (1)

Oij gives the overlap between the ith old orbital and the jth neworbital. The projection of the jth new orbital onto the oldoccupied space is computed as

pj #Xn

i

O2ij $2%

where

Oij #XN

n

XN

m

Xn

i

Coldim

!

Smn

" #

Cnewnj $3%

The occupied orbitals are chosen to be the ones with thelargest projections pj. Consequently, if the initial orbitals forthe Kohn–Sham SCF calculation are chosen such that theydescribe an excited state, the MOM procedure can maintainthe excited state throughout the SCF procedure. In the workpresented here, a long-range corrected hybrid functional hasbeen used for both TDDFT and DKohn–Sham calculations.The exchange part of the functional comprises 20% Hartree–Fock exchange and 80% Coulomb attenuated Becke exchangefunctional49 with an attenuation parameter of 0.3 a!1

0 . TheLYP functional50 is used for the correlation part. TDDFTcalculations were also performed with the oB97 functional.40

The active site model is shown in Fig. 1. For all calculations onplastocyanin with structures drawn from the moleculardynamics simulations, the e!ect of the surrounding proteinincorporated by including point charges for the remainingprotein atoms. Each atom was assigned a point charge takenfrom the CHARMM22 force field.51 All DFT calculationspresented in this work used an unrestricted Kohn–Shamformalism and were performed with the Q-CHEM softwarepackage.52

MRCI calculations have been performed with an activespace comprising the four doubly occupied d orbitals of Cuwith the Cysp, Cyss and singly occupied orbitals, shown inFig. 2. A further two occupied orbitals were also included inthe active space, and this results in an active space of 17 electronsin 9 orbitals. Reference orbitals for the MRCI calculationswere obtained from state averaged multi-configurationalself-consistent field calculations, and the subsequent MRCIcalculations used the projection procedure introduced byKnowles and Werner.53 These calculations were performedusing the MOLPRO suite of programs.54 For all excited statecalculations in the UV region the Stuttgart relativistic smallcore (SRSC) basis set55 was used for copper and the 6-311G*basis set was used for all other atom types.CD spectra were computed at the MRCI level using the

origin independent (velocity) form, where the rotationalstrength for a electronic transition A ’ 0 is given by

R0A # !i

2or0A:LA0 $4%

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where o, r and L represent the excitation energy, momentumand angular momentum, respectively.56 Further calculationsof CD spectra were performed at the single excitationconfiguration interaction (CIS) level with the ORCA softwarepackage.57 For these CIS calculations point charges describedthe extended protein environment were not included. CISexcitation energies are too high, and in the computed spectrumCIS rotational strengths are combined with the MRCIexcitation energies. TDDFT has not been used to computerotational strengths because the calculation of rotationalstrengths with Coulomb attenuated functionals is not currentlyavailable. Furthermore, with standard functionals the order ofthe excited states is not preserved compared to MRCI and,consequently, we have not been able to combine TDDFTrotational strengths with MRCI excitation energies. Graphicalrepresentations of the spectra were generated by representingeach electronic transition with a Gaussian function.

TDDFT can also be applied to study core excited states.Within standard implementations of TDDFT, the calculationof core excited states becomes prohibitively expensive due tothe large number of roots required to obtain the high energycore excited states. A practical solution to this problem is torestrict the single excitation space to include only excitationsfrom the relevant core orbital(s).29,58,59 This makes thecalculation of core excited states of comparable expense tocomputing valence excited states whilst introducing a negligibleerror.60 For core-excitations long-range corrected functionalsdo not improve the calculated excitation energies. This has ledto the development of short-range corrected functionals,which treat the short-range contribution predominantly withHF theory.35 In this work, core-excitation energies and theassociated intensities are computed with TDDFT with theSRC1 form of the short range corrected functional withparameters CSHF = 0.87, mSR = 2.20a!1

o , CLHF = 0.25 andmLR = 1.80a!1

o .35 For the calculation of core excitations, an allelectron basis set is required for copper. For the X-rayabsorption calculations, the 6-31G* basis is used for copper.An additional complication with the computation of coreexcited states is that relativistic e!ects cannot be ignored.Relativistic e!ects lead to a significant lowering of the energyof core orbitals, while the energies of the valence orbitalsremain roughly constant, resulting in an increase in thecore-excitation energy. Corrections of 79.7 eV and 5.9 eVare applied to correct for relativity for the copper and sulfurK edges. These corrections were estimated from lowering inenergy of the core-orbital in relativistic Douglas–Kroll–Hess61

