Efficient estimation of energy transfer efficiency in light-harvesting complexes

Abstract

The fundamental physical mechanisms of energy transfer in photosynthetic complexes is not yet fully understood. In particular, the degree of efficiency or sensitivity of these systems for energy transfer is not known given their non-perturbative and non-Markovian interactions with proteins backbone and surrounding photonic and phononic environments. One major problem in studying light-harvesting complexes has been the lack of an efficient method for simulation of their dynamics in biological environments. To this end, here we revisit the second-order time-convolution (TC2) master equation and examine its reliability beyond extreme Markovian and perturbative limits. In particular, we present a derivation of TC2 without making the usual weak systembath coupling assumption. Using this equation, we explore the long time behaviour of exciton dynamics of Fenna-Matthews-Olson (FMO) portein complex. Moreover, we introduce a constructive error analysis to estimate the accuracy of TC2 equation in calculating energy transfer efficiency, exhibiting reliable performance for environments with weak and intermediate memory and strength. Furthermore, we numerically show that energy transfer efficiency is optimal and robust for the FMO protein complex of green sulphur bacteria with respect to variations in reorganization energy and bath correlation time-scales.

Geometrical effects on energy transfer in disordered open quantum systems

“…29 We showed that oscillatory time evolution of the population of BChls in the FMO using our approach is relatively close to those predicted by HEOM. 11 Here we should emphasize that although Eq. (6) can be applied for any bath correlation function, but our error analysis in Ref.…”

“…11 By providing an error analysis, we could show that TC2 can be employed for highly efficient while reliable estimation of energy transfer efficiency in light-harvesting complexes for both weak and intermediate system-bath coupling strengths and memory time scales. Here, we summarize the main steps of our approach.…”

“…11. ETE measures the likelihood of successful trapping, weighted by trapping rate: it quantifies the excitation availability whenever the reaction center is ready to operate within a period much shorter than the exciton life-time.…”

“…We use ETE as the yield function for performance of these random systems and use a time-convolution master equation (TC2) 22 to estimated energy transport efficiency beyond perturbative and Markovian regimes. 11,12 We extensively explore the effect of spatial compactness on the transport efficiency and robustness due to its potential significance as recently reported in Ref. 12.…”

“…This rational design approach can be influenced by recent observations of Environment-Assisted Quantum Transport (ENAQT) in biological light-harvesting systems. [3][4][5][6][7][8][9][10][11][12][13] Specifically, one might develop radically novel design principles by manipulating delocalized exciton dynamics through engineering coherent couplings of free Hamiltonian and/or the environmental interactions to generate optimal efficiency. If one can fully understand the fundamental microscopic processes involved, it will be in principle possible to use structure for steering the ultrafast migration of excitons via quantum interference effects.…”