Predictions of Novel Two-Photon Absorption Bands in Fluorescent

Nov 21, 2007 - Predictions of Novel Two-Photon Absorption Bands in Fluorescent Proteins ... Yusuf ŞimşekAlex Brown ... M. Alaraby Salem and Alex Bro...
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J. Phys. Chem. B 2007, 111, 14043-14050

14043

Predictions of Novel Two-Photon Absorption Bands in Fluorescent Proteins Riccardo Nifosı`*,† and Yi Luo‡ NEST-CNR INFM and Scuola Normale Superiore, Piazza dei CaValieri 7, Pisa I-56126, Italy, and Department of Theoretical Chemistry, The Royal Institute of Technology, AlbanoVa UniVersity Center, SE-106 91 Stockholm, Sweden ReceiVed: July 16, 2007; In Final Form: September 13, 2007

By means of time-dependent density functional theory, we calculate the two-photon cross-sections for the lowest relevant excitations in some model chromophores of intrinsically fluorescent proteins. The two-photon strength of the first, one-photon active transition varies among the various chromophores, in line with experimental findings. Interestingly, additional transitions with large two-photon cross-sections are found in the 500-700 nm region arising from near-resonant enhancement, as revealed by few-state model analysis. Multiphoton excitation of fluorescent proteins in this spectral region can lead to relevant application for bioimaging.

1. Introduction Despite a rather extensive use in high-resolution imaging of living cells and tissues,1 two-photon excitation properties of fluorescent proteins (FPs) still need to be thoroughly investigated and characterized over a wide range of excitation wavelengths and external conditions (e.g., pH, halide, and, more generally, metabolite concentration). Though, in general, excitation at twice the one-photon wavelength peak effectively results in twophoton absorption and consequent fluorescence,2 other spectral regions that are rather inactive at one-photon excitation can become active when accessed by two-photon excitation. DsRed, a red FP derived from the coral Discosoma,3 displays such “anomalous” behavior: a strong two-photon band appears at fundamental wavelengths shorter than 780 nm. In the corresponding one-photon region (370 nm), the one-photon absorption spectrum is almost completely flat.2,4 In a previous letter, we explained the presence of this band as stemming from a transition to a higher excited state, through coupling with the highest occupied molecular orbital (HOMO)-lowest unoccupied molecular orbital (LUMO) one-photon excitation.5 We shall argue in the following that two-photon excitation bands in the 500-700 nm region are ubiquitous among intrinsically fluorescent proteins (IFPs; i.e., green fluorescent protein (GFP) and its homologues), and might provide interesting spectral windows for multiphoton fluorescence imaging. The light-emitting moiety in IFPs (see refs 3, 6, and 7 for reviews and the references therein) is a chromophore (Table 1) formed autocatalytically from the cyclization of three amino acids in the protein sequence, and positioned inside a compact β-barrel fold.8 In imaging experiments, IFPs are expressed either alone to probe cellular/supercellular structures in vivo,1 or fused to other proteins to study protein localization, trafficking, and interaction with other proteins.9 Several multiphoton imaging applications of IFPs are reported (see ref 1), which combine IFPs’ unique properties as genetically encoded fluorophores with the advantages of multiphoton microscopy (three-dimensional resolution, confined photobleaching, and photodamage). * To whom correspondence should be addressed. E-mail: [email protected]. † NEST-CNR INFM and Scuola Normale Superiore. ‡ The Royal Institute of Technology.

Two-photon excitation spectra of some IFPs have been reported by various authors.2,4,10,11 Investigated FPs include EGFP (a GFP mutant carrying the S65T mutation), ECFP (cyan fluorescent protein (CFP) carrying the Y66W mutation in the chromophore), EYFP (yellow fluorescent protein (YFP) with T203Y), and DsRed (a red-light-emitting GFP homologue). The main one-photon absorption peak (434 nm for CFP, 490-515 nm for GFP mutants, and 555 nm for DsRed) normally also displays a relevant two-photon character at about doubled wavelength, although the limited detection window for two-photon spectra (750 nm up to 1000 nm) does not allow one to follow such behavior completely. A blue shift is observed between one- and two-photon peaks, which is presumably due to different vibronic coupling.2 As already mentioned above, DsRed shows an additional twophoton excitation band. An increasing number (some hundreds) of IFPs have been discovered and produced, and the two-photon spectrum has been measured only in the cases described above. Some IFPs share the same chromophore structure, and a limited number of models are sufficient to exhaust all currently available IFPs. Here we predict the two-photon spectrum of IFPs in some relevant cases, using time-dependent density functional theory (TDDFT) to calculate the two-photon cross-section of the isolated chromophore models. At this stage, we consider purely vertical electronic transitions, thereby neglecting vibronic coupling. The protein matrix crucially influences the photophysics of the chromophore and can shift the spectral peaks by a few tenths of an electronvolt within different mutants/homologues containing the same chromophore structure. Nonetheless, the chromophore models provide simple systems that are the starting point for understanding the optical properties of IFPs. This approach proved successful in the case of DsRed.5 Besides the approximation of using the chromophore as a model of the entire protein, one should also be aware of inherent flaws of the method (i.e., of the approximate exchange and correlation kernels). Various theoretical studies employed TDDFT to calculate the (one-photon) absorption spectrum of the chromophore alone or embedded in the protein matrix within a

