  Photosystem II (PSII) and its associated light-harvesting complex II (LHCII)
are highly concentrated in the stacked grana regions of photosynthetic
thylakoid membranes. Within the membrane, PSII-LHCII supercomplexes can be
arranged in disordered packings, ordered arrays, or mixtures thereof. The
physical driving forces underlying array formation are unknown, complicating
attempts to determine a possible functional role for arrays in regulating light
harvesting or energy conversion efficiency. Here we introduce a coarse-grained
model of protein interactions in coupled photosynthetic membranes, focusing on
just two particle types that feature simple shapes and potential energies
motivated by structural studies. Reporting on computer simulations of the
model's equilibrium fluctuations, we demonstrate its success in reproducing
diverse structural features observed in experiments, including extended
PSII-LHCII arrays. Free energy calculations reveal that the appearance of
arrays marks a phase transition from the disordered fluid state to a
system-spanning crystal, which can easily be arrested by thermodynamic
constraints or slow dynamics. The region of fluid-crystal coexistence is broad,
encompassing much of the physiologically relevant parameter regime. Our results
suggest that grana membranes lie at or near phase coexistence, conferring
significant structural and functional flexibility to this densely packed
membrane protein system.
