Water permeability of gramicidin A-treated lipid bilayer membranes.

Abstract

In membranes containing aqueous pores (channels), the osmotic water permeability coefficient, P f, is greater than the diffusive water permeability coefficient, P d. In fact, the magnitude of P f/P d is commonly used to determine pore radius. Although, for membranes studied to date, P f/P d monotonically declines with decreasing pore radius, there is controversy over the value it theoretically assumes when that radius is so small that water molecules cannot overtake one another within the channel (single-file transport). In one view it should equal 1, and in another view it should equal N, the number of water molecules in the pore. Gramicidin A forms, in lipid bilayer membranes, narrow aqueous channels through which single-file transport may occur. For these channels we find that P f/P d approximately 5. In contrast, for the wider nystatin and amphotericin B pores, P f/P d approximately 3. These findings offer experimental support for the view that P f/P d = N for single-file transport, and we therefore conclude that there are approximately five water molecules in a gramicidin A channel. A similar conclusion was reached independently from streaming potential data. Using single-channel conductance data, we calculate the water permeability of an individual gramicidin A channel. In the Appendix we report that there is a wide range of channel sizes and lifetimes in cholesterol-containing membranes.

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Water Permeability of Gramicidin A-Treated
Lipid Bilayer Membranes
PAUL A. ROSENBERG and ALAN FINKELSTEIN
From the Departments of Physiology, Neuroscience, and Biophysics, Albert Einstein College
of Medicine, Bronx, New York 10461
A B S x R A C X In membranes containing aqueous pores (channels), the osmotic
water permeability coefficient, Ps, is greater than the diffusive water permeability
coefficient, Pa. In fact, the magnitude of Ps/Pa is commonly used to determine
pore radius. Although, for membranes studied to date, Pt/Pa monotonically
declines with decreasing pore radius, there is controversy over the value it
theoretically assumes when that radius is so small that water molecules cannot
overtake one another within the channel (single-file transport). In one view it
should equal 1, and in another view it should equal N, the number of water
molecules in the pore. Gramicidin A forms, in lipid bilayer membranes, narrow
aqueous channels through which single-file transport may occur. For these
channels we find that Ps/Pa ~ 5. In contrast, for the wider nystatin and amphoter-
icin B pores, Ps/Pa ~ 3. These findings offer experimental support for the view
that Ps/Pa = N for single-file transport, and we therefore conclude that there are
approximately five water molecules in a gramicidin A channel. A similar conclusion
was reached independently from streaming potential data. Using single-channel
conductance data, we calculate the water permeability of an individual gramicidin
A channel. In the Appendix we report that there is a wide range of channel sizes
and lifetimes in cholesterol-containing membranes.
INTRODUCTION
The relation between the water permeability of cell membranes as measured,
on the one hand, by tracer diffusion experiments (Pa) and, on the other hand,
by osmotic or hydrodynamic experiments (Ps) has interested physiologists for
over 40 years (Hevesy et al., 1935). It is generally recognized that Ps/Pa -- 1, if
water crosses the membrane by a solubility diffusion mechanism through a
water-poor region such as a lipid bilayer (see Cass, 1968), whereas Ps/Pa > 1 if
water moves through aqueous pores (Mauro, 1957). The inequality arises from
the difference between laminar (or quasi-laminar) flow through a pore, which
occurs when a hydrostatic or osmotic pressure difference exists, and simple
diffusion, which takes place when isotopic water (e.g., THO) exchanges with
unlabeled water (Mauro, 1957). From the magnitude of Pt/Pa, the "equivalent
pore radius" of aqueous channels in biological membranes is calculated (Solo-
mon, 1968).
For macroscopic systems, hydrodynamic theory establishes that Ps/Pa declines
as pore radius decreases. Robbins and Mauro (1960) extended this formulation
J. GEN. PHYSIOL. y The Rockefeller University Press i 0022-1295/78/0901-034151.00 341

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342
THE JOURNAL OF GENERAL PHYSIOLOGY'VOLUME 72" 1978
to pores with radii of tens of angstroms. For nystatin and amphotericin B pores,
whose estimated radii are 4 ~, PflPa ~ 3 (Holz and Finkelstein, 1970). PflPa
therefore appears to approach 1 as the pore radius approaches that of the
solvent molecule. This intuitive feeling was apparently given a theoretical basis
in the analyses by Longuet-Higgins and Austin (1966) 1 and by Manning (1975) of
diffusion and osmosis for single-file transport; i.e., diffusion and osmosis
through pores so narrow that solvent molecules cannot pass one another within
the pore. Implicit, however, in the analyses of Hodgkin and Keynes (1955), Lea
(1963), and Heckmann (1972), and explicit in the analyses of Dick (1966), and
Levitt (1974), is that Pt/Pd is not equal to 1 for single file transport but equal to
N, the number of water molecules in the channel.
The gramicidin A channel offers an opportunity to determine experimentally
PflPa in a very narrow pore. Its permeability to water but not to urea
(Finkelstein, 1974) along with molecular model building (Urry, 1972) suggest
that the radius of the channel is about 2 ]k and that transport occurs via a single-
file process. In this paper we show that Ps/Pa ~ 5 for gramicidin-treated
membranes, and from comparison with the electrokinetic results in the preced-
ing paper (Rosenberg and Finkelstein, 1978) we argue that 5 is approximately
the number of water molecules in the pore. We discuss the interesting implica-
tions of this result for water transport through biological channels, particularly
those induced by antidiuretic hormone (ADH) in toad urinary bladder and
mammalian collecting tubles.
MATERIALS AND METHODS
Strategy
There are two major problems in measuring water permeability of gramicidin A
channels: (a) the significant water permeabilities of unmodified bilayers; and (b) the very
low resistances at which gramicidin-induced water permeability becomes significant.
(a) If the water permeability of the unmodified bilayer is too great, it is very difficult to
measure gramicidin A-induced Pa, because unstirred layer corrections are so large that
impossible accuracies are required for meaningful data. To minimize this problem, we
initially chose a high cholesterol-containing membrane-forming solution (lecithin: choles-
terol molar ratio of 1:4), because cholesterol greatly reduces bilayer water permeability
(Finkelstein and Cass, 1967). After completing a series of experiments, we were
chagrined to discover an enormous spread in single channel sizes and lifetimes with
membranes formed from this mixture. 2 Because this obscured any interpretation of the
results, we turned instead to cholesterol-free bacterial phosphatidylethanolamine (PE),
whose membranes yield classical single-channel behavior in the presence of gramicidin
A. The resultant water permeability, although considerably larger than that of the
lecithin-cholesterol membranes, is still low enough that Pd measurements on gramicidin-
treated membranes are feasible. Unstirred layer corrections were maximally a factor of
2, which was acceptable, inasmuch as they could be determined simultaneously with Pa
(see "Tactics").
(b) When membrane resistances are small relative to the access resistance (the resistance
This paper is frequently cited as implying that PflPd = 1. It is not clear to us, however, that this is
a correct implication.
z This phenomenon, occurring in cholesterol-rich bilayers, is described in the Appendix.

