The Dynamic Origin of Color Tuning in ProteinsRevealed by a Carotenoid Pigment

Daniele Loco,† Francesco Buda,∗,‡ Johan Lugtenburg,‡ and BenedettaMennucci∗,†

†Dipartimento di Chimica e Chimica Industriale, University of Pisa, via G. Moruzzi 13,56124, Pisa, Italy

‡Leiden Institute of Chemistry, Leiden University, Einsteinweg 55, 2300 RA Leiden, TheNetherlands

E-mail: f.buda@chem.leidenuniv.nl; benedetta.mennucci@unipi.it

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Abstract

Understanding the microscopic origin of the color tuning in pigment-protein complexes isa challenging yet fundamental issue in photoactive biological systems. Here, we propose apossible interpretation by using a state-of-the-art multiscale strategy based on the integrationof quantum chemistry and polarizable atomistic embeddings into a dynamic description. Bymeans of such a strategy we are able to resolve the long-standing dispute over the colorationmechanism in the crustacyanin protein. It is shown that the combination of the dynamicalflexibility of the carotenoid pigments (astaxanthin) with the responsive protein environment isessential to obtain quantitative predictions of the spectral tuning. The strong linear correlationbetween the excitation energies and the bond length alternation in the long-chain carotenoidsmodulated by the dynamical protein environment is a novel finding explaining the high colortunability in crustacyanin.

Color tuning of chromophores by the embed-ding protein is an extremely effective strategythat nature has developed and optimized toactivate different biological functions.1 Manyexamples are known from simple microorgan-isms to complex systems and various mecha-nisms have been suggested both from experi-mental and theoretical investigations.2–14 Thesemechanisms are mostly based on the electro-static interactions of protein residues surround-ing the chromophore that, either through netcharges or large polarity effects, can differen-tially stabilize ground and excited states. Theother mechanism which is often suggested is theconformational change of the chromophore ex-erted by the confinement in the protein bind-ing pocket. However, in most cases, electrostat-ics and conformational effects can only qualita-tively explain the observed color change.11,15,16

It is therefore more likely that multiple effectsare simultaneously active making the elucida-tion of the mechanism of tuning still an un-solved problem. Here we show that an exhaus-tive explanation is indeed achievable throughadvanced computational approaches.

The specific case here selected is one of thelargest and most spectacular color changes in-duced by a protein matrix. When heatingthe lobster (Homarus Gammarus), the darkblue color of its carapace is changed intobright red. Lobster carapaces contain a keto-carotenoid pigment called astaxanthin (AXT),which, when embedded in the α-crustacyaninprotein, gives a π− π∗ absorption maximum atλmax ∼ 630 nm. Upon protein denaturation,the released AXT appears as a red pigment,

with a maximum absorption between 475 and500 nm, depending on the solvent. Although itis clear that the color change is due to the for-mation of the carotenoid-protein complex, theexact mechanism inducing this large spectralshift has not been established. The elucidationof the crystal structure of the dimeric subunitof the protein (β-crustacyanin)17 has revealedthe 6-s-trans conformation of AXT in the bind-ing pocket, contrary to the 6-s-cis conformationobserved in solution. The X-ray structure of β-crustacyanin has also shown the close proximityof the two AXT molecules in the dimeric sub-unit (Figure 1) with a center-to-center inter-molecular distance of about 7 A.17 Moreover,the AXT carotenoids appear to be bent withinthe binding pocket and their carbonyl groupsform hydrogen bonds with a nearby histidineand a water molecule, respectively.

