Parametric Mapping of Quantum Regime in Fenna–Matthews–Olson Light-Harvesting Complexes: A Synthetic Review of Models, Methods and Approaches

Abstract

Developments in ultrafast-spectroscopy techniques have revealed notably long-lived quantum coherence between electronic states in Fenna–Matthews–Olson complex bacteriochlorophylls, a group of molecules setting a nanoscale structure responsible of the coherent energy transfer in the photosynthetic process of green sulfur bacteria. Despite the experimental advances, such a task should normally be complemented with physical computer simulations to understand its complexity. Several methods have been explored to model this quantum phenomenon, mainly using the quantum open systems theory as a first approach. The traditional methods used in this approach do not take into account the memory effects of the surroundings, which is commonly approximated as a phonon bath on thermal equilibrium. To surpass such an approximation, this article applies the Hierarchical Equations of Motion method, a non-markovian approach also used to analyze the dynamic of such a complex, for the modeling of the system evolution. We perform a parametric analysis about some physical features in the quantum regime involved during the quantum excitation process in order to get a comprehension about its non-trivial dependence on operation parameters. Thus, the analysis is conducted in terms of some relevant physical parameters in the system to track the complex global behavior in aspects as coherence, entanglement, decoherence times, transference times, and efficiency of the main process of energy capturing. As a complementary analysis from the derived outcomes, we compare those features for two different species as a suggestive possible roadmap to track genetic differences in the photosynthetic performance of the complex through its biological nature.

Temperature Dependence of Entanglement and Coherence in Fenna-Matthews-Olson Complex

“…Developed by [6] for phononic media and then applied to FMO by [12], HEOM method follows by switching into the interaction picture of H S−B in order to trace the bath system considering non-markovian considerations. It becomes in recursive equations considering D previous temporal stages of the bath, each one labeled by a vector n of degree s = 0, 1, ..., D (accounting the number of elements different of zero in the description) and by N for the BChl considered (see [8] for a more detailed explanation). There, ρ n with n = (0, .., 0) is the approximation to the density matrix for the system and other ρ n are auxiliary ones in each step of the recursive method, each one corresponding to all vectors n = (n 1 , n 2 , ..., n N ) with 0 ≤ n i ∈ Z + ∪ {0} such as N i=1 n i = s. It is a recursive procedure to better fit the evolution of the system under a non-markovian regime.…”

“…See [8] for a more detailed description. BChls 1, 6 and 8, work as FMO antennas while BChls 3 and 4 drive the energy oscillations to the RC at the trapping rate, r trap .…”

“…Clearly, the treatment of the HEOM method is completely numerical. In addition, it is computationally convenient translate this equation into a superoperator-supervector version as it is detailed in [3,8] dealing mainly with the model for N = 7. Despite N = 7 model was the first exploited by the research in the field, the eighth BChl was discovered as an important part…”

Non-Markovianity between Site Pairs in FMO Complex Using Discrete-Time Quantum Jump Model

“…Photosynthesis usually occurs at ambient temperature, and the presence of quantum coherence at such a temperature for 300–500 fs led to numerous research efforts in the direction of exploring environment-assisted quantum transport to find further evidence for the presence of quantum coherence for high transport efficiency . Numerous studies have outlined the structural details of the FMO complex and that has been used to study and understand the dynamics in quantum-mechanical framework . In the widely accepted form, the FMO complex is a trimer formed by three identical monomers that each bind seven Bacteriochlorophyll-a (BChla) molecules, since monomers function independently, without loss of generality, studies are restricted to a single monomer.…”

“… 14 Numerous studies have outlined the structural details of the FMO complex and that has been used to study and understand the dynamics in quantum-mechanical framework. 15 In the widely accepted form, the FMO complex is a trimer formed by three identical monomers that each bind seven Bacteriochlorophyll-a (BChla) molecules, since monomers function independently, without loss of generality, studies are restricted to a single monomer. There are seven sites in the FMO complex, and it is assumed that there is at most one exciton in the complex at any time.…”