Computational Methods.

The modeling is based on the Hamiltonian and spectral densities used in a previous study of LHCII (7, 35). The fluorescence spectra are calculated from the steady state of the excitonic populations P_i following the kinetic equations:

where k_ij are the population transfer rates, Γ_i are the population relaxation rates, χ_i(ω) is the absorption spectrum of the ith exciton (see below), and W(ω) is the spectrum of the incident light. These equations can be rigorously derived from the Liouville–von Neumann equation for the reduced density matrix using second-order perturbation theory for the interaction with light, the Markovian and secular approximations, and the fact that the populations vary much slower than the optical coherences. Under these assumptions, the equations have general validity and allow calculation of excitation dynamics (47).

The excitonic absorption spectrum is given by the transition dipole strength, which can be calculated from the structure and coupling between pigments, and the calculated lineshape. The lineshape and population transfer rates are given by the bath properties, which are expressed by means of the spectral density. The absorption and fluorescence spectra are then calculated as follows (35):

Here, |µ_i0|² is the transition dipole moment strength for the ith exciton, ω_i is the optical transition frequency of the ith exciton, and g_ii(τ) = ∑_n|c_in|⁴g_n(τ) is the lineshape function of the ith exciton, where c_in are coefficients of the site ↔ exciton basis transformation, and |c_in|² is the participation of the nth site in the ith exciton. The lineshape function of the nth site is given by gn(τ)=∫0τdt∫0tdt'Cn(t'), where C_n(t) is the bath correlation function related to the spectral density C_n(ω) by Fourier transformation. We assume the same but uncorrelated bath dynamics on all of the different sites here. The reorganization energy of the ith exciton is given by λ_i = ∑_n|c_in|⁴λ_n, where λn=1/π∫0∞dωCn(ω)/ω is the reorganization energy of the nth site. The population transfer rates were calculated by Redfield theory, k_ij = ∑_n|c_in|²|c_jn|²C_n(ω_ji), where ω_ij = (ω_i − λ_i) − (ω_j − λ_j) is the energy gap between the ith and jth exciton.

Based on the LHCII crystal structure determined by ref. 23, the excitonic coupling between pigments is calculated in the dipole–dipole approximation. For the calculated distributions and spectra, the orientation of Chl a611 is first changed (or it is removed) and its coupling to the other pigments is calculated. The fluorescence spectrum is then calculated for 2,000 realizations of the energetic disorder of the pigment site energies.