Fragment Molecular Orbital Calculations on Red Fluorescent Proteins

Jan 7, 2009 - Takeshi Ishikawa,# Minoru Sakurai,. ∇ and Shigenori ..... ability has been augmented by Mochizuki et al., on the basis of efficient in...
0 downloads 0 Views 709KB Size
Download PDF
J. Phys. Chem. B 2009, 113, 1153–1161

1153

Fragment Molecular Orbital Calculations on Red Fluorescent Proteins (DsRed and mFruits) Naoki Taguchi,† Yuji Mochizuki,*,†,‡ Tatsuya Nakano,‡,§ Shinji Amari,| Kaori Fukuzawa,⊥ Takeshi Ishikawa,# Minoru Sakurai,∇ and Shigenori Tanaka‡,O Department of Chemistry and Research Center for Smart Molecules, Faculty of Science, Rikkyo UniVersity, 3-34-1 Nishi-ikebukuro, Toshima-ku, Tokyo 171-8501, Japan, CREST, Japan Science and Technology Agency, 4-1-8 Honcho, Kawaguchi, Saitama 332-0012, Japan, DiVision of Safety Information on Drugs, Food, and Chemicals, National Institute of Health Sciences, 1-18-1 Kamiyoga, Setagaya-ku, Tokyo 158-8501, Japan, Computational Science Department, Science & Technology Systems DiVision, Ryoka Systems, Inc., 1-28-38 Shinkawa, Chuo-ku, Tokyo 104-0033, Japan, Mizuho Information and Research Institute, Inc., 2-3 Kanda Nishiki-cho, Chiyoda-ku, Tokyo 101-8443, Japan, CEID, Gifu UniVersity, 1-1 Yanagido, Gifu 501-1194, Japan, Center for Biological Resources and Informatics, Tokyo Institute of Technology, B-62 4259 Nagatsuta-cho, Midori-ku, Yokohama 226-8501, Japan, and Graduate School of Human DeVelopment and EnVironment, Kobe UniVersity, 1-1 Rokkodai, Nada-ku, Kobe 657-8501, Japan ReceiVed: September 13, 2008; ReVised Manuscript ReceiVed: NoVember 17, 2008

We have performed a series of fragment molecular orbital (FMO) calculations for a family of red fluorescent proteins, DsRed and mFruits. The electronic transition energies were evaluated by the method of configuration interaction singles with perturbative doubles [CIS(D)] including higher-order corrections. The calculated values were in good agreement with the corresponding experimental peak values of spectra. Additionally, the chromophore environment was systematically analyzed in terms of the interaction energies between the pigment moiety and neighboring residues. It was theoretically revealed that the electrostatic interactions play a dominant role in the DsRed chromophore, whereas the color tunings in mFruits are controlled in a more delicate fashion. 1. Introduction From Tsien’s pioneering work1 on the green fluorescent protein (GFP) derived from Aequorea Victoria jellyfish, GFPlike photofunctional proteins with different colors have been developed in diverse ways as useful fluorescent markers in the field of bioengineering. One such protein is red fluorescent protein (RFP), which was first isolated by Matz et al.2 from Discosoma coral and then by Tsien’s group.3,4 Its characteristic excitation and emission energy peaks are 558 nm (2.22 eV) and 583 nm (2.13 eV), respectively.2,3 This RFP has thus been called drFP583 or DsRed. Extensive experimental studies have been conducted on DsRed2-15 and derived mutants,16-22 as summarized below. The crucial pigment of DsRed is the deprotonated p-hydroxybenzylideneimidazolinone moiety, which is autocatalytically formed from the three residues of Gln66-Tyr67-Gly68 through slow maturation.4-6,9-12 Gross et al.4 discussed that the energetic shift from green to red is attributable to the elongated π conjugation with an oxidized peptide bond toward Phe65, and they examined this consideration by using time-dependent density functional theory (TDDFT)23,24 for several model * To whom correspondence should be addressed. Address: Department of Chemistry, Faculty of Science, Rikkyo University, 3-34-1 Nishiikebukuro, Toshima-ku, Tokyo 171-8501, Japan. Tel.: +81-3-3985-2407. Fax: +81-3-3985-2407. E-mail: [email protected]. † Rikkyo University. ‡ Japan Science and Technology Agency. § National Institute of Health Sciences. | Ryoka Systems, Inc. ⊥ Mizuho Information and Research Institute, Inc. # Gifu University. ∇ Tokyo Institute of Technology. O Kobe University.

pigments. Meanwhile, Boye´ et al.14,15 measured the gas-phase absorption spectra for several model pigments, denoted GFP, RFP(1), and RFP(2), whose conjugation lengths are gradually elongated, based on their heavy-ion-storage technique [electrostatic ion storage ring at Aarhus (ELISA)]. Their observed results were consistent with the discussion by Gross et al.4 The importance of electrostatic interaction between the anionic pigment and its neighboring charged residues was pointed out by Yarbrough et al.,5 who analyzed the X-ray structure, particularly addressing the roles of Lys163 and Glu215. Habuchi et al.7,8 reported that the coplanar cis configuration of the pigment is converted to the trans configuration (or super-red form) by high irradiation of light and also that this change is associated with a considerable deformation of the chromophore structure by the decarboxylation of Glu215. DsRed is known to be a tetramer protein, with each monomer having the form of a β-barrel in which the pigment is located at the center of barrel.1,2,5,10-13 Although the effect of tetramerization on electronic transition energies is small, as expected from the central position of the pigment,11 such oligomer formation is not favorable in actual applications to living cells. To overcome this deficiency, Tsien and co-workers developed a monomeric DsRed, mRFP1,16 and also a second series of mutants, mFruits17,18 (“m” meaning “monomeric”). The mFruits proteins yield a variety of colorful emissions named after edible fruits, and therefore, they have names such as mCherry.17 Shu et al.18 determined X-ray structures of mCherry, mStrawberry, and mOrange and presented speculative discussions on the environmental differences of the chromophore. The artificial mutations in these three mFruits involve not only the pigment part but also the neighboring residues. The Tyr67-Gly68 part that forms the π-conjugated system of the pigment is retained

10.1021/jp808151c CCC: $40.75  2009 American Chemical Society Published on Web 01/07/2009

1154 J. Phys. Chem. B, Vol. 113, No. 4, 2009

Figure 1. Chemical structures of the pigments for mCherry and mStrawberry.

as in the progenitor DsRed, but the terminal Gln66 is replaced by Met in mCherry and by Thr in mStrawberry and mOrange.17,18 Figure 1 depicts the chemical structures of the pigments for mCherry and mStrawberry. In mOrange, the oxidized peptide bond is altered by making a five-membered ring with Thr66 during an additional maturation and some apparent structural modification by covalent bonding is thus caused.18 Whereas Lys163 in DsRed should play a primary role in electrostatically stabilizing the anionic pigment, it is replaced by Gln in mCherry and by Met in mStrawberry and mOrange.18 Glu215 is kept negatively charged (or deprotonated) in DsRed, but it is neutralized (protonated at high pH) in mCherry and mStrawberry, where the attached proton position directed toward the nitrogen atom in the imidazolinone ring is of special interest in the formation of hydrogen bonds.18 Battad et al.21 and Hendix et al.22 also discussed the key role of Glu215. The different chromophores in these three mFruits from DsRed5 yield shifted excitation (emission) energies. The peak values in spectra are 2.11 (2.03) eV for mCherry, 2.16 (2.08) eV for mStrawberry, and 2.26 (2.21) eV for mOrange.17,18 The quantum yield of mCherry, used most popularly, is lower than that of DsRed,17-20 in accord with some distortion in the coplanarity of the pigment.18 Several quantum mechanical (QM) studies have been conducted with fluorescent proteins. For GFP, Olivucci’s group25-27 reported calculations at the complete-active-space self-consistentfield (CASSCF)28 and second-order perturbation correction (CASPT2) levels,29 taking the protein environment into account in a hybrid manner with classical molecular mechanics (MM), denoted as the so-called QM/MM approach. Rubio et al. applied TDDFT-QM/MM calculations to GFP30 and also to the blue mutant31 and compared the simulated photoabsorption cross sections with the experimental spectra. GFP was also investigated by Nakatsuji and co-workers,32,33 who used the original excited states method of symmetry-adapted cluster and configuration interactions (SAC-CI)34 in combination with QM/MM. Both excitation and emission energies have been evaluated in SAC-CI calculations for yellow, blue, and cyan mutants,1 as well as for GFP.33 Olsen et al.35 examined the charge states and cis/trans configurations of the Rtms5 pigment, which is essentially the same as RFP, through TDDFT calculations on the modeled molecules. Olsen and Smith36 performed extensive CASSCF and multireference second-order perturbation (MRPT2) calculations37 on an anionic RFP model pigment, in order to analyze the photoisomerization pathways. Then, we performed the first full QM treatment of the DsRed monomer,38 based on the fragment molecular orbital (FMO) scheme.39,40 In this predecessor of the present article, the transition energies were obtained by the calculations at the configuration interaction singles (CIS)41 and perturbative doubles [CIS(D)]42 levels under

Taguchi et al. the multilayer variant of FMO43,44 implemented in our original FMO program.45-51 Nifosı´ et al.52 made a systematic TDDFT investigation of the pigment variations of various GFP mutants, and Timerghazin et al.53 recently carried out a series of TDDFT, CIS, CIS(D), and CASSCF calculations along the same lines. Through past theoretical studies,5,25-27,32,33,35,36,38,52,53 the excited state, which is responsible for the principal photoabsorption/ emission of GFP, RFP, and related mutants, has been well characterized by a single-electron transition between the highest occupied MO (HOMO) and the lowest unoccupied MO (LUMO) or a valence ππ* transition with a large oscillator strength. In the present article, we evaluate the excitation energies of three mFruits proteins whose X-ray structures are available,18 namely, mCherry, mStrawberry, and mOrange, employing multilayer FMO-based43,44 CIS50 and CIS(D)51 calculations as in our previous report on DsRed.38 Some modified CIS(D) corrections54 were employed here to obtain good correspondences with the experimental data within an error of 0.1 eV. The biochemical conditions of the chromophore are furthermore analyzed in terms of the interaction energies between the pigment moiety and the neighboring residues, by comparing DsRed and these three mFruits. These comparative analyses are informative in understanding the delicate color tuning mechanisms. To the authors’ knowledge, the present theoretical investigation is the first attempt to treat entire mFruits proteins in a full QM manner. The remaining parts of this article are organized as follows. In section 2, we briefly introduce the FMO methodologies and also our program for later convenience. The details of the computational procedures are also described in this section. The results for DsRed are first given in section 3, demonstrating the improvement over the previous results38 through the modified CIS(D) approach.54 The results for mCherry, mStrawberry, and mOrange are then presented on the same footing as those for DsRed, and the differences in chromophore environment are discussed. 2. Theoretical Calculations 2.1. FMO Methodology. The QM/MM approach has been a practical recipe for treating the active regions of large-scale systems, as just employed for photoactive proteins.26,27,30,31,33 Although the MM technique makes the inclusion of environmental effects feasible, many force-field (FF) parameters must be empirically adjusted to reproduce various experimental quantities. The parameter set for hydrogen bonding, which should play a crucial role in proteins, has unfortunately not yet been established. The flexibility in descriptions of local polarization and electron delocalization are still limited, as well. These difficulties in the MM scheme should lead to an inherent ambiguity in QM/MM calculations, even if highly correlated QM methods were applied to the active regions of the proteins, i.e., the chromophores. Thus, full QM treatments would be desirable to provide cross-reference data for QM/MM results. The FMO scheme proposed by Kitaura et al.39,40 is a promising approach to enable full QM calculations of proteins. In the two-body FMO scheme for the ground state of a given system, a series of Hartree-Fock (HF) calculations is performed for the fragment monomers and dimers under the environmental electrostatic potential (ESP), which is essential to ensure chemical reliability.46 The introduction of bond-detachment atoms (BDAs) with projection techniques is another key point, by which no artificial hydrogen capping is needed for the fragmentations.45 In these ways, both local polarization and electron delocalization can be incorporated at the FMO-HF level. The electron correlation energies are straightforwardly corrected

Fragment MO Calculations on Red Fluorescent Proteins for the respective monomers and dimers through the secondorder Møller-Plesset perturbation (MP2) theory with size consistency.55 There have been two major programs for FMO calculations. One is the GAMESS program56 whose various MO methods have been continuously adapted by Fedorov et al. through extensive modifications: the first adaption for FMOHF57 and the second for FMO-MP2.58 Another is our ABINITMP program, which was originally developed by Nakano et al.45,46 for FMO-HF calculations. FMO-MP2 ability has been augmented by Mochizuki et al., on the basis of efficient integraldirect parallelism.47-49 From the nature of FMO, well-defined fragmentwise interaction energies are naturally obtained, which are useful to grasp insightful pictures of proteins. These quantities for analysis purposes are called interfragment interaction energies (IFIEs) in ABNINT-MP59,60 and pair interaction energies (PIEs) in GAMESS.61 The IFIE/PIE values at the HF level are obtained by using the differential density matrix and ESP matrix, and the MP2 correlation energies can be corrected in an additive manner.59-61 Additionally, an orbitalwise picture of site-specific dispersionlike interactions can be obtained through the local MP262 calculations by our program, as a tool of fragment interaction analysis based on local MP2 (FILM).63,64 Under the multilayer FMO framework,43,44 we made parallelized integral-direct implementations for CIS41 calculations50 and then for CIS(D)42 calculations.51 In these calculations, the FMO-HF procedure was first carried out to determine the ESP distributions of whole protein, and then layer 2, or the chromophore containing the pigment and also some important residues, was subjected to CIS and CIS(D) calculations. Although the corresponding procedures were previously called MLFMO-CIS and MLFMO-CIS(D),38,50,51 we use the alternative notations FMO-HF:CIS and FMO-HF:CIS(D) in the present article, in accordance with Fedorov et al.43,44 It is well-known that typical overestimations of 1-2 eV in CIS excitation energies41 can be remedied by the size-consistent CIS(D) correction,42 which consists of both the orbital relaxation energy in a given excited state and the differential correlation energy from the ground state correlated at the MP2 level. Such a remediation by CIS(D) was demonstrated previously for DsRed.38 Head-Gordon et al.42 showed that the CIS(D) method can be considered as a noniterative second-order approximation of coupled-cluster excited-state method. Mochizuki et al.54 proposed some CIS(D) modifications in which a partial renormalization (PR) of MP2 doubles amplitudes65 (related to the differential correlation energy) and an extra inclusion of MP2 singles66,67 differential relaxation energy (s) are involved, and thus the combined version is denoted as PR-CIS(Ds). Furthermore, the self-energy55,66,67 shift (SS) was utilized to modify the relaxation energy through a sort of renormalization, providing CIS(D)SS.68 Some higher-order correlations can be effectively incorporated into these modified CIS(D) corrections,54,68 by keeping the fifth-power scaling of computational cost as in the original CIS(D).42 FMO-HF:CIS and FMO-HF:CIS(D) calculations (with/without modifications) are now available in an extended version of ABINIT-MP, recently designated as ABINIT-MPX. It would be fair to note that the ability to perform FMO-based TDDFT calculations has been provided by Chiba et al.69-71 in the GAMESS program, where countermeasures for the notorious issue of spurious charge-transfer states72 was taken. Several reviews73-75 of FMO methodologies and related applications have been published. A variety of calculations of realistic proteins and other large molecular systems were

