A poster presentation version of http://arxiv.org/abs/1302.6323, presented by Anna Schneider at the Mini Statistical Mechanics conference in Berkeley, CA in January 2013.

1. Coexistence between fluid and crystalline phases of proteins in photosynthetic membranes
Anna R. Schneider and Phillip L. Geissler.
Biophysics Graduate Group and Department of Chemistry, UC Berkeley. aschn@berkeley.edu
Abstract
In photosynthetic thylakoid membranes, solar energy conversion efficiency is tuned by dynamic rearrangements of photosystem II (PSII) and its associated light-harvesting complex II (LHCII) during nonphotochemical quenching.
While some rearrangements are within disordered packings, PSII complexes in stacked grana membranes are also frequently observed to form co-crystals with LHCII. The determinants and functional relevance of these
morphologies remain elusive. Here we identify a thermodynamic phase transition between fluid and crystalline phases in a coarse-grained model of PSII and LHCII that features experimentally-motivated interactions both within
and between membrane layers. Simulations with this model capture clear signatures of a range of known structural motifs. Free energy calculations produce a phase diagram featuring a broad coexistence region that spans much
of the physiologically relevant parameter regime. It appears that grana membranes are poised at coexistence, conferring significant structural and functional flexibility to this densely packed membrane protein system.
Background Structural characterization of self-assembled arrays
= 3.36, = 0.70 = 4.22, = 0.75
• Photosynthesis in plants and green algae takes place in the thylakoid membrane,
which includes tightly appressed grana stacks a d Canonical ensemble simulations of a coupled pair of grana membrane layers g 0.6 0.5 0.5
• Photosystem II (PSII), the site of water-splitting, and light-harvesting complex II a-c: PSII interlayer motifs. Green and blue outlines: LHCII and PSII particles in 0.5 0.4 0.4
(LHCII), the primary chlorophyll-binding protein, are densely concentrated in
with stacking
the upper (lumen-side-up) layer; purple and red outlines: LHCII and PSII
grana stacks (packing fraction 65–85%) ~20° 0.4
probability
particles in the lower (stroma-side-up) layer. Black lines drawn parallel to the 0.3 0.3
• LHCII stromal faces have net attractive electrostatic interactions between long axis of selected rods highlight orientational relationships between PSII
0.3
0.2 0.2
membrane layers that contribute to stack integrity particles in different layers (compare to panel g). Scale bars = 10 nm. 0.2
• PSII–LHCII complexes can form 2D arrays 0.1 0.1
b
0.1
d: Snapshot of the top layer from a simulation at ρ = 0.75 showing a
‣ sporadically observed, not always reproducible, only in stacked membranes representative array. Color scheme as in “Model and simulations,” except arrayed 0.0 0.0 0.0
0 2 4 6 8 10 12 14 0 5 10 15 20 25 0 15 30 45 60 75 90
‣ many different unit cells (with and without extra LHCIIs) PSII are colored red. Arrays are identified by a recursive clustering algorithm.
• Short-range order affects the efficiency of exciton energy transfer from antenna >60° Scale bar = 50 nm. 0.6 0.5 0.5
= 2.4, = 0.55
Chl in LHCII to reaction center in PSII
without stacking
0.5 = 3.4, = 0.60
e and f: Magnified views of the boxed region in panel d. Scale bars = 20 nm. The 0.4 0.4 = 4.4, = 0.65
• Long-range order may affect diffusive first-passage times between membrane role of intralayer attractions is highlighted in e by showing only particles in the 0.4 = 5.4, = 0.70
probability
0.3 0.3 = 6.4, = 0.75
regions, which is essential for dynamic regulatory phenomena (state transitions top layer and indicating the locations of PSII–LHCII interaction sites on each 0.3
and PSII repair) c PSII. The stabilizing role of stacking is highlighted in f by showing particles from 0.2 0.2
e f both layers in outline form (as in panels a-c).
0.2
0.1 0.1
surface charge on LHCII 0.1
crystal structure ~65° g: Structural correlation functions between membrane layers, with and without
LHCII 0.0 0.0 0.0
( Standfuss et al 2005) aq. stroma coupling through LHCII stacking. Stacking has a large effect on the interlayer 0 2 4 6 8 10 12 14 0 5 10 15 20 25 0 15 30 45 60 75 90
PSII correlations of LHCII and PSII at all densities. No arrays are observed in the distance to nearest distance to nearest rotation to nearest
PSI
absence of stacking interactions. stacked LHCII (nm) stacked PSII (nm) stacked PSII (degrees)
aq. lumen
thylakoid membrane bilayer
ATP synthase
Phase diagram has large
PSII organization:
Evidence for a crystal-fluid phase transition
crystalline array, linear, disordered
coexistence region
‡ 0.85
0.0710 f c
!
