Fluorescence polarization measures energy funneling in single light-harvesting antennas—LH2 vs conjugated polymers

Numerous approaches have been proposed to mimic natural photosynthesis using artificial antenna systems, such as conjugated polymers (CPs), dendrimers, and J-aggregates. As a result, there is a need to characterize and compare the excitation energy transfer (EET) properties of various natural and artificial antennas. Here we experimentally show that EET in single antennas can be characterized by 2D polarization imaging using the single funnel approximation. This methodology addresses the ability of an individual antenna to transfer its absorbed energy towards a single pool of emissive states, using a single parameter called energy funneling efficiency (ε). We studied individual peripheral antennas of purple bacteria (LH2) and single CP chains of 20 nm length. As expected from a perfect antenna, LH2s showed funneling efficiencies close to unity. In contrast, CPs showed lower average funneling efficiencies, greatly varying from molecule to molecule. Cyclodextrin insulation of the conjugated backbone improves EET, increasing the fraction of CPs possessing ε = 1. Comparison between LH2s and CPs shows the importance of the protection systems and the protein scaffold of LH2, which keep the chromophores in functional form and at such geometrical arrangement that ensures excellent EET.

carefully chosen wide-field lens (WFL, Figure S1-B), to a diameter small enough to be fully reflected by the small mirror. The focal distance of the WFL is selected in such a way that the excitation light is focused by the microscope objective lens above its focal distance, and generates wide-field illumination of the sample. The fluorescence collected by the microscope objective results in a beam of much larger diameter than the small mirror. Therefore, the light obstruction by the mirror is negligible. The birefringence of the universal beam splitter proved to be much smaller than that of the dichroic mirror for the near IR light.

Reasoning behind the approximations done in the Single Funnel Approximation
In order to extract information from a polarization portrait, which only has 9 degrees of freedom, when the organization and detailed spectroscopic information of each transition in the multichromophoric system is unknown, several approximations have to be made. As mentioned in the main text these approximations are: (1) the EET drives the excitations towards a fixed set of chromophores called EET-emitter (a common pool of emitting states), (2) the unknown N-dipole system is represented by a new group of Ñ standard dipoles with equal fluorescence excitation cross sections (σ ex~σ ×Φ), and (3) each dipole transfers in average the same amount of energy towards the single EET-emitter.
Approximation 1) means that the SFA does not consider time changes in the transfer efficiency between chromophores, and that the experiment is done under steady state conditions. Approximation 2) is a change in coordinate system. As a consequence of this change, the SFA cannot keep track of how many excitations get lost through non-radiative decays for each chromophore. Finally, approximation 3), which can be seen as the biggest approximation of the SFA, is used because this is exactly the property that the SFA is designed to measure (the ability of a system to directionally transfer their energy to a specific set of dipoles). In case that approximation 3) does not hold for the measured multichromophoric system, then the SFA will measure a low funneling efficiency or will not be able to fit the data, which is an acceptable result for the SFA.

Description of the Single Funnel Approximation fitting procedure
A detailed description about the single funnel approximation and the equations used for data fitting can be found in reference 30 of the main text and Camacho, R. Polarization Portraits of Light-Harvesting Antennas: From Single Molecule Spectroscopy to Imaging, Lund University, 2014, p. 202. DOI: 10.13140/2.1.4852.5607. In the following section we briefly describe the equations used for data fitting.
As mentioned in the main text, the polarization portrait, I(φex, φem), can be split into two components using the single funnel approximation (SFA): where A and B describe the behavior of an independent group of chromophores and a single EET-emitter, respectively. Ñ is the number of standard dipoles (having equal fluorescence excitation cross sections) used to represent the unknown experimental system of N dipoles. φex and φem are the excitation polarization plane orientation and the orientation of the emission analyzer, respectively. αi is the in plane orientation of the standard dipole 'i'. Mf and θf are the polarization degree and main orientation of the EET-emitter, respectively. In order to use equations 2-4 to fit a polarization portrait we have to define a methodology to find the number and orientation of standard dipoles to be used. The methodology we have chosen is based in a symmetric threedipole-model. [27, 30 from main text] In this approach, the system of Ñ dipoles with identical fluorescence excitation cross section (σ ex ) is represented by three dipoles with the following properties: 1) A main dipole (i=1), which defines the main orientation of the system and has orientation α1 and fluorescence excitation cross section σ ex 1.
2) Two side dipoles (i=2 and 3) of identical fluorescence excitation cross section (σ ex 2 = σ ex 3) and symmetrically oriented around the main dipole (α2 = α1 + δ, α3 = α1 -δ). Such three dipole model possesses the following degrees of freedom: orientation of the main dipole (α1), orientation of the side dipoles respective to the main dipole (δ) and the ratio between the excitation cross section of the main and side dipoles (Γ = 1 / 2 = 1 / 3 ). Note that this three-dipole-model is identical to a systems composed of (Γ + 2) dipoles of identical σ ex , where: i) ( × Γ) dipoles are oriented along α1. ii) dipoles are oriented along α2 iii) dipoles oriented along α3 iv) is a factor to make Γ an integer. Moreover, the use of the symmetric three-dipole-model is preferred because it simplifies the equations used for data fitting.
Using the symmetric three-dipole-model equations 3 takes the form: In equation S01, α1 ≡ , where is the experimentally determined fluorescence excitation polarization phase. This is because the orientation of the main dipole in the symmetric three-dipole-model must be equal to the main orientation axis of the transition dipoles responsible for fluorescence excitation.
Further, it can be shown that the last summation of equation 4 can be written as: where Mex is the experimentally determined fluorescence excitation modulation depth. Using S02 and after a normalization step (̃= 2 + Γ), equation 3 and 4 can be written as: where δ is given by: Equations S03 and S04 are used for fitting experimentally determined polarization portraits, ( , ). During the fitting procedure 4 parameters are changed: Γ, Mf, θf, and ε. Moreover, these parameter are bounded in the following way: 0 ≤ Γ ≤ 2 1 + 1 − ( 09) Note that equation S09, and as a consequence S05, are not defined for Mex = 1. Therefore, a special case is defined for multichromophoric systems with Mex = 1. In this special case the absorbing dipoles are modelled by a single dipole oriented at α = (instead of the symmetric three-dipole-model), and equations S03 and S04 take the form: