Conclusions•The stacked nature of photosynthetic membranes is integral to the organization

and function of the light-harvesting and reaction center components within each membrane layer.

•Stacking and in-plane interactions promote orthogonal modes of crystal self-assembly; both are required for crystal growth at physiological conditions.

•Ordered PSII-LHCII crystals and disordered PSII-LHCII fluids are both pure thermodynamic phases; experimentally-observed arrays are finite fragments of the crystal phase.

•Fluid-coexistence boundary is at ~70% protein packing fraction, putting many experimental conditions in the coexistence region.

•The photosynthetic apparatus may dynamically regulate its position within the phase diagram to fine-tune its light-harvesting capacity and the mobility of various pigment-protein species.

Background• Photosynthesis in plants and green algae takes place in the thylakoid membrane,

which includes tightly appressed grana stacks• Photosystem II (PSII), the site of water-splitting, and light-harvesting complex II

(LHCII), the primary chlorophyll-binding protein, are densely concentrated in grana stacks (packing fraction 65–85%)• LHCII stromal faces have net attractive electrostatic interactions between

membrane layers that contribute to stack integrity• PSII–LHCII complexes can form 2D arrays‣ sporadically observed, not always reproducible, only in stacked membranes‣ many different unit cells (with and without extra LHCIIs)

• Short-range order affects the efficiency of exciton energy transfer from antenna Chl in LHCII to reaction center in PSII• Long-range order may affect diffusive first-passage times between membrane

regions, which is essential for dynamic regulatory phenomena (state transitions and PSII repair)

surface charge on LHCII crystal structure

( Standfuss et al 2005)

aq. lumen

aq. stroma

PSI

PSII

LHCII

thylakoid membrane bilayer

grana stack(~500 nm diameter)

stroma lamellae(connect to other grana stacks)

PSII organization:crystalline array, linear, disordered

ATP synthase

Kirchhoff et al 2007

Phase diagram has large coexistence region

•Each phase transition point (µLHCII*,p*) maps to two points and a corresponding tie line. One point lies at the boundary of the homogeneous fluid phase (blue), the other at the boundary of the fully crystalline state (red). Example tie lines are drawn as dashed lines connecting these boundaries for selected values of p*.

•Coexistence (green) and pure-phase regions extend beyond the shaded areas determined by our limited data.

•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 protein system is at coexistence in many physiologically relevant conditions.

coexistence

crystal

0.60

0.65

0.70

0.75

0.80

0.85

1 2 3 4 5 6

packin

g fra

ction

LHCII:PSII ratio

fluidModel and simulations

• Modeled LHCII and PSII particles move in two coupled 2D membrane planes (a)• 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.• PSII have two interaction sites that bind in-plane LHCII via a square-well

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• LHCII are 6.5-nm hard discs with the stacking potential in panel d• Particles move within their own membrane planes via Monte Carlo single-

particle moves, but can interact with particles in adjacent membrane planes• Acceptance criteria for constant chemical potential (insertion) and constant

pressure moves in a system of nl coupled 2D layers:

acc(Nα → Nα + 1) = min�

1,nlV

(Nα + 1)Λ2e−β(∆U−µα)

�

acc(Vo → Vn) = min

�1,

�Vn

Vo

�Ntot+1

e−β(∆U+nlp∆V )

�

d

C

S

C

S

C

S

C

S

C

S

C

S

b

stroma

PSII-LHCII intralayer attraction

simulation

layers

pa

ire

d g

ra

na

me

mb

ra

ne

s

LHCII-LHCII interlayer (stacking) attraction

lumensimulation

lumen

LHCII PSII

+ - + -

alumen

C

S

C

SM

M

(C2S2)2 C2S2M2

c

-4

-3

-2

-1

0

0 6.5

ener

gy (k

BT)

distance (nm)10 nm

Structural characterization of self-assembled arraysCanonical ensemble simulations of a coupled pair of grana membrane layers

a-c: PSII interlayer motifs. Green and blue outlines: LHCII and PSII particles in the upper (lumen-side-up) layer; purple and red outlines: LHCII and PSII particles in the lower (stroma-side-up) layer. Black lines drawn parallel to the long axis of selected rods highlight orientational relationships between PSII particles in different layers (compare to panel g). Scale bars = 10 nm.