10.1021/jp075545v CCC: $37.00 © 2007 American Chemical Society Published on Web 11/21/2007

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Nifosı` and Luo

TABLE 1: Models of FP Chromophores, Along with the Name of the Corresponding Protein(s)and References

quantum mechanical/molecular mechanical (QM/MM) approach, in the cases of GFP,12-15 asFP595,16,17,18 and blue fluorescent protein (BFP),19 in most cases yielding a rather good agreement with experiments. A recent TDDFT (with either BLYP or B3LYP exchange and correlation kernels) study on the whole series of IFP chromophores20 shows that the theory quite accurately predicts the excitation energies for “blue” (such as the ones with Y66H and Y66F) chromophores and “red” anionic chromophores (DsRed, and asFP595), while performing less reliably for the anionic GFP chromophore and neutral DsRed. Within such ranges of validity, we expect that the method yields

reasonably accurate results also for two-photon absorption (TPA) cross-sections. 2. Methods 2.1. Models. Model chromophore structures are reported in Table 1. They were obtained by cutting the connections to the protein backbone at the appropriate positions (i.e., preserving the part of the structure that supports the π-conjugated electronic system) and saturating the dangling bonds with methyl groups. CFP and BFPF are neutral at a reasonable pH range, and so is BFP.21,31 The latter can exist in two neutral protonation states,

Predictions of Novel TPA Bands in FPs

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Figure 1. Calculated (B3LYP/6-31G*) two-photon cross-section (σTPA) and oscillator strength (f) for the lowest-energy excitations of the neutral model chromophores of BFPF (Y66F), BFP (Y66H) in the two possible forms, CFP (Y66W) and GFP. In all graphs the wavelength of the twophoton spectra is halved for easier comparison with the one-photon spectra. The [number f number] indicates the KS MOs transitions that compose the excitation, with the coefficients given in parentheses. Only contributions with absolute values larger than 0.4 are shown.

depending on whether the protonated nitrogen in the imidazole ring is Nδ or N. The GFP chromophore can be either neutral or anionic within the protein matrix. Both states are fluorescent in wild-type GFP: the anionic through direct fluorescent, and the neutral through excited-state proton transfer followed by fluorescence from the anionic excited state.32 In the case of DsRed,33 Kaede,30 zFP538,3 and mOrange,25 the main peak corresponds to the anionic form. Some DsRed mutants and other homologues also have neutral states. Their fluorescent properties are, however, less investigated, so we limit our analysis to the anionic states of the red FP chromophores (also because TDDFT-B3LYP was shown to perform better in these cases).20 2.2. Theory. Excitation energies and one- and two-photon cross-sections can be calculated with TDDFT34 using linear35 and quadratic response theory.36,37 In particular, in the space of transitions between occupied and unoccupied Kohn-Sham (KS) molecular orbitals (MOs), excitations are identified as the solutions of a secular equation.35 When in the next section we shall mention the “decomposition” of an excitation in transitions between KS orbitals, we are referring to the secular-equation framework. The reference quantity for two-photon calculations is the transition moment

δTPA )

1 15

∑ij SiiS/jj + 2SijS/ij

(throughout the paper it is assumed that polarization of incident light is linear). Sij is the two-photon transition matrix, expressed in terms of the expectation values of the dipole moment operator µi between the ground (|0〉) and the excited states (|n〉) as

Sij )

∑n

[

〈0|µi|n〉〈n|µj|f〉 ω0n - ω

+

]

〈0|µj|n〉〈n|µi|f〉 ω0n - ω

(1)

where |f〉 is the final state, and the sum runs over all excited states. Sij is determined from the residues of the quadratic

response function.38,36 Within the same framework, it is possible to calculate permanent and transition dipole moments between excited states. These are useful for evaluating which terms dominate the expansion in eq 1, in a few-state model analysis. The two-photon (absorption) cross-section σTPA is obtained from δTPA by

σTPA )

4π3a05R ω2 TPA δ 15c Γ

(2)

