Tight inner ring architecture and quantum motion of nuclei enable efficient energy transfer in bacterial light harvesting

Abstract

The efficient, directional transfer of absorbed solar energy between photosynthetic light-harvesting complexes continues to pose intriguing questions. In this work, we identify the pathways of energy flow between the B800 and B850 rings in the LH2 complex of Rhodopseudomonas molischianum using fully quantum mechanical path integral methods to simulate the excited-state dynamics of the 24 bacteriochlorophyll molecules and their coupling to 50 normal mode vibrations in each chromophore. While all pigments are identical, the tighter packing of the inner B850 ring is responsible for the thermodynamic stabilization of the inner ring. Molecular vibrations enable the 1-ps flow of energy to the B850 states, which would otherwise be kinetically inaccessible. A classical treatment of the vibrations leads to uniform equilibrium distribution of the excitation, with only 67% transferred to the inner ring. However, spontaneous fluctuations associated with the quantum motion of the nuclei increase the transfer efficiency to 90%.

Coherence Maps and Flow of Excitation Energy in the Bacterial Light Harvesting Complex 2

“…48 The path integral results showed that while the stronger excitonic couplings in the tightly packed inner ring create the necessary thermodynamic drive for inward ring-to-ring energy transfer, the efficient interring energy transfer pathway in the LH2 complex is kinetically enabled by nuclear fluctuations. 45 In this Letter, we supplement our earlier findings with an analysis of the excitation energy transfer (EET) pathways based on coherence maps. 49 A coherence map (C-map) is a pair of snapshots that depict the real and imaginary parts of the system's reduced density matrix (RDM) ρ(t) on the square grid of system states at a particular time t. The temporal evolution of the C-map offers a very effective visualization of a dynamical process in a multistate system because the magnitude and distribution of real and imaginary components encodes a wealth of dynamical information: 49 Further, when the coupling to the environment is diagonal in the basis of system states, as in the case of the Frenkel-type exciton−vibration Hamiltonian, 50,51 the time evolution of site populations is completely determined by the imaginary components of off-diagonal RDM elements weighted by state-to-state electronic couplings H jk e according to the relations 52…”

“…The absence of such superpositions from the perfectly symmetric B800 ring is the consequence of vibrational motion, which is a relatively more effective source of decoherence on the weakly coupled peripheral pigments in comparison to the tightly bound inner ring. 45 As time progresses, the imaginary parts of intra-B850 RDM elements gradually begin to fade, while the corresponding real components stabilize. Strong inter-ring coherences remain within the row and column that contain BChl 17, whose population decays over a time scale of ∼1 ps.…”

“…Figure shows the dynamics of excitation energy transfer at room temperature following excitation of a single monomer, BChl 17. The left panel shows results obtained in our recent calculations using the fully quantum-mechanical small matrix path integral (SMatPI) method, − which found that the portion of excitation energy transferred to the inner ring in the absence of exciton–vibration coupling is less than 15%. The time scale of ring-to-ring energy transfer obtained from these numerically exact calculations is in good agreement with experimental results, suggesting that the parameters of the exciton Hamiltonian are sufficiently accurate for the EET dynamics.…”

“…No such superposition is formed on the outer ring, except for the small population of nearby pigments. The absence of such superpositions from the perfectly symmetric B800 ring is the consequence of vibrational motion, which is a relatively more effective source of decoherence on the weakly coupled peripheral pigments in comparison to the tightly bound inner ring …”

Impact of Spatial Inhomogeneity on Excitation Energy Transport in the Fenna-Matthews-Olson Complex

“…EET prob-lems have also been studied using semiclassical methods [25][26][27][28][29]. Advances in path integral-based methods [30,31] have recently made them lucrative for studying EET systems [32][33][34][35][36]. Among these advances, there have been developments that combine ideas from tensor network and influence functional to help alleviate the cost of path integral calculations in different ways [34,[37][38][39][40][41][42].…”