J. Phys. Chem. B, Vol. 113, No. 4, 2009 1155

Figure 2. Graphic representations of DsRed (first monomer chain of 1ZGO). The pigment moiety located at the center of the β-barrel is shown in yellow.

exhaustively addressed in these documents. The interested reader can learn more about FMO methods through such examples. 2.2. Computational Procedures. We again used the molecular geometry data of DsRed that were prepared in the previous investigation of DsRed.38 For convenience, the preparations are denoted here. The fundamental structure of 1ZGO9 was downloaded from the Protein Data Bank (PDB) server76 for the estimation of excitation energies. The first monomer chain was extracted from this tetramer set, based on the fact that the shift of peak positions between the tetramer and monomer is known to be small.11 From Figure 2, the central location of the pigment in the β-barrel wall1,2,5,10-13 can be seen. The combination of the Molecular Operating Environment (MOE)77 and the FF set of AMBER78 (version 99) was employed to attach the hydrogen atoms and relax their positions appropriately. Two water molecules were retained in the chromophore. The geometrical adequacy of the crucial pigment part was precisely verified by comparison with a model pigment (Model B introduced by Boye´ et al.15) whose structure was separately optimized by the MP2/6-31G* procedure with the Gaussian program.79,80 The good coplanarity between the p-hydroxybenzyl (six-membered) block and the imidazolinone (five-membered) block as a result of π conjugation was also confirmed by this comparison. The numbers of spatial nodes on the crucial conjugation plane were found to be five for the HOMO (π) and six for the LUMO (π*), as shown in Figure 3. The bond elongation could thus be induced in the ππ* excited state. To estimate the energy of photoemission from the excited state, we prepared the 1ZGO(EX) structure in which the CIS/631G*-optimized geometry32,79,80 for the ππ* state of Model B15 was imported. By measuring two torsion angles of twisting and tilting from the X-ray structures, Shu et al.18 found that, in contrast to the case for DsRed,5 the coplanarity of the parts of the pigments in the three mFruits (mCherry, mStrawberry, and mOrange) is deformed by some distortions of the chromophore cavity. They also pointed out that smaller deformation lead to higher quantum yields of emission, e.g., 0.79 for DsRed versus 0.22 for mCherry. The quantitative evaluation of emission energies for mFruits would be desirable if possible, including the differences in quantum yield from that of DsRed. However, the simple insertion technique of the CIS-optimized pigment model should not be adopted unlike for the case of DsRed,38 because the

1156 J. Phys. Chem. B, Vol. 113, No. 4, 2009

Figure 3. Graphic representations of (top) HOMO (π-type) and (bottom) LUMO (π*-type) in DsRed pigment. The fundamental structure was taken from the 1ZGO data set, and then two dangling bonds to the peptide chain were terminated with a methyl group. The HF/6-31G* procedure was used for this figure. Orbital phases are colored in red and green.

structural deformation of the chromophore in the excited states could be more delicate and complicated for the mFruits. Such a difficulty might be partly solved by QM/MM-type geometry optimizations, but both the definition of the QM part and the proper FF parametrization could be other demanding tasks. Thus, we decided to evaluate only the excitation energies for mCherry, mStrawberry, and mOrange17,18 and discuss the environmental differences of the chromophore from the viewpoint of color tuning, as the first step toward tackling the problems of these mFruits proteins. The corresponding PDB76 data sets of 2H5Q, 2H5P, and 2H5O were cast into the standard molecular modeling procedures as in the case of DsRed.38 For the mOrange data set of 2H5O, Shu et al.18 claimed that there was a possibility of uncertainty in the X-ray structure, because unusual bond modifications through additional maturations could be incomplete for the formation of the five-membered ring related to Phe65 and Thr66 and the crystal could statistically contain both reacted and unreacted samples as a consequence. On the basis of the experimental data on structure and pH dependence,18 it was speculated that the hydrogen-bonding networks involving the chromophore could be relatively more important in color tuning for mFruits than for DsRed.5 All water molecules within 5.5 Å of the pigment moiety were thus preserved, where the numbers of corresponding water molecules for mCherry, mStrawberry, and mOrange were 11, 8, and 10, respectively. In the modeling of mCherry from 2H5Q, we took an extra manipulation that the geometries of Glu215 and some important water molecules were optimized by Gaussian at the MP2/631G* level79,80 and then carefully imported. This care was needed for the special situation of mCherry where the attached proton of Glu215 should be crucial in the color tuning through hydrogen bonding to the nitrogen atom in the imidazolinone ring yielding π conjugation.18,22 Nevertheless, the state of Glu215 has been of interest from the experimental side,18,21,22 and all possible cases were considered in our calculations for mCherry, mStrawberry, and mOrange.

