Fragment molecular orbital calculations on red fluorescent proteins (DsRed and mFruits)

Analytic Gradient for Time-Dependent Density Functional Theory Combined with the Fragment Molecular Orbital Method

The analytic energy gradient of energy with respect to nuclear coordinates is derived for the fragment molecular orbital (FMO) method combined with time-dependent density functional theory (TDDFT). The response terms arising from the use of a polarizable embedding are derived. The obtained analytic FMO-TDDFT gradient is shown to be accurate in comparison to both numerical FMO-TDDFT and unfragmented TDDFT gradients, at the level of two- and three-body expansions. The gradients are used for geometry optimizations, molecular dynamics, vibrational calculations, and simulations of IR and Raman spectra of excited states. The developed method is used to optimize the geometry of the ground and excited electronic states of the photoactive yellow protein (PDB: 2PHY).

Fragment-Based Excited-State Calculations Using the GW Approximation and the Bethe-Salpeter Equation

Herein, we present a fragment-based approach for calculating the charged and neutral excited states in molecular systems, based on the many-body Green's function method within the GW approximation and the Bethe-Salpeter equation (BSE). The implementation relies on the many-body expansion of the total irreducible polarizability on the basis of fragment molecular orbitals. The GW quasi-particle energies in complex molecular environments are obtained by the GW calculation for the target fragment plus induced polarization contributions of the surrounding fragments at the static Coulomb-hole plus screened exchange level. In addition, we develop a large-scale GW/BSE method for calculating the delocalized excited states of molecular aggregates, based on the fragment molecular orbital method and the exciton model. The accuracy of fragment-based GW and GW/BSE methods was evaluated on molecular clusters and molecular crystals. We found that the accuracy of the total irreducible polarizability can be improved systematically by including two-body correction terms, and the fragment-based calculations can reasonably reproduce the results of the corresponding unfragmented calculations with a relative error of less than 100 meV. The proposed approach enables efficient excited-state calculations for large molecular systems with reasonable accuracy.

Local Electric Field Controls Fluorescence Quantum Yield of Red and Far-Red Fluorescent Proteins

Genetically encoded probes with red-shifted absorption and fluorescence are highly desirable for imaging applications because they can report from deeper tissue layers with lower background and because they provide additional colors for multicolor imaging. Unfortunately, red and especially far-red fluorescent proteins have very low quantum yields, which undermines their other advantages. Elucidating the mechanism of nonradiative relaxation in red fluorescent proteins (RFPs) could help developing ones with higher quantum yields. Here we consider two possible mechanisms of fast nonradiative relaxation of electronic excitation in RFPs. The first, known as the energy gap law, predicts a steep exponential drop of fluorescence quantum yield with a systematic red shift of fluorescence frequency. In this case the relaxation of excitation occurs in the chromophore without any significant changes of its geometry. The second mechanism is related to a twisted intramolecular charge transfer in the excited state, followed by an ultrafast internal conversion. The chromophore twisting can strongly depend on the local electric field because the field can affect the activation energy. We present a spectroscopic method of evaluating local electric fields experienced by the chromophore in the protein environment. The method is based on linear and two-photon absorption spectroscopy, as well as on quantum-mechanically calculated parameters of the isolated chromophore. Using this method, which is substantiated by our molecular dynamics simulations, we obtain the components of electric field in the chromophore plane for seven different RFPs with the same chromophore structure. We find that in five of these RFPs, the nonradiative relaxation rate increases with the strength of the field along the chromophore axis directed from the center of imidazolinone ring to the center of phenolate ring. Furthermore, this rate depends on the corresponding electrostatic energy change (calculated from the known fields and charge displacements), in quantitative agreement with the Marcus theory of charge transfer. This result supports the dominant role of the twisted intramolecular charge transfer mechanism over the energy gap law for most of the studied RFPs. It provides important guidelines of how to shift the absorption wavelength of an RFP to the red, while keeping its brightness reasonably high.

Assessment of Functionals for TDDFT Calculations of One- and Two-Photon Absorption Properties of Neutral and Anionic Fluorescent Proteins Chromophores

