Optimal fold symmetry of LH2 rings on a photosynthetic membrane

Abstract

An intriguing observation of photosynthetic light-harvesting systems is the N-fold symmetry of light-harvesting complex 2 (LH2) of purple bacteria. We calculate the optimal rotational configuration of N-fold rings on a hexagonal lattice and establish two related mechanisms for the promotion of maximum excitation energy transfer (EET). (i) For certain fold numbers, there exist optimal basis cells with rotational symmetry, extendable to the entire lattice for the global optimization of the EET network. (ii) The type of basis cell can reduce or remove the frustration of EET rates across the photosynthetic network. We find that the existence of a basis cell and its type are directly related to the number of matching points S between the fold symmetry and the hexagonal lattice. The two complementary mechanisms provide selection criteria for the fold number and identify groups of consecutive numbers. Remarkably, one such group consists of the naturally occurring 8-, 9-, and 10-fold rings. By considering the inter-ring distance and EET rate, we demonstrate that this group can achieve minimal rotational sensitivity in addition to an optimal packing density, achieving robust and efficient EET. This corroborates our findings i and ii and, through their direct relation to S, suggests the design principle of matching the internal symmetry with the lattice order.P hotosynthesis lies at the heart of all life on the planet. Excitation energy created in a peripheral light-harvesting antenna complex, upon absorption of a photon, is efficiently transferred via an exciton mechanism, sometimes over hundreds of angstroms, to a reaction center where charge separation takes place, creating a transmembrane electrochemical potential difference that ultimately drives the production of ATP. Light-harvesting antenna complexes, whose primary function is to increase the effective crosssection for photon absorption, while maintaining an efficient energy transfer network, consist of well-ordered membrane-associated arrays of light-absorbing pigments, namely chlorophyll or bacterichlorophyll (BChl), embedded in a protein environment (1-4).Perhaps the most intriguing aspect of light-harvesting systems is the N-fold symmetry displayed by light-harvesting complex 2 (LH2) of purple nonsulfur bacteria. Fold symmetry occurs in systems as diverse as carbon nanotubes, tubular dye aggregates, and the mosaic virus protein, as well as in snow flakes, tori, and nonperiodic tilings (5). In LH2, the N-fold symmetry arises from the N repetitions of a basic heterodimer subunit consisting of two transmembrane polypeptides, α and β, arranged in a circular structure (6-8). Each αβ-heterodimer subunit noncovalently binds one B800 BChl and two B850 BChls (Fig. 1A), so named according to their respective room-temperature absorption bands in the infrared region of the spectrum. In most bacterial species, the αβ-heterodimer repeats eight or nine times to form an octameric or nonameric ring structure (in Rhodopseudomonas paulisterium 10-fold rings have also been observ...

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

“…Recent work in this direction has already demonstrated how the symmetry propensity of light-harvesting complex II leads to inherently efficient EET, 19 while the role of delocalized coherent exciton dynamics and localized exciton trapping has been investigated in analytical models of light-harvesting systems. 20 Furthermore, extensive work has been carried out to investigate the efficiency and robustness of the FennaMatthews-Olson (FMO) PPC with respect to fluctuations in the protein environment, with findings showing that thermal fluctuations can enhance EET via so-called environmentassisted quantum transport (ENAQT).…”

Distinguishing the roles of energy funnelling and delocalization in photosynthetic light harvesting

“…We describe this approach through its application to the strikingly symmetric antenna complexes of purple bacteria [16], which feature tightly packed bacteriochlorophylls and considerable excitonic delocalization [17][18][19][20][21][22][23][24][25][26][27][28]. This delocalization is known to give rise to supertransfer, in particular for EET within the LH2 complex [29][30][31].…”

Photosynthetic pigment-protein complexes as highly connected networks: implications for robust energy transport

“…For example, by developing network-based models of EET in multi-chromophore systems which can be solved analytically, these models have demonstrated the subtle interplay between environmental noise and chromophore coupling strengths, demonstrating that typical parameters observed in biological PPCs lie well within the regime in which EET is predicted to be highly efficient. Furthermore, the role of symmetry in PPC trimers was also considered [46]; here, a network-based viewpoint helped to demonstrate that symmetric ring-structures of the order of those found in nature are predicted to enable optimized and minimally frustrated EET dynamics and optimal packing density. Finally, we highlight interesting results which focused on mapping a quantum-mechanical density matrixbased model of a PPC onto a classical kinetic master equation [36].…”

“…For example, is there any inherent advantage to symmetric chromophore network organization compared with random chromophore network arrangements, as found in FMO [46]? Are there particular features of the electronic couplings, spatial arrangements or orientations of chromophores in biological PPCs which are common across different PPC structures?…”

“…Of course, addressing such fundamental questions is not possible using approximate quantum simulations of highly simplified models of PPCs. For example, given evolutionary time scales, it is tempting to ask whether PPCs are in any way optimized for their role in photosynthesis [34,36,[45][46][47]49,56,67] or whether external factors, such as ease of biological synthesis [21], are instead responsible for the observed molecular organization in PPCs. Such questions are impossible to address from the standpoint of molecular simulations alone, but addressing these issues and better understanding the rationale behind natural PPC structural motifs could, in turn, lead to a better understanding of how to construct improved artificial photosynthetic systems for water-splitting or more efficient light-harvesting devices for solar energy applications [1,68].…”