stroma lamellae
(connect to other grana stacks)
# 0.80
fluid-crystal interface
packing fraction
grana stack coexistence
pressure (kBT/nm2)
(~500 nm diameter)
0.0705 0.75
Kirchhoff et al 2007
crystal
0.70
0.0700 p*
Model and simulations cooperativity
0.65 fluid
0.0695 0.60
a PSII-LHCII intralayer attraction
lumen 1 2 3 4 5 6
simulation
lumen = c = ‡ LHCII:PSII ratio
0.0690
paired grana
membranes
" • Each phase transition point (µLHCII*,p*) maps to two points and a corresponding
+-+- stroma simulation 50 two free energy basins tie line. One point lies at the boundary of the homogeneous fluid phase (blue), the
layers other at the boundary of the fully crystalline state (red). Example tie lines are
LHCII PSII
free energy (kBT)
40 drawn as dashed lines connecting these boundaries for selected values of p*.
lumen
• Coexistence (green) and pure-phase regions extend beyond the shaded areas
30 determined by our limited data.
LHCII-LHCII interlayer (stacking) attraction p > p*
20 • The range of reported values of ϕ and ρ from in vivo and in vitro experiments lies
predominantly inside the coexistence region. Thus, our model of the LHCII-PSII
b S c d 0
p = p* protein system is at coexistence in many physiologically relevant conditions.
energy (kBT)
C
C
S M
-1 10
S C
S -2
C C p < p*
C S
M S -3 0
Conclusions
S C -4
f
10 nm
(C2S2)2 C
C2S2M2 0 distance (nm) 6.5 0.60 0.65 0.70 0.75 0.80 0.85 0.90
=
S
• Modeled LHCII and PSII particles move in two coupled 2D membrane planes (a) packing fraction
• PSII supercomplexes (including two chirally-embedded LHCIIs) are 12×26.5-
nm hard rods, as shown in panels b and c. Scale bars = 10 nm. • The stacked nature of photosynthetic membranes is integral to the organization
and function of the light-harvesting and reaction center components within each
• PSII have two interaction sites that bind in-plane LHCII via a square-well Umbrella sampling free energy calculations in the osmotic (NPSIIµLHCIIpT) ensemble membrane layer.
potential to form (C2S2)2 (b) and C2S2Mx (c) complexes; binding embedded
LHCIIs to form (C2S2)2 also requires the PSIIs be close to parallel a: Applied pressure p versus packing fraction b: Free energy as a function of ρ for a system at fixed • Stacking and in-plane interactions promote orthogonal modes of crystal self-
ρ along a line of constant chemical potential chemical potential and three values of pressure near assembly; both are required for crystal growth at physiological conditions.
• LHCII are 6.5-nm hard discs with the stacking potential in panel d shows a sharp crossover at p* from a low- coexistence: within the fluid phase (blue), within the
ρ = packing fraction
• Particles move within their own membrane planes via Monte Carlo single- pressure, low-density regime to a high- crystalline phase (red), and at coexistence (green). Error ϕ = mole ratio of free LHCII to • Ordered PSII-LHCII crystals and disordered PSII-LHCII fluids are both pure
particle moves, but can interact with particles in adjacent membrane planes PSII supercomplex thermodynamic phases; experimentally-observed arrays are finite fragments of
pressure, high-density regime. Means (line bars estimated from the MBAR method are smaller than
the crystal phase.
• Acceptance criteria for constant chemical potential (insertion) and constant and points) and root-mean-squared the symbols. Because the zero of free energy is arbitrary
p = 2D “pressure”
pressure moves in a system of nl coupled 2D layers: fluctuations (whiskers) of ρ at each pressure at each pressure, curves are vertically offset for clarity. • Fluid-coexistence boundary is at ~70% protein packing fraction, putting many
are calculated from probability distributions Dotted lines are guides to the eye. µLHCII = LHCII chemical potential experimental conditions in the coexistence region.
nl V derived from free energy surfaces like those
acc(Nα → Nα + 1) = min 1, e−β(∆U −µα )
(Nα + 1)Λ2 in panel b. Fluctuations, and therefore c: Snapshots taken from umbrella sampling simulations µLHCII*,p* = phase transition • The photosynthetic apparatus may dynamically regulate its position within the
whiskers, are large in the vicinity of p*. biased to the stated densities. Scale bars = 50 nm. phase diagram to fine-tune its light-harvesting capacity and the mobility of various
Ntot +1
Vn pigment-protein species.
acc(Vo → Vn ) = min 1, e−β(∆U +nl p∆V )
Vo