Alamethicin aggregation in lipid membranes.

Abstract

X-ray scattering features induced by aggregates of alamethicin (Alm) were obtained in oriented stacks of model membranes of DOPC(diC18:1PC) and diC22:1PC. The first feature obtained near full hydration was Bragg rod in-plane scattering near 0.11 A(-1) in DOPC and near 0.08 A(-1) in diC22:1PC at a 1:10 Alm:lipid ratio. This feature is interpreted as bundles consisting of n Alm monomers in a barrel-stave configuration surrounding a water pore. Fitting the scattering data to previously published molecular dynamics simulations indicates that the number of peptides per bundle is n = 6 in DOPC and n >or= 9 in diC22:1PC. The larger bundle size in diC22:1PC is explained by hydrophobic mismatch of Alm with the thicker bilayer. A second diffuse scattering peak located at q(r) approximately 0.7 A(-1) is obtained for both DOPC and diC22:1PC at several peptide concentrations. Theoretical calculations indicate that this peak cannot be caused by the Alm bundle structure. Instead, we interpret it as being due to two-dimensional hexagonally packed clusters in equilibrium with Alm bundles. As the relative humidity was reduced, interactions between Alm in neighboring bilayers produced more peaks with three-dimensional crystallographic character that do not index with the conventional hexagonal space groups.

Full text

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ORIGINAL ARTICLES
Alamethicin Aggregation in Lipid Membranes
Jianjun Pan Æ Æ Stephanie Tristram-Nagle Æ Æ
John F. Nagle
Received: 13 August 2009/Accepted: 2 September 2009/Published online: 30 September 2009
? Springer Science+Business Media, LLC 2009
Abstract
of alamethicin (Alm) were obtained in oriented stacks of
model membranes of DOPC(diC18:1PC) and diC22:1PC.
The first feature obtained near full hydration was Bragg rod
in-plane scattering near 0.11 A˚-1in DOPC and near 0.08
A˚-1in diC22:1PC at a 1:10 Alm:lipid ratio. This feature is
interpreted as bundles consisting of n Alm monomers in a
barrel-stave configuration surrounding a water pore. Fitting
the scattering data to previously published molecular
dynamics simulations indicates that the number of peptides
per bundle is n = 6 in DOPC and n C 9 in diC22:1PC. The
larger bundle size in diC22:1PC is explained by hydro-
phobic mismatch of Alm with the thicker bilayer. A second
diffuse scattering peak located at qr& 0.7 A˚-1is obtained
for both DOPC and diC22:1PC at several peptide con-
centrations. Theoretical calculations indicate that this peak
cannot be caused by the Alm bundle structure. Instead, we
interpret it as being due to two-dimensional hexagonally
packed clusters in equilibrium with Alm bundles. As the
relative humidity was reduced, interactions between Alm in
neighboring bilayers produced more peaks with three-
dimensional crystallographic character that do not index
with the conventional hexagonal space groups.
X-ray scattering features induced by aggregates
Keywords
Hydrophobic mismatch ? Water pore ? Helix bundle ?
Ion channel
Alamethicin ? Aggregation ?
Introduction
It is becoming increasingly appreciated that lipids play an
important role in membrane biochemistry (Phillips et al.
2009) by modulating protein function (Brown 1994) and
lateral organization (Baumgart et al. 2003). Differences in
the curvature stress (Gruner and Shyamsunder 1991) or the
lateral pressure profile (Cantor 1997) in bilayers of different
lipids likely alter the energy of the transition state and the
kineticsofproteinconformationchanges.Theenergycostof
membrane deformation caused by hydrophobic mismatch
betweenthehydrophobiccoreofthelipidmembraneandthe
protein’s hydrophobic domain depends on membrane
thickness, bending elasticity, area stretch modulus and
intrinsic curvature (Huang 1986; Andersen and Koeppe
2007). Therefore, membrane protein structure and function
can be modulated by varying the mechanical and structural
properties of lipid bilayers (McIntosh and Simon 2006).
One particular interest here was to investigate how the
size of the ion channels (bundles) formed by the antimi-
crobial peptide alamethicin (Alm) changes as a function of
lipid properties. Macroscopic and single-channel (Hall
et al. 1984; Sansom 1991; Woolley and Wallace 1992;
Cafiso 1994) conductance measurements have indicated
that the conductance behavior of the Alm channel depends
on lipid properties. A larger probability for higher con-
ductance states (larger n) has been observed when Alm
inserts into PE lipids, which have a smaller headgroup than
the typical bilayer forming PC lipids (Keller et al. 1993).
Stable barrel-stave (Baumann and Mueller 1974) Alm
bundles have been observed by applying neutron (He et al.
1995, 1996) and X-ray (Constantin et al. 2007; Qian et al.
2008) scattering techniques where no external voltage was
present. The neutron studies showed that the bundles
encompassed a water pore. These stable bundles may be
J. Pan ? S. Tristram-Nagle ? J. F. Nagle (&)
Department of Physics, Carnegie Mellon University,
Pittsburgh, PA 15213, USA
e-mail: nagle@cmu.edu
J. F. Nagle
Department of Biological Sciences, Carnegie Mellon University,
Pittsburgh, PA 15213, USA
123
J Membrane Biol (2009) 231:11–27
DOI 10.1007/s00232-009-9199-8

