Site-dependence of van der Waals interaction explains exciton spectra of double-walled tubular J-aggregates.

The simulation of the optical properties of supramolecular aggregates requires the development of methods, which are able to treat a large number of coupled chromophores interacting with the environment. Since it is currently not possible to treat large systems by quantum chemistry, the Frenkel exciton model is a valuable alternative. In this work we show how the Frenkel exciton model can be extended in order to explain the excitonic spectra of a specific double-walled tubular dye aggregate explicitly taking into account dispersive energy shifts of ground and excited states due to van der Waals interaction with all surrounding molecules. The experimentally observed splitting is well explained by the site-dependent energy shift of molecules placed at the inner or outer side of the double-walled tube, respectively. Therefore we can conclude that inclusion of the site-dependent dispersive effect in the theoretical description of optical properties of nanoscaled dye aggregates is mandatory.

Towards a structure-based exciton Hamiltonian for the CP29 antenna of photosystem II.

The exciton Hamiltonian pertaining to the first excited states of chlorophyll (Chl) a and b pigments in the minor light-harvesting complex CP29 of plant photosystem II is determined based on the recent crystal structure at 2.8 Å resolution applying a combined quantum chemical/electrostatic approach as used earlier for the major light-harvesting complex LHCII. Two electrostatic methods for the calculation of the local transition energies (site energies), referred to as the Poisson-Boltzmann/quantum chemical (PBQC) and charge density coupling (CDC) method, which differ in the way the polarizable environment of the pigments is described, are compared and found to yield comparable results, when tested against fits of measured optical spectra (linear absorption, linear dichroism, circular dichroism, and fluorescence). The crystal structure shows a Chl a/b ratio of 2.25, whereas a ratio between 2.25 and 3.0 can be estimated from the simulation of experimental spectra. Thus, it is possible that up to one Chl b is lost in CP29 samples. The lowest site energy is found to be located at Chl a604 close to neoxanthin. This assignment is confirmed by the simulation of wild-type-minus-mutant difference spectra of reconstituted CP29, where a tyrosine residue next to Chl a604 is modified in the mutant. Nonetheless, the terminal emitter domain (TED), i.e. the pigments contributing mostly to the lowest exciton state, is found at the Chl a611-a612-a615 trimer due to strong excitonic coupling between these pigments, with the largest contributions from Chls a611 and a612. A major difference between CP29 and LHCII is that Chl a610 is not the energy sink in CP29, which is presumably to a large extent due to the replacement of a lysine residue with alanine close to the TED.

Computational protein design: the Proteus software and selected applications.

We describe an automated procedure for protein design, implemented in a flexible software package, called Proteus. System setup and calculation of an energy matrix are done with the XPLOR modeling program and its sophisticated command language, supporting several force fields and solvent models. A second program provides algorithms to search sequence space. It allows a decomposition of the system into groups, which can be combined in different ways in the energy function, for both positive and negative design. The whole procedure can be controlled by editing 2-4 scripts. Two applications consider the tyrosyl-tRNA synthetase enzyme and its successful redesign to bind both O-methyl-tyrosine and D-tyrosine. For the latter, we present Monte Carlo simulations where the D-tyrosine concentration is gradually increased, displacing L-tyrosine from the binding pocket and yielding the binding free energy difference, in good agreement with experiment. Complete redesign of the Crk SH3 domain is presented. The top 10000 sequences are all assigned to the correct fold by the SUPERFAMILY library of Hidden Markov Models. Finally, we report the acid/base behavior of the SNase protein. Sidechain protonation is treated as a form of mutation; it is then straightforward to perform constant-pH Monte Carlo simulations, which yield good agreement with experiment. Overall, the software can be used for a wide range of application, producing not only native-like sequences but also thermodynamic properties with errors that appear comparable to other current software packages.

Structure-based modeling of energy transfer in photosynthesis.

We provide a minimal model for a structure-based simulation of excitation energy transfer in pigment-protein complexes (PPCs). In our treatment, the PPC is assembled from its building blocks. The latter are defined such that electron exchange occurs only within, but not between these units. The variational principle is applied to investigate how the Coulomb interaction between building blocks changes the character of the electronic states of the PPC. In this way, the standard exciton Hamiltonian is obtained from first principles and a hierarchy of calculation schemes for the parameters of this Hamiltonian arises. Possible extensions of this approach are discussed concerning (i) the inclusion of dispersive site energy shifts and (ii) the inclusion of electron exchange between pigments. First results on electron exchange within the special pair of photosystem II of cyanobacteria and higher plants are presented and compared with earlier results on purple bacteria. In the last part of this mini-review, the coupling of electronic and nuclear degrees of freedom is considered. First, the standard exciton-vibrational Hamiltonian is parameterized with the help of a normal mode analysis of the PPC. Second, dynamical theories are discussed that exploit this Hamiltonian in the study of dissipative exciton motion.