Taguchi et al. We employed the PR-CIS(Ds) method54 to obtain the ππ* transition energy of the pigment more accurately than by the original CIS(D) method.42 Before the calculations on the mFruits,18 the improvement due to higher-order corrections in PR-CIS(Ds) was examined for the two free pigment models RFP(1) and RFP(2),14,15 as well as for DsRed.38 The 6-31G* basis set55,80 was used throughout, because the use of such a polarized double-ζ set is a reasonable option for describing the lowest ππ* states of GFP-derived pigments.25-27,32,33,36,38 The total number of 6-31G* basis functions was more than 30000 for both DsRed and the mFruits. The frozen-core restriction was imposed in correlated treatments. As in the previous investigation of DsRed,38 three ways of setting layer 2 were tried for the FMO-HF:CIS(D)-type calculations.51,54 Letting X be the pigment consisting of the essential 66-68 residues, these three layer-2 settings are labeled X (pigment only), F+X (adding Phe65), and F+X+S (also adding Ser69). Both the oxidized peptide bond to Phe65 and the regular peptide bond to Ser69 were included in the X region because the fragmentation should be properly made at the sp3 carbon atom as the bond-detachment atom (BDA).45 Each residue was treated as the fragment monomer (as well as water molecule), except for layer 2. The total number of fragments was 220 for the DsRed case of X setting. All FMO calculations were carried out using the ABINIX-MPX program mainly on an in-house computer cluster equipped with 16 cores of Intel Core 2 Duo (2.93 GHz, 4GB/ core). We note here as a typical timing that the FMO-HF:PRCIS(Ds)/6-31G* job with the largest F+X+S setting could be completed with 3.0 days for an mFruits protein, indicating the practical applicability of our FMO-based method to photoactive proteins. We separately performed a series of FMO-MP2/6-31G* calculations,47-49 in order to analyze the chemical environments of the chromophore in terms of IFIE quantities.59,60 Then, the simple setting of X was adopted for convenience of analysis. Negative and positive IFIE values indicate stabilization and destabilization interactions, respectively. The IFIE analyses revealed the interesting difference that the pigment-residue interactions were electrostatically characterized for DsRed5,38 whereas they were controlled in more delicate ways for mFruits.18 To illuminate the local dispersion-type interactions, the recently developed FILM technique63,64 was also applied to mCherry. 3. Results and Discussion 3.1. DsRed. Before addressing the FMO-HF:PR-CIS(Ds) results for DsRed, we first verify the improved accuracy by the PR-CIS(Ds) treatment for the anionic RFP(1) and RFP(2) models whose excitation energy peaks were measured by Boye´ et al. in ELISA experiments.14,15 The formal length of π conjugation in RFP(2) is equivalent to that of the wild-type DsRed, but the oxidized peptide bond is replaced by the usual carbon-carbon double bond (see Boye´ et al.’s original paper15). Table 1 lists the excitation energies of RFP(1) and RFP(2), where the CIS and CIS(D) values are the same as those found in our previous report.38 It can be immediately seen that the PR-CIS(Ds) treatment provides better values than does the unmodified CIS(D). In other words, the higher-order correlations from the partial renormalization of the MP2 doubles amplitudes and the inclusion of the MP2 singles contribution54 are shown to be effective in fine improvements. In particular, a close correspondence between the calculated energy (2.29 eV) and the experimental value (2.26 eV) for RFP(2) is favorable, with a good correspondence also expected for the real DsRed from the previous discussions with free pigment models.38

Fragment MO Calculations on Red Fluorescent Proteins

J. Phys. Chem. B, Vol. 113, No. 4, 2009 1157

TABLE 1: Excitation Energies (eV) of RFP(1) and RFP(2) Model Pigments Obtained by Various Methods Such as CIS, CIS(D), and CIS(Ds) with and without Partial Renormalization (PR)a without PR RFP(1) RFP(2)

with PR

without PR

CIS

CIS(D)

CIS(Ds)

CIS(D)

CIS(Ds)

expt

3.49 3.18

2.62 2.42

2.65 2.43

2.49 2.28

2.53 2.29

2.38 2.26

a

Experimental values obtained by Boye´ et al. with ELISA experiments.14,15 Molecular geometries optimized by the MP2/ 6-31G* procedure (see also our previous report38). Computational excitation energies evaluated with the 6-31G* basis set.

TABLE 2: Excitation and Emission Energies (eV) of DsRed Obtained by Various Methods Such as CIS, CIS(D), and CIS(Ds) with and without Partial Renormalization (PR)a without PR CIS

CIS(D)

X F+X F+X+S expt

3.35 3.27 3.26

2.49 2.30 2.28

X F+X F+X+S expt

3.25 3.20 3.18

2.41 2.21 2.21

TABLE 3: Excitation Energies (eV) of mCherry, mStrawberry, and mOrange Obtained by Various Methods Such as CIS, CIS(D), and CIS(Ds) with and without Partial Renormalization (PR)a

CIS(Ds)

CIS

CIS(D)

X F+X F+X+S expt

3.32 3.19 3.24

2.40 2.22 2.27

X F+X F+X+S expt X F+X F+X+S expt

CIS(D)

CIS(Ds)

Excitation 2.54 2.37 2.34

2.36 2.18 2.16

2.41 2.24 2.22 2.22

Emission 2.45 2.27 2.26

2.28 2.09 2.09

2.32 2.15 2.14 2.13

a Experimental values correspond to the peak value (or the so-called λmax) of observed spectra.2,3 Three types of the layer 2 settings are labeled X, F+X, and F+X+S (see section 2.2). Computational excitation (and emission) energies were evaluated with the 6-31G* basis set.

Table 2 compiles the series of calculated results from FMOHF:CIS to FMO-HF:PR-CIS(Ds) calculations for both excitation and emission energies, compared with the experimental peak values.2,3 As expected, the PR-CIS(Ds) calculations yield better results than does CIS(D)38 for all three settings of layer 2. The smallest setting of X is shown to be not sufficient in evaluating the excitation energy even with the higher contributions.54 This indicates that the associated relaxation of phenyl electrons in Phe65 is substantial: recall that Phe65 commits the oxidized peptide bond as the conjugation tail of DsRed.4 Consistently, the F+X results are much better than the X values. The proper reservation of the margin, by which the orbital relaxations associated with the excitation in the pigment moiety are taken into account, is essential to make quantitative estimations through the multilayer-type calculations of the FMO scheme.38,51,69,70,81 Now, it is remarkable that the error of about 0.1 eV remaining in the best CIS(D) value with the largest F+X+S setting38 is reduced to almost zero at the PR-CIS(Ds) level, and the Stokes shift is well estimated. That is, the best results for the excitation and emission energies were obtained as 2.22 and 2.14 eV, respectively, at the FMO-HF:PR-CIS(Ds)/6-31G* level. These values are almost perfectly coincident with the experimental values of 2.22 and 2.13 eV,2,3 indicating not only the validity of the modeled 1ZGO and 1ZGO(EX) structures38 but also the reliability of our FMO-HF:PR-CIS(Ds) approach including higher-order corrections.51,54 Although the empirical FF parameters were used at the molecular modeling stage, this satisfactory agreement between theory and experiment could demonstrate the promising power of excited-state calculations based on the FMO scheme where no empirically adjusted parameters were

with PR CIS(D)

CIS(Ds)

mCherry 2.44 2.26 2.31

2.27 2.09 2.13

2.31 2.13 2.18 2.11

3.13 3.01 3.04

mStrawberry 2.32 2.37 2.20 2.25 2.22 2.27

2.17 2.05 2.07

2.22 2.10 2.12 2.16

3.56 3.47 3.48

2.66 2.54 2.56

mOrange 2.68 2.56 2.58

2.53 2.41 2.43

2.55 2.43 2.45 2.26

with PR

CIS(Ds)

a Experimental values correspond to the peak values (or the so-called λmax) of observed spectra.17,18 Three types of the layer 2 settings are labeled X, F+X, and F+X+S (see section 2.2). Computational excitation energies were evaluated with the 6-31G* basis set. For mCherry and mStrawberry, Glu215 was protonated, and the attached proton was directed toward the nitrogen atom in the imidazolinone ring for hydrogen bonding. In contrast, Glu215 was kept deprotonated for mOrange. See ref 18.

