Protein-Protein Interaction in Purple Membrane
Maikel C. Rheinsta
¨
dter,
1,2,4,
*
Karin Schmalzl,
3
Kathleen Wood,
4,5,†
and Dieter Strauch
6
1
Department of Physics and Astronomy, McMaster University, Hamilton, Ontario, L8S 4M1, Canada
2
Canadian Neutron Beam Centre, Chalk River, Ontario, K0J 1J0, Canada
3
Institut fu
¨
r Festko
¨
rperforschung, Forschungszentrum Ju
¨
lich GmbH, JCNS at ILL, F-38042 Grenoble, France
4
Institut Laue-Langevin, F-38042 Grenoble Cedex 9, France
5
Institut de Biologie Structurale Jean Pierre Ebel CEA-CNRS-UJF, F-38027 Grenoble, France
6
Theoretische Physik, Universita
¨
t Regensburg, D-93040 Regensburg, Germany
(Received 7 April 2009; published 18 September 2009)
We present experimental evidence for a long-range protein-protein interaction in purple membrane
(PM). The interprotein dynamics were quantified by measuring the spectrum of the acoustic phonons in
the 2D bacteriorhodopsin (BR) protein lattice using inelastic neutron scattering. Phonon energies of about
1 meV were determined. The data are compared to an analytical model, and the effective spring constant
for the interaction between neighboring protein trimers are determined to be k ¼ 53 N=m. Additional,
optical-like excitations at 0.45 meV were found and assigned to intraprotein dynamics between
neighboring BR monomers.
DOI: 10.1103/PhysRevLett.103.128104 PACS numbers: 87.15.km, 83.85.Hf, 87.16.dj
The high protein concentration in biological membranes
may lead to long-range protein-protein interactions, which
were speculated some time ago [1]. Motions in proteins
occur on various length and time scales [2,3], and the
functional behavior of membrane proteins is likely to
depend on the lipid bilayer composition and physical prop-
erties, such as hydrophobic thickness and elastic moduli.
How the variety of inter- and intraprotein motions, occur-
ring over different time and length scales, interact to result
in a functioning biological system remains an open field for
those working at the interface of physics and biology. The
dynamical coupling between proteins, i.e., cooperative
protein dynamics, may be important for the understanding
of macromolecular function in a cellular context because
it can lead to an effective interprotein communication.
Recently, interprotein motions in a carboxymyoglobin pro-
tein crystal were reported from a molecular dynamics
simulation [4,5]. Experimentally, phononlike excitations
of proteins in hydrated protein powder were reported [6].
Here, we report collective interprotein excitations in a
biological membrane, the purple membrane (PM).
PM occurs naturally in the form of a two-dimensional
crystal, consisting of 75% (wt/wt) of a single protein,
bacteriorhodopsin (BR), that functions as a light-activated
proton pump, and 25% various lipid species (mostly
phospho- and glycolipids) [7]. BR is a proton transporting
membrane protein, formed of seven transmembrane alpha
helices arranged around the photosensitive retinal mole-
cule. The protein in the lipid matrix is organized in trimers
that form a highly ordered 2D hexagonal lattice with lattice
parameter a 62
A. The structure of PM is well estab-
lished by electron microscopy, neutron and x-ray diffrac-
tion experiments as reviewed for instance in [7–12]. Here
we present the unprecedented determination of collective
protein-protein dynamics, i.e., acoustic phonons, in the 2D
protein lattice in PM using coherent inelastic neutron
scattering. The results allow the determination of the ef-
fective coupling constant by comparison to an analytical
model.
The experiments were performed on the IN12 cold-
triple-axis spectrometer at the Institut Laue-Langevin
(ILL, Grenoble, France). IN12 turned out to be highly
suited for elastic and inelastic investigations in oriented
biological samples because of its flexibility, good energy
resolution, and extremely low background. It allows the
measurement of diffraction and inelastic scattering in the
same run without changing the setup, which is crucial to
assign dynamical modes to structural properties and mo-
lecular components. IN12 was equipped with a vacuum
box to avoid air scattering at small scattering angles and
with vertically focusing monochromator and analyzer to
increase the neutron flux at the sample position. There
was no horizontal focusing, but the beam was collimated
to 40
0
—monochromator—30
0
—sample—30
0
—analyzer—
60
0
—detector. All scans were done in the W configuration
with fixed k
f
¼ 1:25
A
1
resulting in a q resolution of
q ¼ 0:005
A
1
, and an energy resolution of @! ¼
25 eV.