d: Snapshot of the top layer from a simulation at ρ = 0.75 showing a representative array. Color scheme as in “Model and simulations,” except arrayed PSII are colored red. Arrays are identified by a recursive clustering algorithm. Scale bar = 50 nm.

e and f: Magnified views of the boxed region in panel d. Scale bars = 20 nm. The role of intralayer attractions is highlighted in e by showing only particles in the top layer and indicating the locations of PSII–LHCII interaction sites on each PSII. The stabilizing role of stacking is highlighted in f by showing particles from both layers in outline form (as in panels a-c).

g: Structural correlation functions between membrane layers, with and without coupling through LHCII stacking. Stacking has a large effect on the interlayer correlations of LHCII and PSII at all densities. No arrays are observed in the absence of stacking interactions.

wit

h s

tack

ing

wit

hou

t st

acki

ng

g

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0 2 4 6 8 10 12 14

prob

abilit

y

0.0

0.1

0.2

0.3

0.4

0.5

0 5 10 15 20 250.0

0.1

0.2

0.3

0.4

0.5

0 15 30 45 60 75 90

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0 2 4 6 8 10 12 14

prob

abilit

y

distance to neareststacked LHCII (nm)

0.0

0.1

0.2

0.3

0.4

0.5

0 5 10 15 20 25distance to neareststacked PSII (nm)

0.0

0.1

0.2

0.3

0.4

0.5

0 15 30 45 60 75 90rotation to nearest

stacked PSII (degrees)

= 2.4, = 0.55 = 3.4, = 0.60 = 4.4, = 0.65 = 5.4, = 0.70 = 6.4, = 0.75

d

e f

= 3.36, = 0.70 = 4.22, = 0.75

~20°

>60°

~65°

a

b

c

Coexistence between fluid and crystalline phases of proteins in photosynthetic membranesAnna R. Schneider and Phillip L. Geissler.

Biophysics Graduate Group and Department of Chemistry, UC Berkeley. aschn@berkeley.edu

AbstractIn 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.

Evidence for a crystal-fluid phase transition

ρ = packing fraction

ϕ = mole ratio of free LHCII to PSII supercomplex

p = 2D “pressure”

µLHCII = LHCII chemical potential

µLHCII*,p* = phase transition

b: Free energy as a function of ρ for a system at fixed chemical potential and three values of pressure near coexistence: within the fluid phase (blue), within the crystalline phase (red), and at coexistence (green). Error bars estimated from the MBAR method are smaller than the symbols. Because the zero of free energy is arbitrary at each pressure, curves are vertically offset for clarity. Dotted lines are guides to the eye.

c: Snapshots taken from umbrella sampling simulations biased to the stated densities. Scale bars = 50 nm.

a: Applied pressure p versus packing fraction ρ along a line of constant chemical potential shows a sharp crossover at p* from a low-pressure, low-density regime to a high-pressure, high-density regime. Means (line and points) and root-mean-squared fluctuations (whiskers) of ρ at each pressure are calculated from probability distributions derived from free energy surfaces like those in panel b. Fluctuations, and therefore whiskers, are large in the vicinity of p*.

Umbrella sampling free energy calculations in the osmotic (NPSIIµLHCIIpT) ensemble

= c = ‡

=

f

!

"

#

p < p*

p = p*

p > p*

‡ c f

p*

0.0690

0.0695

0.0700

0.0705

0.0710

pres

sure

(kBT

/nm

2 )

0

10

20

30

40

50

0.60 0.65 0.70 0.75 0.80 0.85 0.90

free

ener

gy (k

BT)

packing fraction

fluid-crystal interface

two free energy basins

cooperativity