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Biophys J, July 2002, p. 219-228, Vol. 83, No. 1
*Institute for Chemical Research, Kyoto University, Uji, Kyoto
611-0011, Japan; and
Faculty of Pharmaceutical
Science, Kyoto University, Sakyo-ku, Kyoto 606-0001, Japan
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ABSTRACT |
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To evaluate the role of charged residues facing a pore lumen in stability of channel structure and ion permeation, we studied electrical properties of ion channels formed by synthesized native alamethicins (Rf50 (alm-Q7Q18) and Rf30 (alm-Q7E18)) and their analogs with Glu-7 (alm-E7Q18 and alm-E7E18). The single-channel currents were measured over a pH range of 3.5 to 8.7 using planar bilayers of diphytanoyl PC. The peptides all showed multi-level current fluctuations in this pH range. At pH 3.5 the channels formed by the four peptides were similar to each other irrespective of the side chain differences at positions 7 and 18. The ionization of Glu-7 (E7) and Glu-18 (E18) above neutral pH reduced the relative probabilities of low-conductance states (levels 1 and 2) and increased those of high-conductance states (levels 4-6). The channel conductance of the peptides with E7 and/or E18, which was distinct from that of alm-Q7Q18, showed a marked pH-dependence, especially for low-conductance states. The ionization of E7 further reduced the stability of channel structure, altered the current-voltage curve from a superlinear relation to a sublinear one, and enhanced cation selectivity. These results indicate that ionized E7 strongly influences the channel structure and the ion permeation, in contrast to ionized E18.
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INTRODUCTION |
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Alamethicin isolated from Trichoderma
viride is a mixture of 20-residue amphipathic peptides with eight
-aminoisobutyric acids (Aib) and a phenylalaninol at the C-terminus.
The major components are called Rf50 and Rf30, which differ only in
whether residue 18 is either Gln or Glu.
Both Rf50 and Rf30 form
voltage-gated ion channels in bilayer lipid membranes, which have been
extensively studied (for reviews, Latorre and Alvarez, 1981
; Woolley
and Wallace, 1992
; Sansom, 1991
, 1993
; Cafiso, 1994
). In the ion
channels, peptide helices are supposed to be packed together in
parallel around a central ion permeable pore. This channel structure,
called the "helix-bundle" model or the "barrel-stave" model
(Baumann and Mueller, 1974
; Boheim, 1974
), resembles a structural motif of pore regions in some biological ion channels such as nAChR, and
therefore alamethicin provides a simple model system for exploring structure-function relationships in ion channels. In the alamethicin ion channels, hydrophilic residues, Gln-7 and Glu-18 (or Gln-18), face
the pore lumen and probably form hydrogen-bonded rings, being expected
to play a key role in the channel stability and the ion permeation (Fox
and Richards, 1982
). In particular, Gln-7 located at the narrowest part
of the pore might be more important.
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To examine this idea, functional modifications of alamethicin
channels have been studied by replacing Gln-7 and Gln-18 by other amino
acid residues. Gln-7 was replaced by Ala in Rf30 (Kaduk et al., 1998
);
by Ala, Asn, or Ser in synthetic des-Aib alamethicin analogs in which
all Aib residues are replaced by Leu (Molle et al., 1996
); and by Ala
in trichosporin-B-Via, having a sequence similar to alamethicin
(Nagaoka et al., 1996a
). These modifications did not diminish
channel-forming activity except for the replacement of Gln-7 by Ala in
des-Aib alamethicin analogs, but reduced the lifetime of channel
opening and changed the channel conductance. The replacement of Gln-18
by Lys in covalent dimers of alamethicin altered the charge selectivity
of ion permeation from weakly cation-selective to weakly
anion-selective at neutral pH (Starostin et al., 1999
; Borisenko et
al., 2000
).
In this paper we have studied the effects of the replacement of Gln-7 by Glu-7 in Rf50 and Rf30 on channel formation and ion permeation. Four peptides, Rf50 (alm-Q7Q18), Rf30 (alm-Q7E18), alm-E7Q18, and alm-E7E18 (see Table 1) were synthesized by a solid-phase method and their single-channel recordings were carried out using planar bilayer lipid membranes. Because our main concern was to reveal the effects of the ionization of Glu-7 and Glu-18 on channel properties, the pH of the membrane-bathing solutions was varied from 3.5 to 8.7.
