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Biophys J, February 2002, p. 908-914, Vol. 82, No. 2
*Department of Physics, National Central University, Chung-Li,
Taiwan 32054; and
Department of Physics & Astronomy, Rice
University, Houston, Texas 77251
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ABSTRACT |
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The transition of the state of alamethicin from its
inactive state to its active state of pore formation was measured as a function of the peptide concentration in three different membrane conditions. In each case the fraction of the alamethicin molecules occupying the active state,
, showed a sigmoidal concentration dependence that is typical of the activities of antimicrobial peptides.
Such a concentration dependence is often interpreted as due to peptide
aggregation. However, we will show that a simple effect of aggregation
cannot explain the data. We will introduce a model based on the
elasticity of membrane, taking into consideration the membrane-thinning
effect due to protein inclusion. The elastic energy of membrane
provides an additional driving force for aggregation. The model
produces a relation that not only predicts the correct concentration
dependence but also explains qualitatively how the dependence changes
with membrane conditions. The result shows that the membrane-mediated
interactions between monomers and aggregates are essential for the
strong cooperativity shown in pore formation.
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INTRODUCTION |
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It is well known that the activities of
membrane-active antimicrobial peptides, whether on bactericide,
hemolysis, or liposome lysis, often exhibit a sigmoidal (sometimes
described as all-or-none) dependence on the peptide concentration
(Steiner et al., 1988
; Boman et al., 1994
; Shai, 1999
). These phenomena
are often interpreted as an aggregation effect of the peptides,
although the data were rarely analyzed quantitatively. In this paper,
we will use the example of alamethicin to measure and analyze the
concentration dependence of the peptide activity. We conclude that the
sigmoidal dependence cannot be explained as a simple aggregation effect of peptide, rather the phenomenon requires an additional driving force
that is provided by a membrane-thinning effect induced by the peptide inclusion.
Gene-encoded membrane-active antimicrobial peptides, such as
alamethicin, magainin, and protegrin (also bee venom toxin melittin), have been shown to exhibit two distinct oriented circular dichroism spectra (Olah and Huang, 1988
; Wu et al., 1990
), clearly indicating that there are two distinct states of binding to lipid bilayers (Huang,
2000
). In one state, the I state, the peptide molecules induce
formation of transmembrane pores as shown by neutron diffraction (He et
al., 1995
, 1996a
), presumably that is how the antimicrobial peptides
kill the target cells. The other state, the S state, is an inactive
state because no transmembrane pores were detected (Yang et al., 2001
).
Thus, the factors that determine the state of a peptide in a cell
membrane will determine the susceptibility of the cell to the peptide.
At present, these factors are not well understood.
One important factor appears to be the concentration of the peptide
molecules bound to the membrane. In all the cases we have studied
(Huang and Wu, 1991
; Ludtke et al., 1994
; Heller et al., 1998
; Yang et
al., 2001
), we found that a peptide at low concentrations favors the S
state, whereas at high concentrations favors the I state. This is
consistent with the above-mentioned sigmoidal dependence of the peptide
activity on the peptide concentration. Our purpose here is to study
what causes such a cooperative phenomenon, that is, a superlinear
increase of peptide activity with concentration.
We measured the transition of alamethicin from the S state to the
I state as a function of the peptide concentration through a
coexistence region by using the method of oriented circular dichroism
(OCD). The measurement was done in three different conditions: in fully
hydrated diphytanoyl phosphatidylcholine (DPhPC) bilayers, in slightly
dehydrated DPhPC bilayers, and in fully hydrated 5:1 DPhPC and
diphytanoyl phosphatidylethanolamine (DPhPE) mixture bilayers. In each
case the fraction of alamethicin molecules occupying the I state shows
a sigmoidal dependence on the peptide concentration. We compared the
data with a Debye's model for micelles that has satisfactorily
described the micellization of soap solutions (Debye, 1949
;
Blankschtein et al., 1986
). We found that a simple effect of
aggregation is insufficient to explain the strong cooperativity exhibited by the pore formation of alamethicin. We will introduce an
elasticity model based on the fact that a bilayer membrane in its fluid
state is an elastic body. The inclusion of a protein in the membrane
induces a strain field around the protein. This strain field mediates
protein-protein interactions at a distance (Harroun et al., 1999
) and
contributes to a peptide concentration-dependent elastic energy that
influences the relative energy level between the S state and the I
state. We will show that the experimental data can be described by a
phenomenological relation based on the elasticity theory of membrane
(Huang, 1986
, 1995
).