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ROSENBERG AND FINKELSTEIN Water Permeability in Gramicidin Channels
343
measured in the absence of a membrane), they cannot be evaluated accurately, because
their determination involves subtraction of two nearly identical numbers; under inaus-
picious circumstances, for example, a 10% error in the total resistance can result in a
fivefold error in membrane resistance. We minimized this problem by our choice of salt
solution--0.01 M NaC1 plus 0.1 M choline chloride. The 0.1 M choline chloride reduced
the access resistance by about a factor of 10 from that in 0.01 M NaCI alone, without
altering channel resistance, in that choline is an impermeant of the gramicidin channel,3
and thus we could easily determine membrane resistance with reasonable accuracy.
(Access resistance was 1200 fl; the lowest measured resistance was 1700 1~, thus giving a
membrane resistance of 500 fl.)
Tactics
All membranes described in the body of this report were formed from bacterial
phosphatidylethanolamine (2.5% PE in 2,2,4,6,6-pentamethylheptane). The aqueous
solutions bathing the membrane were 0.01 M NaCI + 0.1 M choline chloride + 10 -4 M
EDTA (pH 7). The gramicidin A used in most experiments was a sample obtained from
the late Dr. Lyman Craig; similar results were obtained with gramicidin purchased from
ICN Pharmaceuticals, Inc. (Irvine, Calif.), a mixture of 72% A, 9% B, and 19% C
(Glickson et al., 1972). Bacterial PE was obtained from Supelco, Inc. (Bellafonte, Pa.);
2,2,4,6,6-pentamethylheptane was from Analabs, Inc. (North Haven, Conn.).
TRACER EXPERIMENTS (Pd)
Membranes were formed at room temperature (23 ~ +-
2 ~ C) by the brush technique (Mueller et al., 1963) across a 0.78 mm 2 circular hole in a
Teflon partition (125/xm thick) separating two lucite compartments each containing 3 ml
of solution. After the membrane formed, gramicidin was added (from stock methanol or
ethanol solutions) to one or both compartments to a final concentration of from 0.2 to 1
/zg/ml. In some instances the membrane was formed in the presence of gramicidin in the
aqueous solutions. When conductance became stable, THO was added to one compart-
ment and its flux, dO*, measured as described previously (Holz and Finkeistein, 1970).
(Sometimes dO* was first measured for an unmodified membrane, gramicidin A then
added, and dO* again determined.) The observed permeability coefficient, (Pn)obs, was
calculated from the equation:
dO* = -- (Pa)obsAAc*,
(1)
where A is the membrane area and Ac* is the difference in concentration of isotope in
the two compartments; it was corrected for unstirred layers as described previously (Holz
and Finkelstein, 1970). The unstirred layer thickness was found, using [14C]butanol (Hotz
and Finkelstein, 1970), to be 100/~m; in some experiments THO and [14C]butanol fluxes
were determined simultaneously. Both compartments were stirred continuously with
magnetic fleas.
Resistance (R = AV/A1) was measured using two pairs of Ag/AgCI electrodes, one pair
to apply a current step, AI, and the other to record the resulting initial 4 potential
difference, AV. The recording electrodes were connected to a high input impedance
amplifier, and its output was displayed on an oscilloscope face. The membrane
3 Gramicidin-treated membranes separating 0.1 M choline chloride solutions had a conductance of
about 7% that occurring in 0.01 M NaCI. This conductance was produced by a contaminant (possibly
NH~') in the choline.
4 At the high conductances of most experiments, the response to a step of current was an initial
jump of voltage followed by a further rise with time to some steady-state value. This further rise was
a polarization voltage resulting from the accumulation of NaCI at one interface and its depletion
from the other. The initial jump measures the membrane (plus access) resistance.

