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Equilibrium and Dynamical Path Integral Methods in Bacterial Photosynthesis

  • Chapter
Biophysical Techniques in Photosynthesis

Part of the book series: Advances in Photosynthesis and Respiration ((AIPH,volume 26))

Classical molecular dynamics simulations have provided a wealth of information on processes in biological systems. In spite of the spectacular success and the insights gained from such simulations, processes involving electron or exciton transfer are inherently quantum mechanical and thus not amenable to a classical description. This chapter focuses on the use of path integral methods for simulating the equilibrium and dynamical properties of charged particles in dissipative environments.

Feynman’s path integral theory is an exact formulation of time-dependent quantum mechanics and quantum statistical mechanics that circumvents the use of wave functions, whose storage requirements are prohibitive for systems of more than a few atoms. The calculation of thermal equilibrium properties in non-fermionic systems is possible with the well-established path integral Monte Carlo method. Dynamical processes involve multidimensional integrals of rapidly oscillating functions; Monte Carlo methods converge extremely slowly in such cases, and thus fully quantum mechanical simulations of real-time processes generally remain out of reach. In the case of electron (or exciton) transfer processes, the so-called linear response approximation makes it possible to replace the vast majority of nuclear coordinates by an effective dissipative environment of harmonic oscillators. This simplifi cation allows a fully quantum mechanical treatment of the dynamics using an iterative decomposition of the path integral developed in the mid-1990s.

Applications of these methods to determine the exciton coherence length in the B850 ring of the light harvesting complex (LH2) and the mechanism of primary charge separation in the photosynthetic reaction center are reviewed. Path integral calculations, along with a visual inspection of statistically signifi cant paths, led to the conclusion that the exciton is delocalized over two to three chlorophyll monomers at room temperature. Iterative evaluation of the real-time path integral for a three-state model comprising the excited special pair, the reduced accessory bacteriochlorophyll, and the reduced bacteriopheophytin, offers evidence in support of the sequential mechanism, where the electron is fi rst transferred to the accessory chlorophyll.

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  1. Departments of Chemistry and Physics, University of Illinois, 601 S. Goodwin Avenue, 61801, Urbana, IL, USA

    Nancy Makri

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Makri, N. (2008). Equilibrium and Dynamical Path Integral Methods in Bacterial Photosynthesis. In: Aartsma, T.J., Matysik, J. (eds) Biophysical Techniques in Photosynthesis. Advances in Photosynthesis and Respiration, vol 26. Springer, Dordrecht. https://doi.org/10.1007/978-1-4020-8250-4_23

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