Deuterated PM was produced and hydrated by H
2
O in
order to suppress the contribution of the membrane hydra-
tion water to the phonon spectrum in the coherent inelastic
neutron scattering experiments. Because of the minuteness
of the coherent inelastically scattered signals, the prepara-
tion of appropriate samples and experimental setups is
challenging in this type of experiments. We used a com-
pletely deuterated PM to enhance the collective protein-
protein excitations over other contributions to the inelastic
scattering cross section. 200 mgs of deuterated PM sus-
PRL 103, 128104 (2009)
PHYSICAL REVIEW LETTERS
week ending
18 SEPTEMBER 2009
0031-9007=09=103(12)=128104(4) 128104-1 Ó 2009 The American Physical Society
pended in H
2
O was centrifuged down and the obtained
pellet spread onto a 40 30 mm aluminum sample holder.
This was then partially dried to 0.5 g water per gram of
membrane over silica gel in a desiccator. The PM patches
naturally align along the surface of the sample holder as
they dry. The silica gel was then replaced by water, and the
sample left to hydrate to a lamellar spacing of d
z
¼ 65
A at
303 K (30
C).
A sketch of the scattering geometry is shown in
Fig. 1(a). The experiments were carried out on PM stacks,
i.e., PM samples with a regular repeat distance d
z
. The
mosaicity of the sample (the distribution of normal vectors
with respect to the substrate) was checked by rocking scans
to about 17
. Figure 1(b) shows a reflectivity curve mea-
sured at T ¼ 30
C. From the three well developed Bragg
peaks, the lamellar spacing d
z
was determined to be d
z
¼
65:1
A, corresponding to an average inter membrane water
layer of 16 A
˚
, since the thickness of a dry PM fragment is
49 A
˚
. For the inelastic scans, Q was placed in the plane of
the membranes (q
jj
).
The in-plane diffraction pattern of the 2D hexagonal
protein lattice was measured and is shown in Fig. 2.
Although the normal vectors of the membranes are well
aligned with respect to the substrate, the (x, y) orientation
of the membrane layers is statistical and the signal a
superposition of the different domains (powder average).
All reflections can be indexed by a hexagonal unit cell with
a lattice parameter of 61:78 0:73
A. Correlations and
motions in membranes are often well separated in recip-
rocal space because of the largely different length and time
scales involved. The prominent distances in PM, such as
lipid-lipid and BR-BR monomers and trimers for instance
lead to spatially well-separated signals. The same holds for
the different time scales involved from the picosecond
(molecular reorientations) to the nano- or microsecond
(membrane undulations, large protein motions). The use
of oriented samples further allows the separation of corre-
lations in the plane of the membranes, and perpendicular to
the bilayers. Dynamics between different protein trimers is
expected to be dominant where the 2D BR diffraction
pattern is observed, i.e., in a q
jj
range of about 0:1
A
1
to 0:6
A
1
. Because elastic and inelastic scattering at small
momentum transfers was dominated by the rather strong
(1,0) and (1,1) reflections, systematic inelastic scans were
taken at q
jj
values in the third Brillouin zone of the 2D
pattern, between 0:34
A
1
and 0:46
A
1
. The inset in
Fig. 2 shows the Bragg peaks in the third Brillouin zone
in magnification and marks the positions of inelastic scans
at constant q
jj
values. Figure 3 depicts constant-q
jj
scans
at selected values between q
jj
¼ 0:35
A
1
and q
jj
¼
0:45
A
1
. The total inelastic signal consists of a
Gaussian central peak due to instrumental resolution,
a quasielastic broadening, which is described by a
Lorentzian peak shape, and pairs of excitations, described
by damped harmonic oscillator peak profiles. Because of
the pronounced and symmetric inelastic signals, we are
sure that the observed peaks are not spurious effects. The
quasielastic signal most likely stems from coherent and
incoherent diffusive motions.
The excitation spectrum of the 2D protein lattice was
modeled analytically. The protein trimers were taken as the
centers of a primitive hexagonal lattice with lattice con-
stant a ¼ 62
A, and the spectrum of the acoustic phonons
FIG. 1 (color online). (a) Sketch of the triple-axis scattering
geometry. q
jj
is the in-plane component of the scattering vector
Q. (b) Reflectivity curve measured at T ¼ 30
C. The dotted line
is a fit of Lorentzian peak profiles including a q
4
term. (c) BR
trimers are arranged on a hexagonal lattice of lattice constant
a 62
A. (d) The interaction between the protein trimers is
depicted as springs with effective spring constant k.