Computational design of protein-ligand binding: modifying the specificity of asparaginyl-tRNA synthetase.

A method for computational design of protein-ligand interactions is implemented and tested on the asparaginyl- and aspartyl-tRNA synthetase enzymes (AsnRS, AspRS). The substrate specificity of these enzymes is crucial for the accurate translation of the genetic code. The method relies on a molecular mechanics energy function and a simple, continuum electrostatic, implicit solvent model. As test calculations, we first compute AspRS-substrate binding free energy changes due to nine point mutations, for which experimental data are available; we also perform large-scale redesign of the entire active site of each enzyme (40 amino acids) and compare to experimental sequences. We then apply the method to engineer an increased binding of aspartyl-adenylate (AspAMP) into AsnRS. Mutants are obtained using several directed evolution protocols, where four or five amino acid positions in the active site are randomized. Promising mutants are subjected to molecular dynamics simulations; Poisson-Boltzmann calculations provide an estimate of the corresponding, AspAMP, binding free energy changes, relative to the native AsnRS. Several of the mutants are predicted to have an inverted binding specificity, preferring to bind AspAMP rather than the natural substrate, AsnAMP. The computed binding affinities are significantly weaker than the native, AsnRS:AsnAMP affinity, and in most cases, the active site structure is significantly changed, compared to the native complex. This almost certainly precludes catalytic activity. One of the designed sequences has a higher affinity and more native-like structure and may represent a valid candidate for Asp activity.

Computational protein design: software implementation, parameter optimization, and performance of a simple model.

Computational protein design will continue to improve as new implementations and parameterizations are explored. An automated protein design procedure is implemented and applied to the full redesign of 16 globular proteins. We combine established but simple ingredients: a molecular mechanics description of the protein where nonpolar hydrogens are implicit, a simple solvent model, a folded state where the backbone is fixed, and a tripeptide model of the unfolded state. Sequences are selected to optimize the folding free energy, using a simple heuristic algorithm to explore sequence and conformational space. We show that a balanced parametrization, obtained here and in our previous work, makes this procedure effective, despite the simplicity of the ingredients. Calculations were done using our Proteins @ Home distributed computing platform, with the help of several thousand volunteers. We describe the software implementation, the optimization of selected terms in the energy function, and the performance of the method. We allowed all amino acids to mutate except glycines, prolines, and cysteines. For 15 of the 16 test proteins, the scores of the computed sequences were comparable to those of natural homologues. Using the low energy computed sequences in a BLAST search of the SWISSPROT database, we could retrieve natural sequences for all protein families considered, with no high-ranking false-positives. The good stability of the designed sequences was supported by molecular dynamics simulations of selected sequences, which gave structures close to the experimental native structure.

Theory of FRET "Spectroscopic Ruler" for Short Distances: Application to Polyproline.

Förster resonance energy transfer (FRET) is an important mechanism for the estimation of intermolecular distances, e.g., in fluorescent labeled proteins. The interpretations of FRET experiments with standard Förster theory relies on the following approximations: (i) a point-dipole approximation (PDA) for the coupling between transition densities of the chromophores, (ii) a screening of this coupling by the inverse optical dielectric constant of the medium, and (iii) the assumption of fast isotropic sampling over the mutual orientations of the chromophores. These approximations become critical, in particular, at short intermolecular distances, where the PDA and the screening model become invalid and the variation of interchromophore distances, and not just orientations, has a critical influence on the excitation energy transfer. Here, we present a quantum chemical/electrostatic/molecular dynamics (MD) method that goes beyond all of the above approximations. The Poisson-TrEsp method for the ab initio/electrostatic calculation of excitonic couplings in a dielectric medium is combined with all-atom molecular dynamics (MD) simulations to calculate FRET efficiencies. The method is applied to analyze single-molecule experiments on a polyproline helix of variable length labeled with Alexa dyes. Our method provides a quantitative explanation of the overestimation of FRET efficiencies by the standard Förster theory for short interchromophore distances for this system. A detailed analysis of the different levels of approximation that connect the present Poisson-TrEsp/MD method with Förster theory reveals error compensation effects, between the PDA and the neglect of correlations in interchromophore distances and orientations on one hand and the neglect of static disorder in orientations and interchromophore distances on the other. Whereas the first two approximations are found to decrease the FRET efficiency, the latter two overcompensate this decrease and are responsible for the overestimation of the FRET efficiency by Förster theory.

