Knowledge of a detailed picture of the events occurring in the chromophore-containing domains of photosensing proteins at atomic resolution is important for a rational design of novel fluorescent proteins with improved properties. Modern molecular modeling tools including quantum chemistry methods are of considerable value in this research contributing considerably to this field [1-30]. When performing such simulations, questions of accuracy and speed of calculations are the important issues for quick prediction of spectral bands in mutated proteins, which is a typical request from experimentalists. At one extreme, elaborate approaches based on quantum mechanics-molecular mechanics (QM/MM) optimization of geometry coordinates in the chromophore-containing domains, followed by expensive ab initio calculations of excitation energies (e.g., by using versions of configuretion interaction (CI) and perturbation theory-based methods, CASPT2 and MCQDPT2), are described in the literature [4,10,13,14,20,22,27,30-32]. The significance of these approaches is highly recognized; however, time and computational resources are quite demanding for these approaches to be routinely applied to a series of calculations. At another extreme, multiple attempts to apply inexpensive TD DFT [33] and ZINDO [34] methods to evaluate vertical excitation energies for model systems composed of the chromophore and small fractions of the environmental molecular groups of protein have often resulted in uncertain conclusions. Since the first calculations for the DsRed protein [1], in which the authors demonstrated that ZINDO provided reasonable estimates for absorption bands, and TD DFT was highly inferior to ZINDO, the progress along this line has been fairly slow.

In this work we demonstrate that higher accuracy in ZINDO-based calculations may be achieved by considering fairly large molecular clusters mimicking chromophore-containing domains of proteins with a careful optimization of geometry coordinates by using the coordinate-locking scheme. The latter is widely applied in a related field, i.e., in simulations of enzymatic reactions [35]. In this approach, a model molecular system has been constructed, as taken from the protein matrix, and certain atomic coordinates at the periphery of the model are fixed, as in the reference moieties, such as crystal or other reliable structures, upon optimization of geometry coordinates. For the systems with carefully optimized geometry parameters, ZINDO has been found to be very efficient in computing bands in optical spectra. As shown in our previous applications for several classes of fluorescent proteins [19,21,24], such a strategy in fact leads to accurate results that are comparable to the experimenttal values. In this work we show that an elaborate selection of model clusters in the coordinate-locking scheme and an application of fairly inexpensive quantum chemistry methods allow us to calculate bands both in the absorption and in the emission spectra of proteins. Such clusters can be designed when starting from the coordinates of heavy atoms of relevant structures deposited to the Protein Data Bank (PDB). After the addition of hydrogen atoms, a model system can be equilibrated by using classical molecular dynamics (MD) simulations, followed by geometry optimization using the QM/MM technique with a relatively small quantum subsystem. These preliminary steps allow one to achieve general relaxation of atomic coordinates in the chromophore-conining domain. The final treatment of a large cluster alows one to describe interaction of the chromophore with an extended environment at the exclusive quantum level and to eliminate ambiguous effects of the QM/MM boundary.

Colored protein asFP595, a natural protein from Anemonia sulcata, and its Ala143Gly variant called kindling fluorescent protein (KFP) [36-44], are important members of the GFP family. Upon light illumination at low intensities, asFP595 and KFP are weakly fluorescent with a very low quantum yield. However, high-intensity irradiation with green light leads to a nonlinear dependence of the fluorescence intensity on excitation energy and to a drastic increase of the quantum yield. Such kindling is reversible, since upon blue light illumination or in the dark, the proteins return to the initial nonfluorescent state. The reversible photoswitching is highly attractive for developments in optical microscopy much below the diffraction limit. Also, KFP is considered a convenient acceptor partner in the Förster resonance energy transfer (FRET) pair with brightly fluorescent red protein TagRFP. Employing FRET between these two proteins connected by an appropriate peptide linker opens new perspectives for monitoring biological and physiological mechanisms and for creating novel diagnostic tools [45, 46].

Beyond promising practical applications, studies of asFP595 are of considerable importance, due to challenging puzzles in its photophysical behavior. The reasons for increased red fluorescence of the initially non-fluorescent species upon intense green light illumination are not yet fully understood. The current working hypothesis relates the photoswitching phenomenon in asFP595 and KFP to the light-induced tran-cis isomerization of the chromophore inside the protein matrix. In spite of certain evidence provided in favor of this viewpoint by the crystal structures of asFP595 and KFP [39-41], especially in the work of Andresen et al. [40], no direct proof has been found to demonstrate such a trans-cis isomerization route in the protein environment. The MD-created movie in ref. [40] for the trans-cis transformations may be considered as a nice visualization but not as a strong argument. Even more intriguing is a recent demonstration of protein kindling in the experiments in solutions by varying pH [25]. Namely, it has been demonstrated that at physiological pH the KFP variant is still a weakly fluorescent species; however, the intensity of fluorescence is considerably increasing upon shifting pH to alkaline values. Tentative mechanisms of pH-induced kindling were discussed in ref. [25] which did not exclude increase of population of proteins with the cis-isomer of the chromophore.