Hartree–Fock calculations relative to analogous unrelativisticcalculations.30

Classical molecular dynamics simulations were performedwith CHARMM.62 For plastocyanin, the simulation protocoldescribed by Ungar et al.4 was followed with some minormodifications. The simulations were carried out at constantvolume and temperature (300 K). The SHAKE constraint63

was applied to all bonds to hydrogen and a time step of 1 fswas used. A 10 A cuto! for nonbonded interactions and longrange electrostatics were accounted for by the particle-mesh-Ewald (PME) method using default values for the parameters.Equilibrium lasted for 140 ps, followed by production dynamicsfor 1 ns. 114 structural snapshots were extracted at equal timeintervals for subsequent quantum chemical calculations.64,65

Simulations of cucumber basic protein were performed withexplicit solvent and cubic periodic boundary conditions,although solvent should have a limited e!ect on the structureof the active site.4

3. Results and discussion

A. CuCl2!4

The electronic structure of the CuCl2!4 ion is a model for theelectronic structure of the active site of oxidised blue copperproteins. The absorption spectrum of CuCl2!4 with a D4h

configuration has been reported,7 and this provides a usefulsystem to explore the accuracy of the DFT based techniques.Table 1 shows the computed excitation energies and oscillatorstrengths for transitions in the UV region with TDDFT and

Fig. 2 Molecular orbitals of plastocyanin.

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MOM approaches. For these calculations CuCl2!4 is consideredin the D4h configuration with a bond length of 2.361 A. All thecalculations predict a singly occupied orbital of b1g symmetrythat is a mixture of the Cu dx2!y2 and Cl p orbitals, inagreement with experiment. Experiment shows three ligandfield excitations at low energy with LMCT excitations athigher energy. TDDFT with the B3LYP exchange–correlationfunctional provides a reasonable description of the ligand fieldexcitations, although the excitation energy for the b1g ’ b2gtransition is too high. The primary deficiency of this approachis the excitation energies for the charge transfer transitions areconsistently too low. For example, transition energies for theexcitations from the eu orbitals are over 8000 cm!1 too low.Furthermore, the b1g ’ a2g transition is predicted to lieamongst the ligand field excitations. These transitions aregenuinely charge transfer in nature and the use of the long-range corrected functional does result in an improvement inthe description of the UV spectrum. The charge transferexcitations are shifted up in energy and are closer to experiment.However, the description of the ligand field excitations is lesssatisfactory. For these transitions there is little di!erence in thepredicted excitation energies, whereas in experiment they canbe distinguished clearly.

Also shown in Table 1 are analogous calculations with theMOM approach. This approach, in conjunction with theB3LYP functional, gives good agreement with experimentfor the ligand field excitations, predicting excitation energieswithin 1500 cm!1 of experiment. Formally, charge transferexcitations should not problematic with the MOM approach,and should be described adequately with hybrid functionals.However for the results presented here, while the excitationenergies for the charge transfer bands are higher than forTDDFT with the B3LYP functional, they are too lowcompared with experiment. The MOM calculations are alsoimproved with the use of the long-range corrected functional.Overall, the MOM approach predicts excitation energies incloser agreement with experiment than TDDFT providing amore balanced treatment between ligand field and chargetransfer excitations. This is, in part, a reflection of the natureof the electronic excitations, which involve doublet states, thatcan be described well by the single determinant based MOMapproach. All of the calculations predict significant intensity(oscillator strength Z 0.005) only for excitations from the

eu orbitals, with the higher energy excitation more intense.For the TDDFT and MOM calculations with the long-rangecorrected functional, the oscillator strength of the higherenergy b1g ’ eu excitation is about three times greater thanthe lower energy one, which is consistent with experiment.