Such X-ray structural information has fur-ther stimulated several theoretical and exper-imental investigations.10,11,15,16,18–22 The originof the large bathochromic shift of the order of0.5 eV has been related to (i) planarization ofthe chromophore in the protein binding pocketinducing an extension of the conjugated system;(ii) polarization effects due to either chargedresidues in the vicinity of the chromophore ordue to long-range polarization effects; (iii) ex-citonic coupling due to the proximity of thetwo bound chromophore (as also suggested byCD spectra15,23), or a combination of the abovemechanisms. The hypothesis of a strong exci-tonic splitting, originally proposed on the ba-sis of a simple dipole-dipole model approxima-tion,15 has been more recently discarded based

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on more accurate theoretical calculations16,21

as well as 2D electronic spectroscopy investi-gations, which give an exciton coupling of 250cm−1 (0.03 eV).22

Figure 1: β-crustacyanin protein scaffold with thetwo AXT carotenoids inside it, in the configurationrepresented in the cristallographic structure.17

Another long-debated idea is the presence ofa net charge on the AXT end rings or a nearbycharged residue inducing a strong charge po-larization of the conjugated chain, thus ex-plaining the large spectral shift compared tothe chromophore in nonpolar solvent.21 Re-cently, a work combining experimental dataand quantum-chemical calculations on a modelcompound has proposed the enolization of AXTwithin the protein environment to explain thelarge bathochromic shift.10 However, it is diffi-cult to reconcile this suggestion with the solidstate 13C NMR data on α-crustacyanin thathave shown rather small chemical shifts dif-ferences compared to 13C NMR data in solu-tion.15,16 These data quite convincingly indicateno evidence of enolization that would result inmuch larger chemical shifts.

In a recent computational study, Gamiz-Hernandez et al. employed an hybrid QM/MMapproach using correlated ab initio calculationsfor the excitation energies and they showed theimportance of properly including the specificityof the different protein residues surrounding thepigment.11 Their predicted color shift of about0.3 eV, however, accounts for about 60% of theobserved experimental shift from hexane to β-crustacyanin. The question is what are the

missing elements in the theoretical model fora quantitative prediction?

In this work, we provide the answer by com-paring a hierarchy of models of increasing com-pleteness which combine a quantum chemicalcharacterization of the structure, the dynamicsand the optical response of the chromophore(s)with a classical description of the environment.This comparative study not only allows us toresolve the long-lasting dispute over colorationmechanism in crustacyanin but it also clarifiesthe limits of the commonly used computationalstrategies to study the effects of the protein onthe response of the embedded chromophore tolight.

It is well known that the quantum chemi-cal description of the electronic excitations incarotenoids is extremely challenging due to thespecific character of the different π − π∗ ex-cited states. Indeed, from theoretical stud-ies comparing single– and multi– reference ap-proaches,24–27 it comes out that contributionsfrom multiple excitations are crucial for thedescription of the lowest (dark) excited state,whereas the (bright) second state is dominatedby single excitations.28 For that excitation,Time Dependent Density Functional Theory(TDDFT) has shown to be a valid approachespecially when used in combination with opti-mized long-range corrected hybrid density func-tionals. This is exactly the level of QM descrip-tion that will be used here to describe the brightexcitation of AXT in terms of the ωB97x func-tional.29 The validity of the selected functionalhas been further confirmed by comparing theresults obtained for AXT to those of anothercarotenoid, violoerythrin (VIO), which has thesame length of AXT but with isopentenonerings instead of ionone rings. VIO shows al-ready a blue color in hexane solution (λmax=530nm for VIO compared to λmax=472 nm forAXT).30,31 In Section S2 of the Supporting Info(SI) we provide validation tests on the ωB97xfunctional and show that it is able to quantita-tively predict the experimental spectral shift forAXT and VIO carotenoids in solution. In thefollowing, all the computed excitation energyshifts will refer to the unbound AXT in cis– con-formation in cyclohexane represented through

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the Polarizable Continuum Model (PCM).32 Infact, while AXT in the protein crystal is in thetrans form, in solution the cis conformation isknown to be dominant (see also Table S1 inSI).11,19