Red/Green Color Tuning of Visual Rhodopsins: Electrostatic Theory Provides a Quantitative Explanation.

We present a structure-based theory of the long-wavelength (red/green) color tuning in visual rhodopsins and its application to the analysis of site-directed mutagenesis experiments. Using a combination of electrostatic and molecular-mechanics methods, we explain the measured mutant-minus-wild-type absorption shifts and conclude that the dominant mechanism of the color tuning in these systems is electrostatic pigment-protein coupling. An important element of our analysis is the independent determination of protonation states of titratable residues in the wild type and the mutant protein as well as the self-consistent reoptimization of hydrogen atom positions, which includes the relaxation of the hydrogen bonding network and the reorientation of water molecules. On the basis of this analysis, we propose a "dipole-orientation rule" according to which both the position and the orientation of a polar group introduced in the protein environment determine the direction of the transition energy shift of the retinal chromophore.

Structure Prediction of Self-Assembled Dye Aggregates from Cryogenic Transmission Electron Microscopy, Molecular Mechanics, and Theory of Optical Spectra.

Cryogenic transmission electron microscopy (cryo-TEM) studies suggest that TTBC molecules self-assemble in aqueous solution to form single-walled tubes with a diameter of about 35 Å. In order to reveal the arrangement and mutual orientations of the individual molecules in the tube, we combine information from crystal structure data of this dye with a calculation of linear absorbance and linear dichroism spectra and molecular dynamics simulations. We start with wrapping crystal planes in different directions to obtain tubes of suitable diameter. This set of tube models is evaluated by comparing the resulting optical spectra with experimental data. The tubes that can explain the spectra are investigated further by molecular dynamics simulations, including explicit solvent molecules. From the trajectories of the most stable tube models, the short-range ordering of the dye molecules is extracted and the optimization of the structure is iteratively completed. The final structural model is a tube of rings with 6-fold rotational symmetry, where neighboring rings are rotated by 30° and the transition dipole moments of the chromophores form an angle of 74° with respect to the symmetry axis of the tube. This model is in agreement with cryo-TEM images and can explain the optical spectra, consisting of a sharp red-shifted J-band that is polarized parallel to to the symmetry axis of the tube and a broad blue-shifted H-band polarized perpendicular to this axis. The general structure of the homogeneous spectrum of this hybrid HJ-aggregate is described by an analytical model that explains the difference in redistribution of oscillator strength inside the vibrational manifolds of the J- and H-bands and the relative intensities and excitation energies of those bands. In addition to the particular system investigated here, the present methodology can be expected to aid the structure prediction for a wide range of self-assembled dye aggregates.

The quest for energy traps in the CP43 antenna of photosystem II.

To identify energy traps in CP43, a subcomplex of the photosystem II antenna system, site energies and excitonic couplings of the QY transitions of chlorophyll (Chl) a pigments bound to CP43 are computed using electrostatic models of pigment-protein and pigment-pigment interactions. The computations are based on recent crystal structures of the photosystem II core complex with resolutions of 1.9 and 2.1Å and compared to earlier results obtained at 2.9Å resolution. Linear optical spectra (i.e., absorption, linear dichroism, circular dichroism, and fluorescence) are simulated using the computed excitonic couplings, a refinement fit for the site energies, and a dynamical theory of optical lineshapes. A comparison of the obtained root mean square deviation of about 100 cm(-1) between directly calculated and refined site energies with the maximum range of about 350 cm(-1) of directly calculated site energies shows that the combined quantum chemical/electrostatic approach provides a semi-quantitative agreement with experiment. Possible reasons for the deviations are discussed, including limits of the electrostatic models and the lineshape theory as well as structural alterations of CP43 upon detachment from the core complex. Based on the simulations, an assignment of the two low-energy exciton states A and B of CP43, that where observed earlier in hole burning studies, is suggested. State A is assigned to a localized exciton state on Chl 37 in the lumenal layer of pigments. State B is assigned to an exciton state that is delocalized over several pigments in the cytoplasmic layer. The delocalization explains the smaller inhomogeneous width of state B compared to state A observed in hole burning spectra, which is proposed to be due to exchange narrowing. The assignment of states A and B largely confirms our earlier suggestion that was based on a fit of linear optical spectra and electrostatic calculations using the 2.9Å resolution structure. Interestingly, for the latter structure, the site energy of Chl 37 is obtained closer to the refined value than for 1.9 and 2.1Å resolution. This is explained by a variation of the site energy due to the influence of lipids that might be different in the core complex and isolated CP43. To remove remaining uncertainties in the assignment of states A and B, target sites for mutagenesis experiments are proposed based on the electrostatic computations. In particular, it is suggested to mutate Trp C63 close to Chl 37 to probe the identity of state A and to mutate Arg C41 close to Chl 47 to probe state B.

