Excited state dynamics in photosynthetic reaction center and light harvesting complex 1

Abstract

Key to efficient harvesting of sunlight in photosynthesis is the first energy conversion process in which electronic excitation establishes a trans-membrane charge gradient. This conversion is accomplished by the photosynthetic reaction center (RC) that is, in case of the purple photosynthetic bacterium Rhodobacter sphaeroides studied here, surrounded by light harvesting complex 1 (LH1). The RC employs six pigment molecules to initiate the conversion: four bacteriochlorophylls and two bacteriopheophytins. The excited states of these pigments interact very strongly and are simultaneously influenced by the surrounding thermal protein environment. Likewise, LH1 employs 32 bacteriochlorophylls influenced in their excited state dynamics by strong interaction between the pigments and by interaction with the protein environment. Modeling the excited state dynamics in the RC as well as in LH1 requires theoretical methods, which account for both pigment-pigment interaction and pigment-environment interaction. In the present study we describe the excitation dynamics within a RC and excitation transfer between light harvesting complex 1 (LH1) and RC, employing the hierarchical equation of motion method. For this purpose a set of model parameters that reproduce RC as well as LH1 spectra and observed oscillatory excitation dynamics in the RC is suggested. We find that the environment has a significant effect on LH1-RC excitation transfer and that excitation transfers incoherently between LH1 and RC.

Figure 1

(a) Position of bacteriochlorophylls (P_M, P_L, B_M, B_L) and bacteriopheophytins (H_M, H_L) in the reaction center (RC) from Rhodobacter sphaeroides. (b) RC equilibrium infrared absorption spectrum from Ref. . (c) Light harvesting complex 1 surrounding the RC; shown is also the B875 ring of pigments. (d) Orientation of bacteriochlorophyll and bacteriopheophytin transition dipole moments in the RC.

Figure 2

Comparison of 300 K linear equilibrium absorption spectra calculated by the HEOM and observed experimentally as reported in Ref. .

Figure 3

Excitation dynamics of the reaction center calculated with system and bath parameters taken from Table 1, where parameter set 1 (a) assumes high dynamic disorder and parameter set 2 (b) assumes low dynamic disorder. Populations are shown for the pigments initially excited in each calculation.

Figure 4

Reaction center exciton states. The exciton states, $\widetilde{|\nu ⟩}$, are defined as eigenstates of the stationary state density matrix, namely, ${\rho }_e\widetilde{|\nu ⟩}=P_{\nu }\widetilde{|\nu ⟩}$; parameters were taken from Table 1, where parameter set 1 (a) assumes high dynamic disorder and parameter set 2 (b) assumes low dynamic disorder. Orange circles (radius scales with diagonal elements of $\widetilde{|\nu ⟩}\widetilde{⟨\nu |}$) indicate the participation of each pigment in an exciton state, and blue lines (thickness scales with absolute value of off-diagonal elements of $\widetilde{|\nu ⟩}\widetilde{⟨\nu |}$) indicate inter-pigment coherence. Listed are also the steady-state population P_ν and energy ε_ν of each exciton state. The numbering of the states is in energetically ascending order.

Figure 5

(a) LH1 absorption spectrum. Shown is a comparison of spectra from Ref. and calculated here using the HEOM approach, but excluding static disorder. (b) Excitation transfer from LH1 to RC. Excitation transfer was determined both for parameter sets 1 and 2. Shown are close comparisons between the HEOM results and descriptions in terms of the kinetic model in Eq. 10 where t_f is the LH1→RC transfer time and t_b is the RC→LH1 transfer time.