Robust and fragile quantum effects in the transfer kinetics of delocalized excitons between B850 units of LH2 complexes

TL;DR

Application of a generalized master equation to pairs of the B850 units of LH2 complexes provides quantitative information on how the inter-LH2 exciton transfer depends on the distance, relative rotational angle, and the relative energies of the two LH2s.

Abstract

Aggregates of light harvesting 2 (LH2) complexes form the major exciton-relaying domain in the photosynthetic unit of purple bacteria. Application of a generalized master equation to pairs of the B850 units of LH2 complexes, where excitons predominantly reside, provide quantitative information on how the inter-LH2 exciton transfer depends on the distance, relative rotational angle, and the relative energies of the two LH2s. The distance dependence demonstrates significant enhancement of the rate due to quantum delocalization of excitons, the qualitative nature of which remains robust against the disorder. The angle dependence reflects isotropic nature of exciton transfer, which remains similar for the ensemble of disorder. The variation of the rate on relative excitation energies of LH2 exhibits resonance peaks, which however is fragile as the disorder becomes significant. Overall, the average transfer times between two LH2s are estimated to be in the range of 4 - 25 ps for physically plausible inter-LH2 distances.

Figures (5)

• Figure 1: The range of inter-LH2 distances estimated from AFM images.Scheuring-Science309sturgis-biochemistry48olsen-jbc283Sumino-jpcb117 Note that $d_{\rm LH2-LH2}=l_c+2R_\beta$ (see Eq. (\ref{['eq:r-beta-1']})). Each LH2 complex here consists of 27 bactreiochlorophylls (BChls). Nine of them facing up in the plane (red) form the B800 unit. Eighteen of them showing sideways (blue) for the B850 unit.
• Figure 2: (a) Dependence of GME-MED and MC-FRET rates on the LH2-LH2 distances. The value of $A$ for T=200 K is 78190 and that for T=300 K is 48215. (b) Dependence of rates on relative angles between two B850 complexes at T= 200 K (upper panel) and 300 K (lower panel) with $l_c=2\ {\rm nm}$, for which $d_{LH2-LH2}=7.506\ {\rm nm}$. The GME-MED rates and the MC-FRET rates are compared for each case. (c) Dependence of rates on relative energies between two B850 complexes at T= 200 K (upper panel) and 300 K (lower panel) with $l_c=2\ {\rm nm}$, for which $d_{LH2-LH2}=7.506\ {\rm nm}$. The GME-MED rates and the MC-FRET rates are compared for each case.
• Figure 3: Dependences of average values of GME-MED rates and MC-FRET rates at ${\rm 300\ K}$. Each point was determined by averaging over an ensemble of 10,000 realizations of the disorder in site excitation energies of BChls with standard deviation, $200\ {\rm cm^{-1}}$. (a) The distance dependence for $\gamma=0$ and $E_{LH2(1)}-E_{LH2(2)}=0$. (b) The dependence on relative angle for $d_{LH2-LH2}=7.506\ {\rm nm}$ and $E_{LH2(1)}-E_{LH2(2)}=0$. (c) The dependence on $E_{LH2(1)}-E_{LH2(2)}$, the bias of average excitation energies between two LH2 complexes, for $d_{LH2-LH2}=7.506\ {\rm nm}$ and $\gamma=0$.
• Figure 4: Distributions of inter-LH2 transfer rates for $d_{LH2-LH2}=7.506\ {\rm nm}$ and $\gamma=0$ at ${\rm 300\ K}$.
• Figure S1: Time dependent population of the exciton in the initial B850 unit calculated from the GME-MED method (blue solid line) and the exponential decay based on the MC-FRET rate (red dashed line). The left column is for the case where there is no disorder. The right column shows the average population dynamics for the entire ensemble of the disorder as specified in the text.