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MATERIALS AND METHODS |
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Peptide synthesis
The peptides whose sequences are shown in Table 1 were
synthesized by the solid-phase method with Fmoc-amino acid fluorides described by Wenschuh et al. (1995)
. The solid support used was an
o-chlorotrityl resin, to which the C-terminal
phenylalaninol, Pheol, was directly anchored. To assemble sterically
hindered
-aminoisobutyric acid (Aib) and amino acids next to Aib,
their Fmoc-amino acid fluorides were used as coupling agents, which were prepared from the Fmoc-amino acids using cyanuryl fluoride (Bertho
et al., 1991
). The other amino acids were assembled by the standard
method with Fmoc-amino acids. After completion of the assemblage
followed by acetylation of the N-terminus, the peptides were cleaved
from the resin. The peptides were purified through a column of Sephadex
LH-20 (Amersham Bioscience, Uppsala, Sweden) with methanol and
then by reverse-phase HPLC on a YMC-ODS column (YMC, Kyoto, Japan) with
elutes containing 63-68% CH3CN, 37-32%
H2O, and 0.05% TFA. The HPLC chromatograms of
the purified peptides showed single peaks whose retention times at
40°C were 33 min for alm-Q7Q18 (with a
CH3CN/H2O ratio of 63:37),
29 min for alm-Q7E18 (65:35), 29 min for alm-E7Q18 (65:35) and 31 min for alm-E7E18 (68:32). The purified peptides were characterized by
ESI-MS with an API-3000 (Perkin-Elmer Sciex, Wellesley, MA) as follows:
m/z 982.2 [M+2H+] and 655.1 [M+3H+] for alm-Q7Q18 (MW = 1962.4); m/z
982.7 [M+2H+] and 655.4 [M+3H+] for alm-Q7E18 (MW = 1963.3); m/z
983.0 [M+2H+] and 656.0 [M+3H+] for alm-E7Q18 (MW = 1963.3); m/z
983.2 [M+2H+] for alm-E7E18 (MW = 1964.3).
Fig. 1 show the ESI-MS charts and the
HPLC traces of purified alm-E7Q18 and alm-E7E18, indicating that those
are of adequate purity. Similar ESI-MS charts and HPLC traces were
obtained for alm-E7Q18 and alm-E7E18 (not shown).
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Single-channel measurement
Single ion channel recordings were performed with planar bilayer
lipid membranes prepared by the monolayer-folding technique (Montal and
Mueller, 1972
), as described in previous papers (Nagaoka et al., 1996b
;
Koide et al., 1997
). Lipid membranes were formed from diphytanoyl
phosphatidyl choline (diphy-PC) (Avanti Polar Lipids, Alabaster, AL) in
1 M KCl buffered with 10 mM MES-KOH (pH 3.5, 4.7, 5.9), 10 mM HEPES-KOH
(pH 6.7-7.0), or 10 mM TRIS-HCl (pH 8.3-8.7). Small amounts of a
peptide solution in ethanol were added only to one side of a membrane
(cis side) to give a final concentration of 1-10 nM.
A pair of Ag-AgCl electrodes was used for current measurement and voltage supply. The cis- and trans-side electrodes were connected to a DC voltage source and to the virtual ground of a homemade current amplifier, respectively. Hence, a positive voltage means that the cis side is positive relative to the trans side. The output voltages of the current amplifier were recorded with a DR-F2a digital recorder (TEAC Corporation, Tokyo, Japan). All measurements were performed at 25 ± 0.5°C.
In the single-channel recordings we carefully adjusted applied voltage not to count plural channels per membrane. The critical applied voltage depended on peptide concentration in the bathing solution, and therefore voltage dependence of single-channel currents was obtained by varying peptide concentration. Relative probabilities of different conductance states were calculated from the single-channel recordings, being almost independent of either peptide concentration or applied voltage.
Ion selectivity of single channels between K+ and
Cl
was measured with solutions of potassium and
chloride salts with bulky counterions that negligibly contribute to the
channel current. This method was the same as described by Starostin et
al. (1999)
. The electrolyte solutions used were 1 M potassium gluconate
(Kgluc) (Wako Pure Chemical Industries, Osaka, Japan) and 1 M
N-methylglucamine chloride (NmgCl) (Tokyo Kasei Kogyo,
Tokyo, Japan) both containing 10 mM HEPES-KOH (pH 7.0). The
conductances of the Kgluc and NmgCl solutions measured using a
HP-4192A LF Impedance Analyzer (Hewlett-Packard, Palo Alto, CA),
were close to each other, 39% and 38% of that of 1 M KCl with 10 mM
HEPES-KOH (pH 7.0), respectively.
Theoretical calculation of single-channel current
Single-channel currents in symmetric KCl solutions were
calculated by a method similar to that described by Dieckmann et al. (1999)
. In their method, the Nernst-Planck equation was used with potential energy profiles for permeating ions in a pore, which were
calculated with a macroscopic pore model by a three-dimensional finite-differential Poisson-Boltzmann (FDPB) method (Sharp and Honig,
1990
). In this study, to save time in FDPB calculation, we adopted an
axial symmetric geometry (Jordan et al., 1989
). The grid dimensions
were 65 (radial) × 75 (axial) whose radial and axial grid spacing
were 0.05 nm and 0.125 nm, respectively. The electrostatic potential
energy for a permeating ion is provided by a sum of the
"desolvation" (or image) energy and the "interaction" energy.
The "desolvation" energy is the self energy difference due to
interactions between a probe ion and charges induced at boundaries
between different dielectrics (Parsegian, 1969
). The "interaction"
energy comes from the interactions of a permeating ion with charges of
ionized residues and dipole moments of helix backbones.
In the calculation with the Nernst-Planck equation, we assumed that a
transmembrane voltage V produces a constant electric field
in the pore. Because both the cis and trans sides
have the same KCl solution of activity,
aKCl, the single-channel current I is simply given by
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(1) |
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(2) |
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(3) |
the electrostatic potential energy of a permeating ion,
D the ion diffusion coefficient, F the Faraday
constant, and subscripts K and Cl refer to K+ and
Cl
ions, respectively.
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RESULTS AND DISCUSSION |
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Single-channel recordings
Single ion channel currents were measured for ion channels formed
in diphy-PC bilayers by two native alamethicins Rf50 (alm-Q7Q18) and
Rf30 (alm-Q7E18) and their analogs with Glu-7 (E7) instead of Gln-7
(Q7) (alm-E7Q18 and alm-E7E18). The effects of the ionization of E7 and
E18 on the ion channel properties were examined by varying pH of the
membrane-bathing solutions (1 M KCl) from 3.5 to 8.7. In this pH range
the headgroup of diphy-PC is electrically neutral and the contributions
of H+ and OH
to the
channel currents are negligible. When the peptides were added to one
side (cis side) of the membrane, multi-level current fluctuations were observed only at cis-positive voltages.
Fig. 2 shows typical examples of current
fluctuations measured at 200 mV and at pH 3.5, 6.7-6.9, and 8.3-8.7.
The corresponding conductance histograms (all-point amplitude
histograms) are shown in Fig. 3. The
current fluctuations of alm-Q7Q18 channels were almost independent of
pH, and four conductance states (levels 1-4) were found besides the
lowest conductance state (level 0) (Hanke and Boheim, 1980
) that was
not properly resolved from the closed state in the histograms. The
relative probabilities of the conductance states decreased with
increasing conductance-level number. Very similar behavior was found
with alm-Q7E18, alm-E7Q18, and alm-E7E18 at pH 3.5, where E7 and E18
were not ionized. This suggests that, when E residues are not ionized,
the channels of the four peptides are similar to each other in
structure and stability, irrespective of the side chain differences.
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For the peptides with E7 and/or E18 at pH 6.7-6.9 and pH
8.3-8.7, the relative probabilities of low-conductance states (levels 1 and 2) decreased significantly, and those of high-conductance states
(levels 4-6) increased. The conductance histograms were "bell-shaped," in which the major conductance state was level 4 for
alm-Q7E18, level 4-5 for alm-E7Q18, and level 5-6 for alm-E7E18. This
indicates that the ionization of E7 and/or E18 inhibits formation of
smaller pores and facilitates that of larger pores, which might be due
to electrostatic repulsion between peptides in a channel. The relative
probabilities of conductance states may be determined by
peptide/peptide and peptide/lipid interactions. The importance of
peptide/lipid interactions has been clearly demonstrated by Keller et
al. (1993)
and Bezrukov et al. (1998)
, i.e., lipid packing stress
promoted higher conductance states. The present findings show that
peptide/peptide interactions are also an important factor that governs
the relative probabilities of conductance levels.
