Mohamed Madjet

α-Helices direct excitation energy flow in the Fenna–Matthews–Olson protein

In photosynthesis, light is captured by antenna proteins. These proteins transfer the excitation energy with almost 100% quantum efficiency to the reaction centers, where charge separation takes place. The time scale and pathways of this transfer are controlled by the protein scaffold, which holds the pigments at optimal geometry and tunes their excitation energies (site energies). The detailed understanding of the tuning of site energies by the protein has been an unsolved problem since the first high-resolution crystal structure of a light-harvesting antenna appeared >30 years ago [Fenna RE, Matthews BW (1975) Nature 258:573–577]. Here, we present a combined quantum chemical/electrostatic approach to compute site energies that considers the whole protein in atomic detail and provides the missing link between crystallography and spectroscopy. The calculation of site energies of the Fenna–Matthews–Olson protein results in optical spectra that are in quantitative agreement with experiment and reveals an unexpectedly strong influence of the backbone of two α-helices. The electric field from the latter defines the direction of excitation energy flow in the Fenna–Matthews–Olson protein, whereas the effects of amino acid side chains, hitherto thought to be crucial, largely compensate each other. This result challenges the current view of how energy flow is regulated in pigment–protein complexes and demonstrates that attention has to be paid to the backbone architecture.

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.

Structure-Based Calculations of Optical Spectra of Photosystem I Suggest an Asymmetric Light-Harvesting Process

Optical line shape theory is combined with a quantum-chemical/electrostatic calculation of the site energies of the 96 chlorophyll a pigments and their excitonic couplings to simulate optical spectra of photosystem I core complexes from Thermosynechococcus elongatus. The absorbance, linear dichroism and circular dichroism spectra, calculated on the basis of the 2.5 A crystal structure, match the experimental data semiquantitatively allowing for a detailed analysis of the pigment-protein interaction. The majority of site energies are determined by multiple interactions with a large number (>20) of amino acid residues, a result which demonstrates the importance of long-range electrostatic interactions. The low-energy exciton states of the antenna are found to be located at a nearest distance of about 25 A from the special pair of the reaction center. The intermediate pigments form a high-energy bridge, the site energies of which are stabilized by a particularly large number (>100) of amino acid residues. The concentration of low energy exciton states in the antenna is larger on the side of the A-branch of the reaction center, implying an asymmetric delivery of excitation energy to the latter. This asymmetry in light-harvesting may provide the key for understanding the asymmetric use of the two branches in primary electron transfer reactions. Experiments are suggested to check for this possibility.

Deciphering the Influence of Short-Range Electronic Couplings on Optical Properties of Molecular Dimers: Application to Special Pairs in Photosynthesis

The excited states of chromophore dimers are, in general, delocalized, and the transition energies and transition dipoles are different from those of the monomers. The intermolecular interaction that is responsible for these effects has two contributions: Forster-type Coulomb coupling and a short-range coupling, which depends on the intermolecular overlap of electronic wave functions. The latter contains the Dexter-type exchange coupling and the coupling of excited states to intermolecular charge-transfer (CT) states. Recently, we developed a method (TrEsp) for an accurate and numerically efficient calculation of the Forster-type Coulomb part (Madjet et al. J. Phys. Chem. B 2006, 110, 17268). Here, we combine the latter with quantum chemical calculations to evaluate the short-range contribution, extending a method developed earlier by Scholes et al. (J. Phys. Chem. B 1999, 103, 2543). An effective two-state model is used, which relates the transition energies and transition dipole moments obtained by quantum chemical calculations of the monomers to those calculated for the dimer. From this relation, the short-range excitonic coupling and effective shifts of the local transition energies due to the coupling to intermolecular CT states can be inferred including a consistency check to evaluate quantum chemical methods that differ in the treatment of electron correlation. The method is applied to the special pairs of the reaction centers of purple bacteria (bRC) and photosystem I (PSI). We find that the short-range coupling represents the dominant contribution to the total excitonic coupling in both special pairs (80% in PSI and 70% in the bRC) and exhibits a monoexponential dependence on the distance between the pi-planes of the pigments with an attenuation factor of 2.8 A(-1). We obtain significant red-shifts of the local transition energies, which show a biexponential distance dependence with one attenuation factor being 2.8 A(-1) and another factor being in the range 0.3-0.7 A(-1) for PSI and 0.8-0.9 A(-1) for bRC. Both effects of the short-range coupling determine the excitation energy sink in the reaction centers at the special pairs.