As a first model for the pigment-protein com-plex, we assume that the effect of the proteincan be mimicked with a dielectric medium thatwe represent through PCM. To account for thewater molecules that can penetrate into the pro-tein and contribute to the polarity of the lo-cal environment of each AXT, we have used adielectric constant corresponding to a solventof medium-high polarity, namely ε = 20, incombination with an optical dielectric constantequal to 2.0 as commonly used for proteins.Using such an effective dielectric model, wehave optimized the geometry of the single 6-s-trans AXT in PCM at B3LYP/6–31G(d) level,and computed the excitation energy at theTDωB97x/6–31+G(d) level. To properly ac-count for the differential stabilization of groundand excited state we have also introduced astate-specific correction to the TDDFT excita-tion energies.33

The value of 0.17 eV for the bathochromicshift obtained at the QM/PCM level (seeTable 1) when moving from hexane to β-crustacyanin recovers only a portion of theexperimental value (0.51 eV).17,20 This shiftis mainly associated to the planarization ofthe chromophore in the s-trans conformation.What is clearly missing in this “continuum” pic-ture are both the specific interactions betweenthe AXTs and the protein residues and the pos-sible inhomogeneities in the electrostatic andpolarization effects of the protein matrix. Apossible step forward is thus the inclusion of anatomistic MM method based on the availablecrystal structure of the pigment-protein com-plex. Because the resolution of this structurefor the chromophore is not enough to be safelyused in the QM calculations, we relaxed thegeometry of the two AXTs within the proteinkept frozen in its crystal structure. The geom-etry optimization was performed at B3LYP/6–31G(d)/AMBER level using an electrostaticembedding. The resulting geometries were fi-nally used to calculate the excitation energies

of the chromophores still within the same elec-trostatic embedding for the protein. The result-ing excitation energy shifts, reported in Table 1,show that the two AXTs “feel” a quite differentlocal environment: for one (AXT A), the shiftis more than double than for the other (AXTB) and even larger than the experimental one.A possible improvement to this description isto combine the same relaxed AXTs structureswith a polarizable embedding for the protein.Here the polarizable AMOEBA force field34 hasbeen used in its recent implementation withina TDDFT framework.35 In such an implemen-tation a state-specific correction of the TDDFTexcitation energies can also be included using aformalism similar to what done at PCM level.Through this correction, it is possible to recoverthe effects due to the relaxation of the chro-mophore electronic density upon excitation andcombine it with those due the response of thepolarizable embedding to the excitation (see eq.S7 of the SI).36

The resulting shift increases of ∼0.1 eV forboth AXTs if compared to the non polariz-able QM/MM results. As the AXT geometriesand the protein configuration have not changed,this additional shift is only due to the com-bined effect of (i) the state-specific relaxationof the protein polarization to both ground andexcited states and (ii) its response to the elec-tronic transition.36 In the present case, the for-mer effect is much smaller than the second one,as the π − π∗ excitation does not correspondto a significant reorganization of the electroniccharge.

To investigate the possible sources of the dif-ferent shift shown by the two AXTs in the crys-tal structure, we have dissected the contribu-tion of the various residues surrounding the pig-ments. Two aspects have been considered: howmuch each residue contributes to stabilize theground state (through electrostatics and polar-ization) and how much it responds to the excita-tion through polarization (see Section S1 of theSI for more details). The results are reportedin Fig.2. As it can be seen, for both AXTs theresidues which respond the most to the excita-tion are not homogeneously distributed aroundthe chromophore but they concentrate more on

4

Table 1: Comparison between calculatedand experimental excitation energy shiftsfor different QM/classical models. The shiftis obtained with respect to the cis– form inn–hexane (2.56 eV at TDωB97x/PCM leveland 2.63 eV in the experiments). The exper-imental value is from Ref. 17,20. All valuesare in eV.