Apparently, there is a strong need to provide a detailed picture of the photo-induced processes in asFP595 and KFP at atomic resolution, starting from structural and spectral properties. Reliable theoretical estimates for the emission spectrum are still unknown, and no firm assignment of the observed peak at 595 nm to a specific chromophore isomer has yet been made. We show that the computed band position both in absorption and in emission correlate well with experimentally observed band maxima what provides a solid support to the so far tentative assignments of the spectral bands.

The model clusters mimicking the chromophore containing pocket were prepared as follows. The crystal structure PDB 2A50 [40] of the wild-type asFP595 with the trans-anionic chromophore served as an initial source of coordinates of heavy atoms. After addition of hydrogen atoms assuming a generally accepted protonation scheme for polar amino acid residues Arg, Lys (positively charged), and Asp, Glu (negatively charged), the geometry coordinates were optimized by using the flexible effective fragment potential QM/MM method [47,48]. The QM subsystem described at the restricted Hartree-Fock method with the 6-31G basis set level was composed of Chro, Arg92, Ser158, His197, and Glu215. The MM subsystem was described with the AMBER force field parameters. This level of theoretical approach is suitable for preliminary geometry optimization on the ground state potential surface, but apparently is not sufficient for quantitative predictions, first of all, because of small basis set and absence of correlation contributions. On the other hand, we needed QM/MM minimization as a preliminary step before cluster calculations in order to prepare a better relaxed all-atom model initiated by the coordinates of heavy atoms only in the crystal structure. We examined the superposition of the QM/MM optimized and crystal (PDB 2A50) structures (Figure 1) and found that theoretical coordinates of backbone atoms were well reproduced in simulations. QM/MM calculations were performed by using the modified version of the GAMESS(US) package [49].

Next, we manually selected 20 amino acid residues completely surrounding the chromophore, as well as nine crystallography-resolved water molecules to form a model cluster, as shown in Figure 2. By such selection, first of all, we intended to form a closed shell around the chromophore, and secondly, to maintain the hydrogen

bon network around the chromophore. In total, the system included 308 atoms for the case of anionic chromophore. In Figure 1, the selected carbon atoms whose coordinates were kept frozen in subsequent geometry optimizations were indicated by colored balls. We used the B3LYP/6-31G(d) approximation of the density functional theory (DFT) methodology to find equilibrium coordinates for the ground state. These coordinates were used to compute vertical excitation energies by using the ZINDO method. Model clusters with the chromophore in the cis form were constructed manually, and their coordinates were re-optimized in the same DFT approximation.

As we see below, the position of absorption bands of the protein is well reproduced for the clusters of such size. However, in order to make a feasible location of energy minima on the excited state potential surface by using the configuration interaction with singles (CIS) method with a subsequent estimation of the emission bands, we had to reduce the number of atoms included in calculations. Reduction of the cluster size was performed manually in such a way that the hydrogen bond network spanning the chromophore and the immediate residues should be substantially conserved with respect to the large clusters. Finally, the 214-atomic cluster (for the case of the trans-anionic chromophore) was designed. Figure 3 illustrates the corresponding model system and shows explicitly which of the peripheral carbon atoms coordinates were kept frozen as in the large cluster (Figure 1) upon optimization of internal coordinates, both in the ground state by using B3LYP/6-31G(d) and in the first excited singlet state by using CIS/6-31G(d).

DFT, CIS and ZINDO calculations were performed by

using Gaussian03 [50].

Firstly, we briefly mention the results of calculations performed for the anionic gas-phase chromophore species (2-acetyl-4-(p-hydroxybenzylidene)-1-methyl-5-imidazolone) shown in Figure 4. Equilibrium geometry coordinates of these molecules were obtained in the B3LYP/6- 31 + G(d,p) approximation by using slightly more extended basis sets than those (6-31G(d)) used for the molecular clusters.

The ZINDO results for the absorption band maxima of the isolated chromophores are 556 nm (or 2.23 eV) for the trans isomer and 569 nm (or 2.18 eV) for the cis isomer. Previous calculations of the vertical excitation energies for the asFP595 chromophore in vacuo [5,6,13-15] in fact show a diversity of results, the most reliable of which [13,14] systematically predict the excitation energy of the cis isomer somewhat lower (about 0.09 - 0.15 eV) than that of the trans isomer. In this respect, the present ZINDO//DFT results are consistent with the higherlevel approaches.

Emission band maxima of the isolated chromophores were evaluated as the vertical energy differences between S₀ and S₁ states at the geometry coordinates optimized in the first excited state S₁ by using the CIS/6-31+G(d,p) procedure. We obtained 565 nm (2.19 eV) for the trans isomer and 578 nm (2.14 eV) for the cis isomer. These ZINDO results illustrate a trend showing that the cis form of the chromophore that the CIS vertical energy differences between two electronic states were strongly overestimated; however, ZINDO at the CIS optimized geometry parameters performed well.

Figure 5 illustrates arrangements of the key residues around the chromophore in the trans-configuration (toppanel) and in the cis-configuration (bottom panel), ac