B. Plastocyanin

Fig. 3 shows the computed spectra for the model active site(depicted in Fig. 1) extracted from the 1PLC crystal structure.All three methods predict spectra that are in qualitativeagreement with experiment, with a weaker band arising fromthe ligand field excitations and an intense band at higherenergy arising from the LMCT excitation. The three di!erentmethods consistently predict the LMCT band to occur athigher energy than the experimental value of 16 700 cm!1.Excitation energies of 22729 cm!1, 19 922 cm!1 and 19603 cm!1

are calculated for TDDFT, MOM and MRCI, respectively.Increasing the size of the active space in the MRCI calculationsdoes not lead to better agreement with experiment. Includingan additional five unoccupied orbitals in the active space givesan excitation energy of 20 519 cm!1 for the LMCT band. Thisincrease in the size of the active space leads to a significantincrease in the time for the calculations. Including an additionalfive unoccupied increases the calculation time from 38 h to93 h. This increase in computational cost makes sampling overmany structural snapshots not practical. Overall, the bestspectral profile is predicted by the MOM calculations sincethe relative intensity of the LMCT and ligand field bands isclosest to experiment.Previous theoretical work has shown that the excitation

energy of the LMCT band is sensitive to the structure of theactive site. Therefore, the calculations should be improved byaveraging over structural configurations since this can lead tosignificant changes in the calculated spectra.66,67 The structuralsnapshots drawn from the molecular dynamics simulationwith the parameters of Voth and co-workers4 gives averagebond lengths of 2.09 A and 2.96 A with standard deviations0.05 A and 0.22 A for the Cu–Scys and Cu–Smeth bond lengths,respectively. These and other structural parameters are consistentwith the values reported previously.4 The Cu–Scys bond lengthfrom simulation is marginally longer than in the crystalstructure. This similarity to the crystal structure is inherent

Table 1 Calculated excitation energies (in cm!1) of CuCl2!4 with TDDFT and MOM. Oscillator strengths Z 0.005 in parenthesis

Excitation Exp.a TD-DFT (B3LYP) TD-DFT (LRC) MOM (B3LYP) MOM (LRC)

b1g ’ b2g 12 000 13 550 13 870 10 730 10 650b1g ’ eg 13 500 12 990 13 230 12 180 12 340b1g ’ a1g 16 500 14 760 13 550 15 970 14 440b1g ’ a2g 23 700 13 550 20 410 16 210 20 730b1g ’ eu 26 400 18 230 (0.02) 24 680 (0.05) 20 490 (0.08) 25 250 (0.07)b1g ’ b2u 19 040 26 290 21 620 26 860b1g ’ eg 24 840 30 890 26 700 31 700b1g ’ a2u 19 040 32 100 26 780 32 990b1g ’ b1g 37 670 39 680 31 210 35 730b1g ’ eu 35 900 29 920 (0.11) 35 080 (0.14) 30 810(0.32) 35 970 (0.22)b1g ’ b2g 29 920 37 180 30 730 37 670

a Experiment.7

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in the design and parameterization of the force field, which isoptimized to reproduce the crystal structure. There is a muchlarger fluctuation in the Cu–Smeth bond length. This is a resultof the copper-methionine interaction being treated as a non-bonded interaction in the force field.

Fig. 3 also shows computed spectra derived from averagingover the 114 structural snapshots drawn from the moleculardynamics simulation. The aim of averaging over these structuresis to represent the non-equilibrium structures that will beaccessed during spectral measurements at finite temperature.A classical molecular dynamics simulation with an accuratelyparameterised force field should be su"cient to provide reliablestructures.68 Point charges describing the remainder of theprotein are included, however, we find the inclusion of thesecharges has relatively little e!ect on the location of the LMCTband. This is consistent with the findings of previous theoreticalstudies.23,24 Overall, the change in the resulting spectra is notas large as first expected. While there is a small shift inthe position of the LMCT band towards lower energy, thepredicted excitation energies of 22 140 cm!1, 19 585 cm!1 and18 354 cm!1 for TDDFT, MOM and MRCI remain too high.The ligand field band predicted from the MOM calculationsmatches the experimentally observed band well, while theligand field band is too high in energy in the TDDFT spectrumand too weak in the MRCI spectrum. We have explored thesensitivity of the computed TDDFT spectrum to the exchange–correlation functional. Repeating the TDDFT calculationswith the oB97 functional of Chai and Head-Gordon40 givesvalues of 23 000 cm!1 and 15 200 cm!1 for the LMCT andligand field bands. These values represent only a small changein the computed spectrum.