involved to capture the electronic effects of the protein environment. There has been another demonstrative example of our approach for a photoactive protein having a pigment with a different chemical structure. Very recently, Tagami et al.82 performed a series of FMO-HF:PR-CIS(Ds) calculations51,54 to evaluate the transition energies of firefly bioluminescence. In that investigation of the firefly luciferin-luciferase system, the whole protein consisting of as many as 539 residues was treated after careful molecular modeling. Then, the difference in luminescence colors between the wild-type (yellowish green) and the I288A mutant (red) luciferases was successfully explained. For the excitation energy of DsRed,2,3 we made additional test calculations of a new FMO-HF:PR-CIS(D)SS(2) method for the purpose of cross-checking, where the second-order selfenergy shift [subscripted as SS(2)] was introduced into the denominator of the energy expression for the orbital relaxation energy68 and also the partial renormalization of MP2 doubles was used for the differential correlation energy.54 The results obtained with the F+X and F+X+S settings were 2.25 and 2.22 eV, respectively. These values are comparable to the corresponding values for PR-CIS(Ds) in Table 2. A small but vital role of higher-order correlations in the modified CIS(D) approach54,68 is again exemplified. 3.2. mFruits. The excitation energies calculated for the mFruits are listed in Table 3, where Glu215 was made protonated for mCherry and mStrawberry (the proton was directed toward the nitrogen atom of the imidazolinone ring) but it was kept deprotonated for mOrange according to Shu et al.’s speculation.18 As in the case of DsRed, we obtained the best overall results at the PR-CIS(Ds) level.54 The error relative to the experimental peak energies was maintained as less than 0.1 eV for mCherry and mStrawberry with the F+X and F+X+S settings. Unfortunately, the correspondence between calculation and experiment was less satisfactory for mOrange.

1158 J. Phys. Chem. B, Vol. 113, No. 4, 2009

Taguchi et al.

TABLE 4: Dependence of Excitation Energy (eV) on Condition of Glu215a mCherry mStrawberry mOrange

TABLE 5: IFIE Values (kcal/mol) from FMO-MP2/6-31G* Calculations for DsRed, mCherry, and mStrawberrya

case i

case ii

case iii

expt

2.18* 2.12* 2.44

2.27 2.15 2.43

2.33 2.18 2.45*

2.11 2.16 2.26

a Computational excitation energies were evaluated with the 6-31G* basis set. Only the PR-CIS(Ds) results of the F+X+S setting are compiled here for simplicity. Three possible cases of Glu215 are as follows: (i) attached proton directed toward the nitrogen atom in the imidazolinone ring, (ii) attached proton directed away from the imidazolinone side, (iii) residue deprotonated or kept negatively charged (see ref 18 for details). Asterisk symbols specify the selected values in Table 3 (refer also to footnote a).

Figure 4. Geometrical configuration of the pigment and protonated Glu215 in mCherry. The attached proton is directed toward the nitrogen atom in the imidazolinone ring for hydrogen bonding.

The probable reason for this disagreement is the uncertainty remaining in the X-ray structure of mOrange,38 as mentioned in the previous section. If better X-ray structures were available for mOrange, the computational results could be improved. As repeatedly mentioned, the charge state and the associated proton position of Glu215 have attracted considerable interest.18,21,22 There are three possible cases: (i) attached proton directed toward the nitrogen atom of the imidazolinone ring (mCherry and mStrawberry in Table 3), (ii) attached proton directed away from the imidazolinone side, and (iii) residue deprotonated or kept negatively charged (mOrange). Table 4 compiles the corresponding results calculated with the F+X+S setting. For mCherry, Shu et al.18 speculated the existence of hydrogen bonding between the attached proton of Glu215 and the nitrogen atom of imidazoline. This speculation for mCherry was confirmed by our calculations, as the value for case i is clearly better than that for case ii in Table 4 and case iii is unlikely because of its too-high excitation energy (2.33 eV). Figure 4 illustrates the geometrical configuration of the mCherry pigment and the protonated Glu215 for case i, where a deformed coplanarity of the pigment is also visible. Absolutely, Glu215 should play a key role in the color tuning of mCherry. Shu et al.18 denoted the coexistence of case ii for mStrawberry, from the observed disorder of Glu215 in the electron-density map obtained by X-ray experiments. The similar values obtained in cases i and ii for mStrawberry are consistent with such an experimental argument as well. It is interesting to note that the difference between the protonated and deprotonated cases is small for mOrange, suggesting that the role of Glu215 is rather minor. Table 5 summarizes the IFIE values59,60 with the FMO-MP2 calculations47-49 for DsRed, mCherry, and mStrawberry. In this

83 IFIE 153 IFIE 163 IFIE 196 IFIE 215 IFIE

DsRed

mCherry

mStrawberry

Lys (+) -30.3 Arg (+) -15.8 Lys (+) -85.7 Asp (-) 32.2 Glu (-) 49.9

Met -0.5 Glu (-) 15.7 Gln -9.8 Asn 2.9 Glu (0) -13.2

Met -0.5 Glu (-) 15.2 Met -1.7 Gly 2.1 Glu (0) -14.0

a

Five representative residue positions are compiled here, with the respective mutation and charge state indicated.

table, five representative residue positions are selected to illuminate the clear differences between DsRed and mFruits. Experimental discussions about the mutations in mFruits17,18 are justified by the IFIE results in Table 5. The electrostatic interactions should dominate the electronic character of the chromophore in DsRed.5,38 On the contrary, the role of electrostatic interactions is suppressed by the absence of positively charged Lys163 (as the outstanding contributor38) and the protonation of Glu215 in mCherry and mStrawberry, except for Lys70, Arg95, and Glu148 kept unchanged as in DsRed.17,18 Shu et al.38 suggested that the loss of Lys163 affects the hydrogen-bonding opportunities in the chromophore. The mutation from Arg153 (DsRed) to Glu153 (mFruits) is also associated with the change of direction from stabilization to destabilization, providing an additional contribution. To guess the environmental shifts in excitation energies of DsRed, mCherry, and mStrawberry, we made trial calculations with the following steps: First, the pigment part was extracted from each PDB data set,9,18,76 and the resulting two dangling bonds to peptide chains (sR1 and sR2 in Figure 1) were terminated by adding a sCH3 group; this procedure was adopted also for Figure 3. Second, the geometries of all hydrogen atoms and the two methyl groups added were optimized with the MP2/6-31G* procedure,79,80 by fixing the fundamental structure of the pigment. Third, the PRCIS(Ds)/6-31G* calculations were performed on the thusprepared model systems. The excitation energies of 1.97, 2.03, and 2.05 eV were then obtained for these models of DsRed, mCherry, and mStrawberry, respectively, which are lower than the actually observed values of 2.22 eV (DsRed),2,3 2.11 eV (mCherry), and 2.16 eV (mStrawberry).17,18 As a result, the blue shift was guessed as the energetic shift due to the protein environment. Clearly, such an environmental shift is incorporated into the FMO calculations in a full QM manner, and good agreement with the experimental energies was achieved, as seen in Tables 2 and 3. It is notable that the amount of shift for DsRed is much larger than the amounts for the two mFruits proteins, being in accord with the electrostatics-driven nature of DsRed.5,38 Meanwhile, the environment of the mFruits chromophore is considered to be more delicate. Next, the differences in the three mFruits chromophores are discussed. The MP2 IFIE results for seven residue positions are plotted in Figure 5. The contribution from positively charged Lys70 (kept as in DsRed17,18) is larger for mOrange than for mCherry and mStrawberry. Note here that Arg95 also has a stabilization contribution, but the amounts are almost the same for the three mFruits; the plot is thus omitted in Figure 5 for simplicity. As expected, the contributions from the protonated or neutralized Glu215 are different between mCherry/mStrawberry and mOrange. Other qualitative differences are found in

Fragment MO Calculations on Red Fluorescent Proteins

Figure 5. Plots of IFIE (kcal/mol) between the pigment and residues with FMO-MP2/6-31G* calculations for mCherry, mStrawberry, and mOrange. Seven representative residue positions are presented.