Page 2

different from the dynamic single channels in conductance
measurements (Qian et al. 2008). The average number of
Alm monomers (n) per bundle has been estimated by
model fitting to X-ray scattering (Constantin et al. 2007) or
to neutron scattering (He et al. 1995, 1996). We use similar
model-fitting procedures to our X-ray scattering data to
investigate the Alm bundle size in two lipid model mem-
branes, DOPC and diC22:1PC. These bilayers have similar
properties except that diC22:1PC is about 7 A˚thicker than
DOPC (Kuc ˇerka et al. 2005b).
We observe a second peak that has also been previously
observed and interpreted as due to barrel-stave bundles (He
et al. 1996); but our analysis does not allow us to agree
with this assignment, and we have been forced to consider
an alternative, coexisting structure. Finally, we present data
on partially dehydrated samples, in which the interactions
between neighboring bilayers in our stacked samples
become strong. A confusing variety of crystallographic
packing patterns appears as one proceeds away from the
fully hydrated biological condition, and, while interesting
solid-state physics and crystallographic problems can be
addressed, we conclude that such samples should not be
preferred for determination of Alm bundle structure.
Materials and Methods
Sample Preparation
1,2-Dioleoyl-sn-glycero-phosphatidylcholine (DOPC) and
1,2-dierucoyl-sn-glycero-phosphatidylcholine
were purchased from Avanti Polar Lipids (Alabaster, AL).
Alm was purchased from Sigma-Aldrich (Milwaukee, WI).
This is a natural, purified 20-amino acid peptide from
Trichoderma viride consisting of 85% Alm I and 15% Alm
II. The primary structure of Alm I is acetyl-Aib-Pro-Aib-
Ala-Aib-Ala-Gln-Aib-Val-Aib-Gly-Leu-Aib-Pro-Val-Aib-
Aib-Glu-Gln-Phol. Alm II differs from Alm I in the amino
acid at the sixth position: Aib in Alm II instead of Ala in
Alm I.
Pure lipid (4 mg) was added to a chloroform:trifluoro-
ethanol (TFE) solvent mixture (v:v 2:1 or 1:1) and to this
was added the appropriate amount of Alm from a chloro-
form stock solution (1 mg/ml). Peptide to lipid mole ratios
between 1:75 and 1:10 were studied. The mixture was
plated onto the 1.5 9 3 cm surface of a polished silicon
wafer using the rock-and-roll procedure (Tristram-Nagle
et al. 1993; Tristram-Nagle 2007). The samples were
allowed to dry for 1 day in a glove box with solvent-rich
atmosphere and an additional day in a fume hood. They
were then trimmed to a strip 0.5 9 3 cm in the center of
the silicon wafer and stored at 2?C in a dessicator prior to
X-ray measurements.
(di22:1PC)
Data Collection
Dried, oriented multilayer samples were placed into our
hydration chamber, which permits full hydration through
the vapor (Kuc ˇerka et al. 2005a). Samples usually achieved
full hydration in less than 1 h. Comparison with the repeat
D spacings obtained from multilamellar vesicles (MLVs)
immersed in water showed that full or nearly full hydration
(DD & 1–2 A˚) was achieved in the oriented samples. All
data were obtained at 30?C.
Figure 1 shows two generic ways to take X-ray data.
Most of the grazing incident X-ray scattering data were
taken at the G-1 station of the Cornell High Energy Syn-
chrotron Source (CHESS). Wavelength & 1.18 A˚ was
selected using multilayer monochromators. The beam was
0.28 mm in the horizontal direction and 1.2 mm in the
vertical direction, and the flat sample was rotated by
a = 0.2? about a horizontal axis perpendicular to the hor-
izontal beam. The total exposure time on a sample spot
was limited to 4 min, during which time the scattering
remained constant. Two-dimensional (2-D) scattering
intensities were collected with a Medoptics charge-coupled
device (CCD) with a 1,024 9 1,024 pixel array, 47.19 lm/
pixel. The CCD-to-sample distance (S) was &370 mm for
low-angle X-ray scattering (LAXS) and & 150 mm for wide-
angle X-ray scattering (WAXS), calibrated using an oriented
silver behenate standard. Part of the WAXS data were col-
lected using a Rigaku (Tokyo, Japan) RUH3R rotating copper
anode with wavelength = 1.54 A˚, collimated with a Xenocs
(Sassenage, France) FOX2D multilayer optic. 2D data were
collected with a Rigaku Mercury CCD, 1,024 9 1,024,
68 lm/pixel, with S & 300 mm. Transmission data (Fig. 1c)
were taken with the sample deposited on 35-lm-thick Si
wafers using the in-house rotating anode source. Transmission
wide-angle data were transformed from detector space to
q-space using standard equations (Tristram-Nagle et al. 1993;
Yang et al. 1998; Pan 2009).
Data Analysis
The theoretical scattering intensity induced by peptide
bundles embedded in lipid bilayers, ignoring the Lorentz
factor, is (Guinier 1994)
IPðqÞ ¼ SPðqÞ ? jFpðqÞj2
SP(q) is the structure factor which describes the positional
correlation between the peptide bundles.
X
where Raand Rbare the central positions of bundles a and
b, respectively. Fp(q) in Eq. 1 is the form factor. It is the
Fourier transform of the electron density contrast between
ð1Þ
SPðqÞ ¼ 1 þ
b6¼a
exp½iq ? ðRb? RaÞ?ð2Þ
12J. Pan et al.: Alamethicin Aggregation in Lipid Membranes
123

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the peptide bundle and the lipid background (He et al.
1993).
FPðqÞ ¼
Z
P
½qPðRÞ?qLðRÞ?exp½iq?ðR?RaÞ?dVðRÞð3Þ
where qPis the electron density of the peptide and qLis the
electron density of the lipid background. The resulting
model intensity, IP(q), was fit to the scattering data,
allowing theusualconstant
minimizing the residual sum of squares over the data
points,
scalingfactor,
K, by
RSS ¼
X
Npoints
i¼1
ðKIiðdataÞ ? IiðmodelÞÞ2
ð4Þ
Results and Discussion
Peak 1 at Low q: Bundles
Data
Figure 2 compares the low-angle X-ray scattering images
for DOPC-oriented multilayer samples with and without
Alm at similar hydration levels. With no Alm, there is
diffuse scattering centered on the meridian (qr= 0) that is
caused by fluctuations in the bilayer stacking (Liu and
Nagle 2004). The addition of Alm causes the appearance of
two features centered at qr& ±0.11 A˚-1, and in the qz
direction they extend up to 0.25 A˚-1. Because the mem-
brane is an in-plane fluid, there is only one intrinsic feature
and that one is required to occur at symmetrical locations
in the qrdirection. Although we shall call this feature ‘‘peak
1,’’ it is most accurately described as a ‘‘Bragg rod’’
(Als-Nielsen and McMorrow 2001), which is expected when
the positions of the scattering entities are not correlated
between neighboring membranes in the stack. Bragg rods
have also been observed for Alm using neutron scattering
(Yang et al. 1999). The Dqzrange of the scattering corre-
spondstouniformscatteringentitiesextending *25A˚along
the normal to the bilayer; this length is consistent with Alm
inserted in a transmembrane helix configuration with modest
tilting of the *30 A˚-long Alm helices (Bak et al. 2001).
Features occurring near the same qrhave been reported
previously using X-ray scattering (Constantin et al. 2007).
Because those samples were at much lower hydration, the
scattering was more concentrated in q-space and resembled
diffuse crystal peaks more than the Bragg rod-shaped peaks
shown in Fig. 2b. We confirm this effect of partial dehy-
dration in the final part of ‘‘Results and Discussion.’’
Similar side peaks observed by neutron scattering, in D2O
for good contrast, have been attributed to water columns
formed in the middle of Alm bundles (He et al. 1995). We
will base much of our analysis in this section on the barrel-
stave model.
qz
qr
K
K'
α
K
K'
en
en
(A)
(C)
qz
qr
(D)
(B)
Fig. 1 Grazing incident
scattering (a) and transmission
scattering (c) experimental
setup. K is the incident beam, K0
is the scattered beam, enis the
normal to the bilayer tilted by
angle a from the incident beam
in c. Gray regions in b and d
represent the available
reciprocal space corresponding
to a and c, respectively. Tilted
lines in b indicate the region cut
off by the silicon substrate
J. Pan et al.: Alamethicin Aggregation in Lipid Membranes 13
123

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We first extract quantitative data for the intensity, I1(qr),
of peak 1 from the overlapping diffuse lamellar scattering.
Following Constantin et al. (2007), the experimental raw
data are fit to two Lorentzians, one for the background with
center at qr= 0 and the other for I1(qr) with a center at qr1,
which is a fitting parameter. Figure 3 shows that the center
of peak 1 shifts to smaller qr1values when the Alm:lipid
mole ratio decreases from 1:10 to 1:20. A similar trend was
reported for Alm in 1,2-dimyristoyl-sn-glycerol-phospha-
tidylcholine (DMPC) multilayer samples (Constantin et al.
2007). Other interesting features are that peak 1 becomes
wider when the peptide concentration decreases and peak 1
is wider for DOPC than for diC22:1PC. Most importantly,
the center of peak 1 is at a smaller qr1value for diC22:1PC
than for DOPC at the same concentration.
Analysis Using a Cylindrical Model for Bundles
Figure 4 illustrates a model of a peptide bundle in a lipid
bilayer. The bundle is approximated by a hollow cylinder
(He et al. 1996) with outside radius b and inside water
channel radius a. In Fig. 4 the hydrophobic thickness of the
lipid is greater than the height of the bundle, but the
opposite leads to similar results. A detailed derivation of
the form factor FP(qr, qz) of this model is given in
Appendix I. It shows that FP(qr, qz) is insensitive to the
inner radius a and results in the approximation
FPðqr;qzÞ ¼ bJ1ðqrbÞ=qr? F1ðqzÞ
where J1(x) is the first-order Bessel function of the first
kind and F1(qz) can be approximated by sinc(qzL/2), where
L = 2Z1 is the length of a uniform cylinder in the z
direction.
ð5Þ
−0.2 −0.10 0.10.2
0
0.1
0.2
0.3
0.4
0.5
0.6
−0.2 −0.100.10.2
qr (Å-1)
qr (Å-1)
qz (Å-1)
(A)
(B)
Fig. 2 Low-angle X-ray scattering (glancing angle a = 0.2?) for
DOPC (a) and Alm:DOPC 1:10 (b) at similar hydration level
(lamellar repeat spacing D & 57 A˚) and T = 30?C. The h = 1
(qz= 0.11 A˚-1and qr= 0) and h = 2 (qz= 0.22 A˚-1and qr= 0)
can be seen through the thin molybdenum attenuator that extends to
qz= 0.32 A˚-1
0.05
0.10
0.150.20
0.0
0.5
1.0
1.5
0.050.10
0.150.20
0.0
0.5
1.0
1.5
0.05
0.10
0.150.20
0.0
0.5
1.0
1.5
0.050.100.150.20
0.0
0.5
1.0
1.5
(A)

