Markus Doerr

QM/MM calculation of solvent effects on absorption spectra of guanine

Electronic spectra of guanine in the gas phase and in water were studied by quantum mechanical/molecular mechanical (QM/MM) methods. Geometries for the excited‐state calculations were extracted from ground‐state molecular dynamics (MD) simulations using the self‐consistent‐charge density functional tight binding (SCC‐DFTB) method for the QM region and the TIP3P force field for the water environment. Theoretical absorption spectra were generated from excitation energies and oscillator strengths calculated for 50 to 500 MD snapshots of guanine in the gas phase (QM) and in solution (QM/MM). The excited‐state calculations used time‐dependent density functional theory (TDDFT) and the DFT‐based multireference configuration interaction (DFT/MRCI) method of Grimme and Waletzke, in combination with two basis sets. Our investigation covered keto‐N7H and keto‐N9H guanine, with particular focus on solvent effects in the low‐energy spectrum of the keto‐N9H tautomer. When compared with the vertical excitation energies of gas‐phase guanine at the optimized DFT (B3LYP/TZVP) geometry, the maxima in the computed solution spectra are shifted by several tenths of an eV. Three effects contribute: the use of SCC‐DFTB‐based rather than B3LYP‐based geometries in the MD snapshots (red shift of ca. 0.1 eV), explicit inclusion of nuclear motion through the MD snapshots (red shift of ca. 0.1 eV), and intrinsic solvent effects (differences in the absorption maxima in the computed gas‐phase and solution spectra, typically ca. 0.1–0.3 eV). A detailed analysis of the results indicates that the intrinsic solvent effects arise both from solvent‐induced structural changes and from electrostatic solute–solvent interactions, the latter being dominant.

QM/MM Study of the Absorption Spectra of DsRed.M1 Chromophores

We report geometries and vertical excitation energies for the red and green chromophores of the DsRed.M1 protein in the gas phase and in the solvated protein environment. Geometries are optimized using density functional theory (DFT, B3LYP functional) for the isolated chromophores and combined quantum mechanical/molecular mechanical (QM/MM) methods for the protein (B3LYP/MM). Vertical excitation energies are computed using DFT/MRCI, OM2/MRCI, and TDDFT as QM methods. In the case of the red chromophore, there is a general blue shift in the excitation energies when going from the isolated chromophore to the protein, which is caused both by structural changes and by electrostatic interactions with the environment. For the lowest ππ* transition, these two factors contribute to a similar extent to the overall DFT/MRCI shift of 0.4 eV. An enlargement of the QM region to include active‐site residues does not change the DFT/MRCI excitation energies much. The DFT/MRCI results are closest to experiment for both chromophores. OM2/MRCI and TDDFT overestimate the first vertical excitation energy by 0.3–0.5 and 0.2–0.4 eV, respectively, relative to the experimental or DFT/MRCI values. The experimental gap of 0.35 eV between the lowest ππ* excitation energies of the red (cis‐acylimine) and green (trans‐peptide) forms is well reproduced by DFT/MRCI and TDDFT (0.32 and 0.37 eV, respectively). A histogram spectrum for an equal mixture of the two forms, generated by OM2/MRCI calculations on 450 snapshots along molecular dynamics trajectories, matches the experimental spectrum quite well, with a gap of 0.23 eV and an overall blue shift of about 0.3 eV. DFT/MRCI appears as an attractive choice for calculating excitation energies in fluorescent proteins, without the shortcomings of TDDFT and computationally more affordable than CASSCF‐based approaches.

QM/MM studies of structural and energetic properties of the far-red fluorescent protein HcRed.

The far-red fluorescent protein HcRed was investigated using molecular dynamics (MD) and combined quantum mechanics/molecular mechanics (QM/MM) calculations. Three models of HcRed (anionic chromophore) were considered, differing in the protonation states of nearby Glu residues (A: Glu214 and Glu146 both protonated; B: Glu214 protonated and Glu146 deprotonated; C: Glu214 and Glu146 both deprotonated). SCC-DFTB/MM MD simulations of model B yield good agreement with the available crystallographic data at ambient pH. Bond lengths in the QM region are well reproduced, with a root mean square (rms) deviation between experimental and average MD data of 0.079 A; the chromophore is almost co-planar, which is consistent with experimental observation; and the five hydrogen bonds involving the chromophore are conserved. QM/MM geometry optimizations were performed on representative snapshot structures from the MD simulations for each model. They confirm the structural features observed in the MD simulations. According to the DFT(B3LYP)/MM results, the cis-conformation of the chromophore is more stable than the trans-form by 9.1-12.9 kcal mol(-1) in model B, and by 12.4-19.9 kcal mol(-1) in model C, consistent with the experimental preference for the cis-isomer. However, in model A when both Glu214 and Glu146 are protonated, the stability is inverted with the trans-form being favored. The different protonation states of the titratable active-site residues Glu214 and Glu146 thus critically influence the manner in which the relative stability and degree of planarity of the cis- and trans-conformers vary with pH. Coupled with the known correlation of chromophore conformation with fluorescence efficiency, this work provides a detailed structural basis for the observed phenomenon that red fluorescent proteins such as HcRed, mKate and Rtms5 show bright fluorescence at high pH.