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344 THE JOURNAL OF GENERAL PHYSIOLOGY i VOLUME 72 i 1978
resistance, Rm, was found by subtracting the access resistance from the measured
resistance. The membrane conductance, Gin, is by definition 1/Rm.
THO (5 mCi/ml) and [1-14C]n-butanol (3.7 mCi/mmol) were obtained from New
England Nuclear (Boston, Mass.)
OSMOTIC EXPERIMENTS The net flow of water produced by a concentration
difference of solute (urea) was measured as described by Holz and Finkelstein (1970); the
present arrangement, however, contained two pairs of Ag/AgCI electrodes (one for
stimulating and the other for recording). Membrane area was 1.27 ram2; electrical
resistance was monitored continually as described for the tracer experiments.
Membranes were formed at 23 ~ -+ 2~ After they were completely black, stirring of
the solution in the outer chamber began, and gramicidin was added from stock solutions
to a final concentration of from 0.05 to 0.15 t~g/ml. When the membrane resistance
attained a constant value, a small volume of 8 M urea (in the same salt solution already
present) was added to the outer chamber to a concentration of between 0.43 to 1.64
osmolality, and the movement of water was recorded as described previously (Holz and
Finkelstein, 1970). The osmotic permeability coefficient, Ps, was calculated from the
equation:
c~w = P~Ar
(2)
where el) w is the flux of water (in moles per unit time) across a membrane of area A in the
presence of a concentration difference, Ac,, of impermeant solute (urea); 9 is the osmotic
coefficient of urea (~0.93), obtained from the Handbook of Chemistry and Physics, 57th
Edition.
RESULTS
Pt and Pa each increase linearly with conductance (Fig. 1), and the increase is
attributed to water permeation through gramicidin channels (see below). The
slopes calculated from Fig. 1 give the proportionality of gramicidin-induced
water permeability to gramicidin-induced conductance (ion permeability). From
them we see that P~/Pd = 5.3 for gramicidin channels3
DISCUSSION
Water and Ions Share a Common Pathway through Gramicidin-Treated
Membranes
The analysis of the data in this paper rests on the assumption that increased
water permeability after membranes are treated with gramicidin results from
water flux through the ion-permeable gramicidin channels. Several lines of
evidence strongly support this assumption:
(a) Water permeability is a linear function of conductance; this is predicted if
water and ions share a common pathway.
(b) If gramicidin-induced water permeability occurred through the bilayer
5 The osmotic experiments were performed under open-circuited conditions. In such circumstances
the osmotic flow of water is opposed by an electroosmotic backflow induced by the streaming
potential. It is easily shown from the data in this and the preceding paper (Rosenberg and
Finkelstein, 1978), however, that this effect is small in the present case (0.01 M NaCI), so that there
is no significant difference in the values of Pr obtained under open-circuited and short-circuited
conditions. What this means is that there is little coupling between ion and water flow; this is to be
expected in 0.01 M NaCI, because at any instant most channels have no ion in them.

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ROSENBERG AND FINKELSTEIN Water Permeability in Gramicidin Channels
345
proper (e.g., if gramicidin acted as a detergent and increased membrane
fluidity), it should be accompanied by a proportional increase in nonelectro-
lyte permeability (Finkelstein, 1976). We found, however, that neither n-
butyramide nor urea permeability is significantly increased by gramicidin
action.
(c) If gramicidin-induced water permeability were through the bilayer proper,
then Pf/Pa should equal 1. Inasmuch as Pf/Pa is much greater than 1 (~5),
this provides strong evidence that the gramicidin-induced water permeability
occurs through pores.
(d) The electrokinetic phenomena described in the preceeding paper (Rosen-
berg and Finkelstein, 1978) directly demonstrate that ions and water share a
common pathway through gramicidin-treated membranes.
50
45
40
55
3O
E 25
o
a.
20
0 I
15 ~
Pf
i //0
0 I 2345
I ,o
102G I~'l/crn z}
do
FIGURE 1. (@) PI and (O)Pa of gramicidin-treated membranes as a function of
membrane conductance. Note that for the unmodified membrane (G ~ 0), Ps =
Pa. The slopes of the Ps and Pa lines are 34.2 x 10 -a and 6.5 x 20 -3 cm s-~/l~ -~
cm -2, respectively.
In summary, these considerations strongly suggest that gramicidin-induced
water transport occurs through the ion-permeable gramicidin channels.
P~/Pafor Narrow Pores
The theoretical expectation for the value of PI/Pa in single-file transport is
controversial: in one view it equals 1 (Manning, 1975), and in the other it equals
N, the number of water molecules in the channel (Dick, 1966; Levitt, 1974). In
our opinion, the latter view is correct, and we find Levitt's argument particularly
convincing. But it is not our purpose to undertake a critique of the theoretical
arguments. Our contribution is an experimental one, insofar as experiments
can contribute to theory (which is a doubtful propositon).