Here ω is the excitation energy, and Γ is a phenomenological line width accounting for homogeneous and inhomogeneous broadening. We set Γ ) 0.1 eV, as commonly employed in TPA calculations.39 a0, R, and c are the usual Bohr radius, finestructure constant, and light speed, respectively. Regarding onephoton absorption, we report the dimensionless oscillator strength f, which is simply proportional to the one-photon crosssection. As the exchange and correlation functional in TDDFT calculation, we employed the B3LYP functional,40,41 and performed the calculation with 6-31G* basis functions and with the addition of diffuse function (6-31+G*) for comparison in the case of anions. For the neutral species, the differences employing 6-31G* versus 6-31+G* are less relevant as discussed in the following. Geometry optimization (at the B3LYP 6-31G* level) and excitation energies/oscillator strength calculations were carried out with GAUSSIAN 03,42 while twophoton cross-sections and excited-state dipole moments were computed with DALTON.43 The TPA calculation does not converge if the number of basis functions is too large, while the one-photon analysis is feasible also with bigger basis sets. As a consequence, we had to limit our results to the 6-31G* basis set in the case of Kaede for σTPA, but calculated the excitation energies and oscillator strengths also with diffuse functions for comparison. We also evaluated the effect of implicit solvent, using the polarizable continuum model (PCM)44,45 and methanol as solvent. This analysis was restricted to one-photon properties, and the complete results are reported in the Supporting

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Figure 2. Isosurfaces of KS MOs. For BFPF, HOMO-3 is shown instead of HOMO-2 because the former participates in the relevant excitations.

Information (SI). However, when the excitations are easily mapped between the two calculations (gas-phase vs implicit solvent), it is possible to establish the effect of polarization, in red or blue shifting the excitation energies. The PCM calculation also tells how “robust” a certain excitation is, that is, how sensitive it is to the interaction with external matrices. Regarding the notation, HOMO-i and LUMO+j (or H-i and L+j) indicate the KS MO lying at the ith place below the HOMO and at the jth place above the LUMO, respectively, so that the (energy) order reads [...] H-2, H-1, H, L, L +1, L+2 [...]. 3. Results The results of our calculations are reported in Tables 2-10. For each chromophore, we included the excitation energy (in

Nifosı` and Luo both eV and nm), oscillator strength (f), and σTPA (in GM ) 10-50 cm4s/photon). In Figures 1 and 3, we compare one- and two-photon absorption spectra in the relevant spectral windows. For the strongest excitations, we also indicate the decomposition in terms of transitions between KS MOs. The SI reports the KS MOs components for each excitation and for each level of theory, and the transition dipole moments between excited states in the case of the CFPN chromophore. 3.1. Neutral Chromophores. Blue FPs. The one-photon HOMO f LUMO (H f L) transition of BFPF and BFPδ has a small σTPA around 1 GM, and, in the case of BFP, it is negligible (0.03 GM; Table 2). Such values, together with the low quantum yield of fluorescence for BFPs, point to a rather ineffective two-photon excitation. Below 300 nm (see Figure 1) other excitations appear with much larger σTPA (50-150 GM) and some residual oscillator strength. These excitations are mainly composed by the H f L KS transition in BFPδ/, and by H f L in BFPF. The shape of the H-3 of BFPF is similar to that of the H-2 of BFPPδ/ (see Figure 2). In the case of BFPF, an intermediate additional excitation is present with σTPA around 4 GM, characterized by H f L, with H-2 almost completely localized on the phenyl ring. CFP. The H f L transition has rather large σTPA, around 25 GM. This value agrees with the experimental value of 7.87 for the two-photon excitation (TPE) reported in ref 2, which, when scaled by a CFP fluorescence quantum yield φ of 0.4, gives a value of 19.7 GM for σTPA (σTPE ) φσTPE). An H f L excitation is present at 300 nm with large σTPA, analogous to the TPA strong transition of BFPs. This excitation is red-shifted to 312 nm in the PCM calculation. The smaller TPA peak at 315 nm (331 nm in PCM) is analogous to that of BFPF, with H-1 (MO 62) mainly localized on the Trp66 indole ring. The last peak in the blue wing of the spectrum in Figure 1 comes mainly from an H f L+1 KS transition, with L+1 again completely localized on Trp66, though with π* character. This transition to L+1 is also present in the spectrum of anionic chromophores (see below).

Figure 3. Calculated two-photon cross-section (σTPA, thin filled bars) and oscillator strength (f, thick white bars) for the lowest-energy excitations of the anionic model chromophores of GFP, ZFP, mOrange, DsRed, and Kaede. In all graphs the wavelength of the two-photon spectra is halved for easier comparison with the one-photon spectra. In the case of KAEA and ZFPA, the 6-31G* basis-set results are shown. The gray peaks in the DSRA plot are calculated with the 6-31G* basis sets. All other peaks are from 6-31+G* basis-set calculations. See caption of Figure 1 for the meaning of [number f number].