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MATERIALS AND METHODS |
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1,2-Diphytanoyl-sn-glycero-3-phosphatidylcholine
(DPhPC) and
1,2-diphytanoyl-sn-glycero-3-phosphatidylethanolamine
(DPhPE) were purchased from Avanti Polar Lipids (Alabaster, AL).
Alamethicin was purchased from Sigma-Aldrich Chemical Co. (St. Louis,
MO). It is a mixture of components, principally alamethicin I (85% by
high-performance liquid chromatography) and alamethicin II (12%),
which differ by one amino acid (Pandey et al., 1977
). Polyethylene glycol (PEG20000) was purchased from Merck Co. (Hohenbrunn, Germany). All materials were used as delivered.
Sample preparation followed the method described in Ludtke et al.
(1995)
. Briefly, lipid and peptide mixtures at chosen peptide-to-lipid molar ratios (P/L) were dissolved in a solvent of 1:1 (v/v)
methanol and chloroform. The lipid concentration was ~1 mg per 20 µl solvent. A solution of 10 µl or less (depending on the
P/L) was spread onto a 14-mm diameter area of a thoroughly
cleaned quartz surface. After the deposited sample appeared dry, it was
placed in vacuum to ensure a complete removal of solvent residues. The
vacuumed sample was then slowly hydrated until it became transparent. A good sample was visually smooth and showed up to eight orders of Bragg
diffraction by x-ray, indicating it was a stack of oriented lipid bilayers.
The sample chamber was a cylindrical construction whose cross section is shown in Fig. 1. The light beam of the CD spectropolarimeter was along the cylindrical axis, perpendicular to the two parallel quartz windows. One of the windows was the quartz plate; on its inside surface the sample was deposited. The space between the windows was sealed. The rim of this space was used to hold distilled water for a full hydration measurement or a PEG solution for a partial hydration measurement. The humidity corresponding to a PEG solution was measured by a hygrometer in a calibration chamber provided by the manufacturer (Rotronic Instrument Co., Huntington, NY). A typical concentration used in this study was 4.75 g of PEG20000 in 10.00 g of water, which gave a 98.0% relative humidity at 25°C. The outer part of the sample chamber was a thermostat. The temperature was monitored by a Pt100 thermo-resistor and controlled by a computer via a feedback thermo-electric module. The temperature could be controlled from 10° to 40°C with the stability of ±0.1°C for several days. The cylindrical sample chamber was allowed to rotate around its axis for the purpose of rotational averaging.
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Circular dichroism was measured with light incident normal to the
substrate surface (Olah and Huang, 1988
; Wu et al., 1990
). The resulted
spectrum was the OCD. Data were collected on a Jasco J-810
spectropolarimeter. Because the state of alamethicin is sensitive to
the hydration level, the equilibrium of the sample was ensured by an
agreement of at least three OCD spectra measured over a period of
6 h after each humidity setting. Each OCD spectrum presented in
Figs. 2,
3, and
4 was an average of eight measurements at
eight rotational angles equally spaced in one complete rotation. Such
rotational averaging diminishes possible spectral artifacts due to the
linear dichroism that could be caused by imperfections in the sample,
strain in the quartz plates, or an imperfect alignment of the windows
(Wu et al., 1990
). We did not detect any significant change of spectrum
with temperature from 10° to 40°C. This seems to indicate that the
entropic contribution to the change of state is negligible. All data
presented here were measured at 25°C. The background OCD spectra of
lipid bilayers were measured separately and were removed from the
corresponding spectra of the samples containing alamethicin. An example
of low peptide concentration is shown in Fig. 2.