0 0.2 0.4 0.6 0.8
10
3
10
4
q
||
(Å
−1
)
neutron counts
(1,0)
(1,1)
(2,0)
(2,1)
(3,0)
(2,2)
(3,1)
(4,0)
(3,2)
(4,1)
(5,0)
0.35 0.4 0.45
400
500
600
(3,0)
(2,2)
(3,1)
(4,0)
FIG. 2 (color online). Diffraction pattern of the 2D protein
lattice from q
jj
¼ 0 to 0:75
A
1
. The reflections can be indexed
by a hexagonal unit cell with a lattice parameter of 61:78
0:73
A. The dashed line is a fit of the theoretical peak pattern to
the data. The inset shows the third Brillouin zone in magnifica-
tion. The arrows mark the positions of inelastic scans at constant
q
jj
values.
PRL 103, 128104 (2009)
PHYSICAL REVIEW LETTERS
week ending
18 SEPTEMBER 2009
128104-2
was calculated. The model is depicted in Fig. 1(c). The
basic hexagonal translations are marked by arrows. The
interaction between the protein trimers is contained in
springs with an effective (longitudinal) spring constant k
[Fig. 1(d)]. The calculated longitudinal spectrum C
l
ðq; !Þ,
defined by C
l
ðq; !Þ¼ð!
2
=q
2
ÞSðq; !Þ, is shown in Fig. 4.
The statistical average in the plane of the membrane leads
to a superposition of the different phonon branches, which
start and end in the hexagonal Bragg peaks (at @! ¼ 0).
The positions of excitations, as determined from the fits in
Fig. 3, are marked by the data points. The absolute phonon
energies can not be determined from the model, but depend
on the coupling constant k. So the energy of the phonon
spectrum in Fig. 4 was fitted to best match the experiment.
The experimentally determined excitation energies occur
at the intersections of the inelastic scans with the calcu-
lated phonon branches and well reproduce the features of
the theoretical excitation spectrum (within the given er-
rors). Note that because the proteins trimers were treated as
point masses with an effective mass of M
tr
, the calculations
do not include any contributions from intramonomer or
intratrimer dynamics, i.e., possible optical modes. The
excitations observed in the experiment at q
jj
values around
0:42
A
1
(corresponding to a length scale of about 15 A
˚
)
and energy value of 0.45 meV (marked by the dashed line
in Fig. 4), have no equivalent in the theoretical spectrum
and possibly stem from optical phonon branches. Because
the distance agrees well with the monomer-monomer dis-
tance in the protein trimer this mode can tentatively be
assigned to optical-like monomer dynamics (the corre-
sponding form factor is likely to be maximum at the
corresponding nearest neighbor distance).
The commonly assumed interaction mechanism be-
tween inclusions in membranes is a lipid-mediated inter-
action due to local distortions of the lipid bilayer [13–17],
with a strong dependence on the bilayer properties, in
particular, elastic properties. The PM may, however, be a
special case because there are very few lipids between
neighboring BR proteins [18]. While the nature of the
interaction still will be mainly elastic, it is not likely to
be purely lipid mediated but for the most part a direct
protein-protein interaction. The strength of the interaction
can be determined from the data in Fig. 4. The energy of
the zone-boundary phonon at the M point of the hexagonal
Brillouin zone (for instance at a q
jj
value of 0:35
A
1
)
relates to the coupling constant by M
tr
!
2
¼ 6k. Because
the energy is determined to @! ¼ 1:02 meV, the effective
protein-protein spring constant k is calculated to k ¼
53 N=m [ 19]. The amplitude of this mode of vibration
can be estimated from the equipartition theorem to
ffiffiffiffiffiffiffiffi
hx
2
i
p
¼
ffiffiffiffiffiffiffiffiffiffiffiffiffiffi
k
B
T=k
p
¼ 0:1
A, and the interaction force be-
tween two neighboring trimers to F ¼ k
ffiffiffiffiffiffiffiffi
hx
2
i
p
¼ 0:5nN.