Fig. 4 illustrates the correlation between the bond lengths ofthe two copper-sulfur bonds and the computed excitationenergy of the LMCT band for the MRCI calculations. Thisshows a very strong correlation between the Cu–Scys bond

length, with a correlation coe"cient of over 0.9, while there islittle correlation between the excitation energy and the Cu–Smeth

bond length. This indicates that for theory to correctly predictthe excitation energy of the LMCT band, the average Cu–Scysbond length from the simulation and hence the crystal structureshould be longer. A single calculation in isolation would notprovide suitable justification for suggesting a change in thecrystal structure. However, the fact that three unrelatedapproaches to computing the excitation energies all predictconsistently that the excitation energy is too high coupled withthe very strong correlation between the Cu–Scys bond lengthand the excitation energy does provide a more compelling casefor reviewing the bond length in the crystal structure. TheCu–Scys bond length versus excitation energy graph suggeststhat to correctly predict the energy of the LMCT band, aCu–Scys bond length of about 2.15 A is necessary. This bondlength is similar to the Cu–Scys bond lengths found in therelated blue copper proteins cucumber basic protein (2.16 A)and nitrite reductase (2.19 A). There is only a small variationin the experimentally observed energies of the LMCT band inplastocyanin (16700 cm!1), cucumber basic protein (17550 cm!1)and nitrite reductase (17 100 cm!1), which also indicatesstrongly that the Cu–Scys bond lengths should be similar. Anerror in the Cu–Scys bond length of about 0.8 A is alsoreasonable considering the resolution of the crystal structureof 1.33 A.A more direct computational approach to establishing

the Cu–Scys bond length is to optimize the structure directlywithin a QM/MM approach. We have performed a QM/MMoptimization of the structure in which the active site is modeledusing B3LYP and the 6-31G* basis set with 6!31+G* for thesulfur atoms and the CHARMM force field for the remainderof the protein. These calculations exploit the new interfacebetween CHARMM and Q-CHEM.69 The structure of theactive site from the QM/MM optimization is shown in Table 2.

Fig. 3 Computed UV/vis absorption spectra for plastocyanin. The experimental spectrum adapted from reference17 is shown in red.

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Overall, the QM/MM optimization is in good agreement withthe crystal structure. The bond length for the long Cu–Smeth

bond is predicted accurately and the QM/MM predicts only asmall di!erence between the two Cu–Nhis bond lengths inagreement with the classical simulation. Of particular relevance isthe Cu–Scys bond length is predicted to be longer than in thecrystal structure and consistent with our analysis of theabsorption spectra. This bond length is shorter than the valuepredicted by the QM/MM calculations of Sinnecker andNeese.24 This reason for this di!erence could be the basisset, since we have found that this bond length is sensitive to thebasis set used, in particular the inclusion of polarizationfunctions is important. The Cu–Smeth bond length agrees wellwith the crystal structure. However, the Cu–Nhis bond lengthsshow a notable deviation from the crystal structure. In thecrystal structure there is a significant di!erence between thetwo Cu–Nhis bond lengths while the QM/MM here and byothers24 predict that the two bond lengths are much closer toeach other and lie between the two values given by the crystalstructure. However, we find that these changes are lesssignificant in the spectroscopy than the Cu–Scys bond length.

This increase in the Cu–Scys bond length has been incorporatedinto the molecular dynamics simulation by increasing theequilibrium Cu–S bond length from 2.10 A to 2.15 A in theforce field. The average structural parameters relevant to theactive site resulting from this new simulation are also shown inTable 2 with corresponding values for the 1PLC crystal

structure. The simulation gives an average bond length of2.14 A for the Cu–Scys bond. The remaining structuralparameters remain close to the crystal structure. The mostsignificant deviation is for the two Cu–N bond lengths. Thesimulation predicts these to be similar, while there is asignificant di!erence in the crystal structure. There is also anoticable di!erence in the values for the Cb(cys)–S(cys)–Cu–S(met) dihedral angle. However, there is a large standarddeviation for this angle because of the variation in the positionof the non-bonded methionine residue.Fig. 3 shows the computed spectra arising from the