Predictions of Novel TPA Bands in FPs

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TABLE 2: Excitation Energies (in eV; nm in Parentheses), Oscillator Strengths (f), and TPA Cross-Sections (σTPA, in GM) for the Chromophores of BFPs BFPF (6-31G*)

BFPδ (6-31G*)

BFP (6-31G*)

exc

energy

f

σTPA

energy

f

σTPA

energy

f

σTPA

1 2 3 4 5 6 7 8

3.60 (344) 3.60 (344) 4.18 (297) 4.43 (280) 5.04 (246) 5.18 (239) 5.55 (224) 6.03 (206)

0.55 0.00 0.01 0.22 0.00 0.04 0.04 0.11

0.91 0.00 4.21 134.50 0.08 1.51 203.04 14.22

3.59 (345) 3.77 (329) 4.37 (284) 4.48 (277) 4.98 (249) 5.40 (230) 5.65 (219) 5.99 (207)

0.61 0.00 0.09 0.00 0.01 0.00 0.02 0.04

1.32 0.00 52.70 0.01 3.68 0.14 75.17 216.12

3.62 (343) 3.74 (331) 4.55 (272) 4.77 (260) 5.18 (240) 5.28 (235) 5.58 (222) 6.03 (206)

0.00 0.47 0.25 0.00 0.00 0.12 0.02 0.00

0.00 0.03 89.34 0.01 0.18 4.55 4.86 184.28

TABLE 3: Excitation Energies (in eV; nm in Parentheses), Oscillator Strengths (f), and TPA Cross-Sections (σTPA, in GM) for the Chromophore of CFP CFP (6-31G*)

TABLE 6: Excitation Energies (in eV; nm in Parentheses), Oscillator Strengths (f), and TPA Cross-Sections (σTPA, in GM) for the Chromophore of mOrange

CFP (6-31+G*)

exc

energy

f

σTPA

1 2 3 4 5 6 7 8

3.42 (363) 3.75 (331) 3.93 (315) 4.13 (300) 4.40 (282) 4.94 (251) 5.04 (246) 5.22 (238)

0.62 0.00 0.01 0.00 0.07 0.10 0.16 0.00

25.92 0.00 15.34 144.45 5.67 0.11 94.62 0.10

energy 3.32 (373) 3.77 (329) 3.87 (321) 4.06 (306) 4.25 (292) 4.50 (276) 4.75 (261) 4.83 (257)

ORNA 6-31G*

f

σTPA

exc

energy

0.60 0.00 0.01 0.00 0.07 0.00 0.00 0.03

24.74 0.00 19.70 171.59 5.74 0.39 0.02 11.70

1 2 3 4 5 6 7 8

2.65 (468) 2.79 (445) 3.60 (344) 3.62 (342) 3.99 (311) 4.06 (306) 4.46 (278) 4.49 (276)

TABLE 4: Excitation Energies (in eV; nm in Parentheses), Oscillator Strengths (f), and TPA Cross-Sections (σTPA, in GM) for the Chromophore of GFP, Neutral State GFPN (6-31G*)

ORNA 6-31+G*

f

σTPA

energy

f

σTPA

0.87 0.00 0.03 0.00 0.14 0.14 0.06 0.00

13.71 0.00 5.52 0.04 21.39 45.70 284.8 2.46

2.59 (480) 2.91 (427) 3.58 (347) 3.65 (339) 3.66 (339) 3.91 (317) 4.51 (275) 4.65 (267)

0.90 0.00 0.04 0.00 0.00 0.18 0.00 0.05

12.87 0.00 26.71 5.10 0.018 48.44 -

TABLE 7: Excitation Energies (in eV; nm in Parentheses), Oscillator Strengths (f), and TPA Cross-Sections (σTPA, in GM) for the Chromophore of AsFP595

GFPN (6-31+G*)

ASF A (6-31+G*)

exc

energy

f

σTPA

energy

f

σTPA

exc

energy

f

σTPA

1 2 3 4 5 6 7 8

3.54 (352) 3.66 (338) 4.22 (294) 4.38 (283) 4.94 (251) 5.11 (243) 5.46 (227) 5.83 (213)

0.70 0.00 0.08 0.01 0.07 0.00 0.09 0.10

6.14 0.00 157.16 24.67 3.37 0.08 105.28 54.41

3.46 (358) 3.69 (336) 4.17 (297) 4.30 (288) 4.80 (258) 4.81 (258) 4.96 (250) 5.11 (242)