Using the same approach, the spring constant for graphite
for comparison is calculated to 27 000 N=m for the in-
plane interaction, and 3:5N=m for out-of-plane interac-
tions. The force constant that we measure in PM is 1–2
orders of magnitude larger than the effective van der Waals
force constant in graphite, but 2–3 orders of magnitude
weaker than a C—C bond.
The ‘‘softness’’ of BR proteins in PM was probed by
elastic incoherent neutron scattering [8,20], and force con-
stants of 0:1N=m were reported. The shear modulus in
stacks of PM was determined by x-ray reflectivity to ¼
0:02 N=m [12]. The corresponding amplitudes of vibration
were 2.2 respective 3.8 A
˚
. These techniques were mainly
sensitive to diffusion of proteins (and lipids), and the force
and time constants involved are determined by local fric-
tion and restoring forces. The corresponding force con-
FIG. 4 (color online). Calculated excitation spectrum C
l
ðq; !Þ
in the range of the experimental data. Data points mark the
positions of excitations, as determined from the fits in Fig. 3. The
errorbars give the uncertainty in determining the peak position.
The horizontal line at ! ¼ 0:45 meV marks the position of a
possible optical phonon mode, not included in the calculations.
10
1
10
2
10
3
q
||
=0.35 Å
−1
0.37 Å
−1
0.39 Å
−1
−1 −0.5 0 0.5
10
1
neutron counts (arb. units)
0.41 Å
−1
−1 −0.5 0 0.5
ω (meV)
0.43 Å
−1
−1 −0.5 0 0.5 1
0.45 Å
−1
FIG. 3 (color online). Energy scans at q
jj
values of q
jj
¼ 0:35,
0.37, 0.39, 0.41, 0.43, and 0:45
A
1
. The total inelastic signal
consists of a central peak (Gaussian), a Lorentzian quasielastic
contribution, and the excitations, fitted using damped harmonic
oscillator peak profiles.
PRL 103, 128104 (2009)
PHYSICAL REVIEW LETTERS
week ending
18 SEPTEMBER 2009
128104-3
stants are about 2 orders of magnitude smaller than the one
reported in this study. Energies of collective, phononlike
excitations were also reported for proteins in a protein
crystal (from computer simulations [4,5]) and hydrated
protein powder (from inelastic x-ray scattering [6]), and
energies of about 1 meV for inter-, and even 10 meV for
intraprotein motions were found. The reported energies
cannot be quantitatively compared to the excitations in
this study because the systems are distinctly different.
However, it seems that the energies found for protein
interactions are consistently higher than the force constants
from experiments, which probe the local energy land-
scapes. The amplitudes of diffusive, self-correlated mo-
tions are therefore about one magnitude larger than those
of collective, pair correlated motions. ‘‘Motional coher-
ence’’, i.e., a structurally coherent state, was reported
recently in fluid phospholipid membranes [21]. So while
for a long time motions in biological materials were con-
sidered as thermally activated vibrations or librations in
local potentials, at least part of the fluctuation spectrum
stems from interactions. The future challenge is to under-
stand the impact of collective molecular motions in mem-
branes and proteins on biological function.
The protein coupling reported here may be relevant for
the photo cycle in PM. It was reported [22] that the BR
proteins undergo structural changes during the photo cycle,
involving displacements of up to 1.7 A
˚
. Because of the
elastic coupling of the BR proteins, those distortions can
propagate to neighboring proteins. On the microscopic
level, displacing or distorting a BR trimer by 1.7 A
˚
yields
a force between neighboring trimers of 9 nN (using the
model presented here). It can therefore be speculated that
there is a protein-protein communication during the photo-
cycle in PM. So while thermal fluctuations are dominated
by diffusive motions, collective motions may play a key
role to establish dynamics-function relations in complex
biological materials.
In conclusion we present experimental evidence for
protein-protein interactions in purple membrane. The spec-
trum of the acoustic phonons in the 2D bacteriorhodopsin
lattice was calculated and measured by inelastic neutron
scattering. Phonon energies of about 1 meV were found.
An additional band at energies of about 0.45 meV was
tentatively assigned to optical phonon modes between the
BR monomers. The effective spring constant for the inter-
action between protein trimers was determined from the
acoustic phonon branches to k ¼ 53 N=m. Future experi-
ments will address collective intraprotein trimer and also
intramonomer dynamics. To make a clear relationship to
protein function, protein dynamics of activated proteins,
i.e., the collective dynamics of proteins undergoing the
photo cycle, will be studied [23]. While the protein con-
centration in PM is very high and the proteins are very
close to a 2D crystal, it can be speculated that there is a
protein coupling also in less dense membrane systems.