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The method of obtaining the OCD spectra for the I state and the S
state has been demonstrated for at least four different peptides in
previous publications (Huang and Wu, 1991
; Ludtke et al., 1994
; Heller
et al., 1998
; Yang et al., 2001
). They are defined as two extreme
spectra in the sense that all other spectra fall in between and can be
expressed as linear superpositions of the two. The extreme spectra were
searched by measuring the OCD of a peptide in many different lipid
bilayers and as a function of P/L, temperature, and
hydration. Here one extreme OCD was found in the sample of
P/L = 1/15 in DPhPC in high hydrations (Fig. 3 A). This spectrum represents a helix oriented parallel to
the light or perpendicular to the plane of bilayers, according to the
theory of OCD (Olah and Huang, 1988
; Wu et al., 1990
). When a sample
exhibited this spectrum, it also produced a neutron diffraction pattern
of transmembrane pores (He et al., 1995
, 1996a
). We called this the I
state of alamethicin. Another extreme spectrum was found in the sample
of P/L = 1/150 in DPhPC, independent of the degree of
hydration (Figs. 2 and 3 B). This spectrum represents a
helix oriented perpendicular to the light or parallel to the plane of
bilayers, according to the theory. When a sample exhibited this
spectrum, its diffraction pattern showed no detectable in-plane structures (He et al., 1995
, 1996a
). We called this the S state of
alamethicin. For some peptides, the two extreme spectra could be
obtained from one sample at two different hydrations or temperatures (e.g., melittin see Yang et al., 2001
). In that case, the two spectra
are relatively normalized. However, when the two extreme spectra were
obtained from two separate samples as in this case, there was a problem
of normalization, i.e., the two spectra were not normalized to each
other. This problem was solved as follows. Suppose that there is a
cross point between the I and the S spectra, then this isodichroic
point must be common to all spectra provided that they are all
normalized correctly. We could easily find such a point by varying the
hydration level of the P/L = 1/15 sample (Fig.
3 A). The relative normalization was achieved by adjusting the amplitudes of all other spectra to cross this isodichroic point
(Fig. 3 C). Each normalized spectrum was then fitted by a
linear superposition of the I and S spectra (Fig. 3 C) from which the fraction of alamethicin in the I state,
, was obtained. The example in Fig. 3 C shows that the fit is excellent.
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RESULT AND ANALYSIS |
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Fig. 4 shows the normalized OCD spectra of alamethicin in DPhPC for a series of P/Ls, all in full hydration. The fraction of alamethicin occupying the I state as a function of P/L is shown in Fig. 5, along with the data for alamethicin in DPhPC equilibrated at 98% relative humidity, and alamethicin in 5:1 DPhPC/DPhPE mixtures in full hydration. The error bars, about ±0.05, represent the standard deviations of the numerical fits.
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We make three remarks before we proceed with analyses.
First, the system of alamethicin in DPhPC bilayers has been studied by
one of us (H.W.H.) for over 10 years. When we first discovered the
concentration dependence of the state (or orientation) of alamethicin,
the threshold concentration (P/L)* (at full hydration) was
measured at ~1/120 (Huang and Wu, 1991
). But in our 1995 study (Wu et
al., 1995
) we found (P/L)* shifted to ~1/40. This latter value was again measured in the 1996 (He et al., 1996b
) and in the 1997 (Heller et al., 1997
) studies. In our current study, we found
(P/L)* shifted back to ~1/120 (Fig. 5), the same value originally measured in 1991. We have obtained alamethicin and DPhPC
from the same companies. As far as we know, the source of alamethicin
has been the same. However, according to Avanti (S. Burgess, personal
communication), DPhPC has been made with phytol from different sources
over the years. Whether the different results were due to any
differences in the materials is not clear, although we suspected so in
our previous investigation (Wu et al., 1995
). What is clear is that the
state of a peptide is sensitive to many physical and chemical
variables. Therefore, to study the state of a peptide, one has to take
care in keeping all conditions except the variables of interest constant.