0.69 0.00 0.08 0.00 0.00 0.09 0.00 0.00

5.58 0.00 149.18 53.35 0.01 3.64 -

1 2 3 4 5 6 7 8

2.58 (480) 2.88 (431) 3.43 (361) 3.53 (351) 3.77 (329) 3.89 (318) 3.95 (314) 3.98 (311)

0.80 0.00 0.00 0.01 0.00 0.15 0.00 0.15

6.84 0.00 0.02 12.89 0.80 50.86 -

TABLE 5: Excitation Energies (in eV; nm in Parentheses), Oscillator Strengths (f), and TPA Cross-Sections (σTPA, in GM) for the Chromophore of GFP, Anionic State GFPA 6-31G*

GFPA 6-31+G*

exc

energy

f

σTPA

energy

f

σTPA

1 2 3 4 5 6 7 8

3.09 (401) 3.19 (388) 4.16 (298) 4.32 (287) 4.38 (283) 4.48 (277) 4.75 (261) 4.98 (249)

0.00 0.98 0.00 0.00 0.01 0.06 0.07 0.00

0.00 2.81 0.01 2.63 3.01 22.02 59.39 2.91

2.97 (417) 3.11 (398) 3.22 (385) 3.60 (344) 3.85 (322) 4.08 (304) 4.13 (300) 4.19 (296)

0.00 0.92 0.00 0.00 0.00 0.00 0.00 0.05

0.59 2.18 0.00 1.99 3.19 16.53 -

In this specific case, we also calculated the transition dipole moments within the first five excited states (SI). The large values (around 3-5 D) of 〈1|µ|3〉, 〈1|µ|4〉, 〈3|µ|4〉, and 〈3|µ|5〉 help understanding, through eq 1, the strong TPA of excitations to the third, fourth, and fifth excited states (Table 3). In particular, the very strong σTPA of the fourth excitation stems from various channels, the main one through state 1 (〈0|µ|1〉 and 〈1|µ|4〉 are both large), the others through states 3 and 5 (〈3|µ|4〉 and 〈4|µ|5〉 are relevant). GFPN. The neutral GFP chromophore behaves rather similarly to the BFPs, though with small but still significant σTPA for the H f L excitation and large σTPA for the H f L excitation at around 290 nm (323 nm in PCM). The blue-wing peak at 280 nm is an excitation with contributions coming from both H f

L+1 and H f L KS transitions. H-3 and L+1 are both localized on the tyrosil ring, with π and π* character, respectively. Although the TPA spectrum of GFP mutants with a population of neutral chromophore was measured,46 no absolute value for σTPA is reported. 3.2. Anionic Chromophores. With the exclusion of GFPA, which is treated below, all other anionic chromophores have moderately strong σTPA (7-40 GM) for the first excitation. The largest σTPA for this state belongs to ZFPA and KAEA. The LUMO extends to the conjugated tail rather than to the oxygen and the C-C bond in the imidazolidinone (Figure 4), in contrast to what happens in BFPs, CFP, and GFP. This is the signature of the extended conjugation typical of the “red” chromophores. A second TPA peak is present around 350-380 nm, with contributions from H f L+1 and H f L. H-1 is a σ MO on the phenolate combined with a py on the carbonyl. ZFPA, ORNA, ASFA, and DSRA. These four chromophores share common spectral features (ORNA indeed comes from mOrange FP, a DsRed mutant). Apart from the first two peaks, already addressed above, a third TPA band is present in the spectrum and again contains contributions from H f L+1 and H f L. In the case of ORNA, this band has also an H f L component, with H-4 localized on the imidazolidinone. An H f L component contributes to the third band in ASFA, with H-5 being a π orbital on the phenolate ring, and the H f L contributing only with a 0.22 coefficient. This band also has significant oscillator strength, and is present in the measured

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Nifosı` and Luo

Figure 4. Isosurfaces of KS MOs.