The peptides with E7 (alm-E7Q18 and alm-E7E18) at pH 6.7-6.9 and pH 8.3-8.7 showed rapid transitions between adjacent conductance states in the current fluctuations and broadening and splitting of peaks in the conductance histograms. This behavior implies that the ionization of E7 residues at the narrowest part of the pore destabilizes the channel structure and produces different conformations, in contrast to ionized E18 residues near the pore mouth.
The molecularity of alamethicin per channel in each conductance state
has been discussed by several authors (Hanke and Boheim, 1980
; Sansom,
1991
; Matsubara et al., 1996
; You et al., 1996
). Because the
transitions between adjacent conductance states may be caused by
the uptake and release of a peptide from a helix bundle, the number of
peptides per channel increases one by one with increasing
conductance-level number. Hanke and Boheim (1980)
suggested that the
lowest-conductance channel (termed level 0 channel in this paper) is a
trimeric bundle following macroscopic calculations with a cylindrical
model. Matsubara et al. (1996)
supported this assignment by using
alamethicin molecules tethered with cyclic templates. Their conclusion,
however, should be reconsidered because the cyclic templates are liable
to interfere with normal packing of helices in a channel. You et al.
(1996)
compared the conductance levels between the alamethicin monomer
and its covalent dimer, suggesting that the number of peptides in level
0, 2, and 4 channels (or level 1, 3, and 5 channels in their notation)
is an even number, putatively 4, 5, 6, 7, and 8 for levels 0, 1, 2, 3, and 4, respectively. Our similar studies with N-terminally linked
dimers by a disulfide bond have also supported their conclusion (a
preliminary report was presented at the 39th annual meeting of the
Biophysical Society of Japan, 2001).
pH-dependence of channel conductance
Fig. 4 shows pH-dependence of the conductance of level 2 channels that were commonly observed for all the peptides over the pH range examined. The channel conductance of alm-Q7Q18 was almost independent of pH. The conductance of the alm-Q7E18 channel increased with pH from 3.5 to 6 and leveled off above pH 6, whereas that of the alm-E7Q18 channel started to increase at pH 5 and still increased above pH 6. The conductance of alm-E7E18 channel appeared to be a sum of the contributions of ionized E7 and E18 that were obtained with alm-E7Q18 and alm-Q7E18, respectively. The influence of pH on the channel conductance decreased with increasing conductance-level number (see Fig. 3).
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The pH-dependence of channel conductance is related to the dissociation
of E residues, which is influenced by their surroundings such as
electrolyte shielding and ionized states of their neighbors. The
effective pKa value that was estimated to be
4.5-5 from the pH-dependence of channel conductance for alm-Q7E18 was
close to that of free E residues, indicating small electrostatic
interactions between E18 residues in a channel. The change in channel
conductance for alm-E7Q18, which was distinct from alm-Q7E18, spread
over a wider pH region, suggesting electrostatic interactions between E7 residues in a channel alter the effective pKa
values. Borisenko et al. (2000)
calculated the effective
pKa values of eight Lys residues in an octameric
bundle. The results showed that the effective pKa
was considerably shifted to a lower value with increasing the number of
ionized Lys residues. For acidic residues, the reverse change in
pKa is expected, explaining the broad
pH-dependence of channel conductance for alm-E7Q18 and alm-E7E18. The
electrostatic interactions between adjacent E residues depend on their
positions in the pore. The E7 residues located at the narrowest part of the pore are closer to each other and are less subjected to electrolyte shielding effects than the E18 residues near the pore mouth. This might
explain the difference in pH-dependence of channel conductance between
alm-Q7E18 and alm-E7Q18.
Single-channel current-voltage relationships
Non-ohmic behavior of single channels has been reported for
alamethicin (Eisenberg et al., 1973
; Gordon and Haydon, 1975
; Taylor
and de Levie, 1991
) and for covalent dimers of alamethicin (Woolley and
Wallace, 1992
), providing insights into energy barrier profiles for the
ion permeation. Fig. 5 shows the
I-V relationships of the single channels obtained
for the four peptides at pH 7.0. To compare the
I-V curves among different conductance levels, those were normalized with current values at 200 mV. The normalized I-V curves of alm-Q7Q18 and alm-Q7E18 channels
were similar to each other and changed from a superlinear (concave)
relation to a linear one with increasing conductance-level number.
