Multiscale photosynthetic and biomimetic excitation energy transfer

Journal name:
Nature Physics
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Published online


Recent evidence suggests that quantum coherence enhances excitation energy transfer (EET) through individual photosynthetic light-harvesting protein complexes (LHCs). Its role in vivo is unclear however, where transfer to chemical reaction centres (RCs) spans larger, multi-LHC/RC networks. Here we predict maximum coherence lengths possible in fully connected chromophore networks with the generic structural and energetic features of multi-LHC/RC networks. A renormalization analysis reveals the dependence of EET dynamics on multiscale, hierarchical network structure. Surprisingly, thermal decoherence rate declines at larger length scales for physiological parameters and coherence length is instead limited by localization due to static disorder. Physiological parameters support coherence lengths up to ~ 5nm, which is consistent with observations of solvated LHCs and invites experimental tests for intercomplex coherences in multi-LHC/RC networks. Results further suggest that a semiconductor quantum dot network engineered with hierarchically clustered structure and small static disorder may support coherent EET over larger length scales, at ambient temperatures.

At a glance


  1. Structural hierarchy of the higher-plant light-harvesting machinery and renormalization flow of our analogous dimeric chromophore network hierarchy.
    Figure 1: Structural hierarchy of the higher-plant light-harvesting machinery and renormalization flow of our analogous dimeric chromophore network hierarchy.

    a, Transmission electron micrograph of a sugar- cane chloroplast. Densely stacked grana regions of the thylakoid membrane are visible. Image courtesy of R. Birch, used with permission. b, Cross-sectional representation of a granal membrane stack showing embedded aggregates of photosystem II LHCII (PSII-LHCII) supercomplexes interspersed with other complexes. c, 3D diagram of membrane-embedded semicrystalline aggregate of PSII-LHCII supercomplexes. d, PSII-LHCII supercomplex containing LHCs (green, brown) coupled to RC-containing core complexes (blue). e, Trimeric LHCII. f, Monomeric subunit of LHCII, with chlorophyll crystal structure overlaid. This complex binds 14 chlorophyll (8 chlorophyll a, 6 chlorophyll b) and 4 carotenoid chromophores. g, Strongly coupled dimer (a613-a614) of chlorophyll-a chromophores. h, Chlorophyll-a chromophore. i, Renormalization flow of dimeric chromophore network hierarchy. A tetramer at the 0th level is coarse-grained to an effective dimer at the 1st level through the operator βk(ij). This dimer is paired with a similar effective dimer and the coarse-graining repeated, and so on. The site energies Ek(i), transfer coupling energies Δk(ij)and system–bath coupling energies gk(12)(q) are transformed between levels. Analogous structures from the higher-plant photosynthetic structural hierarchy are presented at each vertical level of the dimeric network hierarchy: 0, chlorophyll a; 1, strongly coupled chlorophyll cluster; 2, LHCII monomer. Typical intersite separations in an LHCII aggregate (c,d) are d0~1nm, d1~2.5nm (corresponding to C=d1/d0=2.5), d2~4nm (Cright arrow2), d3(intertrimer separation) ~ 8.5nm (C=2.13).

  2. Multiscale tunnelling and decoherence rates in an ordered network ([epsi]0(ij)=0), across the first seven hierarchy levels
k (curves labelled by colour), as a function of network clustering
    Figure 2: Multiscale tunnelling and decoherence rates in an ordered network (ε0(ij)=0), across the first seven hierarchy levels k (curves labelled by colour), as a function of network clustering C.

    Vertical green bands indicate clustering range mapped from the higher-plant network. a, Intradimer excitation tunnelling rate. b, Thermal decoherence rate in the Ohmic spectral density case. c, Thermal decoherence rate in the cubic spectral density case.

  3. Scaling of dynamical crossover by thermal decoherence (XTk=Fk(2[Delta]k(12))/(2[Delta]k(12))) and localization by static disorder ().
    Figure 3: Scaling of dynamical crossover by thermal decoherence (XTk=Fk(2Δk(12))/(2Δk(12))) and localization by static disorder ( ).

    Vertical green bands indicate clustering range mapped from the higher-plant network. a, Simulation results for log(XTk) in the Ohmic spectral density case (Jk(ω)=B1Sk(ω)ω), shown for first seven hierarchy levels k(curves labelled by colour) at T=293K in ordered (ε0(ij)=0) networks against network clustering C. Log(XDk) is also plotted against C, assuming σ(ε0(ij))~2.4×1012s−1 (~80cm−1) as in ref. 4. Zero on the vertical axis separates coherent (below) and incoherent (above) dynamical regimes. b, Cubic spectral density case (Jk(ω)=B3Sk(ω)ω3) under the same parameterization. c, Summary of results. The physiological system uses a parameterization mapped from the higher-plant network; the engineered and ordered systems have the zeroth-level static disorder reduced by an order of magnitude and reduced to zero, respectively. Tunnelling rates shown in red are slower than observed rates at which PSII RCs trap excitations in native higher-plant thylakoid membranes (~2.0–3.3×109s−1; ref. 36) and are therefore insignificant to physiological EET in that system.


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Author information


  1. Institute for Molecular Bioscience, University of Queensland, St Lucia, Queensland 4072, Australia

    • A. K. Ringsmuth
  2. Centre for Engineered Quantum Systems, University of Queensland, St Lucia, Queensland 4072, Australia

    • A. K. Ringsmuth,
    • G. J. Milburn &
    • T. M. Stace


A.K.R. suggested the multiscale, hierarchical approach of the study. T.M.S. proposed the renormalization analysis. A.K.R. and T.M.S. completed the calculations. A.K.R. wrote, and T.M.S. and G.J.M. edited, the manuscript. G.J.M. supervised the project and advised on calculations.

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