one-photon excitation spectra of DsRed33 and zFP5383 at around 320-330 nm. In the case of DsRed, the second band is present in the experimental two-photon spectra (see discussion in ref 5). The calculated σTPA for this transition, 24.9 GM, compares nicely with the measured value of around 18 GM for the twophoton excitation cross-section,2 which, when scaled by the DsRed quantum yield of 0.79,33 gives 22.8 GM for σTPA. We would like to point out, however, that the value of 18 GM might be underestimated because only an incomplete portion of the band lies within the measured spectral window.2 The gray peaks in the plot are calculated using 6-31G*. The corresponding 6-31+G* TPA calculation failed to converge for more than six excitations. ZFPA is rather sensitive to the basis set employed (6-31G* results are shown in the ZFPA plot, Figure 3). Using 6-31+G* instead of 6-31G* results in the appearance of a strong TPA excitation at 400 nm (see Table 8). Since this excitation is located at 330 nm in the 6-31+G*/PCM calculation, the large red shift predicted in the gas phase should not be expected in condensed-phase measurements such as in the protein. KAEA. The strongest (230 GM) TPA transition contains the usual H f L+1/H f L contribution, combined with H f L. H-5 has a π character and extends from the imidazolidinone oxygen and nearby nitrogen, down to the imidazole in the tail. The two other transitions (sixth and seventh) arise from H f L (322 nm, 45.3 GM), with H-4 being the π MO on the phenolate, and from H f L+1 (311 nm, 194 GM).

TABLE 8: Excitation Energies (in eV; nm in Parentheses), Oscillator Strengths (f), and TPA Cross-Sections (σTPA, in GM) for the Chromophore of zFP538 ZFPA (6-31G*)

ZFPA (6-31+G*)

exc

energy

f

σTPA

energy

f

σTPA

1 2 3 4 5 6 7 8

2.64 (470) 2.84 (436) 3.61 (343) 3.66 (339) 3.97 (312) 4.10 (302) 4.21 (294) 4.43 (280)

0.86 0.00 0.07 0.00 0.23 0.03 0.00 0.06

37.59 0.00 12.91 0.17 60.20 35.84 1.21 129.74

2.57 (483) 2.97 (417) 3.10 (400) 3.57 (348) 3.67 (338) 3.69 (336) 3.78 (328) 3.81 (325)

0.86 0.00 0.04 0.07 0.00 0.00 0.00 0.00

7.67 0.00 13.12 10.44 4.05 1.11 -

Quite surprisingly, the transitions characterizing the seventh excitation in the gas phase, are found in the third position in the implicit solvent, and the excitation energy drops by more than 0.7 eV, to a 369-nm wavelength. (In the PCM calculation, the order of these states is changed, and some MOs are shuffled, so that H-1 and H-2 in the gas phase become H-2 and H-1 in methanol; see SI.) By contrast, the other two excitations (fifth and sixth in the 6-31G* calculation) undergo negligible shifts. The predicted one-photon spectrum features two peaks in the 300-400 nm region: one at 390 nm and the other at 331 nm (respectively, 400 and 344 nm with 6-31+G*, and 384 and 334 nm with PCM). The measured absorption spectrum contains a structured band at 330-370 nm, which presumably arises from the combinations of these two excitations.47

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TABLE 9: Excitation Energies (in eV; nm in Parentheses), Oscillator Strengths (f), and TPA Cross-Sections (σTPA, in GM) for the Chromophore of DsRed DSRA (6-31G*)

DSRA (6-31+G*)

exc

energy

f

σTPA

energy

f

σTPA

1 2 3 4 5 6 7 8

2.43 (511) 2.63 (471) 3.27 (380) 3.27 (379) 3.32 (374) 3.78 (328) 3.85 (322) 4.22 (294)

0.93 0.00 0.00 0.01 0.00 0.21 0.10 0.00

9.25 0.00 0.45 2.98 0.31 22.46 47.14 72.26

2.36 (524) 2.74 (452) 3.24 (382) 3.29 (377) 3.35 (370) 3.69 (336) 3.80 (326) 3.88 (319)

0.96 0.00 0.02 0.00 0.00 0.23 0.06 0.01

22.7 0.0 24.9 0.7 1.1 -

TABLE 10: Excitation Energies (in eV; nm in Parentheses), Oscillator Strengths (f), and TPA Cross-Sections (σTPA, in GM) for the Chromophore of Kaede KAEA (6-31G*)

KAEA (6-31+G*)

exc

energy

f

σTPA

energy

f

1 2 3 4 5 6 7 8

2.25 (552) 2.66 (466) 3.18 (390) 3.57 (348) 3.74 (332) 3.85 (322) 3.99 (311) 4.22 (294)

0.82 0.00 0.14 0.00 0.26 0.01 0.00 0.04

38.48 0.00 0.60 0.03 230.03 45.30 193.76 50.97

2.15 (577) 2.64 (470) 2.77 (448) 3.10 (400) 3.40 (365) 3.58 (346) 3.60 (344) 3.79 (327)

