Role of non-Condon vibronic coupling and conformation change on two-photon absorption spectra of green fluorescent protein

One- and two-photon absorption spectra of organoboron complexes: vibronic and environmental effects

We synthesized a series of four parent aza-β-ketoiminate organoboron complexes and performed spectroscopic studies using both experimental and computational techniques. We studied how benzannulation influences the vibronic structure of the UV/Vis absorption bands with a focus on the bright lowest-energy π → π* electronic excitation. Theoretical simulations, accounting for inhomogeneous broadening effects using different embedding schemes, allowed gaining in-depth insights into the observed differences in band shapes induced by structural modifications. We observed huge variations in the distributions of vibronic transitions depending on the position of benzannulation. By and large, the harmonic approximation combined with the adiabatic hessian model delivers qualitatively correct band shapes for the one-photon absorption spectra, except in one case. We also assessed the importance of non-Condon effects (accounted for by the linear term in Herzberg-Teller expansion of the dipole moment) for S0 → S1 band shapes. It turned out that non-Condon contributions have no effect on the band shape in one-photon absorption spectra. In contrast, these effects significantly change the Franck-Condon band shapes of the two-photon absorption spectra. For one of the studied organoboron complexes we also performed a preliminary exploration of mechanical anharmonicity, resulting in an increase of the intensity of the 0-0 transition, which improves the agreement with the experimental data compared to the harmonic model.

Nonempirical Simulations of Inhomogeneous Broadening of Electronic Transitions in Solution: Predicting Band Shapes in One- and Two-Photon Absorption Spectra of Chalcones

We have examined several approaches relying on the Polarizable Embedding (PE) scheme to predict optical band shapes for two chalcone molecules in methanol solution. The PE-TDDFT and PERI-CC2 methods were combined with molecular dynamics simulations, where the solute geometry was kept either as rigid, flexible or partly-flexible (restrained) body. The first approach, termed RBMD-PE-TDDFT, was employed to estimate the inhomogeneous broadening for subsequent convolution with the vibrationally-resolved spectra of the molecule in solution determined quantum-mechanically (QM). As demonstrated, the RBMD-PE-TDDFT/QM-PCM approach delivers accurate band widths, also reproducing their correct asymmetric shapes. Further refinement can be obtained by the estimation of the inhomogeneous broadening using the RBMD-PERI-CC2 method. On the other hand, the remaining two approaches (FBMD-PE-TDDFT and ResBMD-PE-TDDFT), which lack quantum-mechanical treatment of molecular vibrations, lead to underestimated band widths. In this study, we also proposed a simple strategy regarding the rapid selection of the exchange-correlation functional for the simulations of vibrationally-resolved one- and two-photon absorption spectra based on two easy-to-compute metrics.

Blue-Shifted Green Fluorescent Protein Homologues Are Brighter than Enhanced Green Fluorescent Protein under Two-Photon Excitation

Fluorescent proteins (FPs) are indispensable markers for two-photon imaging of live tissue, especially in the brains of small model organisms. The quantity of physiologically relevant data collected, however, is limited by heat-induced damage of the tissue due to the high intensities of the excitation laser. We seek to minimize this damage by developing FPs with improved brightness. Among FPs with the same chromophore structure, the spectral properties can vary widely due to differences in the local protein environment. Using a physical model that describes the spectra of FPs containing the anionic green FP (GFP) chromophore, we predict that those that are blue-shifted in one-photon absorption will have stronger peak two-photon absorption cross sections. Following this prediction, we present 12 blue-shifted GFP homologues and demonstrate that they are up to 2.5 times brighter than the commonly used enhanced GFP (EGFP).

Prediction of two-photon absorption enhancement in red fluorescent protein chromophores made from non-canonical amino acids

Two-photon spectroscopy of fluorescent proteins is a powerful bio-imaging tool known for deep tissue penetration and little cellular damage. Being less sensitive than the one-photon microscopy alternatives, a protein with a large two-photon absorption (TPA) cross-section is needed. Here, we use time-dependent density functional theory (TD-DFT) at the B3LYP and CAM-B3LYP/6-31+G(d,p) levels of theory to screen twenty-two possible chromophores that can be formed upon replacing the amino-acid Tyr66 that forms the red fluorescent protein (RFP) chromophore with a non-canonical amino acid. The two-level model for TPA was used to assess the properties (i.e., transition dipole moment, permanent dipole moment difference, and the angle between them) leading to the TPA cross-sections determined via response theory. Computing TPA cross-sections with B3LYP and CAM-B3LYP yields similar overall trends. Results using both functionals agree that the RFP-derived model of the Gold Fluorescent Protein chromophore (Model 20) has the largest intrinsic TPA cross-section at the optimized geometry. TPA was further computed for selected chromophores following conformational changes: variation of both the dihedral angle of the acylimine moiety and the tilt and twist angles between the rings of the chromophore. The TPA cross-section assumed an oscillatory trend with the rotation of the acylimine dihedral, and the TPA is maximized in the planar conformation for almost all models. Model 21 (a hydroxyquinoline derivative) is shown to be comparable to Model 20 in terms of TPA cross-section. The conformational study on Model 21 shows that the acylimine angle has a much stronger effect on the TPA than its tilt and twist angles. Having an intrinsic TPA ability that is more than 7 times that of the native RFP chromophore, Models 20 and 21 appear to be very promising for future experimental investigation.