I (a.u)
Data
Overall Fit
Peak 1
Background


(C)
(D)
(B)

qr (Å-1)qr (Å-1)
Fig. 3 The intensity I(qr) (data
points) for each sample was
obtained by averaging the data
from qz= 0.08 to qz= 0.12
A˚-1for a Alm:DOPC 1:10, b
Alm:DOPC 1:20, c
Alm:diC22:1PC 1:10 and d
Alm:diC22:1PC 1:20. The
intensity I1(qr) of peak 1
(dashed green line) was
separated from the diffuse
scattering Idiffuse(qr) (dotted blue
line). The overall scale factor
was chosen so that the
maximum of I1(qr) = 1. The
sum of I1(qr) and Idiffuse(qr) is
shown as a solid red line close
to the data points. (Color figure
online)
14J. Pan et al.: Alamethicin Aggregation in Lipid Membranes
123

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The second part of the model regards the lateral distri-
bution of the individual bundles in the bilayer. When the
hydration level of the Alm/lipid mixture is high, the posi-
tional correlation between bundles in different layers is
negligible as evidenced by the appearance of Bragg rods
and not Bragg peaks, so we only need to consider the
distribution of bundles in a single lipid bilayer in order to
calculate the structure factor SP(q) (Yang et al. 1999). The
scattering intensity due to the peptide is given by Eq. 1.
Following He et al. (1995, 1996) and Constantin et al.
(2007), we use a 2-D hard disk model, which gives the
SP(q) shown in Appendix II. The model requires two
parameters, the radius (R) of the hard disk and the packing
fraction (g = NpR2/total area), where N is the total number
of bundles in the given area. Although it might seem that
the radius R of the hard disk should be the same as the
outer radius b of the bundle, this resulted in poor fits, so we
followed Constantin et al. (2007) by allowing R to be
greater than b to account for extended lipid-mediated
bundle interactions.
Figure 5 shows the fits of the model to peak 1. The
parameters b, R and g obtained from fitting the cylindrical
model are listed in Table 1. By comparing the fitting
parameters of the two lipids we see that both the disk radius
R and the outside radius b of the peptide bundle are larger
for diC22:1PC than for DOPC. The fitting results for the
same lipid show that the outer bundle radius b barely
changes when the peptide to lipid ratio decreases from 1:10
to 1:20. However, the larger disk radius R increases for
both lipids when the peptide to lipid ratio decreases. This is
related to the shift in the center qr1of peak 1 shown in
a
b
Z1
Z3
Z2
ρC
ρC
ρH
ρW
ρW
ρP
0
Fig. 4 Hollow cylindrical model of an Alm bundle with inside radius
a and outside radius b. qp, qw, qcand qHare the averaged electron
densities of the peptide bundle, water molecules, lipid chain and lipid
headgroup region, respectively. Horizontal dashed line in the center
indicates the center of the bilayer; z1indicates the half-thickness of
the peptide bundle; z2–z1indicates the remaining lipid chain region
above the peptide bundle; z3–z2indicates the lipid headgroup region
0.000.050.10

0.150.20
0.0
0.5
1.0
1.5
0.000.050.10 0.15 0.20
0.0
0.5
1.0
1.5
0.000.050.10 0.15
0.0
0.5
1.0
1.5
0.000.050.100.15
0.0
0.5
1.0
1.5
(A)
(C)
(D)
(B)

I(a.u.)
Data
Fit
S(q)
|F(q)|2
qr (Å-1)qr (Å-1)
Fig. 5 Fits of the cylindrical
model to peak 1. The data points
are the I1(qr) from Fig. 3. The
fitted form factor FP(qr,qz)
(dotted blue line), the structure
factor (dashed green line) from
Eq. A3 and the fitted intensity
(solid red line) from Eq. 1 show
the results of the best fit for a
Alm:DOPC 1:10, b Alm:DOPC
1:20, c Alm:diC22:1PC 1:10
and d Alm:diC22:1PC 1:20.
(Color figure online)
J. Pan et al.: Alamethicin Aggregation in Lipid Membranes15
123

Page 6

Fig. 3. This change in R is likely an artifact of using a hard
core potential to model the lipid-mediated interactions,
which should decrease gradually with distance.
Following Constantin et al. (2007), we attempted to
make the hard core potential somewhat more realistic by
adding a gaussian repulsive energy, G(r) = U0exp(–r2/
2r2), as a perturbation to the hard disk interaction. The
structure factor of the perturbed hard disk model is given in
Appendix II. The fitting results are listed in Table 1. For
the same lipid, the parameters of the gaussian repulsion, U0
and r, are fixed to be the same at the two concentrations.
This perturbation improves the RSS (Eq. 4) considerably.
Although there is a rather small-magnitude U0for the best-
fitted gaussian repulsion, the decay length (r) is large,
consistent with the anticipated potential slowly decaying
over a long range. It is also encouraging that the pertur-
bation only changes the values of b by less than 1 A˚. Most
importantly, it leaves intact the result that the Alm bundle
is larger in diC22:1PC than in DOPC.
Finally, Table 1 gives values for n, the number of Alm
monomers in the bundle. Although this model does not
explicitly consider monomers, we estimate n = p/sin-1[r/
(b-r)] by assuming that each monomer is a cylinder with
radius r = 5 A˚with axis parallel to the bilayer normal and
that the monomers touch the nearest neighbors around the
bundle as in the barrel-stave model. (It may be noted that if
the cylinders are tilted by an angle, b, from the bilayer
normal around a horizontal axis from the center of the
bundle as indicated by Bak et al. [2001], then n decreases
by a factor of cosb in order to keep b the same.)
Analysis Using a Molecular Dynamics Model for Bundles
Alm bundles from n = 4–8 have been simulated at the
atomic level in a POPC lipid bilayer (Tieleman et al. 2002),
and we have used the atomic coordinates from these sim-
ulations, as described in Appendix III, to obtain the more
realistic form factors FP(qr) shown in Fig. 6. We assume
that the structure of a bundle that is constrained to have a
specific number (n) of Alm monomers is essentially the
same for DOPC and diC22:1PC as it would be for the
POPC lipid employed in the simulation. This assumption is
quite different from, and much more likely to be valid than,
assuming that the most probable number is independent of
the lipid. The fitting procedure is similar to that used for the
cylindrical model except that the form factors shown in
Fig. 6 were calculated from molecular dynamics (MD)
simulations. There are two fitting parameters for each
bundle that has n peptides, the disk radius R and the area
packing fraction g, both of which are involved in the
structure factor SP(qr). Fits of this model to the intensity for
DOPC are shown for n = 4, 6 and 8 in Fig. 7.
Quantitative fitting results are listed in Table 2. For
DOPC at both peptide concentrations, RSS first decreases
as n increases from 4 to 6 and then increases as n increases
from 6 to 8, indicating that the MD bundle with n = 6 fits
our data best. The RSS values (0.36 and 0.97 for 1:10 and
1:20, respectively) are comparable to the cylindrical model
(0.29 and 0.49) in Table 1. For diC22:1PC at both peptide
concentrations, RSS decreases monotonically as n increa-
ses from 4 to 8. Although we do not have simulation results
for n[8, it is clear that n[8 would fit better. Indeed, the
RSS values for the octamer (1.39 and 2.82 for 1:10 and
1:20, respectively) are large compared to the cylindrical
model (0.21 and 0.50). As the difference of the RSS
between the pentamer (1.60) and the hexamer (0.36) for
Alm:DOPC 1:10 is very similar to the difference between
the octamer (1.39) and the best fit of the cylindrical model
(0.21) for Alm:diC22:1PC 1:10 (this similarity also applies
to Alm:lipid 1:20), this suggests that n = 9 might provide
the best fit to the scattering data of diC22:1PC. We also
note that the cylindrical model gives n = 4.8 for DOPC,
about Dn = 1.2 smaller than the more realistic MD result.
Since the cylindrical model gives n & 8.5, addition of
Table 1 Fitting parameters and RSS for the cylindrical model with
unperturbed hard disk and perturbed hard disk interactions with fitted
U0and r parameters
b (A˚) nR (A˚) g
U0(kBT) r (A˚) RSS
Alm:DOPC 1:1013.34.9 23.5 0.42 –– 0.29
13.75.1 23.40.40 1.329.50.10
Alm:DOPC 1:2012.94.6 25.40.26 ––0.49
13.65.1 25.90.20 1.329.50.38
Alm:diC22:1PC 1:10 18.68.4 33.20.40 ––0.21
19.08.6 33.1 0.39 1.146.40.11
Alm:diC22:1PC 1:20 18.7 8.4 34.70.33 –– 0.50
19.69.0 35.3 0.34 1.146.4 0.45
0.0 0.10.20.30.4 0.50.6
0.0
0.2
0.4
0.6
0.8
1.0
|F(qr )|2
N=4
N=5
N=6
N=7
N=8
qr (Å-1)
Fig. 6 Form factors for Alm MD bundles with n monomers obtained
from MD simulations (Tieleman et al. 2002). The sequence of curves
is from right to left as n increases from 4 to 8
16J. Pan et al.: Alamethicin Aggregation in Lipid Membranes
123