How the molecular structure determines the flow of excitation energy in plant light-harvesting complex II

Excitation energy transfer in the light-harvesting complex II of higher plants is modeled using excitonic couplings and local transition energies determined from structure-based calculations recently (Müh et al., 2010). A theory is introduced that implicitly takes into account protein induced dynamic localization effects of the exciton wavefunction between weakly coupled optical and vibronic transitions of different pigments. Linear and non-linear optical spectra are calculated and compared with experimental data reaching qualitative agreement. High-frequency intramolecular vibrational degrees of freedom are found important for ultrafast subpicosecond excitation energy transfer between chlorophyll (Chl) b and Chla, since they allow for fast dissipation of the excess energy. The slower ps component of this transfer is due to the monomeric excited state of Chlb 605. The majority of exciton relaxation in the Chla spectral region is characterized by slow ps exciton equilibration between the Chla domains within one layer and between the lumenal and stromal layers in the 10-20ps time range. Subpicosecond exciton relaxation in the Chla region is only found within the terminal emitter domain (Chls a 610/611/612) and within the Chla 613/614 dimer. Deviations between measured and calculated exciton state life times are obtained for the intermediate spectral region between the main absorbance bands of Chla and Chlb that indicate that besides Chlb 608 another pigment should absorb there. Possible candidates, so far not identified by structure-based calculations, but by fitting of optical spectra and mutagenesis studies, are discussed. Additional mutagenesis studies are suggested to resolve this issue.

Thermally Activated Superradiance and Intersystem Crossing in the Water-Soluble Chlorophyll Binding Protein

The crystal structure of the class IIb water-soluble chlorophyll binding protein (WSCP) from Lepidium virginicum is used to model linear absorption and circular dichroism spectra as well as excited state decay times of class IIa WSCP from cauliflower reconstituted with chlorophyll (Chl) a and Chl b. The close agreement between theory and experiment suggests that both types of WSCP share a common Chl binding motif, where the opening angle between pigment planes in class IIa WSCP should not differ by more than 10 degrees from that in class IIb. The experimentally observed (Schmitt et al. J. Phys. Chem. B 2008, 112, 13951) decrease in excited state lifetime of Chl a homodimers with increasing temperature is fully explained by thermally activated superradiance via the upper exciton state of the dimer. Whereas a temperature-independent intersystem crossing (ISC) rate is inferred for WSCP containing Chl a homodimers, that of WSCP with Chl b homodimers is found to increase above 100 K. Our quantum chemical/electrostatic calculations suggest that a thermally activated ISC via an excited triplet state T4 is responsible for the latter temperature dependence.

Theory of solvatochromic shifts in nonpolar solvents reveals a new spectroscopic rule

An expression of unexpected simplicity is derived for the shift in optical transition energies of solute molecules in nonpolar solvents. The expression reveals a new spectroscopic rule that says: The higher the excited state of the solute, the larger the solvatochromic red shift. A puzzle formulated >50 years ago by Bayliss is solved. Bayliss, based on arguments from classical physics, assumed that the shift scales with the oscillator strength of the solute transition, but noted strong quantitative deviations from this rule in experiments. As the present expression shows, the shift does not depend on the oscillator strength of the transition, but reflects the change in dispersive solute–solvent interactions between the ground and excited states of the solute, that are determined by the anisotropy of intramolecular electron correlation. The theory is applied to explain the solvatochromic shifts of the two lowest electronic excitations of bacteriochlorophyll a and bacteriopheophytin a.

Photoionization of C60: a model study

Time-dependent density functional theory is used to calculate the total and subshell photoionization cross sections of C60. The core of 60 C4+ ions is smeared into a classical jellium shell before treating the correlated motion of the 240 valence electrons quantum mechanically. The calculation reveals two collective plasmon resonances in the total cross section in agreement with the experiment. It is found that a phase-coherent superposition of amplitudes leading to enhancements in the ionization from various C60 subshells in two distinct energy regions essentially builds the plasmons. While the result shows good qualitative agreement with the experiments, the limitation of the model to describe the data in quantitative detail is discussed.

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.

Femtosecond polarization resolved spectroscopy: A tool for determination of the three-dimensional orientation of electronic transition dipole moments and identification of configurational isomers

A method is presented that combines femtosecond polarization resolved UV/visible pump-IR probe spectroscopy and density functional theory calculations in determining the three-dimensional orientation of an electronic transition dipole moment (tdm) within the molecular structure. The method is demonstrated on the approximately planar molecule coumarin 314 (C314) dissolved in acetonitrile, which can exist in two ground state configurations: the E- and the Z-isomer. Based on an exhaustive search analysis on polarization resolved measurement data for four different vibrational modes, it is concluded that C314 in acetonitrile is the E-isomer. The electronic tdm vector for the electronic S(0)-->S(1) transition is determined and the analysis shows that performing the procedure for four vibrational modes instead of the minimally required three reduces the 1sigma probability area from 2.34% to 2.24% of the solution space. Moreover, the fastest rotational correlation time tau(c) for the C314 E-isomer is determined to be 26+/-2 ps.