A Kunitz type protease inhibitor related protein is synthesized in Drosophila prepupal salivary glands and released into the moulting fluid during pupation.

From the Drosophila virilis late puff region 31C, we microcloned two neighbouring genes, Kil-1 and Kil-2, that encode putative Kunitz serine protease inhibitor like proteins. The Kil-1 gene is expressed exclusively in prepupal salivary glands. Using a size mutant of the KIL-1 protein and MALDI-TOF analysis, we demonstrate that during pupation this protein is released from the prepupal salivary glands into the pupation fluid covering the surface of the pupa. 3-D-structure predictions are consistent with the known crystal structure of the human Kunitz type protease inhibitor 2KNT. This is the first experimental proof for the extracorporal presence of a distinct Drosophila prepupal salivary gland protein. Possible functions of KIL-1 in the context of the control of proteolytic activities in the pupation fluid are discussed.

Revealing the functional states in the active site of BLUF photoreceptors from electrochromic shift calculations.

Photoexcitation with blue light of the flavin chromophore in BLUF photoreceptors induces a switch into a metastable signaling state that is characterized by a red-shifted absorption maximum. The red shift is due to a rearrangement in the hydrogen bond pattern around Gln63 located in the immediate proximity of the isoalloxazine ring system of the chromophore. There is a long-lasting controversy between two structural models, named Q63A and Q63J in the literature, on the local conformation of the residues Gln63 and Tyr21 in the dark state of the photoreceptor. As regards the mechanistic details of the light-activation mechanism, rotation of Gln63 is opposed by tautomerism in the Q63A and Q63J models, respectively. We provide a structure-based simulation of electrochromic shifts of the flavin chromophore in the wild type and in various site-directed mutants. The excellent overall agreement between experimental and computed data allows us to evaluate the two structural models. Compelling evidence is obtained that the Q63A model is incorrect, whereas the Q63J is fully consistent with the present computations. Finally, we confirm independently that a keto-enol tautomerization of the glutamine at position 63, which was proposed as molecular mechanism for the transition between the dark and the light-adapted state, explains the measured 10 to 15 nm red shift in flavin absorption between these two states of the protein. We believe that the accurateness of our results provides evidence that the BLUF photoreceptors absorption is fine-tuned through electrostatic interactions between the chromophore and the protein matrix, and finally that the simplicity of our theoretical model is advantageous as regards easy reproducibility and further extensions.

Normal mode analysis of the spectral density of the Fenna-Matthews-Olson light-harvesting protein: how the protein dissipates the excess energy of excitons.

We report a method for the structure-based calculation of the spectral density of the pigment-protein coupling in light-harvesting complexes that combines normal-mode analysis with the charge density coupling (CDC) and transition charge from electrostatic potential (TrEsp) methods for the computation of site energies and excitonic couplings, respectively. The method is applied to the Fenna-Matthews-Olson (FMO) protein in order to investigate the influence of the different parts of the spectral density as well as correlations among these contributions on the energy transfer dynamics and on the temperature-dependent decay of coherences. The fluctuations and correlations in excitonic couplings as well as the correlations between coupling and site energy fluctuations are found to be 1 order of magnitude smaller in amplitude than the site energy fluctuations. Despite considerable amplitudes of that part of the spectral density which contains correlations in site energy fluctuations, the effect of these correlations on the exciton population dynamics and dephasing of coherences is negligible. The inhomogeneous charge distribution of the protein, which causes variations in local pigment-protein coupling constants of the normal modes, is responsible for this effect. It is seen thereby that the same building principle that is used by nature to create an excitation energy funnel in the FMO protein also allows for efficient dissipation of the excitons' excess energy.

The Eighth Bacteriochlorophyll Completes the Excitation Energy Funnel in the FMO Protein.