Two-photon absorption of fluorescent protein chromophores incorporating non-canonical amino acids: TD-DFT screening and classical dynamics

Two-photon spectroscopy of fluorescent proteins is a powerful bio-imaging tool characterized by deep tissue penetration and little damage. However, two-photon spectroscopy has lower sensitivity than one-photon microscopy alternatives and hence a protein with a large two-photon absorption cross-section is needed. We use time-dependent density functional theory (TD-DFT) at the B3LYP/6-31+G(d,p) level of theory to screen twenty-two possible chromophores that can be formed upon replacing the amino-acid Tyr66 that forms the green fluorescent protein (GFP) chromophore with a non-canonical amino acid. A proposed chromophore with a nitro substituent was found to have a large two-photon absorption cross-section (29 GM) compared to other fluorescent protein chromophores as determined at the same level of theory. Classical molecular dynamics are then performed on a nitro-modified fluorescent protein to test its stability and study the effect of the conformational flexibility of the chromophore on its two-photon absorption cross-section. The theoretical results show that the large cross-section is primarily due to the difference between the permanent dipole moments of the excited and ground states of the nitro-modified chromophore. This large difference is maintained through the various conformations assumed by the chromophore in the protein cavity. The nitro-derived protein appears to be very promising as a two-photon absorption probe.

Assessment of mode-mixing and Herzberg-Teller effects on two-photon absorption and resonance hyper-Raman spectra from a time-dependent approach

A time-dependent approach is presented to simulate the two-photon absorption (TPA) and resonance hyper-Raman scattering (RHRS) spectra including Duschinsky rotation (mode-mixing) and Herzberg-Teller (HT) vibronic coupling effects. The computational obstacles for the excited-state geometries, vibrational frequencies, and nuclear derivatives of transition dipole moments, which enter the expressions of TPA and RHRS cross sections, are further overcome by the recently developed analytical excited-state energy derivative approaches in the framework of time-dependent density functional theory. The excited-state potential curvatures are evaluated at different levels of approximation to inspect the effects of frequency differences, mode-mixing and HT on TPA and RHRS spectra. Two types of molecules, one with high symmetry (formaldehyde, p-difluorobenzene, and benzotrifluoride) and the other with non-centrosymmetry (cis-hydroxybenzylidene-2,3-dimethylimidazolinone in the deprotonated anion state (HDBI(-))), are used as test systems. The calculated results reveal that it is crucial to adopt the exact excited-state potential curvatures in the calculations of TPA and RHRS spectra even for the high-symmetric molecules, and that the vertical gradient approximation leads to a large deviation. Furthermore, it is found that the HT contribution is evident in the TPA and RHRS spectra of HDBI(-) although its one- and two-photon transitions are strongly allowed, and its effect results in an obvious blueshift of the TPA maximum with respect to the one-photon absorption maximum. With the HT and solvent effects getting involved, the simulated blueshift of 1291 cm(-1) agrees well with the experimental measurement.

Two-Photon Absorption in Fluorescent Protein Chromophores: TDDFT and CC2 Results

Two-photon spectroscopy of fluorescent proteins is a powerful bioimaging tool. Considerable effort has been made to measure absolute two-photon absorption (TPA) for the available fluorescent proteins. Being a technically involved procedure, there is significant variation in the published experimental measurements even for the same protein. In this work, we present a time-dependent density functional theory (TDDFT) study on isolated chromophores comparing the ability of four functionals (PBE0, B3LYP, CAM-B3LYP, and LC-BLYP) combined with the 6-31+G(d,p) basis set to reproduce averaged experimental TPA energies and cross sections. The TDDFT energies and TPA cross sections are also compared to corresponding CC2/6-31+G(d,p) results for excitation to S1 for the five smallest chromophores. In general, the computed TPA energies are less functional dependent than the TPA cross sections. The variation between functionals is more pronounced when higher-energy transitions are studied. Changes to the conformation of a chromophore are shown to change the TPA cross-section considerably. This adds to the difficulty of comparing an isolated chromophore to the one embedded in the protein environment. All functionals considered give moderate agreement with the corresponding CC2 results; in general, the TPA cross sections determined by TDDFT are 1.5-10 times smaller than the corresponding CC2 values for excitation to S1. LC-BLYP and CAM-B3LYP give erroneously large TPA cross sections in the higher-energy regions. On the other hand, B3LYP and PBE0 yield values that are of the same order of magnitude and in some cases very close to the averaged experimental data. Thus, based on the results reported here, B3LYP and PBE0 are the preferred functionals for screening chromphores for TPA. However, at best, TDDFT can be used to semiquantitatively scan chromophores for potential TPA probes and highlight spectroscopic peaks that could be present in the mature protein.