Water Permeability of Gramicidin A-Treated Lipid Bilayer Membranes P A U L A. R O S E N B E R G and A L A N F I N K E L S T E I N From the Departments of Physiology,Neuroscience, and Biophysics, Albert Einstein College of Medicine, Bronx, New York 10461
A B S x R AC 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 amphotericin 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
T h e relation between the water permeability o f cell m e m b r a n e s as m e a s u r e d , o n the one h a n d , by tracer diffusion experiments (Pa) and, on the o t h e r h a n d , by osmotic or h y d r o d y n a m i c e x p e r i m e n t s (Ps) has interested physiologists for over 40 years (Hevesy et al., 1935). It is generally recognized that Ps/Pa -- 1, if water crosses the m e m b r a n e by a solubility diffusion mechanism t h r o u g h a w a t e r - p o o r region such as a lipid bilayer (see Cass, 1968), whereas Ps/Pa > 1 if water moves t h r o u g h aqueous pores (Mauro, 1957). T h e inequality arises f r o m the difference between laminar (or quasi-laminar) flow t h r o u g h a pore, which occurs when a hydrostatic or osmotic pressure difference exists, a n d simple diffusion, which takes place when isotopic water (e.g., T H O ) exchanges with unlabeled water (Mauro, 1957). F r o m the m a g n i t u d e o f Pt/Pa, the "equivalent pore radius" o f a q u e o u s channels in biological m e m b r a n e s is calculated (Solom o n , 1968). For macroscopic systems, h y d r o d y n a m i c theory establishes that Ps/Pa declines as pore radius decreases. Robbins and M a u r o (1960) e x t e n d e d this f o r m u l a t i o n J. GEN. PHYSIOL. 9 T h e Rockefeller University Press 9 0022-1295/78/0901-034151.00
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to pores with radii o f tens o f a n g s t r o m s . For nystatin a n d a m p h o t e r i c i n B pores, whose estimated radii are 4 ~ , PflPa ~ 3 (Holz a n d Finkelstein, 1970). PflPa t h e r e f o r e a p p e a r s to a p p r o a c h 1 as the p o r e radius a p p r o a c h e s that o f the solvent molecule. T h i s intuitive feeling was a p p a r e n t l y given a theoretical basis in the analyses by L o n g u e t - H i g g i n s a n d Austin (1966) 1 and by M a n n i n g (1975) o f diffusion a n d osmosis for single-file t r a n s p o r t ; i.e., diffusion a n d osmosis t h r o u g h pores so n a r r o w that solvent molecules c a n n o t pass o n e a n o t h e r within the p o r e . Implicit, however, in the analyses o f H o d g k i n a n d Keynes (1955), Lea (1963), and H e c k m a n n (1972), a n d explicit in the analyses o f Dick (1966), a n d Levitt (1974), is that Pt/Pd is not equal to 1 for single file t r a n s p o r t but equal to N, the n u m b e r o f water molecules in the channel. T h e gramicidin A channel offers an o p p o r t u n i t y to d e t e r m i n e e x p e r i m e n t a l l y PflPa in a very n a r r o w p o r e . Its permeability to water but not to u r e a (Finkelstein, 1974) a l o n g with m o l e c u l a r m o d e l building (Urry, 1972) suggest that the radius o f the channel is a b o u t 2 ]k a n d that t r a n s p o r t occurs via a singlefile process. In this p a p e r we show that Ps/Pa ~ 5 for g r a m i c i d i n - t r e a t e d m e m b r a n e s , a n d f r o m c o m p a r i s o n with the electrokinetic results in the preceding p a p e r ( R o s e n b e r g a n d Finkelstein, 1978) we a r g u e that 5 is a p p r o x i m a t e l y the n u m b e r o f water molecules in the p o r e . We discuss the interesting implications o f this result for water t r a n s p o r t t h r o u g h biological channels, particularly those induced by antidiuretic h o r m o n e (ADH) in toad u r i n a r y b l a d d e r a n d m a m m a l i a n 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: cholesterol 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 gramicidintreated 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 T h i s p a p e r is f r e q u e n t l y cited as i m p l y i n g t ha t PflPd = 1. It is not clear to us, however, that this is a correct implication. z T h i s p h e n o m e n o n , o c c u r r i n g in cholesterol-rich bilayers, is de s c ri be d in the A p p e n d i x .
ROSENBERGANDFINKELSTEIN Water Permeability in Gramicidin Channels
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measured in the absence of a membrane), they cannot be evaluated accurately, because their determination involves subtraction of two nearly identical numbers; u n d e r inauspicious circumstances, for example, a 10% error in the total resistance can result in a fivefold error in m e m b r a n e resistance. We minimized this problem by our choice of salt solution--0.01 M NaC1 plus 0.1 M choline chloride. T h e 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 i m p e r m e a n t of the gramicidin channel,3 and thus we could easily determine m e m b r a n e resistance with reasonable accuracy. (Access resistance was 1200 fl; the lowest measured resistance was 1700 1~, thus giving a m e m b r a n e 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). T h e aqueous solutions bathing the m e m b r a n e were 0.01 M NaCI + 0.1 M choline chloride + 10-4 M EDTA (pH 7). T h e 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 m m 2 circular hole in a Teflon partition (125/xm thick) separating two lucite compartments each containing 3 ml of solution. After the m e m b r a n e 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. I n some instances the m e m b r a n e was formed in the presence of gramicidin in the aqueous solutions. When conductance became stable, T H O was added to one compartment and its flux, dO*, measured as described previously (Holz and Finkeistein, 1970). (Sometimes dO* was first measured for an unmodified m e m b r a n e , gramicidin A then added, and dO* again determined.) T h e observed permeability coefficient, (Pn)obs, was calculated from the equation: dO* = -- (Pa)obsAAc*,
(1)
where A is the m e m b r a n e 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). T h e unstirred layer thickness was found, using [14C]butanol (Hotz and Finkelstein, 1970), to be 100/~m; in some experiments T H O and [14C]butanol fluxes were determined simultaneously. Both compartments were stirred continuously with magnetic fleas. Resistance (R = A V / A 1 ) was measured using two pairs of Ag/AgCI electrodes, one pair to apply a c u r r e n t step, AI, and the other to record the resulting initial 4 potential difference, AV. T h e recording electrodes were connected to a high input impedance amplifier, and its output was displayed on an oscilloscope face. The m e m b r a n e 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 initialjump measures the membrane (plus access) resistance.