molecular dynamics simulation with the adjusted force field.For all methods there is a shift to lower wavenumber in theLMCT band. For TDDFT, the shift is too small and bothLMCT and ligand field bands are too high in energy. TheMOMandMRCI spectra are in good agreement with experiment.The LMCT band for MRCI lies at 17 260 cm!1, although theintensity of the ligand field band remains too low comparedwith experiment. For the MOM calculations, the LMCT bandis predicted to lie at 18 762 cm!1 and the relative intensities ofthe LMCT and ligand field bands is predicted correctly by theMOM calculations. However, in this spectrum the LMCTband is marginally too high in energy, which suggests a slightlylonger Cu–Scys bond length. Overall, the MOM and MRCIcalculations are as close to the experiment as one can expectfor systems as complex as plastocyanin. These simulationsillustrate a useful synergy between quantum chemical spectro-scopic calculations and classical molecular dynamics forcefields. If the calculated spectra are sensitive to the conformationand there is su"cient confidence in the accuracy of thequantum chemical calculations and sampling, then simulatingexperimentally measured spectra can provide a test of theclassical force field to establish the molecular dynamicssimulation is sampling the correct molecular conformations.This can also provide a mechanism to test and refine theclassical force field.The calculation of CD spectra is more challenging than the

calculation of UV absorption spectra. The rotational strengthis dependent on the product of the electronic and magnetictransition dipole moment,70 and accurate determination of therotational strength requires both transition moments and theangle between them to be calculated correctly. Furthermore,CD spectra are more sensitive to the underlying structure andit has been shown that conformational sampling is importantto achieve good agreement between calculated spectra andexperiment.71 Fig. 5 shows computed CD spectra based onMRCI and CIS calculations. The CIS method is known tooverestimate excitation energies significantly. Consequently,for the CIS based spectra, CIS/6-31G* rotational strengths arecombined with MRCI excitation energies to allow comparisonwith experiment. Initially, CD spectra computed using thecrystal structure are considered. These spectra have beengenerated using gaussian functions with a full width at halfmaximum (fwhm) of 200 cm!1. For both methods, the resultingspectra are very di!erent from experiment. For the CISspectrum, the ligand field and SOMO ’ Cysp band havethe wrong sign, but the SOMO’ Cyss band appears correctlyas a positive band at higher energy. The MRCI spectrum doesshow a marginally better agreement with experiment. Overall

Table 2 Comparison of the structural parameters for the active sitewith the X-ray crystal structures

Crystal MM simulation QM/MM

Distances (A)Cu–S(cys) 2.07 2.14 2.14Cu–N(his87) 2.06 2.04 1.95Cu–N(his37) 1.91 2.04 1.93Cu–S(met) 2.82 2.90 2.90Angles (1)S(cys)–Cu–N(his87) 121 122 126S(cys)–Cu–N(his37) 132 128 127N(his87)–Cu–N(his37) 97 95 98S(cys)–Cu–S(met) 110 111 105Dihedral angles (1)Cb (cys)–S(cys)–Cu–S(met) 2 19 21Cg(his87)–N(his87)–Cu–S(met) 77 74 55Cg(his37)–N(his37)–Cu–S(met) 112 120 120Improper torsions (1)Cu–S(cys)–N(his87)–N(his37) 21 26 23Cu–S(cys)–N(his37)–N(his87) 27 29 22Cu–N(his87)–N(his37)–S(cys) 16 19 16

Fig. 4 Correlation of the computed LMCT excitation energies with

the Cu–S bond lengths.

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the ligand field band is well described and both SOMO’ Cyspand SOMO ’ Cyss are positive. However, the rotationalstrength of the bands is severely underestimated, and theintense SOMO ’ Cysp charge transfer band is barely visible.

