Computational Modeling of Exciton-bath Hamiltonians for LH2 and LH3 Complexes of Purple Photosynthetic Bacteria at Room Temperature

TL;DR

This work integrates all-atom MD and TD-DFT to dissect the molecular origins of the LH2/LH3 spectral shift in purple bacteria and to construct transferable exciton–bath Hamiltonians. It finds that LH3 lacks HB on the $\beta$-BChl and exhibits only modest acetyl-group–rotation differences, with TD-DFT indicating HB absence accounts for a $\sim$500 cm$^{-1}$ blue shift for affected sites, while acetyl rotation contributes little. To reconcile the experimental LH3 lineshape, the authors introduce a common blue shift of $320$ cm$^{-1}$ to both $\alpha$- and $\beta$-BChls plus the $500$ cm$^{-1}$ $\beta$-specific shift, achieving good agreement with ensemble spectra. The resulting compact exciton–bath models enable efficient simulation of exciton dynamics and offer mechanistic insight into how protein environments tune spectral properties in photosynthetic complexes.

Abstract

Light harvesting 2 (LH2) complex is a primary component of the photosynthetic unit of purple bacteria that is responsible for harvesting and relaying excitons. The electronic absorption line shape of LH2 contains two major bands at 800 nm and 850 nm wavelength regions. Under low light condition, some species of purple bacteria replace LH2 with LH3, a variant form with almost the same structure as the former but with distinctively different spectral features. The major difference between the absorption line shapes of LH2 and LH3 is the shift of the 850 nm band of the former to a new 820 nm region. The microscopic origin of this difference has been subject to some theoretical/computational investigations. However, the genuine molecular level source of such difference is not clearly understood yet. This work reports a comprehensive computational study of LH2 and LH3 complexes so as to clarify different molecular level features of LH2 and LH3 complexes and to construct simple exciton-bath models with a common form. All-atomistic molecular dynamics (MD) simulations of both LH2 and LH3 complexes provide detailed molecular level structural differences of BChls in the two complexes, in particular, in their patterns of hydrogen bonding (HB) and torsional angles of the acetyl group. Time-dependent density functional theory calculation of the excitation energies of BChls for structures sampled from the MD simulations, suggests that the observed differences in HB and torsional angles cannot fully account for the experimentally observed spectral shift of LH3. Potential sources that can explain the actual spectral shift of LH3 are discussed, and their magnitudes are assessed through fitting of experimental line shapes.

Figures (6)

• Figure 1: Schematic of the 9-fold LH2 (LH3) complex. The first protomer ($n=1$) and its 2 adjacent ones ($n=2, 9$), are shown appearing as wedges sliced into the cylindrical complex. BChl molecules appear as filled (for $n=1$) or open (for $n=2,9$) circles with bold labels $\alpha_n$, $\beta_n$, and $\gamma_n$ representing each site. Yellow arrows indicate axial $z$-directions. The pigment radial distance from the $z$-axis is depicted by $R$. Red arrows represent BChl transition dipoles. Polar angle $\theta$, shown in orange, is the angle the transition dipole makes with the $z$-axis. The azimuthal angle $\nu$ is the angle the BChl position vectors of the first protomer make with the $x$-axis, while the azimuthal angle $\phi$ is the angle of the $xy$ projection of the transition dipole relative to the radial vector pointing to each BChl on the $xy$-plane. $Z_\gamma$ is the distance separating the plane of B800 BChls from that of B850 (B820) BChls, which are defined to lie on $z=0$ plane.
• Figure 2: Snapshots of the symmetry units for equilibrated (a) LH2 and (b) LH3 complexes.
• Figure 3: Time dependent root mean square displacements (RMSDs) of protein backbones of LH2 and LH3 complexes during the second phase of MD simulations.
• Figure 4: Calculated spectral densities (divided by $\pi\hbar$) in the unit of ${\rm cm^{-1}}$ for $Q_y$ excitation of BChls for LH2 (red) and LH3 (green) averaged over the 9 sites. The top panel is for $\alpha$, the middle panel for $\beta$, and the bottom is for $\gamma$-BChl. Also compared are the spectral density by Jang et al.jang-jpcb111 based on that of Renger and Marcus,renger-jcp116 Olbrich and Kleinekathöfer,olbrich-jpcb114 and a recent one by Freiberg and coworkers.pajusalu-cpc12 Insets show close-ups of regions below $500\ {\rm cm^{-1}}$.
• Figure 5: (a) Structure of a BChl with phytyl chain remove. The atoms ${\rm C2}$, ${\rm C3}$, ${\rm C3^1}$, and ${\rm O3^1}$ defining the dihedral (torsional) angle are highlighted as yellow. (b) Acetyl group dihedral angle distributions of BChls for LH2 (red) and LH3(blue). The upper panel is for $\alpha$-BChls and the lower panel is for $\beta$-BChls.