Quantum refinement of protein structures: implementation and application to the red fluorescent protein DsRed.M1.

Quantum refinement is an improvement upon the molecular mechanics (MM)-based crystallographic refinement. In the latter, X-ray data are supplemented with additional chemical information through MM force fields, whereas quantum refinement describes crucial regions of interest in the macromolecule by quantum mechanics (QM) instead of MM. In this paper, we report the implementation of quantum refinement in the ChemShell QM/MM framework and its application in an investigation of the chromophore structure of the red fluorescent protein DsRed.M1. Both mechanical and electrostatic QM/MM embedding schemes are implemented and tested. In the quantum refinement of DsRed.M1, the anionic red acylimine chromophore adopts a nearly orthogonal arrangement (rather than a cis or trans form), and the bond lengths in the acylimine moiety are more consistent with a phenolate (rather than a quinoid) structure. These findings are in contrast to the structure deduced from a standard crystallographic refinement (PDB: 2VAD), but in agreement with our earlier results from a purely theoretical QM/MM study. On the other hand, the quantum refinement of the anionic acylimine form of DsRed.M1 yields a hydrogen bonding network around the chromophore, especially with regard to the arrangement of the water molecules and the Glu148 residue, that is closer to the 2VAD structure than to the previously optimized QM/MM structure. In our earlier study the initial classical molecular dynamics (MD) simulations during QM/MM setup apparently exaggerated the mobility of the water molecules around the chromophore. On the basis of the present results, it seems likely that the Glu148 residue is protonated in the DsRed.M1 protein. The calculation of electronic excitation energies allows for further assessment of the proposed structures, especially in the chromophore region. Using a combination of density functional theory and multireference configuration interaction (DFT/MRCI), we find excellent agreement between experiment and theory only for the structures obtained from quantum refinement and from QM/MM optimization, but not for the 2VAD structure. The present case study on DsRed.M1 thus demonstrates the merits of combining reliable theoretical and experimental information in the determination of protein structures.

Photophysics of phenalenone: quantum-mechanical investigation of singlet–triplet intersystem crossing

We have examined the electronic and molecular structure of 1H-phenalen-1-one (phenalenone) in the electronic ground state and in the lowest excited states, as well as intersystem crossing. The electronic structure was calculated using a combination of density functional theory and multi-reference configuration interaction. Intersystem crossing rates were determined using Fermis golden rule and taking direct and vibronic spin-orbit coupling into account. The required spin-orbit matrix elements were obtained applying a non-empirical spin-orbit mean-field approximation. Our calculated electronic energies are in good agreement with experimental data. We find the lowest excited singlet states to be of the npi* (S1) and pipi* (S2) type. Energetically accessible from S1 are two triplet states of the pipi* (T1) and npi* (T2) type, the latter being nearly degenerate to S1. This ordering of states is retained when the molecular structure in the electronically excited states is relaxed. We expect very efficient intersystem crossing between S1 and T1. Our calculated intersystem crossing rate is approximately 2 x 10(10) s(-1), which is in excellent agreement with the experimental value of 3.45 x 10(10) s(-1). Our estimated phosphorescence and fluorescence rates are many orders of magnitude smaller. Our results are in agreement with the experimentally observed behavior of phenalenone, including the high efficiency of 1O2 production.

Electronically Excited States of Higher Acenes up to Nonacene: A Density Functional Theory/Multireference Configuration Interaction Study.