0.79 0.00 0.00 0.17 0.00 0.00 0.26 0.00

GFPA. A “dark” excitation is the first one in the case of GFPA (stemming from, respectively, an H f L+1 or transition H f L+1 when using 6-31+G* or 6-31G*). When using timedependent Hartree-Fock (data not shown), this excitation goes up in energy, and the normal situation, where the first excitation is H f L, is restored. The same normal behavior is recovered when using higher level post Hartree-Fock methods48 and when including implicit solvent effects, through PCM, within the TDDFT-B3LYP calculation (see SI). As also observed by Wang et al.49 for dioxaborine heterocycles, TDDFT-B3LYP in the gas phase can yield the wrong order for excited states, and this order is corrected either by the inclusion of PCM effects or in the pure Hartree-Fock method. The σTPA is low (notice that, in Figure 3, the scale for σTPA of the GFPA plot is enhanced). The blue-shifted three TPA peaks come mainly from transitions from HOMO to higher unoccupied MOs. However, these excitations are rather unstable with respect to changes in the method, and their composition changes when adding diffuse functions to the basis set. At variance with the other anionic chromophores, the order of MOs is sensitive to the basis set employed, and L+1 with 6-31+G* is a σ orbital on the two methyl groups. The poor performance of the methods in this case is also reflected in the comparison with experiment. The measured twophoton excitation cross-section (limited to the red wing of the spectrum) is 41.21 GM,2 yielding a value of 68.7 GM for σTPA when scaled with the fluorescent quantum yield (0.7). Our calculated value of around 2 GM clearly reflects a failure of the theory for GFP anionic chromophore. A TPA calculation including implicit solvent effects would probably result in a better agreement with the experiment. Unfortunately, a PCM treatment of a TPA cross-section is currently not straightforward with available quantum chemistry codes. 4. Discussion By comparing the one-photon experimental spectra with our calculations, it is possible to estimate how the predicted twophoton properties would compare with measurements. Indeed,

the theoretical framework for treating one- and two-photon properties is essentially the same (i.e., linear and quadratic response theory, respectively), although the two-photon case is computationally more demanding. The in vacuo TDDFT values for the first H f L excitation energies are generally blue-shifted with respect to the (one-photon) absorption energies of the proteins by a few tenths of an electronvolt, although the amount of shifting is bigger for blue, cyan, and green IFPs than for yellow/red IFPs. For example, CFP absorption peak is at 440 nm (2.82 eV),21 while our prediction on the model chromophore yields 373 nm (3.31 eV); for DsRed we have 558 nm (2.22 eV)27 vs the predicted 524 nm (2.36 eV). The additional one-photon bands found in the blue wing of the spectrum are particularly well reproduced for the yellow/ red anionic chromophores: DsRed (predicted 336 nm vs measured 335 nm33), zFP538 (predicted 312 nm vs 320 nm3; we compare with the 6-31G* result here for the reasons we mentioned above), asFP595 in the bright state (predicted 318 nm vs 338 nm50). Hence, we expect in these cases that our predictions about the two-photon peaks in the 600-750 nm spectral regions are rather reliable. GFPN and CFPN H f L excitation energies are sensibly blueshifted with respect to measured values in the protein, mostly due to interactions with the protein matrix.20 We can expect a similar behavior for the peaks at around 300 nm, that is, they will be presumably red-shifted by 30-40 nm in the experimental spectrum as well. Unfortunately it is not possible to distinguish the presence of these one-photon bands in the spectra because of the strong overlapping absorption of the main H f L peak on one side, and, on the other, the increasing contribution of aromatic amino acid absorption, which peaks at 278 nm. However, an increase of two-photon absorption in the blue wing of the GFP and CFP spectra can be expected. Similar consideration also holds for BFPs, leading to the conclusion that, despite having very low two-photon absorption in the 700 nm (350 nm) region, they should display increasing two-photon absorption approaching the 550 nm (275 nm) wavelength. One issue about the relevance of these excitations is certainly whether their quantum yield of fluorescence is large enough for two-photon excitation experiments. The case of DsRed is particularly encouraging. There, the TPA band at 780 nm is detected in two-photon excitation experiments,2 implying that, upon excitation to this state, the system efficiently relaxes to the first excited state, from which it fluoresces with rather large quantum yield. This suggests that these higher excitations might also be fluorescent in the other fluorophores. As in the one-photon case, where the dominant excitation is H f L for all chromophores, a common MO composition is also found for these higher excitations. They involve H-2 f L, with the addition of H f L+1 in the anionic chromophores. The mechanisms of TPA enhancement for the higher excitation are arguably similar. These excitations, despite having rather low oscillator strength, acquire TPA transition moment mainly from the low-lying H f L excitation. This was explicitly verified in the cases of DsRed (see ref 5) and CFP (in the present article). 5. Conclusions We investigated the two-photon absorption properties of model chromophores of IFPs, in order to rationalize some existing measurements and focus on spectral regions not yet addressed by experiments. For BFPs, CFP, and GFP, we predict unprecedented strong two-photon absorption in the 500-700 nm region. Similarly, for zFP538, mOrange, asFP595, and