We thank Brigitte Kessler and Dieter Oesterhelt (MPI
for Biochemistry) for providing the sample, Martin Weik
(IBS) for help with sample preparation, Giuseppe Zaccai
(ILL) for critical reading of the manuscript, and the Institut
Laue-Langevin for the allocation of beam time.
*rheinstadter@mcmaster.ca
†
Present address: Australian Nuclear Science & Tech-
nology Organisation, Bragg Institute, Menai, Australia.
[1] Structure and Dynamics of Membranes, edited by
R. Lipowsky and E. Sackmann, Handbook of Biological
Physics Vol. 1 (Elsevier, Amsterdam, 1995).
[2] H. Frauenfelder, S. Sligar, and P. Wolynes, Science 254,
1598 (1991).
[3] P. Fenimore, H. Frauenfelder, B. McMahon, and R.
Young, Proc. Natl. Acad. Sci. U.S.A. 101, 14 408 (2004).
[4] V. Kurkal-Siebert, R. Agarwal, and J. C. Smith, Phys. Rev.
Lett. 100, 138102 (2008).
[5] L. Meinhold, J. C. Smith, A. Kitao, and A. H. Zewail,
Proc. Natl. Acad. Sci. U.S.A. 104, 17 261 (2007).
[6] D. Liu, X.-Q. Chu, M. Lagi, Y. Zhang, E. Fratini,
P. Baglioni, A. Alatas, A. Said, E. Alp, and S.-H. Chen,
Phys. Rev. Lett. 101, 135501 (2008).
[7] U. Haupts, J. Tittor, and D. Oesterhelt, Annu. Rev.
Biophys. Biomol. Struct. 28, 367 (1999).
[8] G. Zaccai, Biophys. Chem. 86, 249 (2000).
[9] R. Neutze, E. Pebay-Peyroula, K. Edman, A. Royant,
J. Navarro, and E. Landau, Biochim. Biophys. Acta
1565, 144 (2002).
[10] J. Lanyi, Annu. Rev. Physiol. 66, 665 (2004).
[11] I. Koltover, T. Salditt, J.-L. Rigaud, and C. Safinya, Phys.
Rev. Lett. 81, 2494 (1998).
[12] I. Koltover, J. Ra
¨
dler, T. Salditt, and C. Safinya, Phys. Rev.
Lett. 82, 3184 (1999).
[13] P. A. Kralchevsky, Adv. Biophys. 34, 25 (1997).
[14] K. Bohinc, V. Kralj-Iglic
ˇ
, and S. May, J. Chem. Phys. 119,
7435 (2003).
[15] P. Biscari and F. Bisi, Eur. Phys. J. E 7, 381 (2002).
[16] P. Lagu
¨
e, M. J. Zuckermann, and B. Roux, Biophys. J. 81,
276 (2001).
[17] N. Dan, P. Pincus, and S. Safran, Langmuir 9, 2768
(1993).
[18] J. Baudry, E. Tajkhorshid, F. Molnar, J. Phillips, and
K. Schulten, J. Phys. Chem. 105, 905 (2001).
[19] Hunt et al., determined the molecular weight of a BR
monomer was determined to 26.9 kDa (1kg¼ 6:0221
10
26
dalton); J. F. Hunt, P. D. McCrea, G. Zaccaı
¨
, and
D. M. Engelman, J. Mol. Biol. 273, 1004 (1997).
[20] G. Zaccai, Science 288, 1604 (2000).
[21] M. C. Rheinsta
¨
dter, J. Das, E. J. Flenner, B. Bru
¨
ning,
T. Seydel, and I. Kosztin, Phys. Rev. Lett. 101, 248106
(2008).
[22] H. Luecke, B. Schobert, H.-T. Richter, J.-P. Cartailler, and
J. K. Lanyi, Science 286, 255 (1999).
[23] J. Pieper, A. Buchsteiner, N. A. Dencher, R. E. Lechner,
and T. Hauß, Phys. Rev. Lett. 100, 228103 (2008).
PRL 103, 128104 (2009)
PHYSICAL REVIEW LETTERS
week ending
18 SEPTEMBER 2009
128104-4