While the optical spectra of the acene series up to pentacene provide textbook examples for the annulation principle, the spectra of the larger members are much less understood. The present work provides an investigation of the optically allowed excited states of the acene series from pentacene to nonacene, the largest acene observed experimentally, using the density functional based multireference configuration method (DFT/MRCI). For this purpose, the ten lowest energy states of the B2u and B3u irreducible representations were computed. In agreement with previous computational investigations, the electronic wave functions of the acenes acquire significant multireference character with increasing acene size. The HOMO → LUMO excitation is the major contributor to the (1)La state (p band, B2u) also for the larger acenes. The oscillator strength decreases with increasing length. The (1)Lb state (α band, B3u), so far difficult to assign for the larger acenes due to overlap with photoprecursor bands, becomes almost insensitive to acene length. The (1)Bb state (β band, B3u) also moves only moderately to lower energy with increasing acene size. Excited states of B3u symmetry that formally result from double excitations involving HOMO, HOMO-1, LUMO, and LUMO+1 decrease in energy much faster with system size. One of them (D1) has very small oscillator strength but becomes almost isoenergetic with the (1)La state for nonacene. The other (D2) also has low oscillator strength as long as it is higher in energy than (1)Bb. Once it is lower in energy than the (1)Bb state, both states interact strongly resulting in two states with large oscillator strengths. The emergence of two strongly absorbing states is in agreement with experimental observations. The DFT/MRCI computations reproduce experimental excitation energies very well for pentacene and hexacene (within 0.1 eV). For the larger acenes deviations are larger (up to 0.2 eV), but qualitative agreement is observed.

QM/MM study of the monomeric red fluorescent protein DsRed.M1.

We report a combined quantum mechanical/molecular mechanical (QM/MM) study of the DsRed.M1 protein using as QM component the self-consistent charge density functional tight-binding (SCC-DFTB) method in molecular dynamics (MD) simulations and hybrid density functional theory (DFT, B3LYP functional) in QM/MM geometry optimizations. We consider different variants of the chromophore (including the cis- and trans-acylimine and peptide forms) as well as different protonation states of environmental residues. The QM/MM calculations provide insight into the role of nearby residues concerning their interactions with the chromophore and their influence on structural and spectroscopic properties. QM/MM optimizations yield a single conformer for the anionic acylimine chromophore, whereas there are distinct cis- and trans-conformers in the anionic peptide chromophore, the latter being more stable. The calculated vertical excitation energies (DFT/MRCI) for the anionic chromophores agree well with experiment. The published crystal structure of DsRed.M1 with an anionic acylimine chromophore indicates a quinoid structure, while the QM/MM calculations predict the phenolate form to be more stable.

Isomerization mechanism of the HcRed fluorescent protein chromophore

To understand how the protein achieves fluorescence, the isomerization mechanism of the HcRed chromophore is studied both under vacuum and in the solvated red fluorescent protein. Quantum mechanical (QM) and quantum mechanical/molecular mechanical (QM/MM) methods are applied both for the ground and the first excited state. The photoinduced processes in the chromophore mainly involve torsions around the imidazolinone-bridge bond (τ) and the phenoxy-bridge bond (φ). Under vacuum, the isomerization of the cis-trans chromophore essentially proceeds by τ twisting, while the radiationless decay requires φ torsion. By contrast, the isomerization of the cis-trans chromophore in HcRed occurs via simultaneous τ and φ twisting. The protein environment significantly reduces the barrier of this hula twist motion compared with vacuum. The excited-state isomerization barrier via the φ rotation of the cis-coplanar conformer in HcRed is computed to be significantly higher than that of the trans-non-coplanar conformer. This is consistent with the experimental observation that the cis-coplanar-conformation of the chromophore is related to the fluorescent properties of HcRed, while the trans-non-planar conformation is weakly fluorescent or non-fluorescent. Our study shows how the protein modifies the isomerization mechanism, notably by interactions involving the nearby residue Ile197, which keeps the chromophore coplanar and blocks the twisting motion that leads to photoinduced radiationless decay.

Reverse Monte Carlo modelling of amorphous Si3B3N7 using scattering and 15N NMR data

We present an enhanced reverse Monte Carlo approach that includes fitting to NMR data in the form of chemical shifts in addition to the usually used scattering data. Furthermore, the internal energy is accounted for in the cost function to prevent unphysical structures. This approach was applied to generate structural models of amorphous Si3B3N7, which is a prototype of a new class of high performance ceramics exhibiting interesting features like high thermal and mechanical stability. We fitted our structural models in direct space to radial distribution functions from x-ray, neutron and electron scattering experiments, and to the 15N NMR spectrum of the ceramic. This spectrum could not be interpreted before since it exhibits a broad structureless signal which is a superposition of peaks related to different chemical environments NBxSi3−x (x = 0–3) whose chemical shifts were only partly known experimentally. Therefore we based the calculation of NMR data in the reverse Monte Carlo optimizations on previous theoretical work that was done in our group. All generated models reproduce the experimental radial distribution functions very well. This good agreement does not deteriorate when the NMR data are taken into account. Fitting the models to 15N NMR chemical shifts in addition to scattering data results in structural changes that not only improve the agreement with the experimental magic-angle spinning (MAS) NMR spectrum but yield also significantly better second-nearest neighbour coordination statistics.