14050 J. Phys. Chem. B, Vol. 111, No. 50, 2007 Kaede, we expect similar contributions in the 600-750 nm window. Kaede in particular should display a particularly large TPA cross-section coming from the presence of three strong TPA excitations. DsRed is, at present, the only case where twophoton absorption was detected in the blue wing (780 nm) of the spectrum.2 Our results strongly encourage examining two-photon excitation in these spectral windows for the various FPs available. The predicted TPA features have the advantage of excitation (and emission) wavelengths with better penetration in biological samples due to reduced absorption by water. It may also be possible to uncover interesting photophysical and photochemical phenomena, like in the case of the two-photon induced DsRed greening effect observed by Marchant et al.4 Acknowledgment. We thank Prof. Fabio Beltram, Dr. Valentina Tozzini, and Dr. Stefano Luin for useful discussions. We acknowledge financial support from the Swedish research council (VR) and from MIUR under FIRB Project No. RBLA03ER38, and the allocation of computer resources from INFM Progetto Calcolo Parallelo 2006 Supporting Information Available: KS MO components for each excitation and for each level of theory (6-31G*, 6-31+G*, and PCM). Transition dipole moments between excited states in the case of the CFPN chromophore. This material is available free of charge via the Internet at http:// pubs.acs.org. References and Notes (1) Zipfel, W. R.; Williams, R. M.; Webb, W. W. Nat. Biotechnol. 2003, 21, 1369-1377. (2) Blab, G. A.; Lommerse, P. H. M.; Cognet, L.; Harms, G. S.; Schmidt, T. Chem. Phys. Lett. 2001, 350, 71-77. (3) Matz, M.; Fradkov, A. F.; Labas, Y.; Savitsky, A.; Zaraisky, A.; Markelov, M. L.; Lukyanov, S. A. Nat. Biotechnol. 1999, 17, 969-973. (4) Marchant, J. S.; Stutzmann, G. E.; Leissring, M. A.; LaFerla, F. M.; Parker, I. Nat. Biotechnol. 2001, 19, 645-649. (5) Nifosi`, R.; Luo, Y. J. Phys. Chem. B 2007, 111, 505-507. (6) Tsien, R. Y. Nat. Biotechnol. 1999, 17, 956-957. (7) Nifosı`, R.; Tozzini, V.; Beltram, F. In Encyclopedia of Condensed Matter Physics; Bassani, G., Liedl, G., Wyder, P., Eds.; Academic Press: New York, 2005; p 235. (8) Reid, B. G.; Flynn, G. C. Biochemistry 1997, 36, 6786-6791. (9) Tsien, R. Y. Annu. ReV. Biochem. 1998, 67, 509-544. (10) Heikal, A. A.; Hess, S. T.; Webb, W. W. Chem. Phys. 2001, 274, 37-55. (11) Spiess, E.; Bestvater, F.; Heckel-Pompey, A.; Toth, K.; Hacker, M.; Stobrawa, G.; Feurer, T.; Wotzlaw, C.; Berchner-Pfannschmidt, U.; Porwol, T.; Acker, H. J. Microsc. 2005, 217, 200-204. (12) Tozzini, V.; Nifosı`, R. J. Phys. Chem. B 2001, 105, 5797-5803. (13) Laino, T.; Nifosı`, R.; Tozzini, V. Chem. Phys. 2004, 298, 17-28. (14) Vendrell, O.; Gelabert, R.; Moreno, M.; Lluch, J. M. Chem. Phys. Lett. 2004, 396, 202-207. (15) Marques, M. A. L.; Lopez, X.; Varsano, D.; Castro, A.; Rubio, A. Phys. ReV. Lett. 2003, 90, 258101-1-258101-4. (16) Amat, P.; Granucci, G.; Buda, F.; Persico, M.; Tozzini, V. J. Phys. Chem. B 2006, 110, 9348-9353. (17) Grigorenko, B.; Savitsky, A.; Topol, I.; Burt, S.; Nemukhin, A. Chem. Phys. Lett 2006, 424, 184-188. (18) Scha¨fe, L. V.; Groenhof, G.; Klingen, A. R.; Ullmann, G. M.; Boggio-Pasqua, M.; Robb, M. A.; Grubmu¨ller, H. Angew. Chem. 2007, 119, 536-542. (19) Lopez, X.; Marques, M. A. L.; Castro, A.; Rubio, A. J. Am. Chem. Soc. 2005, 127, 12329-12337. (20) Nifosı`, R.; Amat, P.; Tozzini, V. J. Comput. Chem. 2007, 28, 23662377.

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