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resistance, Rm, was found by subtracting the access resistance from the measured resistance. The m e m b r a n e conductance, Gin, is by definition 1/Rm. T H O (5 mCi/ml) and [1-14C]n-butanol (3.7 mCi/mmol) were obtained from New England Nuclear (Boston, Mass.) OSMOTIC EXPERIMENTS T h e net flow of water produced by a concentration difference of solute (urea) was measured as described by Holz and Finkelstein (1970); the present a r r a n g e m e n t , 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 m e m b r a n e 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). T h e 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 m e m b r a n e of area A in the presence of a concentration difference, Ac,, of i m p e r m e a n t solute (urea); 9 is the osmotic coefficient of urea (~0.93), obtained from the Handbook of Chemistry and Physics, 57th Edition. RESULTS
Pt a n d Pa e a c h i n c r e a s e l i n e a r l y with c o n d u c t a n c e (Fig. 1), a n d the i n c r e a s e is a t t r i b u t e d to w a t e r p e r m e a t i o n t h r o u g h g r a m i c i d i n c h a n n e l s (see below). T h e slopes c a l c u l a t e d f r o m Fig. 1 give t h e p r o p o r t i o n a l i t y o f g r a m i c i d i n - i n d u c e d w a t e r p e r m e a b i l i t y to g r a m i c i d i n - i n d u c e d c o n d u c t a n c e (ion p e r m e a b i l i t y ) . F r o m t h e m we see t h a t P~/Pd = 5.3 for g r a m i c i d i n c h a n n e l s 3 DISCUSSION
Water and Ions Share a Common Pathway through Gramicidin-Treated Membranes T h e analysis o f t h e d a t a i n this p a p e r rests o n t h e a s s u m p t i o n t h a t i n c r e a s e d w a t e r p e r m e a b i l i t y a f t e r m e m b r a n e s a r e t r e a t e d with g r a m i c i d i n r e s u l t s f r o m w a t e r f l u x t h r o u g h t h e i o n - p e r m e a b l e g r a m i c i d i n c h a n n e l s . Several lines o f e v i d e n c e s t r o n g l y s u p p o r t this a s s u m p t i o n : (a) W a t e r p e r m e a b i l i t y is a l i n e a r f u n c t i o n o f c o n d u c t a n c e ; this is p r e d i c t e d if w a t e r a n d ions s h a r e a c o m m o n p a t h w a y . (b) I f g r a m i c i d i n - i n d u c e d w a t e r p e r m e a b i l i t y o c c u r r e d t h r o u g h t h e b i l a y e r 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.
ROSENBERGA N D FINKELSTEIN WaterPermeabilityin GramicidinChannels
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p r o p e r (e.g., if gramicidin acted as a d e t e r g e n t and increased m e m b r a n e fluidity), it should be accompanied by a p r o p o r t i o n a l increase in nonelectrolyte permeability (Finkelstein, 1976). We f o u n d , however, that neither nb u t y r a m i d e n o r u r e a permeability is significantly increased by gramicidin action. (c) I f gramicidin-induced water permeability were t h r o u g h the bilayer p r o p e r , then Pf/Pa should equal 1. I n a s m u c h as Pf/Pa is much greater than 1 (~5), this provides strong evidence that the gramicidin-induced water permeability occurs t h r o u g h pores. (d) T h e electrokinetic p h e n o m e n a described in the p r e c e e d i n g p a p e r (Rosenb e r g and Finkelstein, 1978) directly d e m o n s t r a t e that ions and water share a c o m m o n pathway t h r o u g h gramicidin-treated m e m b r a n e s . 50
45 40
55 3O
9
~
Pf
/
/
0
E 25
o
a.
20 0
I
15
0 I 2345
I
,o
do
102G I~'l/crn z}
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 s u m m a r y , these considerations strongly suggest that gramicidin-induced water transport occurs t h r o u g h the ion-permeable gramicidin channels.
P~/Pafor Narrow Pores T h e theoretical expectation for the value o f PI/Pa in single-file t r a n s p o r t is controversial: in o n e view it equals 1 (Manning, 1975), a n d in the o t h e r it equals N , the n u m b e r o f water molecules in the channel (Dick, 1966; Levitt, 1974). In o u r opinion, the latter view is correct, and we find Levitt's a r g u m e n t particularly convincing. But it is not o u r p u r p o s e to u n d e r t a k e a critique o f the theoretical a r g u m e n t s . O u r contribution is an e x p e r i m e n t a l one, insofar as e x p e r i m e n t s can contribute to t h e o r y (which is a d o u b t f u l propositon).
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Clearly, PflPa * I for the gramicidin channel. By itself this result is not particularly significant. One might argue that single-file transport does not occur through the gramicidin channel, and therefore, as expected for an aqueous channel, Ps/Pa * 1. The result takes on added significance, however, when compared to that obtained for nystatin and amphotericin B channels. For these channels, with radii --~42~,PflPa ~- 3 (Holz and Finkelstein, 1970), whereas for the small gramicidin channel, with a radius -