Performance of DFT functionals with different percentages of exact Hartree-Fock exchange energy (EX) is assessed for recovery of the CC2 reference one- (OPA) and two-photon absorption (TPA) spectra of fluorescent proteins chromophores in vacuo. The investigated DFT functionals, together with their EX contributions are BLYP (0%), B3LYP (20%), B1LYP (25%), BHandHLYP (50%), and CAM-B3LYP (19% at short range and 65% at long range). Our test set consists of anionic and neutral chromophores as naturally occurring in the fluorescent proteins. For the first time, we compare TDDFT and CC2 methods for higher excited states than the S₁ state, exhibiting relatively large TPA intensity. Our TDDFT results for neutral chromophores reveal an increase in excitation energies as well as TPA and OPA intensities errors, compared to CC2-derived results, as the DFT functional contains less exact exchange. The long-range-corrected CAM-B3LYP functional performs the best, closely followed by BHandHLYP, while BLYP usually significantly underestimates all investigated spectral properties, hence being the worst in reproducing the reference CC2 results. The hybrid B3LYP and B1LYP functionals can be roughly placed in between. We propose that TDDFT may underestimate the TPA intensities for neutral chromophores of fluorescent proteins due to underestimated oscillator strengths between some excited states. In the case of anionic chromophores, we find that B3LYP and B1LYP functionals overcome others in terms of reproducing CC2 excitation energies. On the other hand, however, TPA intensity is usually significantly underestimated, and in this respect, CAM-B3LYP functional seems to be again superior. In contrast to the case of neutral chromophores, it seems that a large magnitude of excited-state dipole moments or changes in dipole moments upon excitation may be the driving force behind high TPA transition moments.

Electron-correlated fragment-molecular-orbital calculations for biomolecular and nano systems

Recent developments in the fragment molecular orbital (FMO) method for theoretical formulation, implementation, and application to nano and biomolecular systems are reviewed. The FMO method has enabled ab initio quantum-mechanical calculations for large molecular systems such as protein-ligand complexes at a reasonable computational cost in a parallelized way. There have been a wealth of application outcomes from the FMO method in the fields of biochemistry, medicinal chemistry and nanotechnology, in which the electron correlation effects play vital roles. With the aid of the advances in high-performance computing, the FMO method promises larger, faster, and more accurate simulations of biomolecular and related systems, including the descriptions of dynamical behaviors in solvent environments. The current status and future prospects of the FMO scheme are addressed in these contexts.

Excited state electronic landscape of mPlum revealed by two-dimensional double quantum coherence spectroscopy

Red fluorescent proteins (RFPs) are widely used probes for monitoring subcellular processes with extremely high spatial and temporal precision. In this work, we employed spectrally resolved transient absorption (SRTA) and two-dimensional double quantum coherence (2D2Q) spectroscopy to investigate the excited state electronic structure of mPlum, a well-known RFP. The SRTA spectra reveal the presence of excited state absorption features at both the low- and high-energy sides of the dominant ground state bleach contribution. The 2D2Q spectra measured at several excitation wavelengths reveal a peak pattern consistent with the presence of more than three electronic states (i.e., ground, excited, and doubly excited). Numerical modeling of this response suggests that the features are consistent with a 1-1-2 electronic structure. The two closely spaced (∼1500 cm(-1)) levels in the double quantum manifold appear at opposite anharmonicities relative to twice the energy of the lowest energy transition. These observations explain the excited state absorption contributions observed in spectrally resolved transient grating and transient absorption measurements and demonstrate the utility of multidimensional spectroscopy in unraveling congested spectra relative to conventional one-dimensional methods.

Molecular-Level Insight into the Spectral Tuning Mechanism of the DsRed Chromophore

We present a detailed study of the protein environmental effects on the one- and two-photon absorption (1PA and 2PA, respectively) properties of the S0-S1 transition in the DsRed protein using the polarizable embedding density functional theory formalism. We find that steric factors and chromophore-protein interactions act in concert to enhance the 2PA activity inside the protein while adversely blue-shifting the 1PA maximum. A two-state model reveals that the 2PA intensity gain is primarily governed by the increased change in the permanent dipole moment between the ground and the excited states acquired inside the protein. Our results indicate that this mainly is attributable to counter-directional contributions stemming from Lys163 and the conserved Arg95 with the former additionally identified as a key residue in the color tuning mechanism. The results provide new insight into the tuning mechanism of DsRed and suggest a possible strategy for simultaneous improvement of its 1PA and 2PA properties.

Color tuning in photofunctional proteins

Depending on protein environment, a single photofunctional chromophore shows a wide variation of photoabsorption/emission energies. This photobiological phenomenon, known as color tuning, is observed in human visual cone pigments, firefly luciferase, and red fluorescent protein. We investigate the origin of color tuning by quantum chemical calculations on the excited states: symmetry-adapted cluster-configuration interaction (SAC-CI) method for excited states and a combined quantum mechanical (QM)/molecular mechanical (MM) method for protein environments. This Minireview summarizes our theoretical studies on the above three systems and explains a common feature of their color-tuning mechanisms. It also discuss the possibility of artificial color tuning toward a rational design of photoabsorption/emission properties.