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Dn = 1.2 would give n & 9.7 as the best value for
diC22:1PC. Note, however, that the best value of n to fit
the data need not be an integer as there is likely to be a
distribution of n sizes. The smaller n obtained from the
cylindrical model fit is related to the fact that its form
factor decreases faster, due to its artifactually sharp edges,
than the form factor of the more realistic MD bundle model
with the same n. In order to achieve the same decrease in
FP(qr), which is needed to fit the data, the cylindrical model
needs a smaller b, which requires a smaller n.
Theory for the Effect of Different Lipids on Bundle Size
Our best fit in Table 2 shows that n & 6 for DOPC whose
hydrophobic thickness 2DCis 26.8 A˚. For the thicker lipid
bilayer, diC22:1PC, whose hydrophobic thickness 2DCis
34.4 A˚, the best fit in Table 2 shows that n[8. We pre-
viously obtained an effective hydrophobic thickness of 27–
28 A˚for Alm (Pan et al. 2009a). According to the hydro-
phobic matching mechanism (Killian 1998; Jensen and
Mouritsen 2004), when the hydrophobic thickness of the
lipid bilayer is larger than the transmembrane peptides, the
lipid bilayer becomes thinner in order to avoid exposure of
lipid hydrocarbon chains to water, as illustrated in Fig. 8b.
The local membrane deformation free energy per unit area
has been given as (Huang 1986; Nielsen Goulian and
Andersen 1998)
F ¼ ðKA=2Þðdh=hÞ2þ ðKC=8Þðr2hÞ2
where h is the hydrophobic thickness of the pure lipid
bilayer, dh is the local difference in the thickness at posi-
tion r in the plane of the membrane due to the bundle, KCis
the bending modulus and KAis the area stretch modulus.
Our previous study found an average over r of dh = –4 A˚
in 1:10 Alm:diC22:1PC. Of course, the magnitude of dh for
those lipids in close proximity to Alm should be greater
than for the average lipid, as is consistent with the larger 7
A˚difference in the hydrophobic thickness of Alm and
diC22:1PC. In contrast to diC22:1PC, the average dh was
less than 1 A˚in DOPC, so it is clear that the lipid distortion
ð6Þ
free energy term in Eq. 6 is much larger for diC22:1PC
than for DOPC.
Although the r dependence of the lipid deformation dh
can be quite complicated depending upon boundary con-
ditions at the perimeter of the bundle (Nielsen et al. 1998),
for convenience, let us approximate it roughly as
dhðrÞ?dhðbÞexp½?ðr ? bÞ=n?
where dh(b) is the maximum deformation in those lipids
that are next to Alm. The decay range n has been given as
(Hung et al. 2007).
ð7Þ
n ¼ ð16h2KC=KAÞ1=4
The area stretch moduli KAfor diC22:1PC and DOPC are
263 and 265 mN/m, respectively (Rawicz et al. 2000). The
bending moduli KCfor diC22:1PC and DOPC are 13 and
8 9 10-20J, respectively (Rawicz et al. 2000; Liu and
Nagle 2004; Kuc ˇerka et al. 2005b; Tristram-Nagle and
Nagle 2007; Pan et al. 2008a), and the hydrophobic
ð8Þ
0.000.050.100.15 0.20
0.0
0.5
1.0
1.5
0.000.05 0.100.150.20 0.000.05 0.10 0.150.20
I (a.u.)
(A)

Data
Fit
S(q)
|F(q) |
2

(B)

(C)
qr (Å-1)
Fig. 7 Model fits to Alm:DOPC 1:10 using form factors calculated from MD simulations. a n = 4, b n = 6, c n = 8
Table 2 Fitting parameters and RSS obtained using bundles from
MD simulations
n = 4
n = 5
n = 6
n = 7
n = 8
Alm:DOPC 1:10
R (A˚)
g
RSS
24.424.123.423.122.1
0.430.420.420.420.44
3.611.600.360.857.08
Alm:DOPC 1:20
R (A˚)
g
RSS
27.026.625.0 24.321.0
0.270.270.270.270.30
6.202.330.972.2412.02
Alm:diC22:1PC 1:10
R (A˚)
g
RSS
34.8 34.834.734.634.0
0.410.410.410.410.41
26.3721.2911.488.641.39
Alm:diC22:1PC 1:20
R(A˚)
g
RSS
37.037.137.037.036.3
0.380.38 0.380.38 0.37
34.3628.3216.3012.682.82
J. Pan et al.: Alamethicin Aggregation in Lipid Membranes17
123

