QM/MM Investigation of the Spectroscopic Properties of the Fluorophore of Bacterial Luciferase.

We employ replica-exchange molecular dynamics (REMD) and a hybrid ab initio multiconfigurational quantum mechanics/molecular mechanics (QM/MM) approach to model the absorption and fluorescence properties of bacterial luciferin-luciferase. Specifically, we employ complete active space perturbation theory (CASPT2) and study the effect of active space, basis set, and IPEA shift on the computed energies. We discuss the effect of the protein environment on the fluorophore's excited-state potential energy surface and the role that the protein plays in enhancing the fluorescence quantum yield in bacterial bioluminescence.

An Average Solvent Electrostatic Configuration Protocol for QM/MM Free Energy Optimization: Implementation and Application to Rhodopsin Systems.

A novel atomistic methodology to perform free energy geometry optimization of a retinal chromophore covalently bound to any rhodopsin-like protein cavity is presented and benchmarked by computing the absorption maxima wavelengths (λmax) of distant rhodopsin systems. The optimization is achieved by computing the Nagaoka's Free Energy Gradient (FEG) within an Average Solvent Electrostatic Configuration (ASEC) atomistic representation of the thermodynamic equilibrium and minimizing such quantity via an iterative procedure based on sequential classical MD and constrained QM/MM geometry optimization steps. The performance of such an ASEC-FEG protocol is assessed at the CASPT2//CASSCF/Amber level by reproducing the λmax values observed for 12 mutants of redesigned human cellular retinol binding protein II (hCRBPII) systems; a set of 10 distant wild-type rhodopsins from vertebrates, invertebrates, eubacteria, and archaea organisms; and finally a set of 10 rhodopsin mutants from an eubacterial rhodopsin. The results clearly show that the proposed protocol, which can be easily extended to any protein incorporating a covalently bound ligand, yields correct λmax trends with limited absolute errors.

Modulation of thermal noise and spectral sensitivity in Lake Baikal cottoid fish rhodopsins.

Lake Baikal is the deepest and one of the most ancient lakes in the world. Its unique ecology has resulted in the colonization of a diversity of depth habitats by a unique fauna that includes a group of teleost fish of the sub-order Cottoidei. This relatively recent radiation of cottoid fishes shows a gradual blue-shift in the wavelength of the absorption maximum of their visual pigments with increasing habitat depth. Here we combine homology modeling and quantum chemical calculations with experimental in vitro measurements of rhodopsins to investigate dim-light adaptation. The calculations, which were able to reproduce the trend of observed absorption maxima in both A1 and A2 rhodopsins, reveal a Barlow-type relationship between the absorption maxima and the thermal isomerization rate suggesting a link between the observed blue-shift and a thermal noise decrease. A Nakanishi point-charge analysis of the electrostatic effects of non-conserved and conserved amino acid residues surrounding the rhodopsin chromophore identified both close and distant sites affecting simultaneously spectral tuning and visual sensitivity. We propose that natural variation at these sites modulate both the thermal noise and spectral shifting in Baikal cottoid visual pigments resulting in adaptations that enable vision in deep water light environments.

Toward Automatic Rhodopsin Modeling as a Tool for High-Throughput Computational Photobiology.

We report on a prototype protocol for the automatic and fast construction of congruous sets of QM/MM models of rhodopsin-like photoreceptors and of their mutants. In the present implementation the information required for the construction of each model is essentially a crystallographic structure or a comparative model complemented with information on the protonation state of ionizable side chains and distributions of external counterions. Starting with such information, a model formed by a fixed environment system, a flexible cavity system, and a chromophore system is automatically generated. The results of the predicted vertical excitation energy for 27 different rhodopsins including vertebrate, invertebrate, and microbial pigments indicate that such basic models could be employed for predicting trends in spectral changes and/or correlate the spectral changes with structural variations in large sets of proteins.

Space and Time Evolution of the Electrostatic Potential During the Activation of a Visual Pigment.

Animal and microbial retinal proteins employ the Schiff base of retinal as their chromophore. Here, the possible consequences of the charge translocation associated with the light-induced dynamics of the chromophore of a visual opsin are investigated along a representative semiclassical trajectory. We show that the evolution of the electrostatic potential projected by the chromophore onto the surrounding protein displays intense but topographically localized sudden variations in proximity of the decay region. pKa calculations carried out on selected snapshots used as probes, indicate that the only residue which may be sensitive to the electrostatic potential shift is Glu181. Accordingly, our results suggest that the frail Tyr191/268-Glu181-Wat2-Ser186 hydrogen bond network may be perturbed by the transient variations of the electrostatic potential.

Molecular bases for the selection of the chromophore of animal rhodopsins.

