Limitations of Linear Dichroism Spectroscopy for Elucidating Structural Issues of Light-Harvesting Aggregates in Chlorosomes

Linear dichroism (LD) spectroscopy is a widely used technique for studying the mutual orientation of the transition-dipole moments of the electronically excited states of molecular aggregates. Often the method is applied to aggregates where detailed information about the geometrical arrangement of the monomers is lacking. However, for complex molecular assemblies where the monomers are assembled hierarchically in tiers of supramolecular structural elements, the method cannot extract well-founded information about the monomer arrangement. Here we discuss this difficulty on the example of chlorosomes, which are the light-harvesting aggregates of photosynthetic green-(non) sulfur bacteria. Chlorosomes consist of hundreds of thousands of bacteriochlorophyll molecules that self-assemble into secondary structural elements of curved lamellar or cylindrical morphology. We exploit data from polarization-resolved fluorescence-excitation spectroscopy performed on single chlorosomes for reconstructing the corresponding LD spectra. This reveals that LD spectroscopy is not suited for benchmarking structural models in particular for complex hierarchically organized molecular supramolecular assemblies.


Comparison of LD Reconstruction Methods 1 and 2
For comparing the two methods used to reconstruct the LD spectra, for simplicity we consider only two transitions with spectra and . We first assume that the two transitions are associated with mutually orthogonal transitiondipole moments, both oriented perpendicular with respect to the incidence direction of light. This is the case for perfectly cylindrical aggregates with their axes parallel to the experimental substrate. For definiteness, we identify transition 1 with the direction parallel to the axis of the cylinder. Then the intensity of the polarization resolved spectrum corresponds to , = cos + sin (1) where α denotes the angle of the polarization of the light and α = 0 has been chosen to refer to the orientation of the transition-dipole moment associated with transition 1.
The polarization-averaged spectrum is thus given by For method 1 we selected the photon frequency peak where features its spectral peak and defined the preferential alignment direction as the angle ∥ for which the modulation of peak , reaches its maximum as a function of .
Accordingly, ∥ is found from which yields −2 peak − peak cos ∥ sin ∥ = − peak − peak sin 2 ∥ = 0 (4) Assuming that peak ≠ peak , this is fulfilled for ∥ = 0, which is the polarization angle at which a maximum is found if peak > peak , and for ∥ = π/2, which gives the maximum if peak < peak . Hence, for exactly perpendicular transition-dipole moments, method 1 selects for the preferential alignment direction either ∥ = 0, which agrees exactly with method 2 [where this direction was chosen along the cylinder axis], or ∥ = π/2, which is out of phase relative to method 2 by π/2, resulting in a sign flip for the LD spectrum obtained from method 1 with respect to the spectrum obtained from method 2.
This shows that for a system with two transitions with exactly perpendicular transition dipoles, methods 1 and 2 lead to identical single-system LD spectra, up to a possible overall sign change. By direct extension, the above also holds if we have two pairs of transitions [(1,2) and (3,4)], where within each pair the transition dipoles are exactly perpendicular to each other, while 1 is exactly parallel to 3 and 2 is parallel to 4.
However, if the transitions do not have pairwise perpendicular dipoles, but rather have dipole orientations that differ by + with ≠ 0, the above no longer holds. We then have for the case of two transitions: which yields the same polarization averaged spectrum as above. The angle ∥ for which the modulation of peak , reaches its maximum as a function of now obeys the equation In general, the solutions for ∥ will no longer be given by 0 and π/2; rather, their numerical values will depend on both the ratio of the intensities at the peak frequency, peak / peak ), and the "mismatch angle" β of their associated transition-dipole moments from being orthogonal. Hence, for β ≠ 0 the results for the LD spectrum obtained from method 1 and method 2 are not equivalent to each other.
The above is nicely illustrated in Fig. S1, which shows in addition to Fig. 5 of the main text also the underlying decomposition of the single-chlorosome spectra in four Gaussians and gives for each case the corresponding angles between the dipoles of the four transitions [1,2]. As is seen, indeed the agreement between both methods used to reconstruct the LD spectrum is better if for both pairs these angles get closer to π/2. Figure S1. Examples of LD spectra and snapshots of the decomposition into Gaussians at ∥ for chlorosomes of the WT-group1, the bchR mutant, and the bchQR mutant, from left to right. The spectra have been obtained from method 1 (blue) and method 2 (grey), respectively. The phase differences ΔΦij between the bands i and j (i,j = 1,2,3,4), and the energy of the intensity maximum, hνpeak, are given in the panels. For illustration purposes we will discuss two example spectra that were assigned to groups A and D, respectively, in more detail. Spectrum fig.S1d, right (group D): At the photon energy hν peak where I ν features its spectral peak this spectrum has contributions from A1, A2, and A3. For the corresponding phase differences we find ΔΦ12 = 72°, ΔΦ34 = 86°, ΔΦ13 = 37°, and ΔΦ24 = 30.9°. Hence, the mutual phase differences deviate clearly from the "ideal" situation and therefore the modulation of the total signal as a function of the polarization at hνpeak differs significantly from the modulation of A1. As a consequence of this, the two reconstruction methods will give different results.
To summarize: For (close to) "ideal" polarization properties the two reconstruction methods give similar results. A sign flip between the reconstructed LD spectra is observed if at the peak frequency the sum of the contributions from A2 and A4 is larger than the sum of the contributions from A1 and A3. For strong deviations from the "ideal" geometry of the mutual alignment of the transition dipole moments significantly different LD spectra will be obtained from the two reconstruction methods

Comment on Observing Nodes in the LD Spectra
If we assume the four Gaussians to have "ideal" polarization properties we would expect to observe three nodes in the LD spectra. Whether these can be resolved depends on the spectral separation between the states within each pair, the spectral separation between the pairs, the relative intensity of the individual bands, and the widths of all these bands. This is illustrated in fig.S2 on the example of spectra from individual chlorosomes from the bchR mutant. Concerning the relative abundancies of the nodes across the different types of chlorosomes one has to consider that growing linewidths will wash out the nodes.
Since the widths of the bands are significantly smaller for the mutants the nodes can be observed better for these chlorosomes. The variation of the number of nodes is