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

Abstract

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.

Figure 1

Monomeric subunit of the trimeric FMO protein from P. aestuarii, which connects the outer antenna system (chlorosome) with the reaction center complex in an orientation as indicated in this figure. The protein part is shown in transparent ribbon style, and the pigments are numbered as in PDB file 3EOJ. The phytyl tails of the pigments were truncated for better visibility. The complete structure of the FMO trimer is shown in Figure S1. Graphics were prepared with VMD.

Figure 2

(Left) Distribution of site energy shifts ΔE_m(c) = Σ_k ΔE_m^(k)(c) (eqs 3 and 4) of the eight pigments BChl m (m = 1,..., 8) in one monomeric subunit of the FMO protein, obtained by combining the FRODA MC sampling of protein conformations and the CDC method for the calculation of site energy shifts. The red lines are Gaussian functions fitted to the histograms using the parameters in Table S1. (Right) Analysis of site energy shifts ΔE_m^(k)(c) (eq 4) caused by single amino acid residues k of different types (blue, positively charged; red, negatively charged; orange, polar; green, nonpolar). Panel A contains the correlation between the full width at half-maximum (fwhm) of the distribution function of ΔE_m^(k)(c) and the absolute mean site energy shift |⟨ΔE_m^(k)(c)⟩|. The curves on top and on the right side give the respective distribution functions for the various types of amino acids. Panels B and C contain the dependence of the fwhm and the |⟨ΔE_m^(k)(c)⟩|, respectively, on the distance between amino acid k and pigment m.

Figure 3

Site energy shift of BChl 6 caused by protein residue Gln 143. In panel A, the distribution function of this site energy shift is shown. The red line on top of the histograms was added to guide the eye. Representative conformations of Gln 143 giving rise to the two peaks I and II of the distribution function are given in panels C and D, respectively. Panel B contains the difference electrostatic potential between the excited and ground states of BChl a obtained with TD-DFT calculations using the B3LYP XC functional. Red (blue) regions correspond to a negative (positive) difference potential. Black arrows I and II represent the dipole moment of the amide side chain of Gln 143 in conformations I and II of this residue shown in panels C and D, respectively.

Figure 4

The same as in Figure 3 but for BChl 8 and negatively charged Asp 160. The two negative signs in the upper left corner of panel B illustrate the relative positions of the negative charge of Asp 160 in the two conformations.

Figure 5

Calculations (blue solid lines) of low-temperature (4 K) absorbance (top part), circular dichroism (middle part), and linear dichroism (lower part) spectra of the FMO protein are compared with experimental data (black dashed lines).