Energy flow in the Photosystem I supercomplex: Comparison of approximative theories with DM-HEOM

doi:10.1016/j.chemphys.2018.05.028

Chemical Physics

Volume 515, 14 November 2018, Pages 262-271

https://doi.org/10.1016/j.chemphys.2018.05.028 Get rights and content

Abstract

We analyze the exciton dynamics in Photosystem I from Thermosynechococcus elongatus using the distributed memory implementation of the hierarchical equation of motion (DM-HEOM) for the 96 Chlorophylls in the monomeric unit. The exciton-system parameters are taken from a first principles calculation. A comparison of the exact results with Förster rates and Markovian approximations allows one to validate the exciton transfer times within the complex and to identify deviations from approximative theories. We show the optical absorption, linear, and circular dichroism spectra obtained with DM-HEOM and compare them to experimental results.

Graphical abstract

Section snippets

Photosystem I

The structure of Photosystem I from the thermophilic cyanobacterium Thermosynechococcus elongatus has been resolved by X-ray crystallography to 2.5 Å resolution [13]. The PS I appears in a trimeric structure, each monomeric unit consisting of 12 protein subunits, with 96 cholorophyll (Chl) molecules, 22 carotenoids, three iron-sulfur clusters, two phylloquinones, four lipids, 201 water molecules, and at least one metal ion [14].

Knowledge of the detailed arrangement of the Chls is a big step

Theories for exciton dynamics

The exciton dynamics of the molecular complex is described by the reduced density matrix of the system. For large complexes (PS I with 96 pigments) and for transfer times exceeding tens of picoseconds, the time-propagation of the density matrix is computationally demanding. Previous simulations are based on approximative methods, often reducing the density matrix to a population vector [8], [10], [28]. In the following we study the deviation of the population rate equations from the exact HEOM

Population dynamics

To compare HEOM with the different rate equations, we initialize the density matrix at the outer lying PL01 pigment and track the time-evolution of the populations at all pigments (Fig. 2). A similar initial condition has been used in [10]. We track the energy flow from the outer pigments in the lumenal ring towards the stromal ring and RC of the supercomplex and compare it to other theories. The difference in energy flow between Förster and HEOM theory is shown in Fig. 3 at different times.

Linear absorption

The linear absorption spectra in Fig. 8 are calculated with DM-HEOM following [7], Eq. (56). The transition dipoles of the $Q_{y}$ -band are assumed to be oriented along the nitrogen $N_{B}$ - $N_{D}$ positions in the optimized 1JB0 structure [17], while we ignore the $Q_{x}$ band. To assess the impact of static disorder we consider both, a single realization with the Hamiltonian [17], and in addition the ensemble average of 1000 calculations with uncorrelated diagonal disorder added to the site energies (standard

Conclusion

We have used the DM-HEOM to compute the energy flow in the PSI system and compare it with simplified approaches. The site energies and excitonic couplings are taken from the DFT results and no fitting to experimental spectra has been performed. The analysis of exciton flow in PS I with DM-HEOM reveals a slow transfer, even compared to Förster rates. The HEOM computation validates previous simplified approaches relying on Förster rates, with a priori unknown error bounds [8]. A simplified rate

Acknowledgements

This contribution is dedicated to Prof. Wolfgang Domcke whose work on time-dependent quantum mechanics and time-resolved spectroscopy provides the required tools and methods to analyze chemical reaction dynamics.

We thank G. Laubender, Y. Zelinskyy, and Th. Steinke for helpful discussions. The work was supported by the German Research Foundation (DFG) grants KR 2889 and RE 1389 (“Realistic Simulations of Photoactive Systems on HPC Clusters with Many-Core Processors”) and the Intel Research

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Energy flow in the Photosystem I supercomplex: Comparison of approximative theories with DM-HEOM

Abstract

Graphical abstract

Section snippets

Photosystem I

Theories for exciton dynamics

Population dynamics

Linear absorption

Conclusion

Acknowledgements

Biophys. J.

Biophys. J.

Biochim. Biophys. Acta Bioenerg.

Chem. Phys. Lett.

Chem. Phys.

Biophys. J.

Chem. Phys.

Biochim. Biophys. Acta Bioenerg.

Biophys. J.

Challenges facing an understanding of the nature of low-energy excited states in photosynthesis

Biochim. Biophys. Acta Bioenerg.

Computational model of photocatalytic water splitting

J. Phys. Chem. A

Time evoultion of a quantum system in contact with a nearly Gussian-Markoffian noise bath

J. Phys. Soc. Jpn.

Unified treatment of quantum coherent and incoherent hopping dynamics in electronic energy transfer: reduced hierarchy equation approach

J. Chem. Phys.

High-performance solution of hierarchical equations of motion for studying energy transfer in light-harvesting complexes

J. Chem. Theory Comput.

Efficient calculation of open quantum system dynamics and time-resolved spectroscopy with Distributed Memory HEOM (DM-HEOM)

J. Comput. Chem.

Robustness and optimality of light harvesting in cyanobacterial Photosystem I

J. Phys. Chem. B

From structure to dynamics: modeling exciton dynamics in the photosynthetic Antenna PS1

J. Phys. Chem. B

Exciton delocalization and transport in Photosystem I of cyanobacteria synechococcus elongates: simulation study of coherent two-dimensional optical signals

J. Phys. Chem. B

Three-dimensional structure of cyanobacterial photosystem I at 2.5 resolution

Nature