These I-V curves were well represented by a
hyperbolic sine function as described previously (Mak and Webb, 1995
;
Koide et al., 1997
). Similar I-V curves were also
obtained for alm-E7Q18 and alm-E7E18 at pH 3.5 (not shown).
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The I-V curves of alm-E7Q18 channels at pH 7.0 showed slightly sublinear (convex) relations. The degree of deviation from a linear relation increased with conductance-level number. The channels of alm-E7E18 showed slightly superlinear curves at levels 2-4, a linear one at level 5, and slightly sublinear ones for level 6-7. The results indicated that the ionization of E7 converted the I-V curve from a superlinear relation to a sublinear one, whereas the ionization of E18 little influenced the shape of I-V curves.
The effects of charged E residues on the I-V
relationships depended on their positions in a pore. Here, we attempt
to simulate the effects for the level 2 channels of the four peptides
at pH 6.7-6.9. The precise simulations are, however, not easy at
present because of the following reasons: 1) we don't yet have the
precise molecular model of alamethicin channels in lipid bilayers
under electric fields, and 2) the method for calculating ion flux from a molecular pore model is still controversial (Levitt, 1999
). Hence, we
intended to provide rather a rough explanation following the line
described by Dieckmann et al. (1999)
. The I-V
curves were calculated by the Nernst-Planck equation from the potential energy profiles for a permeating ion that were estimated using macroscopic pore models.
Three pore models were examined, which have different
electrolyte-occupied regions: electrolytes are excluded from the pore (model A), and penetrate the pore entrances (model B) and the entire
pore interior (model C) (Fig. 6). The
pore shape in the models were similar to that obtained by Tieleman et
al. (1999)
for a hexameric bundle of alm-Q7Q18 and alm-Q7E18 using
molecular dynamics simulations. The relative permittivity of the
aqueous phase including the pore interior was assumed to be 80, and
that of the membrane and the pore wall to be 2. The membrane thickness was 3.5 nm. For the sake of simplicity we dealt with only the charges
of ionized groups and the macro dipoles due to the peptide helix
backbones (the dipole moment is 2.4 × 10
28 Cm per peptide helix). The potential
energy profiles for a permeating ion along the pore axis were
calculated by a nonlinear FDPB method, from which single-channel
currents were calculated using the Nernst-Planck equation with the
following parameter values: DK = DCl = 1.9 × 10
9 m2/s (the value is
for bulk KCl solutions), aKCl = 0.6 M
for 1 M KCl, d = 3.5 nm, and T = 298 K. The narrowest radius of the pore model was used for r.
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Simulations were carried out in the following way. First, we used the
three models having different electrolyte shielding effects to
calculate the I-V curve of alm-Q7Q18. The
narrowest pore radius in each model was changed from 0.3 to 0.6 nm by
0.05 nm to obtain a theoretical I-V curve close
to the observed one. The results are shown in Fig. 6, where the pore
radius is 0.55 nm for model A, 0.5 nm for model B, and 0.35 nm for
model C. The theoretical I-V curve seriously
depended on the pore model used, suggesting that electrolyte shielding
is an important factor to determine the energy barrier of ion
permeation as pointed out by Jordan et al. (1989)
. Because model B,
with r = 0.5 nm, provided a better simulation for the
I-V curve of alm-Q7Q18, we used this model for
simulating the I-V curves of the other three
peptides. The I-V curves for alm-Q7E18 and
alm-E7Q18 were calculated by varying the total charge of E18 or E7 in a
hexameric bundle, the best-fit curves being obtained with total charges
of 0.6e for E18 and 1.1e for E7 (e is
the elementary charge) (shown in Fig. 7).
Finally, the I-V curve of alm-E7E18 was
calculated with the same total charges of E7 and E18 that were
estimated for alm-Q7E18 and alm-E7Q18 channels. The resulting potential
profiles are shown in Fig. 8. These
simulations provided a reasonable explanation for the differences in
nonlinearity among the observed I-V curves, irrespective of the simplified calculations that were based on static
potential energy profiles without taking into account interactions between permeating ions. For the more precise simulations, which would
be a future issue, we should take into account dynamic interactions of permeating ions with charged residues and multi-ion
permeation.