Also shown are corresponding conformationally averagedspectra based on the molecular dynamics simulations with theincreased Cu–Scys bond length. These spectra have beengenerated with a fwhm of 500 cm!1. This conformationalaveraging leads to a clear improvement in the computedspectra. For the CIS based spectrum, the ligand field excitationsresult in an intense negative band in agreement with experiment,and the SOMO’ Cyss band at higher energy is also describedwell. However, while the SOMO ’ Cysp charge transfer bandis broadened and has the correct sign, its intensity is too low.The conformationally averaged MRCI spectrum shows thebest agreement with experiment, and while the agreement isnot excellent, the general features of the experimentalspectrum are reproduced. The ligand field and SOMO’ Cyssbands are reproduced well, and a distinct SOMO ’ Cyspcharge transfer band is evident. However, this band remainstoo weak relative to the ligand field and SOMO ’ Cyssbands, and the small positive peak at about 11 000 cm!1 andnegative peak at about 21 000 cm!1 are not reproduced. Fig. 6shows the dependence of the rotational strength of theSOMO ’ Cysp charge transfer band on the Cu–Scys–N–Nimproper torsion angle, which indicates the extent that thecopper atom is raised out of the plane of the two nitrogen andcysteine sulfur atoms. The graph shows a relatively strongcorrelation of 0.67, with the more planar the Cu–Scys–N–Natoms leading to a more intense band. This suggests that theintensity of this band provides some measure of planarity ofthe active site. Observation of the experimental spectra showsthat the intensity of this band relative to the ligand field banddecreases for the related proteins cucumber basic protein andnitrite reductase compared to plastocyanin17,18 and theseproteins have a greater Cu–Scys–N–N angle in their crystalstructures.

C. X-ray absorption spectra

Table 3 shows the computed energies and intensities of thepre-edge features at the copper and sulfur K edges withthe experimental excitation energies for plastocyanin. Thecomputed values are averages over the 114 structural snapshotsdrawn from the simulations with modified Cu–Scys bondlength. For the sulfur K-edge, the computed excitation energyis in excellent agreement with experiment. For the copperK-edge the agreement is less good, but still within an acceptableerror. Comparing the computed excitation energies for plasto-cyanin with cucumber basic protein shows only a smallchange. The most significant aspect of these calculations isthe computed oscillator strengths, since these can be used toextract information about the relative contribution of sulfurp orbital and copper d orbital character in the SOMO.7 Thecalculated oscillator strength for cucumber basic protein islower than the value for plastocyanin, indicating a smaller sulfurp character in the SOMO. There is little variation in the computedoscillator strengths during the simulation and this is the caseacross the simulations. Fig. 7 shows molecular orbital picturesplotted at the same contour surface of SOMOs of plastocyaninand cucumber basic protein taken from the structural snapshots.From these orbitals, the smaller sulfur p component for cucumberbasic protein can be identified clearly.

Fig. 5 Computed CD spectra for plastocyanin. The experimental spectrum adapted from reference18 is shown in red.

Fig. 6 Correlation of the computed LMCT excitation energies with

the Cu–Scys–N–N torsion angle.

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IV. Conclusions

The UV absorption, CD and X-ray absorption spectra of theblue copper proteins plastocyanin and cucumber basic proteinhave been studied with a combination of quantum chemicalexcited state methods in conjunction with classical moleculardynamics simulations. For calculations based on the geometryof the crystal structure, all three excited state methods usedpredict the location of the LMCT band to be too high inenergy. Analysis of the computed spectra for the di!erentstructural snapshots drawn from the molecular dynamicssimulation highlights a strong correlation between theCu–Scys bond length and the excitation energy of the LMCTtransition. This suggests that the Cu–Scys bond length shouldbe larger than observed in the crystal structure. This issupported by the experimental measurements on relatedblue copper proteins which show LMCT bands at energiessimilar to plastocyanin, yet have significantly longer Cu–Scysbond lengths. The computed CD spectra are sensitive toconformation, and conformational averaging is necessary toobtain spectra that reproduce the major features observed inexperiment. The rotational strength of the LMCT band showssome correlation with the extent to which the copper atom isabove the plane containing the cysteine sulfur and histidinenitrogen atoms.

X-ray absorption spectra of the pre-edge feature at thesulfur K-edge, show a lower oscillator strength for cucumberbasic protein compared to plastocyanin. This indicatesa smaller sulfur p orbital character in the SOMO. Overall,these calculations show how quantum chemical calculationscan be applied to complex systems such as the blue copperproteins and provide a useful tool to aid experimentalendeavors.

Acknowledgements

DR is supported by the Engineering and Physical SciencesResearch Council through the award of the grant (EP/F006780).We thank the University of Nottingham for time on the highperformance computing service.

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