SUPPLEMENTING THE PBSA APPROACH WITH QUANTUM MECHANICS TO STUDY THE BINDING BETWEEN CDK2 AND N2-SUBSTITUTED O6-CYCLOHEXYLMETHOXYGUANINE INHIBITORS

Because classical Poisson–Boltzman Surface Area (PBSA) model does not allow re-polarization of charges and does not account for charge transfer when a ligand binds to a protein, we have examined a hybrid approach in which we describe the protein–ligand interface by quantum mechanics and the rest of the system with the classical PBSA model. We found this approach to rank order the binding of five N2 -substituted O6 -cyclohexylmethoxyguanine inhibitors to CDK2 (cyclin-dependent kinase 2) properly. The calculated binding free energy correlated well with experimental Log(IC50) with a correlation coefficient of 0.94. A regression fit between experimental Log(IC50) and calculated binding free energy yielded a root-mean-square error of 0.48 when Log(IC50) spanned a range over three units. In addition, we observed charge transfer between the ligand and the protein at the interface — an effect not accounted for by the classical PBSA model. We also found that the direct interactions between the protein and the ligands provided the dominant factor to distinguish the binding affinity of the five ligands studied here. This hybrid approach can better prioritize derivatives of lead compounds for synthesis and biological evaluation.

Computational strategy for tuning spectral properties of red fluorescent proteins

Computational methods of quantum chemistry are used to characterize structures and vertical excitation energies of the S(0)-S(1) optical transitions in the chromophore binding pockets of the red fluorescent proteins DsRed and of its artificial mutant mCherry. As previously shown, optimizing the equilibrium geometry configurations with B3LYP density functional theory, followed by ZINDO calculations of the electronic excitations, yields positions of the optical bands in good agreement with experimental data. These large scale quantum calculations elucidate the role of the hydrogen bonded network as well as point mutations in the absorption spectra of the DsRed and mCherry proteins. The effect of an external electric field applied to the fluorescent protein chromophores is examined and shows that such fields may result in large shifts in spectral bands. These strategies can be applied for rational design of the fluorescent proteins by site-directed mutagenesis.

Molecular mechanism of a green-shifted, pH-dependent red fluorescent protein mKate variant

Fluorescent proteins that can switch between distinct colors have contributed significantly to modern biomedical imaging technologies and molecular cell biology. Here we report the identification and biochemical analysis of a green-shifted red fluorescent protein variant GmKate, produced by the introduction of two mutations into mKate. Although the mutations decrease the overall brightness of the protein, GmKate is subject to pH-dependent, reversible green-to-red color conversion. At physiological pH, GmKate absorbs blue light (445 nm) and emits green fluorescence (525 nm). At pH above 9.0, GmKate absorbs 598 nm light and emits 646 nm, far-red fluorescence, similar to its sequence homolog mNeptune. Based on optical spectra and crystal structures of GmKate in its green and red states, the reversible color transition is attributed to the different protonation states of the cis-chromophore, an interpretation that was confirmed by quantum chemical calculations. Crystal structures reveal potential hydrogen bond networks around the chromophore that may facilitate the protonation switch, and indicate a molecular basis for the unusual bathochromic shift observed at high pH. This study provides mechanistic insights into the color tuning of mKate variants, which may aid the development of green-to-red color-convertible fluorescent sensors, and suggests GmKate as a prototype of genetically encoded pH sensors for biological studies.

Excited states of fluorescent proteins, mKO and DsRed: chromophore-protein electrostatic interaction behind the color variations

The emitting states of green fluorescent protein (GFP), monomeric Kusabira orange (mKO), and Discosoma red (DsRed) were studied using QM/MM and SAC-CI methods. By comparing the electronic structures among the green-, orange-, and red-emitting states as well as their electrostatic and quantum mechanical interactions within the protein cavity, the basic mechanisms for determining emission colors have been clarified. We found that the orange and red emissions of mKO and DsRed, respectively, result from cancellation between two effects, the pi skeleton extension (red shift) and protein electrostatic potential (blue shift). The extension of the pi skeleton enhances the intramolecular charge-transfer character of the transition, which makes the fluorescence energy more sensitive to the protein's electrostatic potential. On the basis of this mechanism, we predicted amino acid mutations that could red shift the emission energy of DsRed. A novel single amino acid mutation, which was examined computationally, reduced the DsRed emission energy from 2.14 (579 nm) to 1.95 eV (636 nm), which is approaching near-infrared fluorescence.

Autofluorescent proteins with excitation in the optical window for intravital imaging in mammals

Fluorescent proteins have become valuable tools for biomedical research as protein tags, reporters of gene expression, biosensor components, and cell lineage tracers. However, applications of fluorescent proteins for deep tissue imaging in whole mammals have been constrained by the opacity of tissues to excitation light below 600 nm, because of absorbance by hemoglobin. Fluorescent proteins that excite efficiently in the "optical window" above 600 nm are therefore highly desirable. We report here the evolution of far-red fluorescent proteins with peak excitation at 600 nm or above. The brightest one of these, Neptune, performs well in imaging deep tissues in living mice. The crystal structure of Neptune reveals a novel mechanism for red-shifting involving the acquisition of a new hydrogen bond with the acylimine region of the chromophore.