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Cation/anion selectivity
In the determination of ion selectivity of alamethicin channels we
cannot use the "reversal potential" method because the channels
open only at cis-positive voltages and close before reaching the reversal potentials. Hence, the
K+/Cl
selectivity has
been estimated from the single-channel currents in 1 M potassium
gluconate (Kgluc) and 1 M N-methylglucamine chloride (NmgCl), both buffered with 10 mM HEPES-KOH (pH 7.0). Because of the
bulky organic counterions, channel currents through small pores are
mainly carried by K+ or
Cl
, and thus the channel current ratio
IKgluc/INmgCl
indicates the K+/Cl
selectivity. In the calculation of
IKgluc/INmgCl
the assignment of conductance levels is very important. For alm-Q7Q18
and alm-Q7E18, single-channel recordings in 1 M Kgluc and 1 M NmgCl
were not so different from each other, and therefore the conductance
levels were unambiguously assigned. For alm-E7Q18 and alm-E7E18,
however, single-channel recordings were very different between 1 M
Kgluc and 1 M NmgCl, and the probabilities of lower conductance levels in 1 M Kgluc were extremely reduced (Fig.
9). This situation made it difficult to
identify the conductance levels. Hence, we followed the single-channel
conductances by varying the solution composition from 100% NmgCl to
100% Kgluc. The results are shown in Fig.
10. The conductance of each level was
proportional to the Kgluc/NmgCl ratio, which allowed us to identify the
conductance levels unambiguously. Table 2
summarizes mean values of
IKgluc/INmgCl
obtained at 200 mV. Both alm-E7Q18 and alm-E7E18 channels were strongly
cation-selective, i.e., the
IKgluc/INmgCl
was 4-5 for level 1 channels, decreasing with increasing
conductance-level number. Compared with the peptides with E7 (alm-E7Q18
and E7E18), weak cation selectivity was obtained for the peptides with
Q7 (alm-Q7Q18 and alm-Q7E18). These results indicate that negative
charges at position 7 strongly enhance the cation selectivity, whereas
those at position 18 slightly influence the charge selectivity.
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The "current ratio" method usually provides an underestimated value
for the permeability ratio that is calculated by the "reversal potential" method. Starostin et al. (1999)
determined the
K+/Cl
selectivity of
channels formed by the covalent dimer of alamethicin (Rf50)
(di-alm-Q18) and that of its analog with Lys-18 (di-alm-K18) by the two
methods. Because the dimers formed long-lasting channels, the entire
I-V curves of the single channels were obtained
by applying fast voltage ramps during their opening, and thus the reversal potentials were measured in asymmetric KCl solutions. The
permeability ratio
PK/PCl
of the octamer level channel (level 4) was 2.1 (0.1 M/1.3 M KCl) for
di-alm-Q18, and was 0.56 (0.1 M/1.3 M KCl) for di-alm-K18 at pH 6.8. However, the corresponding current ratio
IK/ICl
measured in electrolyte solutions of bulky counterions was 1.1 for
di-alm-Q18 and 0.7 for di-alm-K18 at pH 7.0.
Borisenko et al. (2000)
demonstrated that di-alm-K18 formed
anion-selective, non-selective, and cation-selective channels depending
on pH. The
PK+/PCl
was 0.25 at pH below 7 and was 4 at pH above 11. Lear et al. (1997)
studied electrostatic effects on charge selectivity with ion channels
formed by designed peptides
(Ac-(LSSLLSL)3-CONH2). They
found that a negatively charged Glu introduced at the N-terminus
enhanced the cation selectivity of the channels, and a positively
charged Arg at the N-terminus reduced the cation selectivity. It may be
concluded from these results and the present results that the charge
selectivity can be modified by introducing dissociable residues to
channel-forming peptides and by varying pH of membrane-bathing
solutions. In particular, charged residues in the pore interior are
much more effective than those at the pore mouth.
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FOOTNOTES |
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Address reprint requests to Dr. Koji Asami, Institute for Chemical Research, Kyoto University, Uji, Kyoto 611-0011, Japan. Tel.: +81-774-38-3081; Fax: +81-774-38-3084; E-mail: asami{at}tampopo.kuicr.kyoto-u.ac.jp.
Submitted October 18, 2001, and accepted for publication March 6, 2002.
Y. Nagaoka's current address is Department of Biotechnology, Kansai University, Suita, Osaka 564-8680, Japan.
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REFERENCES |
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Biophys J, July 2002, p. 219-228, Vol. 83, No. 1
© 2002 by the Biophysical Society 0006-3495/02/07/219/10 $2.00
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