The Fenna-Matthews-Olson (FMO) light-harvesting protein connects the outer antenna system (chlorosome/baseplate) with the reaction center complex in green sulfur bacteria. Since its first structure determination in the mid-70s, this pigment-protein complex has become an important model system to study excitation energy transfer. Recently, an additional bacteriochlorophyll a (the eighth) pigment was discovered in each subunit of this homotrimer. Our structure-based calculations of the optical properties of the FMO protein demonstrate that the eighth pigment is the linker to the baseplate, confirming recent suggestions from crystallographic studies.

Computational protein design: validation and possible relevance as a tool for homology searching and fold recognition.

BACKGROUND: Protein fold recognition usually relies on a statistical model of each fold; each model is constructed from an ensemble of natural sequences belonging to that fold. A complementary strategy may be to employ sequence ensembles produced by computational protein design. Designed sequences can be more diverse than natural sequences, possibly avoiding some limitations of experimental databases. METHODOLOGY/PRINCIPAL FINDINGS: WE EXPLORE THIS STRATEGY FOR FOUR SCOP FAMILIES: Small Kunitz-type inhibitors (SKIs), Interleukin-8 chemokines, PDZ domains, and large Caspase catalytic subunits, represented by 43 structures. An automated procedure is used to redesign the 43 proteins. We use the experimental backbones as fixed templates in the folded state and a molecular mechanics model to compute the interaction energies between sidechain and backbone groups. Calculations are done with the Proteins@Home volunteer computing platform. A heuristic algorithm is used to scan the sequence and conformational space, yielding 200,000-300,000 sequences per backbone template. The results confirm and generalize our earlier study of SH2 and SH3 domains. The designed sequences ressemble moderately-distant, natural homologues of the initial templates; e.g., the SUPERFAMILY, profile Hidden-Markov Model library recognizes 85% of the low-energy sequences as native-like. Conversely, Position Specific Scoring Matrices derived from the sequences can be used to detect natural homologues within the SwissProt database: 60% of known PDZ domains are detected and around 90% of known SKIs and chemokines. Energy components and inter-residue correlations are analyzed and ways to improve the method are discussed. CONCLUSIONS/SIGNIFICANCE: For some families, designed sequences can be a useful complement to experimental ones for homologue searching. However, improved tools are needed to extract more information from the designed profiles before the method can be of general use.

One-electron reduction potential for oxygen- and sulfur-centered organic radicals in protic and aprotic solvents.

We estimated one-electron reduction potentials of redox-active organic molecules for a spectrum of eight different functional groups (phenoxyl, p-benzoquinone, phenylthiyl, p-benzodithiyl, carboxyl, benzoyloxyl, carbthiyl, and benzoylthiyl) in protic (water) and aprotic (acetonitrile, N,N-dimethylacetamide) solvents. Electron affinities (EA) were evaluated in a vacuum with high level quantum chemical methods using Gaussian3-MP2 (G3MP2) and Becke 3 Lee, Yang, and Parr functional B3LYP with aug-cc-pVTZ basis set. To evaluate one-electron redox potentials, gas-phase free energies were combined with solvation energies obtained in a two-step computational approach. First, atomic partial charges were determined in a vacuum by the quantum chemical method B3LYP/6-31G(d,p). Second, solvation energies were determined, solving the Poisson equation with these atomic partial charges. Redox potentials computed this way, compared to experimental data for the 21 considered organic compounds in different solvents, yielded overall root-mean-square deviations of 0.058 and 0.131 V using G3MP2 or B3LYP to compute electronic energies, respectively, while B3LYP/6-31G(d,p) was used to compute solvation energies.

Accurate pKa determination for a heterogeneous group of organic molecules.

Single-molecule studies that allow to compute pKa values, proton affinities (gas-phase acidity/basicity) and the electrostatic energy of solvation have been performed for a heterogeneous set of 26 organic compounds. Quantum mechanical density functional theory (DFT) using the Becke-half&half and B3LYP functionals on optimized molecular geometries have been carried out to investigate the energetics of gas-phase protonation. The electrostatic contribution to the solvation energies of protonated and deprotonated compounds were calculated by solving the Poisson equation using atomic charges generated by fitting the electrostatic potential derived from the molecular wave functions in vacuum. The combination of gas-phase and electrostatic solvation energies by means of the thermodynamic cycle enabled us to compute pKa values for the 26 compounds, which cover six distinct chemical groups (carboxylic acids, benzoic acids, phenols, imides, pyridines and imidazoles). The computational procedure for determining pKa values is accurate and transferable with a root-mean-square deviation of 0.53 and 0.57 pKa units and a maximum error of 1.0 pKa and 1.3 pKa units for Becke-half&half and B3LYP DFT functionals, respectively.