Page 8

thicknesses for diC22:1PC and DOPC are 34.4 and 26.8 A˚,
respectively (Kuc ˇerka et al. 2005b; Pan et al. 2008b,
2009b). Therefore, n = 30 A˚in diC22:1 and n = 23 A˚in
DOPC. Integrating dh(r) over the plane for a single bundle
givesatotaldeformation
Although artificial, it is illuminating to divide by the area/
lipid and by dh(b) to obtain nn= 2pn(n ? b)/AL, which
would be the number of perturbed lipids if the lipids were
represented as two disjoint sets, one of maximally per-
turbed lipids and the other of lipids not perturbed at all.
This gives nn& 136/bundle in diC22:1PC and nn& 73/
bundle in DOPC, using the b values from Table 1. The
greater effective number of perturbed lipids nn in
diC22:1PC is another reason the lipid deformation energy
is larger than in DOPC.
We next emphasize that the values for the decay lengths
n for the perturbed lipid are similar to the values of the hard
disk radii R for the two lipids given in Tables 1, 2. This
supports the claim that the R values represent lipid-medi-
ated interactions between the bundles, provided that it can
be shown that such an interaction is repulsive. Naively, one
might argue that the interaction is attractive because
bringing two bundles close together decreases the total
amount of affected lipid that is in the circles of influence of
all the bundles. Disregarding those lipids that are not in two
circles of influence, there are only half as many affected
lipids when the bundles are close together. However, those
lipids that are in the circles of influence of two bundles
would, in first approximation, be perturbed twice as much,
so their dh2would be twice as large as the dh1that the same
lipid would have when the bundles are far apart. The first
term in the deformation energy in Eq. 6 is proportional to
dh2, so the energy of those lipids in the circle of influence
of two bundles increases by a factor of four, which more
than offsets there being only half as many of them as when
volume
dh(b)2pn(n ? b).
the bundles are separated. Therefore, the lipid-mediated
interaction between bundles should be expected to be
repulsive, which supports the use of a repulsive interaction
in analyzing the data.
We now return to the question of why the larger
deformation energy in diC22:1PC leads to bundles with
larger n. Integrating equation 7 and focusing on the first
term in Eq. 6, the total deformation energy per Alm
monomer is proportional to n[n ? b(n)]/n = n[(n ? r) ?
(r/sin(p/n))/n, which to order 1/n equals n(n ? r)/n ? nr/p.
This shows that the lipid deformation energy decreases
monotonically as n increases, so it favors large bundles. Of
course, n is limited to a finite value because there are other
terms in the free energy that increase with increasing n.
The most obvious is the translational entropy that decreases
as n increases because there are fewer bundles for a fixed
concentration of Alm. Another is the interaction of Alm
with the water in the center of the barrel-stave bundle. As n
increases, the fraction of the Alm surface exposed to water
monotonically increases. This decreases the free energy
until n becomes large enough that this fraction exceeds the
fraction of hydrophilic residues and then this term increa-
ses for larger n because hydrophobic residues would have
to be exposed to water. Importantly, both these free energy
terms that limit n are the same for both lipids, whereas the
lipid deformation term that increases n is larger for
diC22:1PC. Therefore, the sum of the free energies has its
minimal value for larger n for diC22:1PC than for DOPC.
This makes the most probable values of n larger for
diC22:1PC, consistent with our analysis of our data.
Comparison to Previous Results
Alm bundle size in lipid membranes has also been studied
by other groups. Using the same model fitting procedure
shown here and similar in-plane scattering induced by the
Alm bundle structure at qr& 0.1 A˚-1, it has been reported
that n & 7 in Alm/DMPC mixtures (Constantin et al.
2007). Because their samples were at a much lower hydra-
tion level, their estimated n could have been affected by the
correlation between the Alm bundles along the bilayer
normal, which we treat below. However, the DMPC bilayer
is nearly as thick as DOPC, so our value of n = 6 for
DOPC is in good agreement with the previous DMPC
result. Neutron scattering using D2O contrast gave a
Bragg rod at qr& 0.1 A˚-1, which was used to obtain the
radius of the water pore in the middle of the Alm bundle;
assuming a barrel-stave model gave n = 8–9 in Alm/DLPC
and n & 11 in Alm/DiPhyPC (He et al. 1995, 1996).
The hydrophobic core of the DLPC bilayer is about 6 A˚
thinner than the hydrophobic core of Alm (Pan et al.
2009a), which would presumably cause considerable tilt in
Alm momoners and that could change the size of the
(B)
(A)
Fig. 8 a Similar hydrophobic thickness between the lipid bilayer and
the peptide bundle. b The hydrophobic thickness of the lipid bilayer is
larger than the peptide bundle, in which case the lipid molecules at the
circumference of the peptide bundle deform their molecular shape in
order to avoid exposure of hydrocarbon chains to water
18 J. Pan et al.: Alamethicin Aggregation in Lipid Membranes
123

Page 9

bundle. However, the hydrophobic core of DiPhyPC is
close to that of DOPC (Lee et al. 2005), so we have no easy
explanation for the larger n value in this lipid. Qian et al.
(2008) reported n & 8 in a brominated DSPC bilayer using
Fourier transform analysis of the crystal-like peaks
obtained in extremely dehydrated conditions. The thickness
of DSPC is between that of DOPC and diC22:1PC, so their
value of n fits the pattern that n increases with increasing
bilayer thickness. Conductance measurements on mono-
glyceride black lipid membranes prepared in squalene
solvent with the hydrocarbon chain sequence 14:1, 16:1,
18:1 and 20:1 were interpreted to give values of n = 2, 3, 7
and 11, respectively (Hall et al. 1984). Their channels were
not open at zero voltage, and a rather different model
involving strongly tilted helices that did not go all the way
through the membrane in the off state was used to explain
the thickness dependence on n.
Peak 2 at High q: Clusters
Data
Figure 9 shows the background-subtracted WAXS images
for DOPC and for Alm:DOPC 1:10. The comparison shows
that the chain wide-angle scattering peak at q & 1.4 A˚-1is
well preserved when Alm is incorporated into DOPC
bilayers. This is very different from a report that another
antimicrobial peptide, magainin, severely decreases the
chain wide-angle scattering and consequently disrupts the
bilayer structure (Mu ¨nster et al. 2002). Figure 9 also shows
that the addition of Alm causes the appearance of two
additional peaks. The first one, peak 1, is located at
qr& 0.1 A˚-1. The second, weaker one, which we call
‘‘peak 2,’’ is located at qr& 0.7 A˚-1.
Other peptide concentrations have also been investi-
gated, with quantitative results shown in Fig. 10. Even for
the pure lipid, there is a shoulder at qr& 0.7 A˚-1, which is
likely due to weak correlations between the largely
disordered positions of the lipid headgroups (Hub et al.
2007). However, a genuine peak appears with the addition
of Alm. The fitting indicated in Fig. 10 suggests that the
total background-subtracted intensity under the peak is
roughly proportional to the concentration of peptide; when
a small lipid contribution is subtracted, the ratio of the peak
intensities of the 1:10 to the 1:20 samples is 2.4 instead of
2.0.
Origin of Peak 2
One hypothesis might be that peak 2 is due to stronger
headgroup correlations induced by Alm. It has been shown
that both the electron density distribution of the lipid
headgroups and the area/lipid are very little affected by the
incorporation of Alm peptides in a DOPC bilayer (Pan et al.
2009a). Together, these suggest that enhanced lipid head-
group correlations are not responsible for the enhanced peak
intensity at qr& 0.7 A˚-1.
He et al. (1996) reported a similar peak to our peak 2 in
an Alm:DLPC 1:10 sample and interpreted it as originating
from the nearest neighbor peptide–peptide packing dis-
tance within a bundle. In order to test their hypothesis, we
carried out the following analysis. The form factor of an
Alm bundle can be expressed by |F(q)|2= |Fmon(q)|29
|Fpos(q)|2, where |Fmon(q)|2is the form factor of a monomer
and |Fpos(q)|2describes the positional correlation between
the peptides within the bundle. Assuming n peptides sit at
the vertices of a polygon within the bundle, |Fpos(q)|2can be
calculated as follows (Constantin et al. 2007):
jFposðqÞj2¼ 1 þ 2
X
N
k¼1
ð1 ? k=NÞJ0ð2qd ? sinðkp=NÞÞ
ð9Þ
where d is the distance between each vertex and the
polygon center. Figure 11 shows that |Fpos(qr)|2does have a
strong peak at qr& 0.7 A˚-1for the hexamer due to the
well-defined peptide–peptide distance 2r within the bundle.
0 0.51.0
qr (Å-1)
1.52.0
0 0.51.0
qr (Å-1)
1.52.0
0
0.5
1.0
1.5
qz (Å-1)
(A) (B)
Fig. 9 Background-subtracted
wide-angle X-ray scattering
images for a DOPC and b
Alm:DOPC 1:10 at T = 30?C.
Narrow black region in the left
bottom corner is where a piece
of molybdenum attenuator was
used to attenuate the direct
beam and the lamellar peaks.
The broad peak at q & 1.4 A˚-1
is the well-known lipid
hydrocarbon chain wide-angle
scattering
J. Pan et al.: Alamethicin Aggregation in Lipid Membranes 19
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Page 10