The functions of microbial and animal rhodopsins are triggered by the isomerization of their all-trans and 11-cis retinal chromophores, respectively. To lay the molecular basis driving the evolutionary transition from the all-trans to the 11-cis chromophore, multiconfigurational quantum chemistry is used to compare the isomerization mechanisms of the sensory rhodopsin from the cyanobacterium Anabaena PCC 7120 (ASR) and of the bovine rhodopsin (Rh). It is found that, despite their evolutionary distance, these eubacterial and vertebrate rhodopsins start to isomerize via distinct implementations of the same bicycle-pedal mechanism originally proposed by Warshel [Warshel A (1976) Nature 260:678-683]. However, by following the electronic structure changes of ASR (featuring the all-trans chromophore) during the isomerization, we find that ASR enters a region of degeneracy between the first and second excited states not found in Rh (featuring the 11-cis chromophore). We show that such degeneracy is modulated by the preorganized structure of the chromophore and by the position of the reactive double bond. It is argued that the optimization of the electronic properties of the chromophore, which affects the photoisomerization efficiency and the thermal isomerization barrier, provided a key factor for the emergence of the striking amino acid sequence divergence observed between the microbial and animal rhodopsins.

A conical intersection controls the deactivation of the bacterial luciferase fluorophore.

The photophysics of flavins is highly dependent on their environment. For example, 4a-hydroxy flavins display weak fluorescence in solution, but exhibit strong fluorescence when bound to a protein. To understand this behavior, we performed temperature-dependent fluorescent studies on an N(5)-alkylated 4a-hydroxy flavin: the putative bacterial luciferase fluorophore. We find an increase in fluorescence quantum yield upon reaching the glass transition temperature of the solvent. We then employ multiconfigurational quantum chemical methods to map the excited-state deactivation path of the system. The result reveals a shallow but barrierless excited state deactivation path that leads to a conical intersection displaying an orthogonal out-of-plane distortion of the terminal pyrimidine ring. The intersection structure readily explains the observed spectroscopic behavior in terms of an excited-state barrier imposed by the rigid glass cavity.

Comparison of the isomerization mechanisms of human melanopsin and invertebrate and vertebrate rhodopsins.

Comparative modeling and ab initio multiconfigurational quantum chemistry are combined to investigate the reactivity of the human nonvisual photoreceptor melanopsin. It is found that both the thermal and photochemical isomerization of the melanopsin 11-cis retinal chromophore occur via a space-saving mechanism involving the unidirectional, counterclockwise twisting of the =C11H-C12H= moiety with respect to its Lys340-linked frame as proposed by Warshel for visual pigments [Warshel A (1976) Nature 260(5553):679-683]. A comparison with the mechanisms documented for vertebrate (bovine) and invertebrate (squid) visual photoreceptors shows that such a mechanism is not affected by the diversity of the three chromophore cavities. Despite such invariance, trajectory computations indicate that although all receptors display less than 100 fs excited state dynamics, human melanopsin decays from the excited state ∼40 fs earlier than bovine rhodopsin. Some diversity is also found in the energy barriers controlling thermal isomerization. Human melanopsin features the highest computed barrier which appears to be ∼2.5 kcal mol(-1) higher than that of bovine rhodopsin. When assuming the validity of both the reaction speed/quantum yield correlation discussed by Warshel, Mathies and coworkers [Weiss RM, Warshel A (1979) J Am Chem Soc 101:6131-6133; Schoenlein RW, Peteanu LA, Mathies RA, Shank CV (1991) Science 254(5030):412-415] and of a relationship between thermal isomerization rate and thermal activation of the photocycle, melanopsin turns out to be a highly sensitive pigment consistent with the low number of melanopsin-containing cells found in the retina and with the extraretina location of melanopsin in nonmammalian vertebrates.

Shape of Multireference, Equation-of-Motion Coupled-Cluster, and Density Functional Theory Potential Energy Surfaces at a Conical Intersection.

