Static Disorder in Excitation Energies of the Fenna-Matthews-Olson Protein: Structure-Based Theory Meets Experiment.

Inhomogeneous broadening of optical lines of the Fenna-Matthews-Olson (FMO) light-harvesting protein is investigated by combining a Monte Carlo sampling of low-energy conformational substates of the protein with a quantum chemical/electrostatic calculation of local transition energies (site energies) of the pigments. The good agreement between the optical spectra calculated for the inhomogeneous ensemble and the experimental data demonstrates that electrostatics is the dominant contributor to static disorder in site energies. Rotamers of polar amino acid side chains are found to cause bimodal distribution functions of site energy shifts, which can be probed by hole burning and single-molecule spectroscopy. When summing over the large number of contributions, the resulting distribution functions of the site energies become Gaussians, and the correlations in site energy fluctuations at different sites practically average to zero. These results demonstrate that static disorder in the FMO protein is in the realm of the central limit theorem of statistics.

Evidence of Correlated Static Disorder in the Fenna-Matthews-Olson Complex.

Observation of excitonic quantum beats in photosynthetic antennae has prompted wide debate regarding the function of excitonic coherence in pigment-protein complexes. Much of this work focuses on the interactions of excitons with the femto-to-picosecond dynamical fluctuations of their environment. However, in experiments these effects can be masked by static disorder of the excited-state energies across ensembles, whose microscopic origins are challenging to predict. Here the excited-state properties of ∼2000 atom clusters of the Fenna-Matthews-Olson complex are simulated using a unique combination of linear-scaling density functional theory and constrained geometric dynamics. While slow, large amplitude protein motion leads to large variations in the Qy transitions of two pigments, we identify pigment-protein correlations that greatly reduce variations in the energy gap across the ensemble, which is consistent with experimental observations of suppressed inhomogeneous dephasing of quantum beats.

Residue Geometry Networks: A Rigidity-Based Approach to the Amino Acid Network and Evolutionary Rate Analysis.

Amino acid networks (AANs) abstract the protein structure by recording the amino acid contacts and can provide insight into protein function. Herein, we describe a novel AAN construction technique that employs the rigidity analysis tool, FIRST, to build the AAN, which we refer to as the residue geometry network (RGN). We show that this new construction can be combined with network theory methods to include the effects of allowed conformal motions and local chemical environments. Importantly, this is done without costly molecular dynamics simulations required by other AAN-related methods, which allows us to analyse large proteins and/or data sets. We have calculated the centrality of the residues belonging to 795 proteins. The results display a strong, negative correlation between residue centrality and the evolutionary rate. Furthermore, among residues with high closeness, those with low degree were particularly strongly conserved. Random walk simulations using the RGN were also successful in identifying allosteric residues in proteins involved in GPCR signalling. The dynamic function of these residues largely remain hidden in the traditional distance-cutoff construction technique. Despite being constructed from only the crystal structure, the results in this paper suggests that the RGN can identify residues that fulfil a dynamical function.

Constrained geometric dynamics of the Fenna-Matthews-Olson complex: the role of correlated motion in reducing uncertainty in excitation energy transfer.

The trimeric Fenna-Mathews-Olson (FMO) complex of green sulphur bacteria is a well-studied example of a photosynthetic pigment-protein complex, in which the electronic properties of the pigments are modified by the protein environment to promote efficient excitonic energy transfer from antenna complexes to the reaction centres. By a range of simulation methods, many of the electronic properties of the FMO complex can be extracted from knowledge of the static crystal structure. However, the recent observation and analysis of long-lasting quantum dynamics in the FMO complex point to protein dynamics as a key factor in protecting and generating quantum coherence under laboratory conditions. While fast inter- and intra-molecular vibrations have been investigated extensively, the slow, conformational dynamics which effectively determine the optical inhomogeneous broadening of experimental ensembles has received less attention. The following study employs constrained geometric dynamics to study the flexibility in the protein network by efficiently generating the accessible conformational states from the published crystal structure. Statistical and principle component analyses reveal highly correlated low frequency motions between functionally relevant elements, including strong correlations between pigments that are excitonically coupled. Our analysis reveals a hierarchy of structural interactions which enforce these correlated motions, from the level of monomer-monomer interfaces right down to the α-helices, ß-sheets and pigments. In addition to inducing strong spatial correlations across the conformational ensemble, we find that the overall rigidity of the FMO complex is exceptionally high. We suggest that these observations support the idea of highly correlated inhomogeneous disorder of the electronic excited states, which is further supported by the remarkably low variance (typically <5%) of the excitonic couplings of the conformational ensemble.