Model Shift

PCM 0.17MM 0.59a & 0.19b

AMOEBA 0.72a & 0.29b

<AMOEBA>MD 0.50

Experiment 0.51a AXT A; b AXT B

one side, namely the side with the H-bondedwater molecule. However, the relative contri-butions are different in the two AXTs: in par-ticular, AXT A (i.e. the AXT showing thelargest shift) not only feels a much larger effectfrom all the residues which are common to bothAXTs (such as phenylalanine PHE, and tyro-sine, TYR) but it has additional residues con-tributing significantly (such as an asparagine,ASN and a glutamine, GLN). What mostlydifferentiate the two chromophores, however,are the electrostatic (and polarization) effectsof the residues on the ground state. It ap-pears that AXT B feels a strong effect due tocharged (ASP) and polar (SER, THR) residuesfrom both sides of the chain while for AXT Athe most interacting residues are placed alongthe chain (the charged ASP) and on one side(GLN). This asymmetry can explain the muchlarger bathochromic shift found for AXT A.

This analysis clearly shows that a static repre-sentation in terms of a single “frozen” arrange-ment of the residues leads to significant differ-ences between the two AXTs. To verify if thisis physically sound or an artifact, we need tointroduce temperature-dependent fluctuationsof the system leading to many different AXT–environment configurations.

To do that, a Born-Oppenheimer (BO) MDsimulation has been performed where the twoAXTs are described at B3LYP/6-31G level

while the protein is represented in terms of thepolarizable AMOEBA force field. To performthe QM/AMOEBA BOMD simulation, the re-cently implemented interface between a locallymodified version of Gaussian37 and Tinker38

has been used (see Section S3 of the SI for moredetails).39

As a preliminary analysis, possible excitoniceffects have been checked, calculating the exci-tation energies of the dimer and the separatemonomers on structures randomly extractedfrom the BO-MD trajectory. In the monomericcalculation, the second AXT is treated on anequal footing with the protein residues. Theobtained excitation properties are almost un-changed switching from the dimer to monomers(see also NTO in Section S2 of the SI) andthe excitation energies differing for less than∼ 0.01 eV. This confirms the previous stud-ies showing a negligible contribution of exci-tonic interactions in the observed shift.11,16,21,22

Once validated the monomeric model, we haveconsidered 40 uncorrelated configurations ex-tracted from the BO-MD and used them tocalculate the electronic excitations of the twoAXTs within the polarizable AMOEBA embed-ding. The results are reported in Figure 3.

5

TYR

ASP

SER

THR

PHE

ILE

WAT

TYR

TYR

ILE

ASN

PHEPHE

ASP

ASP

GLN

WAT

AXT B

AXT Acm-1

cm-1

Figure 2: Left: contribution of each residue to the excitation energy of the two AXTs (in cm−1). Right:The residues which contribute most are indicated by colored surfaces. A threshold of 40 cm−1 has beenused and the depicted residues are those contained in the black box. The residues reported as tubes arethose with the largest electrostatic and polarization interaction energy (> 5 Kcal/mol) with each AXT inthe ground state.

The resulting band maximum has been finallyused to calculate the <AMOEBA>MD shift re-ported in Table 1. The obtained result (0.50eV) is in excellent agreement with the experi-mental one of 0.51 eV. The remarkable agree-ment is not limited to the energy shift but italso applies to the absolute value of the excita-tion energy (2.06 eV vs. 2.10 eV) and to theband width: the FWHM calculated on the con-volution reported in Fig.3 is 0.51 eV while fromthe experimental spectrum we get 0.54 eV.15

The simultaneous excellent reproduction ofthese three main features of the protein-inducedspectral changes cannot be due to error cancel-lations but instead confirms the validity of themodel thus allowing us to propose a molecularmechanism for the tuning.