Second, in our samples, all of the alamethicin molecules appeared to be
bound to lipid bilayers. Negligible amounts of alamethicin, if any,
were in the water layers between lipid bilayers. This is because the
thickness of the water layer between two lipid bilayers is generally
less than the width of the alamethicin helix (Wu et al., 1995
; Hung et
al., 2000
). Furthermore, the samples showed a pure I state in which all
peptide molecules were perpendicularly oriented to the bilayers,
indicating that all were participating in the S to I transition.
Third, each of the three types of sample produced a single series of Bragg diffraction peaks (data not shown), indicating that the peptide and lipids were mixed into homogeneous bilayers.
Model analysis
Micellar model
The fraction of alamethicin molecules occupying the active state of pore formation,
, shows a sigmoidal concentration dependence in
each of the three conditions we have measured (Fig. 5). The most
commonly invoked interpretation for a sigmoidal concentration dependence is that there is molecular aggregation. In the case under
consideration, one would assume that the peptide aggregates to form
pores in the I state. Indeed, transmembrane pores were detected by
neutron diffraction when alamethicin was in the I state (He et al.,
1995
|
(1) |
|
(2) |
|
(3) |
C
|
(4) |
(C1/Cc). In this case, the density of
pores is negligible and so we have C1
C. But for C > Cc, the
Cn terms dominates Eq. 4.
C1 needs to exceed Cc by
only a very small amount in order that almost all of C
Cc be accommodated entirely by the pore density.
Cc is called the critical micellization
concentration, equivalent to (P/L)* here. Thus, the
essential implication of a simple aggregation effect is
C1
C, Cn
0 for
C < Cc and C1
Cc, nCn
C
Cc for C > Cc. Therefore,
the prediction of the micellar model in the S-to-I transition region is
|
(5) |
Elasticity model
We know that what makes alamethicin bind to a lipid bilayer is the hydrophobic interaction, the attraction between the hydrophobic surface of the alamethicin helix (Fox and Richards, 1982
s. This is, however, not the total free energy of binding. For a peptide to adsorb on the interface, it needs to be embedded in the headgroup region of the lipid bilayer. This has a consequence of expanding the area of the bilayer and causing
a local thinning in the hydrocarbon region (Wu et al., 1995
|
(6) |
(P/L)2 is the elastic energy of membrane
thinning mentioned above with
as the proportionality constant. Then
the chemical potential of the S state contains a positive term of
elastic energy that increases linearly with P/L. We have
proposed that this is the reason the chemical potential of the S state
crosses over that of the I state as P/L increases and that
explains the S to I transition at high peptide concentrations (Huang,
1995
(P/L), form pores, and the rest, (1
)(P/L), remain in the S state. We propose the
following phenomenological energy in the fashion of the Landau theory
(Landau and Lifshitz, 1969
|
(7) |
|

I is the interaction energy for a
peptide in a pore, and we assume that pores also cause membrane
thinning. But the thinning effect of a pore (normalized to per peptide)
is different from that of a peptide adsorbed in the headgroup region.
We express this difference by the factor
. Minimization of the free
energy with respect to
,
F/
= 0, gives the
relation between
and P/L.
|
(8) |
= 0 when P/L = (P/L)*, we have
|
(9) |
|
(10) |
S >
I, because at
very low concentrations, where the quadratic term is absent (Huang,
1995
< 1. This makes sense. The contribution of a
pore to membrane thinning (normalized to per peptide) should be less
than the contribution by a peptide in the S state, otherwise the
insertion transition would not occur by increasing the concentration.
As seen from Eq. 10,
is the ratio of the lower boundary to the
higher boundary of the transition (or coexistence) region,
= (P/L)*/(P/L)**. (P/L)** is the threshold
concentration for all of the alamethicin molecules to form pores.
