First-Principles Models for Biological Light-Harvesting: Phycobiliprotein Complexes from Cryptophyte Algae

Abstract

There have been numerous efforts, both experimental and theoretical, that have attempted to parametrize model Hamiltonians to describe excited state energy transfer in photosynthetic light harvesting systems. The Frenkel exciton model, with its set of electronically coupled two level chromophores that are each linearly coupled to dissipative baths of harmonic oscillators, has become the workhorse of this field. The challenges to parametrizing such Hamiltonians have been their uniqueness, and physical interpretation. Here we present a computational approach that uses accurate first-principles electronic structure methods to compute unique model parameters for a collection of local minima that are sampled with molecular dynamics and QM geometry optimization enabling the construction of an ensemble of local models that captures fluctuations as these systems move between local basins of inherent structure. The accuracy, robustness, and reliability of the approach is demonstrated in an application to the phycobiliprotein light harvesting complexes from cryptophyte algae. Our computed Hamiltonian ensemble provides a first-principles description of inhomogeneous broadening processes, and a standard approximate non-Markovian reduced density matrix dynamics description is used to estimate lifetime broadening contributions to the spectral line shape arising from electronic-vibrational coupling. Despite the overbroadening arising from this approximate line shape theory, we demonstrate that our model Hamiltonian ensemble approach is able to provide a reliable fully first-principles method for computation of spectra and can distinguish the influence of different chromophore protonation states in experimental results. A key feature in the dynamics of these systems is the excitation of intrachromophore vibrations upon electronic excitation and energy transfer. We demonstrate that the Hamiltonian ensemble approach provides a reliable first-principles description of these contributions that have been detailed in recent broad-band pump-probe and two-dimensional electronic spectroscopy experiments.

Determination of the protonation preferences of bilin pigments in cryptophyte antenna complexes

“…The changes observed in PC645 indicate that the relative intensity of the low energy band is reduced. This is consistent with the spectral changes predicted recently by Lee and coworkers arising from deprotonation of MBVs, 15 which increases the energy of the π→π* transition. As expected by the lack of a coordinating anionic residue, MBV pigments are predicted to be the least basic bilins in the complex.…”

“…6 An additional complication in the study of phycobiliproteins is the need to understand the protonation preferences of bilin pigments in the complex, as they can considerably impact their electronic transition properties, and also their degree of coupling to the environment. 15 Moreover, protonation/deprotonation of the pigments is also important because, unlike other photosynthetic organisms where antenna complexes are bound to the thylakoid membrane, cryptophyte biliproteins are suspended in the lumen, 16 where the varies on the range ~5-7, depending on the prolongation of the incident sunlight. 17 The uncertainty regarding this issue leaves open questions: can the protonation state of the pigments change upon variations of available sunlight?, and can changes in the bilin protonation patterns alter the light-harvesting pathways and dynamics in the system?…”

“…the Coker group has studied the protonation state of the MBVs in PC645 by comparing experimental and theoretical spectra derived from quantum chemical calculations. 15 Their results indicate that the PC645 complex with unprotonated MBVs displays better maximum intensities in the two main absorption peaks compared to the protonated case. However, the low-energy edge of the predicted spectra is slightly too broad, so that the assignment of the protonation preferences still remains open.…”

Delocalized excitons in natural light-harvesting complexes

“…However, the intermolecular motions may not be well described by harmonic potentials, and the energy gap could be highly nonlinear with the intermolecular coordinates. Very recently, an extension of the method has been presented by combining VG with force-field based MD (Lee et al, 2017): the sampled configurations are used to initiate QM ground state optimization of chromophore geometries in the presence of the instantaneous local fields provided by the MM partial charges of the surrounding protein environment. Ground and excited state properties are then computed at these optimized geometries to parametrize an ensemble of instantaneous local systembath model Hamiltonians.…”

Successes & challenges in the atomistic modeling of light-harvesting and its photoregulation

“…Structures extracted from the MD can be refined through a geometry optimization at the QM/MM level of the pigments, keeping the environment frozen in its configuration following from the MD trajectory. This strategy should allow to locate "inherent structures" of the pigments in the protein, that is, the accessible local minima in the pigment potential energy surface [111]. This method requires, however, a large number of QM/MM optimizations whose cost is not negligible compared to the cost of sampling structures.…”