First of all, the temperature-dependent fluc-tuations of the AXT-protein complex act to re-duce the large differences found between thetwo AXTs when simulated within a frozen en-vironment. Now, the chromophores are al-lowed to explore a common range of local en-vironments as shown by the large overlap of

the excitation energies calculated for the twoAXTs (see Figure 3). To better understand therole of these structural fluctuations of the chro-mophores coupled to those of the embeddingprotein, it is useful to introduce a geometricalparameter largely used in conjugated systemsto relate electronic properties to the structure.This parameter is called Bond Length Alter-nation (BLA) and it is defined as the differ-ence between the average single and the aver-age double bond length along the conjugatedchain. The BLA parameter has been success-fully used to explain the optical properties ofvarious pigment-protein complexes3,6,40–43 butit has never been applied to crustacyanin.

The correlation between the calculated exci-tation energies and the BLA of the correspond-ing structures is reported in Figure 3 for the twoAXTs. As expected due to the high sensitiv-ity of the excitation energies of carotenoids tochanges in the conjugation path,44 a linear cor-relation appears for both AXTs. The slightlydifferent slopes and spread are likely due to thedifferent local environment which we have pre-

6

O

HO

OH

O

HO

HO

O

OH

a)

b)

HO

CO

O

O

O

HO

c)

HO

O

OHd)

e)

O

OH

O

OH

BLA (Å)

Exci

tatio

n en

ergy

(eV

)

1.5 1.8 2.1 2.4 2.7

Excitation energy (eV)

AXT AAXT B

1.5Excitation energy (eV)1.8 2.1 2.4 2.7

Figure 3: Top: Distribution of theTDDFT/AMOEBA excitation energies onthe snapshots extracted along the BOMD: theheights of the sticks are proportional to thesquared modulus of the corresponding transitiondipoles. The black curve is obtained as the sumof Gaussian convoluted bandshapes centered oneach excitation energy and having a FWHM of500 cm−1 (changing the width from 500 to 1000cm−1 has a negligible effect on the position of themaximum). Bottom: correlation diagram betweenthe excitation energies (in eV) of the two AXTswith their respective BLA (in A) defined usingthe single and double bonds underlined in gray inthe AXT structure. The empty dots refer to theoptimized structures within the crystal.

viously discussed in the analysis of the crystal.What is quite unexpected is instead the largewindow of energies (around 1.0 eV) that thesefluctuations in the BLA allow both AXTs toexplore.

To better understand this finding, in Fig. 4

we report the set of residues which mostly actson AXT A in the crystal structure and in a con-figuration extracted from the BOMD trajectorywhich presents characteristics (both in terms ofBLA and excitation energy) similar to the av-erage values. The color scheme is the same asthe one used in Fig. 2: the residues reportedas tubes are those with the largest electrostaticand polarization interaction energy with AXTin the ground state, whereas the residues re-ported as colored surfaces are those showingthe largest response to the excitation. Here,to make the picture more complete, we haveused a smaller value for the ground state in-teraction energy threshold and we have usedred(blue) color to indicate residues giving a neg-ative(positive) interaction energy.

As it can be seen, the structure of the chro-mophore is very different in the two configu-rations: while in the relaxed crystal structureit is almost straight (with BLA=0.051 A) inthe BOMD configuration it is much more bent(with BLA=0.078 A). This structural differenceis accompanied by a change in the number andthe type of interacting residues. In particular,the number of residues having strong interac-tions (e.g. above the selected threshold) withthe ground state is much larger in the crystalstructure than in the selected snapshot. Wethus expect a much larger stabilization of theground state in the former. Some differences arealso present in the response of the polarizableresidues to the excitation: we see that in thecrystal structure there are five strongly respon-sive residues (plus the H-bonded water) while,in the configuration from the BOMD, these re-duce to three (and water is no more within theselected threshold). These differences are re-flected in the very different energy shift whichreduces from 0.83 eV (in the crystal configura-tion) to 0.46 eV in the BOMD configuration.We can better explain this reduction in termsof different contributions. By calculating theexcitation energy of the isolated AXT in thetwo different geometrical structures we obtainca. 62% of the whole reduction. By switch-ing on the effects of the residues we can assigna further 23% to the different stabilization ofthe ground state and the remaining 15% to the