However, when it is multiplied by the monomer form
factor |Fmon(qr)|2, which is calculated from the monomer
crystal structure (Fox and Richards 1982), there is no
noticeable peak at qr& 0.7 A˚-1because the monomer
form factor is very small at large qrvalues. Furthermore,
Fig. 11 shows that the barrel-stave model predicts a peak
centered at 0.38 A˚-1, primarily due to next nearest
neighbor Alm distances in the bundle. This peak should be
stronger than peak 2 near 0.7 A˚-1. The failure to observe
experimentally any peak near 0.38 A˚-1is therefore
inconsistent with explaining peak 2 with the barrel-stave
bundle model.
In contrast, we propose that the source of peak 2 is
hexagonally packed clusters of Alm with no water chan-
nels, as illustrated on the left side of Fig. 12. A very large
hexagonally packed cluster would have a peak at qr= 2p/
2rcos(30?) = 0.73 A˚-1, where r = 5 A˚is the radius of the
Alm monomer. Although the monomeric form factor
would still be very small, the structure factor for an infinite
lattice is a delta function. The observed broad width of
peak 2 in the qrdirection has two likely causes, the finite
size of the clusters and positional disorder within each
cluster. Both of these would also weaken the peak, as
observed. An analogy is that the wide-angle lipid scattering
occurs at roughly twice the qrvalue because the hydro-
carbon chains have roughly half the radius. The difference
is that fluid chains have much more orientational disorder,
so the wide-angle lipid scattering extends much further into
0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8
qr (Å-1)
0.0
0.5
1.0
1.5
2.0
0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8
qr (Å-1)
0.0
0.5
1.0
1.5
2.0


Intensity (a.u)

(D)(C)
(B)
Data
Fit
Gaussian 1
Gaussian 2
Background

(A)
Fig. 10 Scattering intensity
along the qrdirection at qznear
zero for Alm:DOPC at ratios a
0:1, b 1:75, c 1:20 and d 1:10.
Each data set is fit by the sum of
three components: two gaussian
functions representing the two
peaks centered at qr& 0.7 and
1.4 A˚-1and a second order
polynomial background. The
chain wide-angle scattering
peak at qr& 1.4 A˚-1is
normalized to 1.0
0.00.20.40.6
qr (Å-1)
0.8 1.01.2
0.0
0.2
0.4
0.6
0.8
1.0

|F(qr) | 2 (a.u.)
|Fmon(q) |
|Fmon(q) |
|Fpos(q) |
2x|Fpos(q) |
2
2
2
Fig. 11 The overall form factor of a barrel-stave bundle with number
of peptide per bundle n = 6 shown by the solid red curve. The
monotonically decreasing dashed green curve is the form factor for
the monomer, and the dotted blue curve with a local maximum near
qr& 0.7 A˚-1is the positional factor. (Color figure online)
Fig. 12 Top view of Alm (large gray circles) packing model in a
lipid bilayer (small open circles represent hydrocarbon chains). A
hexagonally packed cluster is shown on the left side and a coexisting
barrel-stave bundle (n = 7) is shown at the right side
20J. Pan et al.: Alamethicin Aggregation in Lipid Membranes
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Page 11

the qzdirection (Mills et al. 2008). The much more rapid
decrease in intensity of peak 2 with increasing qzis con-
sistent with transmembrane Alm helices oriented nearly
along the bilayer normal.
The type of cluster indicated in Fig. 12 is unusual in the
Alm literature, although it may be noted that a recent report
combiningcoarse-grained
described Alm peptides forming large clusters spontane-
ously (Thøgersen et al. 2008). The usually assumed driving
force for barrel-stave bundle formation is that amphipathic
helices have a hydrophilic side and a hydrophobic side, as
shown in Fig. 13a, and the bundle forms because the
hydrophilic side of each monomer faces the water channel.
Of course, amphipathic helices can generally form other
structures that do not have a water channel, such as the
seven-helix transmembrane structure of bacteriorhodopsin.
Figure 13b emphasizes that hydophilicity might also be
satisfied in an Alm cluster.
A logical question at this point is, can the putative
clusters that explain peak 2 also explain peak 1? To address
this question, we calculated the internal structure factor of
hexagonally packed clusters numerically. An example for a
60-monomer cluster is shown in Fig. 14. There is a strong
peak at qr& 0.7 A˚-1due to the Alm packing structure that
corresponds to peak 2 in our experiment. Although this
peak is narrower in Fig. 14 than peak 2, lateral disorder and
smaller clusters would broaden it. There is a strong peak
centered at qr= 0 in Fig. 14, but this peak is artifactually
high and would be much reduced by employing a minus
fluid model for the lipid solvating the clusters, which
involves some technical challenges. As the clusters become
larger, this peak becomes even more confined to qrnear
zero, and it clearly cannot account for peak 1, whose center
is at nonzero qr. For 0\q\q2there are also the familiar
andall-atomsimulations
ripples that occur from small samples of uniform size;
these would be smeared out by the likely dispersion of
cluster sizes, and their intensity also becomes smaller when
the cluster size becomes larger. We therefore believe that
clusters cannot predict peak 1 but do predict peak 2.
Model for the Aggregation of Alm in Lipid Bilayers
Because peaks 1 and 2 require different structural origins,
we now consider a model in which Alm bundles and Alm
clusters coexist as shown in Fig. 12. We first note that there
also is generally a surface fraction with Alm lying in the
plane of the bilayer, but we have previously concluded that
the surface fraction is negligible for DOPC and diC22:1PC
(Pan et al. 2009a). In this subsection we deduce logical
(A)
U16
V9
P2
F20-OH
U13
A6
U17
U10
U3
P14
Q7
E18
G11
A4
V15
U8
Q19
U1
L12
U5
(B)
12
3
H
H
H
H
H
Fig. 13 a Helical wheel of an Alm monomer obtained from its crystal
structure. Dashed line separates the smaller hydrophilic (blue online)
and the larger hydrophobic (red online) faces. b The same hexagonally
packed cluster in Fig. 12 with hydrophilic strips (blue online) facing
each other around the cavities marked by H and with hydrophobic
portions (red online) facing other hydrophobic portions or facing the
lipid. The motif composed of the three circles numbered 1, 2 and 3 is
the building block for clusters of any size. (Color figure online)
0.00.20.4 0.60.81.0
0.00
0.05
0.10
0.15
cluster structure factor (a.u.)
qr (Å-1)
Fig. 14 Internal structure factor of a hexagonally packed cluster with
60 Alm monomers
J. Pan et al.: Alamethicin Aggregation in Lipid Membranes21
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Page 12