J. Phys. Chem. B, Vol. 113, No. 4, 2009 1159 formational fluctuation of proteins in realistic conditions at finite temperatures. The method of classical molecular dynamics (MD) simulations (with FF parameters) could be a straightforward option to sample a series of fluctuating conformations. Yamato et al.84,85 reported a statistical estimate for the excitation energy of photoactive yellow protein (PYP),86 by averaging 10 MDgenerated conformations. A hybrid approach of coupled-cluster equation-of-motion (EOMCC)87 and MD sampling was applied to the cytosine moiety in a model DNA, in order to obtain the average values of ππ* and nπ* excitation energies.88 Recently, the utilization of MD simulations for FMO calculations was started in our research group.81,82,89,90 Such MD-based techniques could be used to manage multiple structure samples of DsRed and mFruits, as long as a rich resource for simulations is provided. A sufficient number of samples could then produce the distributions of excitation energies, resembling the actual spectral shapes observed experimentally.81 If proper parameter sets for excited states were available, a systematic estimation of emission energies of mFruits as a currently demanding task would also be tractable. Another issue to be addressed is the hydration effect, which was omitted in our calculations. For PYP,86 Chiba et el.71 assessed the shift in excitation energy due to hydration by using FMO/TDDFT calculations with the polarizable continuum model (PCM).91 They obtained an energy shift of 0.1 eV as the result of the assessment. By considering the situation in which the pigment of PYP was located at a relatively outer region of the protein structure,50,51,71,84-86 smaller amount of shifts could be expected for DsRed and mFruits in which the pigment is placed at the center of the β-barrel.1,2,5,10-13 We posit that modeling with explicit water molecules92,93 would be straightforward if the hydration effect was examined in conjunction with conformational fluctuations through MD simulations. 4. Conclusions

Figure 6. Graphical representations of two localized orbital pairs in FILM calculations with the 6-31G* basis set. These pairs concern CH/π interactions between the pigment and Pro63 in mCherry. Each pair gains -0.2 kcal/mol as the leading stabilization, where the net stabilization is -5.0 kcal/mol by FILM and is slightly smaller than -6.2 kcal/mol by the usual MP2 calculation; the chemical discussion is unchanged. Orbital phases are colored in red (yellow) and blue (green) for the π-conjugated p-hydroxybenzylidene part of the pigment (C-H bond of Pro63).

positions 163, 174, and 214. Pro63 and Ser146 should provide stabilization due to dispersion-type interactions with the pigment part. Particularly, the so-called CH/π type interaction83 is expected to be a principal source of stabilization. The FILM technique63,64 is convenient for grasping the local orbitalwise picture of CH/π attractive interactions. Figure 6 demonstrates two orbital pairs that gain the leading stabilization energies for mCherry; see the figure caption for details. The corresponding localized orbital pairs are visible between a CsH bond of Pro63 and the p-hydroxybenzylidene part of pigment. Shu et al.18 argued that the chromophore situation is substantially more hydrophobic in mFruits than in DsRed, and their argument has now been supported by our analyses through FMO calculations. Finally, we address a fundamental issue related to future investigations of DsRed and mFruits. This concerns the con-

In this work, we applied FMO-HF:PR-CIS(Ds) calculations51,54 to DsRed2,3 and three mFruits mutants, namely, mCherry, mStrawberry, and mOrange.17,18 For DsRed, the best excitation and emission energies estimated with the F+X+S setting were 2.22 and 2.14 eV, respectively, satisfactorily reproducing the corresponding experimental values of 2.22 and 2.13 eV.2,3 The excitation energy was evaluated to be 2.18 eV for mCherry, where the protonated Glu215 with a hydrogen bond to the imidazolinone ring was found to be essential to obtain a close agreement with the experimental excitation energy of 2.11 eV.17,18 A reasonable excitation energy was obtained also for mStrawberry: 2.12 eV (our calculation) versus 2.16 eV (experiment17,18). A relatively large error of 0.2 eV remained for the case of mOrange unfortunately, but it can be attributed to the issue of some uncertainty in the X-ray structure.18 The supplemental IFIE analyses59,60 with FMO-MP2 calculations47-49 revealed the environments of the chromophores in detail. Specifically, it was shown that the DsRed chromophore is characterized well by electrostatic interactions38 whereas the mFruits chromophores are controlled in more delicate ways through hydrogen bonding and dispersion-type interactions. Such differences in color tunings had been speculated experimentally,5,18 and our systematic calculations confirmed them on the basis of quantitative estimates of transition energies. We hope that such FMO-based computational methods can be helpful in developing new fluorescent proteins with several color variations. Acknowledgment. Y.M. and T.N. thank Mr. Katsumi Yamashita for technical contributions to the ABINIT-MPX pro-