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Configuration@CRYSTAL

Configuration@BOMD

Figure 4: Comparison between AXT(A) in thecrystal (top) and in a configuration extracted fromthe BOMD (bottom). The residues reported astubes are those with the largest interaction en-ergy with the AXT in its ground state. Only theresidues having an interaction energy of more than3 kcal/mol (absolute value) are shown: red meansa negative energy while blue means a positive en-ergy. Colored surfaces indicates the residues withthe largest response to the excitation.

differential response to the excitation.This analysis clearly says that the protein de-

termines the optical response of the embeddedAXTs through fluctuations of the geometricalstructure. The resulting conjugation paths willin fact correspond to a different ground statestabilization through the electrostatic (and po-larization) effects of the surrounding residueswhich will differently respond to the excitationprocess. Without the inclusion of the dynam-ics, none of these coupled effects can be prop-erly described and only a qualitative picture canbe obtained. Moreover, we argue that cumu-lative electrostatic/polarization effects can alsoexplain the further red shift of ≈ 0.15 eV fromβ-crustacyanin to the octamer α-crustacyanin.

To further validate the accuracy of the simu-lations in reproducing the coupling between ge-ometry and environment we have run a shortBOMD using a larger basis set (namely 6-311G): as shown in Section S4 of the SI, the re-sulting structures reproduce the same range ofBLAs and consequently the same distributionof excitation energies. We have also checkedthe effect of using a polarizable FF by selectingfour snapshots from the QM/AMOEBA BOMDcharacterized by a quite different value of theBLA and, keeping frozen the environment, op-timizing the structure of AXT within a non-polarizable (AMBER) and the AMOEBA pro-tein. As the environment is kept fixed, onlythe different charges and the presence of po-larization will affect the final geometry of theembedded carotenoid. The data (reported inthe SI) confirm a non-negligible effect of thepolarizable environment: without including po-larization, BLA values are always larger whichmeans a larger localization into single and dou-ble bonds. These differences in the BLA finallycorrespond to a 0.1-0.2 eV differences (towardsthe blue) in the excitation energies.

In conclusion, with the present study we haveshown that the color tuning in proteins is acomplex phenomenon and its modeling requiresto go beyond the methodological approachescommonly used to describe embedded systems.In particular, the popular strategy based ona single relaxed structure (generally obtainedfrom crystal data) cannot be used. Both the

8

electronic and the nuclear structure of highlyconjugated pigments are in fact so sensitiveto the details of the surrounding that a sin-gle configuration of the environment necessar-ily induces artifacts that cannot be removedneither by using a high-level QM descriptionfor the pigment and/or introducing an accurateatomistic and polarizable model for the envi-ronment. Unfortunately, also the other popularstrategy based on the use of a configurationalsampling obtained from classical MD simula-tions presents serious limitations. In this case,in fact, an accurate enough description of thecoupled torsional and bond-length distorsionsof the pigments’ conjugated structure is difficultto be achieved.45 A complete and reliable pic-ture can be obtained only if the pigment’s elec-tronic and structural fluctuations induced bythe dynamic electrostatic fields of the proteinand the residue-dependent polarization interac-tions can be accurately included in all the stepsof the simulation. This necessarily requires toapply dynamic QM/classical approaches wherethe classical models include all the main fea-tures which define the embedding effects of aprotein, namely an atomistic detail combinedwith an accurate description of electrostaticsand polarization.

Supporting Information Avail-

able

Details on the approach employed to includethe effect of the polarizable environment on theelectronic excitation. Test calculations for theωB97X DFT functional and details about theQM/MM BOMD. ωB97X DFT NTOs of AXT.Test calculations on the effect of the basis setand the polarizable FF

Acknowledgement FB acknowledges theuse of supercomputer facilities at SURFsarasponsored by NWO Physical Sciences, with fi-nancial support from the Netherlands Organi-zation for Scientific Research (NWO).

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