We report and characterize ground-state and excited-state potential energy profiles using a variety of electronic structure methods along a loop lying on the branching plane associated with a conical intersection (CI) of a reduced retinal model, the penta-2,4-dieniminium cation (PSB3). Whereas the performance of the equation-of-motion coupled-cluster, density functional theory, and multireference methods had been tested along the excited- and ground-state paths of PSB3 in our earlier work, the ability of these methods to correctly describe the potential energy surface shape along a CI branching plane has not yet been investigated. This is the focus of the present contribution. We find, in agreement with earlier studies by others, that standard time-dependent DFT (TDDFT) does not yield the correct two-dimensional (i.e., conical) crossing along the branching plane but rather a one-dimensional (i.e., linear) crossing along the same plane. The same type of behavior is found for SS-CASPT2(IPEA=0), SS-CASPT2(IPEA=0.25), spin-projected SF-TDDFT, EOM-SF-CCSD, and, finally, for the reference MRCISD+Q method. In contrast, we found that MRCISD, CASSCF, MS-CASPT2(IPEA=0), MS-CASPT2(IPEA=0.25), XMCQDPT2, QD-NEVPT2, non-spin-projected SF-TDDFT, and SI-SA-REKS yield the expected conical crossing. To assess the effect of the different crossing topologies (i.e., linear or conical) on the PSB3 photoisomerization efficiency, we discuss the results of 100 semiclassical trajectories computed by CASSCF and SS-CASPT2(IPEA=0.25) for a PSB3 derivative. We show that for the same initial conditions, the two methods yield similar dynamics leading to isomerization quantum yields that differ by only a few percent.

Mapping the Excited State Potential Energy Surface of a Retinal Chromophore Model with Multireference and Equation-of-Motion Coupled-Cluster Methods.

The photoisomerization of the retinal chromophore of visual pigments proceeds along a complex reaction coordinate on a multidimensional surface that comprises a hydrogen-out-of-plane (HOOP) coordinate, a bond length alternation (BLA) coordinate, a single bond torsion and, finally, the reactive double bond torsion. These degrees of freedom are coupled with changes in the electronic structure of the chromophore and, therefore, the computational investigation of the photochemistry of such systems requires the use of a methodology capable of describing electronic structure changes along all those coordinates. Here, we employ the penta-2,4-dieniminium (PSB3) cation as a minimal model of the retinal chromophore of visual pigments and compare its excited state isomerization paths at the CASSCF and CASPT2 levels of theory. These paths connect the cis isomer and the trans isomer of PSB3 with two structurally and energetically distinct conical intersections (CIs) that belong to the same intersection space. MRCISD+Q energy profiles along these paths provide benchmark values against which other ab initio methods are validated. Accordingly, we compare the energy profiles of MRPT2 methods (CASPT2, QD-NEVPT2, and XMCQDPT2) and EOM-SF-CC methods (EOM-SF-CCSD and EOM-SF-CCSD(dT)) to the MRCISD+Q reference profiles. We find that the paths produced with CASSCF and CASPT2 are topologically and energetically different, partially due to the existence of a "locally excited" region on the CASPT2 excited state near the Franck-Condon point that is absent in CASSCF and that involves a single bond, rather than double bond, torsion. We also find that MRPT2 methods as well as EOM-SF-CCSD(dT) are capable of quantitatively describing the processes involved in the photoisomerization of systems like PSB3.

Quantum chemical modeling of rhodopsin mutants displaying switchable colors.

We look at the possibility to compute and understand the color change occurring upon mutation of a photochromic protein. Accordingly, ab initio multiconfigurational quantum chemical methods are used to construct basic quantum-mechanics/molecular-mechanics (QM/MM) models for a small mutant library of the sensory rhodopsin of Anabaena (Nostoc) sp. PCC7120 cyanobacterium. Together with the wild-type forms, a set of 26 absorption maxima spanning a ca. 80 nm range is obtained. We show that these models can be used to capture the electrostatic change controlling the computed color variation and the change in the ionization of specific side chains.

Origin of Fluorescence in 11-cis Locked Bovine Rhodopsin.

The excited state lifetime of bovine rhodopsin (Rh) increases from ca. 100 fs to 85 ps when the C11═C12 bond of its chromophore is locked by a cyclopentene moiety (Rh5). To explain such an increase, we employed ab initio multiconfigurational quantum chemistry to construct computer models of Rh and Rh5 and to investigate the shape of their excited state potential energy surfaces in a comparative way. Our results show that the observed Rh5 fluorescence (λmax(f) = 620 nm) is due to a previously unreported locally excited intermediate whose lifetime is controlled by a small energy barrier. The analysis of the properties and decay path of such an intermediate provides useful information for engineering rhodopsin variants with augmented fluorescence efficiencies.

Using the computer to understand the chemistry of conical intersections.

The application of computational chemistry in resolving photochemical and photobiological problems depends on theoretical models and calculation strategies that allow an understanding of how and when the energy contained in a photon can be used or dissipated by a molecule. Progress in this arena has been the result of a scientific journey that can be traced from the 1960s and 1970s with the development of the concept of the "photochemical funnel", and again from the 1980s and 1990s with the development and application of ab initio multiconfigurational quantum chemistry. Mainly following the viewpoint and contributions of the corresponding author (together with others), here we show that both the early and the ongoing research points to a central role of conical intersections in the molecular-level control of the selectivity and efficiency of photochemical reactions and internal conversion processes.