1160 J. Phys. Chem. B, Vol. 113, No. 4, 2009 gram. Y.M. and S.T. are also grateful to Dr. Mika Ito for fruitful comments on the manuscript. The work reported here was supported by the CREST project operated by the Japan Science and Technology Agency (JST). Additionally, Y.M. acknowledges a Grant-in-Aid for Scientific Research on Priority Area “Molecular Theory for Real Systems” from the Ministry of Education, Culture, Sports, Science and Technology of Japan (MEXT). References and Notes (1) Tsien, R. J. Annu. ReV. Biochem. 1998, 67, 509–44. (2) Matz, M. V.; Fradkov, A. F.; Labas, Y. A.; Savitsky, A. P.; Zaraisky, A. G.; Markelov, M. L.; Lukyanov, S. A. Nat. Biotechnol. 1999, 17, 969–973. (3) Baird, G. S.; Zacharias, D. A.; Tsien, R. Y. Proc. Natl. Acad. Sci. U.S.A. 2000, 97, 11984–11989. (4) Gross, L. A.; Baird, G. S.; Hoffman, R. C.; Baldridge, K. K.; Tsien, R. Y. Proc. Natl. Acad. Sci. U.S.A. 2000, 97, 11990–11995. (5) Yarbrough, D.; Wachter, R. M.; Kallio, K.; Matz, M. V.; Remington, S. J. Proc. Natl. Acad. Sci. U.S.A. 2001, 98, 462–467. (6) Mizuno, H.; Mal, T. K.; Tong, K. I.; Ando, R.; Furuta, T.; Ikura, M.; Miyazaki, A. Mol. Cell 2003, 12, 1051–1058. (7) Habuchi, S.; Cotlet, M.; Gensch, T.; Bednarz, T.; Harber-Pohlmeier, S.; Rozenski, J.; Dirix, G.; Michiels, J.; Vanderleyden, J.; Heberle, J.; de Schryver, F. C.; Hofkens, J. J. Am. Chem. Soc. 2005, 125, 8977–8984. (8) Loos, D. C.; Habuchi, S.; Flors, C.; Hotta, J.; Wiedenmann, J.; Nienhaus, G. U.; Hofkens, J. J. Am. Chem. Soc. 2006, 128, 6270–6271. (9) Tubbs, J. L.; Tainer, J. A.; Getzoff, E. D. Biochemistry 2005, 12, 1051–1058. (10) Remington, S. J. Curr. Opin. Struct. Biol. 2006, 16, 714–721. (11) Shrestha, S.; Deo, S. K. Anal. Bioanal. Chem. 2006, 386, 515– 524. (12) Strongin, D. E.; Bevis, B.; Khuong, N.; Downing, M. E.; Strack, R. L.; Sundaram, K.; Glick, B. S.; Keenan, R. J. Protein Eng. Des. Sel. 2007, 20, 525–534. (13) Schleifenbaum, F.; Blum, C.; Elgass, K.; Subramaniam, V.; Meixner, A. J. J. Phys. Chem. B 2008, 112, 7669–7674. (14) Boye´, S.; Krogh, H.; Nielsen, I. B.; Nielsen, S. B.; Pedersen, S. U.; Pedersen, U. V.; Andersen, L. H. Phys. ReV. Lett. 2003, 90, 118103-1– 118103-4. (15) Boye´, S.; Nielsen, S. B.; Krogh, H.; Nielsen, I. B.; Pedersen, U. V.; Bell, A. F.; He, X.; Tonge, P. J.; Andersen, L. H. Phys. Chem. Chem. Phys. 2003, 5, 3021–3026. (16) Campbell, R. E.; Tour, O.; Palmer, A. E.; Steinbach, P. A.; Baird, G. S.; Zacharias, D. A.; Tsien, R. Y. Proc. Natl. Acad. Sci. U.S.A. 2002, 99, 7877–7882. (17) Shaner, N. C.; Campbell, R. E.; Steinbach, P. A.; Giepmans, B. N. G.; Palmer, A. E.; Tsien, R. Y. Nat. Biotechnol. 2004, 22, 1567– 1572. (18) Shu, X.; Shaner, N. C.; Yarbrough, C. A.; Tsien, R. Y.; Remington, S. J. Biochem. 2006, 45, 9639–9647. (19) Merzlyak, E. M.; Goedhart, J.; Shcherbo, D.; Bulina, M. E.; Shcheglov, A. S.; Fradkov, A. F.; Gaintzeva, A.; Lukyanov, K. A.; Lukyanov, S.; Gadella, T. W. J.; Chudakov, D. M. Nat. Methods 2007, 4, 555–557. (20) Li, Y.; Sierra, A. M.; Ai, H.-w.; Campbell, R. E. Photochem. Photobiol. 2008, 84, 111–119. (21) Battad, J. M.; Wilmann, P. G.; Olsen, S.; Byres, E.; Smith, S. C.; Dove, S. G.; Turcic, K. N.; Devenish, R. J.; Rossjohn, J.; Prescott, M. J. Mol. Biol. 2007, 368, 998–1010. (22) Hendrix, J.; Flors, C.; Dedecker, P.; Hofkens, J.; Engelborghs, Y. Biophys. J. 2008, 94, 4103–4113. (23) Runge, E.; Gross, E. K. U. Phys. ReV. Lett. 1984, 52, 997–1000. (24) Bauernschmitt, R.; Ahlrichs, R. Chem. Phys. Lett. 1996, 256, 454– 464. (25) Martin, M. E.; Nergi, F.; Olivucci, M. J. Am. Chem. Soc. 2004, 126, 5452–5464. (26) Sinicropi, A.; Andruniow, T.; Ferre, N.; Basosi, R.; Olivucci, M. J. Am. Chem. Soc. 2005, 127, 11534–11535. (27) Sinicropi, A.; Basosi, R.; Olivucci, M. J. Phys. Conf. Ser. 2008, 101, 012001-1–012001-11. (28) Roos, B. O.; Taylor, P. R.; Siegbahn, P. E. M. Chem. Phys. 1980, 48, 157–173. (29) Andersson, K.; Malmqvist, P. Å; Roos, B. O.; Sadlej, A. J.; Wolinski, K. J. Phys. Chem. A 1990, 94, 5483–5488. (30) Marques, M. A. L.; Lopez, X.; Varsano, D.; Castro, A.; Rubio, A. Phys. ReV. Lett. 2003, 90, 258101-1–258101-4. (31) Lopez, X.; Marques, M. A. L.; Castro, A.; Rubio, A. J. Am. Chem. Soc. 2002, 102, 759–781.