The first thing to notice in Eq. 10 is that if we did not include the
contribution of pores in the membrane thinning effect, i.e., if
= 0, the two models would predict the same
vs.
P/L relation. The equivalence of these two models is
reminiscent of the equivalence of the Bragg-Williams approximation and
the Landau theory for the Ising model (Huang, 1987
is linear to the reciprocal of P/L that is
born out by the measurement. Replotting
as a function of (P/L)
1, we found the data in the transition
region falling on a straight line (Fig.
6). From the intercept of the line
fitting to the transition data with the line of
= 0, we obtain
the threshold concentration (P/L)* for each of the three
cases. Here the micellar model predicts the data to fall on a line of
slope
(P/L)* (the dotted line) that does not agree with
the data. The elasticity model predicts a steeper slope
(P/L)*/(1
) and also allows the slope to vary with
representing different bilayer conditions, both agree with the
measurement. The values of
are listed in the inset of Fig. 6 for
three different conditions. We also show the relative magnitudes of
by using Eq. 9 assuming a constant value for (
S
I).
|
and
(P/L) holds for three different conditions is significant.
That means the relation predicted by Eq. 10 is general and is strongly supported. In one sample we made a partial substitution of DPhPC with
DPhPE. (We could not use pure DPhPE because it will result in a
nonbilayer phase.) The purpose was to reduce the average size of the
lipid headgroup, noting that the headgroup PE is substantially smaller
than PC (Heller et al., 1997
is the quantity that represents the effect
of peptide raising elastic energy in membrane (per peptide molecule).
We expect this quantity to decrease with the average size of the
headgroup. This is born out by the result shown in the inset of Fig. 6.
In another sample, the DPhPC bilayers were kept at a slightly
dehydrated condition, i.e., being equilibrated with a water vapor of
98% relative humidity. In this case there were fewer water molecules
adsorbed in the headgroup region compared with the case of 100%
relative humidity. This should have a consequence similar to reducing
the average size of the lipid headgroup. Again the experimental result
supports the prediction. All of these results are consistent with our
hypothesis that the membrane thinning effect is the driving force for
the peptide's S to I transition.
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CONCLUSION |
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|
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We have presented a measurement of the sigmoidal concentration
dependence for the change of the state of alamethicin, from its
inactive state of adsorbing in the headgroup region of a lipid bilayer
to the active state of forming transmembrane pores. Our quantitative
analysis shows that a simple aggregation effect does give rise to a
sigmoidal concentration dependence. However, the experiment shows that
the cooperativity of pore formation is stronger (steeper increase in
) than that predicted by a simple aggregation model. Thus, a
micellar model as described by Eq. 3 that includes no interactions
between monomers and aggregates does not agree with the experiment.
Many investigators have proposed that the energetics of
peptide-membrane interaction must include a term arisen from the
elastic deformation in membrane caused by the peptide inclusion (for
review, see Aranda-Espinoza et al., 1996
). Here we show that this
elastic energy produces a membrane-mediated interaction between
monomers and pores, and this is essential for the action of pore
formation by alamethicin.
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ACKNOWLEDGMENTS |
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FYC was supported by a grant from the National Science Council (Taiwan), NSC 89-2112-M-008-035, and by the National Central University. HWH was supported by the NIH grant GM55203 and by the Robert A. Welch Foundation.
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FOOTNOTES |
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Address reprint requests to Dr. Huey W. Huang, Rice University, Department of Physics & Astronomy, Houston, TX 77251. Tel.: 713-348-4899; Fax: 713-348-4150; E-mail: hwhuang{at}rice.edu.
Submitted August 15, 2001 and accepted for publication October 22, 2001.
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J. Chem. Phys.
89:2531-2538
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Biochim. Biophys. Acta.
1462:55-70
Biophys J, February 2002, p. 908-914, Vol. 82, No. 2
© 2002 by the Biophysical Society 0006-3495/02/02/908/07 $2.00
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