consequences of this model and use our data to test these
consequences.
Because the number of monomers would be larger in a
cluster than in a bundle, entropic considerations suggest
that the ratio of clusters to bundles would increase as the
total monomer concentration increased. Unfortunately,
when Alm concentration is decreased below 1:20, peak 1,
even though it is much more intense than peak 2, is difficult
to extract from the very intense diffuse scattering of the
lipid bilayer, so there is an insufficient range of concen-
trations to prove using peak intensities that there are two
populations with a nontrivial equilibrium constant. How-
ever, our analysis in Fig. 10 found that the ratio of peak 2
to the lipid bilayer wide-angle scattering peak increases by
a factor of 2.4 instead of a factor of 2 in going from 1:20 to
1:10 Alm:DOPC, indicating that the fraction of Alm in
clusters grows more rapidly than the Alm concentration,
which is consistent with entropic considerations.
Comparison of the area packing fraction g obtained by
fitting in Table 2 with the mole ratio of Alm to lipid
strongly supports our model that Alm is partitioned into
bundles and clusters that coexist. The bundle area Abun-
dle= pb2for different n can be estimated from the MD
simulations (Tieleman et al. 2002). It is about 600 A˚2for
the hexamer and 1,050 A˚2for the octamer (Pan 2009).
Assuming that there are only barrel-stave bundles and lipid,
the area packing fraction gBis (Constantin et al. 2007)
pR2
Abundleþn
where R is the disk radius; n is the number of peptides per
bundle; L/P is lipid to peptide ratio and ALis the lateral
area per lipid molecule, which is 72 A˚2for DOPC and
69 A˚2for diC22:1PC (Kuc ˇerka et al. 2005b). The second
term in the denominator is the total lipid area per bundle;
the number 2 arises because Alm is transmembrane,
whereas each bilayer is formed by two lipid monolayers.
The calculated area packing fractions gBbased on Eq. 10
are listed in Table 3. They are considerably larger than the
experimental values given as g in Table 3 using composite
values from Tables 1, 2.
gB¼
2?L
PAL
ð10Þ
The discrepancy between g and gBin Table 3 means
there is at least one incorrect assumption in Eq. 10. It
cannot be the hard disk radius R or the number of peptides
per bundle n as they are related to the structure factor and
the form factor, which basically determine the position and
the width of peak 1. It cannot be the bundle radius b either
because it contributes\35% to the denominator. The
bilayer thickness measurement indicates that with the
addition of 10% Alm peptide, the area per lipid differs at
most 10% for diC22:1PC and there is negligible difference
for DOPC (Pan et al. 2009a). The only adjustable param-
eter is then the effective peptide to lipid ratio (P/L)Bfor the
bundles. Table 3 lists the required (P/L)B in order for
Eq. 10 to achieve gB= g, and they are all smaller than the
experimental P/L. This is consistent with having a sub-
stantial fraction of Alm that is not included in bundles and
that is included in structures, such as clusters, that have less
associated lipid than the bundles. If we assume that the
clusters have negligible associated lipid, we can calculate
the ratio C/B of Alm in clusters C to Alm in bundles B
using (C ? B)/L = P/L with B/L = (P/L)B. The last col-
umn of Table 3 shows the ratio C/B. The result that C/B is
higher for diC22:1PC than for DOPC is consistent with
clusters requiring less adjacent lipid on a per monomer
Alm basis, so the greater lipid deformation energy in
diC22:1PC favors clusters compared to DOPC. The result
that C/B decreases with decreased P/L for both lipids is
consistent with the entropic free energy favoring smaller
aggregates at low P/L. These results are therefore consis-
tent with our new model in which Alm clusters coexist with
Alm bundles.
Crystallography of Partially Dried Samples
As stacks of bilayers are partially dehydrated, the water
cushion between bilayers becomes thinner and interactions
between neighboring membranes become stronger. Fig-
ure 15 shows that peak 1 gradually changes from a Bragg
rod, appropriate for 2-D scattering, to more discrete peaks
that indicate 3-D correlations. In this section we briefly
report our results when we further dehydrated our samples
to obtain crystallographic patterns.
For this purpose we employed transmission geometry
(Fig. 1c), with the result shown in Fig. 16. Although there
are broad widths and considerable mosaic spread, six peaks
are easily identified. We have indexed these peaks to four
possible space groups (Pan 2009). If Alm forms cylindrical
bundles, one would suppose that the space group would
have an in-plane hexagonal structure and that the Alm
would be displaced in neighboring layers either in an
ABCABC…stacking pattern (rhombohedral) (Qian et al.
2008) or in an ABAB…stacking pattern (Salditt et al.
2006). However, neither of these space groups predicts
Table 3 Area packing fraction gBfor disks based on Eq. 10 using
experimental P/L ratios for each sample, fitted g from Tables 1 and 2,
effective (P/L)Bfor bundles required to obtain gB= g and ratio C/B
of Alm in clusters to bundles assuming negligible lipid associated
with the clusters
Alm:Lipid P:L
gB
g
(P/L)B
C/B
Alm:DOPC 1:10 0.620.421:160.6
Alm:DOPC 1:200.40 0.27 1:310.55
Alm:diC22:1PC 1:10 0.950.41 1:281.8
Alm:diC22:1PC 1:200.630.381:370.85
22J. Pan et al.: Alamethicin Aggregation in Lipid Membranes
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Page 13

peak IV, which is even stronger than peaks II and III.
However, all the observed peaks are predicted by a body-
centered tetragonal (BCT) space group, in which the in-
plane packing is in a square array with lattice spacing
a = 37 A˚. Neighboring membranes are then located a
distance c = 43 A˚along the out-of-plane direction, and
they have their in-plane square array shifted by a/2 in both
in-plane directions. This BCT pattern is not so surprising.
If there are repulsive interactions between Alm bundles,
both in-plane and between neighboring planes, then there
should be a shift of the in-plane array between neighboring
planes in order to fit the bundles in one plane into the
interstices between the bundles in the neighboring plane.
Of course, if there is a high concentration of bundles in
each plane, then the in-plane packing must be hexagonal
and the best that the neighboring plane can do is to fit into
half those small interstices. However, if the concentration
is smaller to allow enough room for a square in-plane
packing array, then neighboring planes can come closer
together and reduce their repulsive interaction energy by a
relative shift of the square array of bundles by (a/2,a/2),
which neatly places the bundles of one plane into all the
interstices of the other plane.
While the BCT space group is clearly better at repre-
senting our data than the ABC or AB hexagonal space
groups, it is nevertheless worrying that all three space
groups allow many peaks that we do not observe. Of
course, peaks allowed by space groups may be extinct
because of small form factors (usually called ‘‘structure
factors’’ in crystallography), but the number of required
extinctions casts some doubt on the BCT assignment. (A
full listing of all peaks compatible with these structures is
available [Pan 2009].) It may be noted that some of the
additional peaks could be indexed to the band of intensity
that occurs at qr& 0.75 A˚-1. Because of the many
extinctions, we have also considered a 2-D monoclinic
space group that has been proposed for protegrin (Yang
et al. 2000). This predicts all the observed peaks and
requires many fewer extinctions. However, that structure
would require ribbons of Alm running uniformly in the y
direction in the plane of each horizontal (x, y) layer, and
such layers would be stacked in the z direction. We find
such a structure hard to rationalize, and if it were true, it
would be irrelevant to obtaining the structure of the bundle
or cluster aggregates that occur in well-hydrated samples.
It is clear from the literature that partially dried samples
result in different space groups depending delicately upon
the conditions of the experiment. Salditt et al. (2006)
reported the hexagonal AB space group at T = 20?C in
DMPC bilayers, but the observed q range did not include
−0.2
−0.10 0.10.2
0.5
0.4
0.3
0.2
0.1
0
−0.2
−0.10 0.10.2
−0.2
−0.100.10.2
qr (Å-1)
qz (Å-1)
(A)(B)(C)
Fig. 15 Background-subtracted
grazing incident scattering
images for Alm:diC22:1PC 1:10
at a D = 64.1 A˚, b D = 61.3 A˚
and c D = 58.5 A˚at T = 30?C
00.10.20.3 0.40.50.60.70.8
−0.35
−0.25
−0.15
−0.05
0.05
0.15
0.25
0.35
I
II
III
IV
V
VI
qr (Å-1)
qz (Å-1)
Fig. 16 Transmission scattering for Alm:DOPC 1:10 at D = 43 A˚
with sample rotated by a = 45oand converted to q-space. The two
triangular (red online) regions of q-space, one in the upper left and
one in the lower left, touching at q = 0, are inaccessible in this
transmission geometry. The scattering peaks are indicated by open
white circles and are given roman numerals. Peak VI was observed
using a = 30?. The white intensities are brightest, and the red (color
online) pixels correspond to the smallest intensities after background
subtraction. Peaks II and III appear darker than the surrounding
background in the noncolor figure. (Color figure online)
J. Pan et al.: Alamethicin Aggregation in Lipid Membranes23
123