Taguchi et al. (32) Das, A. K.; Hasegawa, J.; Miyahara, T.; Ehara, M.; Nakatsuji, H. J. Comput. Chem. 2003, 24, 1421–1431. (33) Hasegawa, J.; Fujimoto, K.; Swerts, B.; Miyahara, T.; Nakatsuji, H. J. Comput. Chem. 2007, 28, 2443–2452. (34) Nakatsuji, H. Chem. Phys. Lett. 1978, 59, 362–364. (35) Olsen, S.; Prescott, M.; Wilmann, P.; Battad, J.; Rossjohn, J.; Smith, S. C. Chem. Phys. Lett. 2006, 420, 507–511. (36) Olsen, S.; Smith, S. C. J. Am. Chem. Soc. 2007, 129, 2054–2065. (37) Celani, P.; Werner, H.-J. J. Chem. Phys. 2000, 112, 5546–5557. (38) Mochizuki, Y.; Nakano, T.; Amari, S.; Ishikawa, T.; Tanaka, K.; Sakurai, M.; Tanaka, S. Chem. Phys. Lett. 2007, 433, 360–367. (39) Kitaura, K.; Sawai, T.; Asada, T.; Nakano, T.; Uebayasi, M. Chem. Phys. Lett. 1999, 312, 319–324. (40) Kitaura, K.; Ikeo, E.; Asada, T.; Nakano, T.; Uebayasi, M. Chem. Phys. Lett. 1999, 313, 701–706. (41) Foresman, J. B.; Head-Gordon, M.; Pople, J. A.; Frisch, M. J. J. Phys. Chem. 1992, 96, 135–149. (42) Head-Gordon, M.; Rico, R. J.; Oumi, M.; Lee, T. J. Chem. Phys. Lett. 1994, 219, 21–29. (43) Fedorov, D. G.; Kitaura, K. J. Chem. Phys. 2005, 122, 0541081–054108-10. (44) Fedorov, D. G.; Ishida, T.; Kitaura, K. J. Phys. Chem. A 2005, 109, 2638–2646. (45) Nakano, T.; Kaminuma, T.; Sato, T.; Akiyama, U.; Uebayasi, M.; Kitaura, K. Chem. Phys. Lett. 2000, 318, 614–618. (46) Nakano, T.; Kaminuma, T.; Sato, T.; Fukuzawa, K.; Akiyama, Y.; Uebayasi, M.; Kitaura, K. Chem. Phys. Lett. 2002, 351, 475–480. (47) Mochizuki, Y.; Nakano, T.; Koikegami, S.; Tanimori, S.; Abe, Y.; Nagashima, U.; Kitaura, K. Theor. Chem. Acc. 2004, 112, 442–452. (48) Mochizuki, Y.; Koikegami, S.; Nakano, T.; Amari, S.; Kitaura, K. Chem. Phys. Lett. 2004, 396, 473–479. (49) Mochizuki, Y.; Yamashita, K.; Murase, T.; Nakano, T.; Fukuzawa, K.; Takematsu, K.; Watanabe, H.; Tanaka, S. Chem. Phys. Lett. 2008, 457, 396–403. (50) Mochizuki, Y.; Koikegami, S.; Amari, S.; Segawa, K.; Kitaura, K.; Nakano, T. Chem. Phys. Lett. 2005, 406, 283–288. (51) Mochizuki, Y.; Tanaka, K.; Yamashita, K.; Ishikawa, T.; Nakano, T.; Amari, S.; Segawa, K.; Murase, T.; Tokiwa, H.; Sakurai, M. Theor. Chem. Acc. 2007, 117, 541–553. (52) Nifosı´, R.; Amat, P.; Tozzini, V. J. Comput. Chem. 2007, 28, 2366– 2377. (53) Timerghazin, Q. K.; Carlson, H. J.; Liang, C.; Cambell, R. E.; Brown, A. J. Phys. Chem. B 2008, 112, 2533–2541. (54) Mochizuki, Y.; Tanaka, K. Chem. Phys. Lett. 2007, 443, 389–397. (55) Szabo, A.; Ostlund, N. S. Modern Quantum Chemistry; MacMillan: New York, 1982. (56) Schmidt, M. W.; Baldridge, K. K.; Boatz, J. A.; Elbert, S. T.; Gordon, M. S.; Jensen, J. H.; Koseki, S.; Matsunaga, N.; Nguyen, K. A.; Su, S. J.; Windus, T. L.; Dupuis, M.; Montgomery, J.A. J. Comput. Chem. 1993, 14, 1347–1363; see also http://www.msg.ameslab.gov/GAMESS/. (57) Fedorov, D. G.; Olson, R. M.; Kitaura, K.; Gordon, M. S.; Koseki, S. J. Comput. Chem. 2004, 25, 872–880. (58) Fedorov, D. G.; Kitaura, K. J. Chem. Phys. 2004, 121, 2483–2490. (59) Fukuzawa, K.; Mochizuki, Y.; Tanaka, S.; Kitaura, K.; Nakano, T. J. Phys. Chem. B 2006, 110, 16102–16110; Errata 2006, 110, 24276. (60) Amari, S.; Aizawa, M.; Zhang, J.; Fukuzawa, K.; Mochizuki, Y.; Iwasawa, Y.; Nakata, K.; Chuman, H.; Nakano, T. J. Chem. Inf. Comput. Sci. 2006, 46, 221–230. (61) Fedorov, D. G.; Kitaura, K. J. Comput. Chem. 2007, 28, 222–237. (62) Pulay, P.; Saebø, S. Theor. Chim. Acta 1986, 69, 357–368. (63) Ishikawa, T.; Mochizuki, Y.; Amari, S.; Nakano, T.; Tokiwa, H. S.; Tanaka, S.; Tanaka, K. Theor. Chem. Acc. 2007, 118, 937–945. (64) Ishikawa, T.; Mochizuki, Y.; Amari, S.; Nakano, T.; S; Tanaka, S.; Tanaka, K. Chem. Phys. Lett. 2008, 463, 189–194. (65) Dykstra, C. E.; Davidson, E. R. Int. J. Quantum Chem. 2000, 78, 226–236. (66) Pickup, B. T.; Goscinski, O. Mol. Phys. 1973, 4, 1013–1035. ¨ hrn, Y. Propagators in Quantum Chemistry, 2nd (67) Linderberg, K.; O ed.; Wiley: New York, 2004. (68) Mochizuki, Y. Chem. Phys. Lett. 2008, 453, 109–116. (69) Chiba, M.; Fedorov, D. G.; Kitaura, K. Chem. Phys. Lett. 2007, 444, 346–350. (70) Chiba, M.; Fedorov, D. G.; Kitaura, K. J. Chem. Phys. 2007, 127, 104108-1–104108-11. (71) Chiba, M.; Fedorov, D. G.; Kitaura, K. J. Comput. Chem. 2008, 29, 2667–2676. (72) Dreuw, A.; Weisman, J. L.; Head-Gordon, M. J. Chem. Phys. 2003, 119, 2943–2946. (73) Modern Methods for Theoretical Physical Chemistry of Biopolymers; Starikov, E. B., Lewis, J. P., Tanaka, S., Eds.; Elsevier: Amsterdam, 2006. Extensive documentation on the FMO methodology and application can be found in this book (see Chapter 1 by Fedorov et al. and also Chapter 2 by Nakano et al., for example).

Fragment MO Calculations on Red Fluorescent Proteins (74) Fedorov, D. G.; Kitaura, K. J. Phys. Chem. A 2007, 111, 6904– 6914. (75) Theory and Applications of the Fragment Molecular Orbital Method; Kitaura, K., Fedorov, D. G., Eds.; CRC Press: Boca Raton, FL, 2009. (76) Protein Data Bank (PDB), http://www.rcsb.org/pdb/ (2006–2007). (77) Molecular Operating Environment (MOE), http:// www.compchem.com/ (2007). (78) AMBER, http://amber.scripps.edu/ (1999). (79) Gaussian, revision D.01; http://www.gaussian.com. (80) Foresman J. B.; Frisch A. Exploring Chemistry with Electronic Structure Methods, 2nd ed.; Gaussian Inc.: Pittsburgh, PA, 1996. (81) Mochizuki, Y.; Komeiji, Y.; Ishikawa, T.; Nakano, T.; Yamataka, H. Chem. Phys. Lett. 2007, 437, 66–72. (82) Tagami, A.; Ishibashi, N.; Kato, D.; Taguchi, N.; Mochizuki, Y.; Watanabe, H.; Ito, M.; Tanaka, S. To be submitted. (83) Nishio, M.; Hirota, M.; Umezawa, Y. The CH/π Interaction; WileyVCH: New York, 1998. (84) Kawaguchi, K.; Yamato, T. Chem. Phys. Lett. 2006, 430, 386– 390.

J. Phys. Chem. B, Vol. 113, No. 4, 2009 1161 (85) Yamato, T.; Ishikura, T.; Kakitani, T.; Kawaguchi, K.; Watanabe, H. Photochem. PhotoBiol. 2007, 83, 323–327. (86) Meyer, T. E. Biochim. Biophys. Acta 1985, 23, 175–183. (87) Kowalski, K.; Piecuch, P. J. Chem. Phys. 2001, 120, 1715–1738. (88) Valiev, M.; Kowalski, K. J. Chem. Phys. 2006, 125, 211101-1– 211101-3. (89) Ito, M.; Fukuzawa, K.; Mochizuki, Y.; Nakano, T.; Tanaka, S. J. Phys. Chem. A 2008, 112, 1986–1998. (90) Ito, M.; Fukuzawa, K.; Ishikawa, T.; Mochizuki, Y.; Nakano, T.; Tanaka, S. J. Phys. Chem. B 2008, 112, 12081–12094. (91) Tomasi, J.; Mennucci, B.; Cammi, R. Chem. ReV. 2005, 105, 2994– 3094. (92) Ishikawa, T.; Mochizuki, Y.; Mori, H.; Honda, H.; Fujita, T.; Amari, S.; Komeiji, Y.; Tokiwa, H.; Tanaka, S.; Nakano, T.; Tanaka, K.; Miyoshi, E. Chem. Phys. Lett. 2006, 427, 159–165. (93) Komeiji, Y.; Ishida, T.; Fedorov, D. G.; Kitaura, K. J. Comput. Chem. 2007, 28, 1750–1762.

JP808151C