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Pigment-protein complexes (PPCs) play a central role in facilitating excitation energy transfer (EET) from light-harvesting antenna complexes to reaction centres in photosynthetic systems; understanding molecular organisation in these biological networks is key to developing better artificial light-harvesting systems. In this article, we combine quantum-mechanical simulations and a network-based picture of transport to investigate how chromophore organization and protein environment in PPCs impacts on EET efficiency and robustness. In a prototypical PPC model, the Fenna-Matthews-Olson (FMO) complex, we consider the impact on EET efficiency of both disrupting the chromophore network and changing the influence of (local and global) environmental dephasing. Surprisingly, we find a large degree of resilience to changes in both chromophore network and protein environmental dephasing, the extent of which is greater than previously observed; for example, FMO maintains EET when 50% of the constituent chromophores are removed, or when environmental dephasing fluctuations vary over two orders-of-magnitude relative to the in vivo system. We also highlight the fact that the influence of local dephasing can be strongly dependent on the characteristics of the EET network and the initial excitation; for example, initial excitations resulting in rapid coherent decay are generally insensitive to the environment, whereas the incoherent population decay observed following excitation at weakly coupled chromophores demonstrates a more pronounced dependence on dephasing rate as a result of the greater possibility of local exciton trapping. Finally, we show that the FMO electronic Hamiltonian is not particularly optimised for EET; instead, it is just one of many possible chromophore organisations which demonstrate a good level of EET transport efficiency following excitation at different chromophores. Overall, these robustness and efficiency characteristics are attributed to the highly connected nature of the chromophore network and the presence of multiple EET pathways, features which might easily be built into artificial photosynthetic systems.

Robustness, efficiency, and optimality in the Fenna-Matthews-Olson photosynthetic pigment-protein complex