Page 14

peak IV, so their available data could also be fit with the
BCT space group. Qian et al. (2008) also did not obtain
data for as large values of qras ours, but their small qr
data clearly did not fit the BCT space group and did fit
the rhombohedral ABC space group. Qian et al. (2008)
also reported a tetragonal phase at relative humidity 54–
58%. We have explored assigning phases to our observed
peaks to obtain electron density profiles, but the results
are ambiguous; this is another reason that we are not
generally enthusiastic about using partially dried samples
to elucidate the structure of Alm aggregates in lipid
bilayers.
Summary
Although we do not directly confirm that Alm bundles
have the barrel-stave configuration, our modeling of our
observed peak 1 is consistent with it. This is the case both
for our simple cylindrical model, in which the water pore
is inessential to our analysis, and for our use of the MD
simulations, which do contain a water pore. We find that
the number n of Alm monomers in the bundle increases
when the thickness of the original bilayer increases,
which is consistent with some previous results, and we
explain this as the effect of greater lipid deformation
energy in the thicker bilayers. Contrary to a previous
conclusion, we do not believe that peak 2 can be
explained by barrel-stave bundles. We propose that there
are also coexisting clusters (Fig. 12), and this picture is
supported by the Alm concentration dependence and by
the packing fraction results obtained by fitting to peak 1.
Also, crystallographic analysis was applied to partially
dried samples, and the results lead us to suggest that such
samples are not to be preferred for analysis of peptide
aggregates in membranes.
Acknowledgements
the MD simulation results of Alm bundles. We acknowledge Dr.
Thalia Mills for helping to acquire some of the scattering data at the
Cornell High Energy Synchrotron Source (CHESS), which is sup-
ported by the National Science Foundation and the National Institutes
of Health/National Institute of General Medical Sciences under
National Science Foundation award DMR-0225180. This research
was supported by NIH Institute of General Medical Sciences grant
GM44976 (to J. F. N.).
We thank Prof. Peter Tieleman for providing
Appendix I: Form Factor of a Hollow Cylindrical
Bundle
The form factor of a hollow cylindrical bundle model
embedded in lipid bilayer shown in Fig. 4 in the text can be
calculated as follows:
The electron density is qp& 0.4 e/A˚3for Alm peptide
(Pabst et al. 2007), qC& 0.3 e/A˚3for hydrocarbon chains
and qW= 0.33 e/A˚3for water molecules at 30?C. Because
the headgroup region is composed of both lipid headgroups
FPðqr;qzÞ ¼
2
Zz1
Zz1
Zz2
Zz3
0
Zb
Za
Zb
Zb
a
qP? qC
ðÞexp½iqr? r?cosðqzzÞþ
2
0
0
qW? qC
ðÞexp½iqr? r?cosðqzzÞþ
2
z1
0
qW? qC
ðÞexp½iqr? r?cosðqzzÞþ
2
z2
0
qW? qH
ðÞexp½iqr? r?cosðqzzÞ
?2ðqP? qCÞsinðqzz1Þ
qz
?2ðqW? qCÞsinðqzz1Þ
qz
0
8
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
<
>
:
>
>
9
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
=
>
;
>
>
d2rdz
¼
bJ1ðqrbÞ ? aJ1ðqraÞ
qr
þ
aJ1ðqraÞ
qr
þ
bJ1ðqrbÞ
qr
?
2ðqW? qCÞ ? sinðqzz2Þ ? sinðqzz1Þ
2ðqW? qHÞ ? sinðqzz3Þ ? sinðqzz2Þ
??þ
??
@
1
A=qz
8
>
>
>
>
>
>
>
>
>
>
:
>
<
>
>
>
>
>
>
>
>
>
9
>
>
>
>
>
>
>
>
>
>
;
>
=
>
>
>
>
>
>
>
>
>
ðA1Þ
24J. Pan et al.: Alamethicin Aggregation in Lipid Membranes
123

Page 15

(q & 0.5 e/A˚3) and water molecules with v:v & 1:1, the
averaged electron density of the headgroup region is
qH& 0.4 e/A˚3.
For a hexamer bundle, b = r/sin(p/6) ? r = 15 A˚and
a = r/sin(p/6) – r = 5 A˚based on the barrel-stave model
(Baumann and Mueller 1974); r = 5 A˚is the radius of the
helical peptide. Figure 17 shows the behavior of bJ1(qrb)/qr
and aJ1(qra)/qrat the qrrange of 0–0.2 A˚-1, which is the
fittingrangeofpeak1.FromthefigureweseethatbJ1(qrb)/qr
changes significantly while aJ1(qra)/qr acts almost as a
constantasafunctionofqrandissmallcomparedtobJ1(qrb)/
qr.WealsonoticethatthetwotermscontainingaJ1(qra)/qrin
Eq. A1haveoppositesignsbasedonthenumericalvaluesof
the electron densities, which makes their contribution to the
overall form factor even smaller. For these two reasons, the
twotermscontainingaJ1(qra)/qrareignored,andEq. A1can
be approximated by
FPðqr;qzÞ ?
bJ1ðqrbÞ
qr
>
>
¼bJ1ðqrbÞ
?2ðqP? qCÞsinðqzz1Þ
0
qz
þ
bJ1ðqrbÞ
qr
?
2ðqW? qCÞ ? sinðqzz2Þ ? sinðqzz1Þ
2ðqW? qHÞ ? sinðqzz3Þ ? sinðqzz2Þ
??þ
??
@
1
A=qz
8
<
>
>
>
>
>
>
>
>
:
9
=
>
>
>
>
>
>
>
>
>
>
;
qr
? F1ðqzÞ
ðA2Þ
Appendix II: Structure Factor
The analytical expression of the structure factor for the 2-D
hard disk model has been derived (Rosenfeld 1990) and
utilized (Constantin et al. 2007) to estimate Alm bundle
size in DMPC lipid bilayers.
S?1
0ðqrÞ
¼1þ4g A
J1ðqrRÞ
qrR
??2
þBJ0ðqrRÞJ1ðqrRÞ
qrR
þGJ1ð2qrRÞ
qrR
"#
G¼ 1?g
v¼
1?g
A¼g?11þ 2g?1
B¼g?11?g
where g is the area packing fraction of the disks (the area
occupied by the disks divided by the total area) and R is the
disk radius.
By treating the long-range interaction G(r) as pertur-
bation to the hard disk interaction, the perturbed structure
factor can be expressed by the following equation based on
random phase approximation (Hansen and McDonald
1976).
ðÞ?3=2
1þg
ðÞ3
ðÞvþ2gG
½
½
?
ðÞv?1?3gG
?ðA3Þ
SPðqÞ ¼
S0ðqÞ
?ðqÞ ? S0ðqÞ
1 ? nbG
ðA4Þ
where S0(q) is the structure factor of the unperturbed state
(hard disk interactions), n is the number density of the disks
(n = g/pR2), b = 1/kBTandG
the perturbation G(r).
?ðqÞis the Fourier transform of
Appendix III: Form Factor Calculation for Bundles
from MD Simulations
The main idea of calculating the electron density contrast
between the Alm bundle and the lipid background (He
et al. 1993) is to select two patches with the same size from
a simulation snapshot (Constantin et al. 2007). One con-
tains every atom belonging to the bundle, including water
molecules located in the lumen of the bundle, and the other
contains only lipid molecules. The form factor can then be
calculated by the following equation:
FPðqÞ ¼
Z
P
½qPðrÞ ? qLðrÞ?exp½iq ? ðr ? raÞ?dVðrÞ
X
where rmdenotes the position of the mth atom within the
bundle patch with electron number Qmand rndenotes the
position of the nth atom within the lipid patch with electron
number Qn. In practice, we chose two circular patches, one
¼
m
Qmexp iq ? rm
½ ? ?
X
n
Qnexp iq ? rn
½?ðA5Þ
0.000.050.10
qr (Å-1)
0.150.20
0
20
40
60
80
100
120


bJ1(qrb)/qr
aJ1(qra)/qr
Fig. 17 Bessel functions of bJ1(qrb)/qrwith b = 15 A˚and aJ1(qra)/qr
with a = 5 A˚
J. Pan et al.: Alamethicin Aggregation in Lipid Membranes 25
123