Water Movement through Membrane Channels

Water Movement through Membrane Channels

CURRENT TOPICS IN MEMBRANES A N D 'TRANSPORT. VOLUME ?I Water Movement through Membrane Channels ALAN FINKELSTEIN Departments of Physiology and Bioph...

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CURRENT TOPICS IN MEMBRANES A N D 'TRANSPORT. VOLUME ?I

Water Movement through Membrane Channels ALAN FINKELSTEIN Departments of Physiology and Biophysics nnd of Neuroscience Albert Einstein College of Medicine Bronx, N e w York

.................................

296

...................................

298

I.

11.

A.

Unmodified Membrane.. ,

111. IV. Summary . . . . . . . . .

..........

The movement of ions and water across plasma membranes has been of interest to physiologists for over 100 years. It is now clear that most, if not all, ionic conductance associated with these membranes is attributable to channels, that is, to high dielectric constant, hydrophilic regions spanning the low dielectric constant, hydrophobic bilayers of cell membranes. Presumably these same channels are also permeable to water, although at present there are no data bearing directly on this point. Ion-conducting channels also occur in artificial lipid bilayer membranes; indeed, the first studies of single-channel behavior were made on channels in these model membranes (Ehrenstein et af., 1970; Hladky and Haydon, 1972). For two of these channels, those formed by gramicidin A and the polyene antibiotics nystatin and amphotericin B , water permeabilities have also been determined (Rosenberg and Finkelstein, 1978b; Holz and Finkelstein, 1970), providing the only direct data on water transport through "biological-like'' channels. In addition, water permeabilities of unmodified lipid bilayers are known. This article is a review of the findings from water permeability studies on both unmodified and channel-modified planar 295 Copyright B 1984 by Academic Press, Inc All nghts of reproduction in any form reserved

ISBN 012-153321-2

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ALAN FINKELSTEIN

lipid bilayers, with particular emphasis on the latter, and a discussion of their implications for water transport across plasma membranes. The interesting topic of water-ion interaction within channels is also touched upon in the course of the discussion; a more extensive treatment is given in the article by Levitt in this volume. I. WATER PERMEABILlTY COE FFlClENTS

Before considering water permeability studies on lipid bilayer membranes, let us recall some general definitions and interpretations of water permeability coefficients. On any membrane, two different water permeability measurements can be made, each giving rise to a different water permeability coefficient. In one, a difference in concentration, Ac,, of an impermeant solute is placed across the membrane, causing an osmotic flow of water, @, (expressed as moles per unit time). The relation between @, and Acs is expressed through the osmotic, or filtration, water permeability coefficient ( P I )by the equation @,

=

P f A Ac,

(1)

where A is the membrane area. [In principle, Pf can be obtained by applying a hydrostatic pressure difference (AP),instead of an osmotic pressure difference (AT = RT Acs; where R is the gas constant and T is absolute temperature), across the membrane; that is why the osmotic permeability coefficient is also called the filtration permeability coefficient. In practice, water flow is almost always experimentally generated across lipid bilayers and cell membranes by osmotic pressure differences.] In the other type of measurement, a difference in concentration, Ac*, of isotopic water is placed across the membrane, giving rising to an isotopic flux, @*. The diffusional water permeability coefficient Pd expresses the proportionality between @* and Ac* through the equation @* = -PdA Ac*

(2)

If water transport across a membrane occurs through channels, the corresponding equations are Qw = t ~ p lAc, Q * = -I

Ac*

Z ~ J

(la) (221)

where n is the number of channels in the membrane, and pl and pd are the

WATER MOVEMENT THROUGH MEMBRANE CHANNELS

297

water permeability coefficients p r r d w m i d . These single-channel permeability coefficients, having dimensions of cubic centimeters per second, are related to the corresponding macroscopic permeability coefficients, having dimensions of centinieters per sccond. by the identities p, =

rj,~i~~

(3a)

Pd = PcjA/n

(3b) From the ratio of Pf to P d , interferences can be drawn about the physical nature of the water transpart pathway. If the membrane consists of an organic phase in which water is poorly soluble, then both bulk and isotopic water movement occur by a solubility-diffusion mechanism, and it can easily be shown that PflPd = 1 (Cass, 1968). On the other hand, if water transport is through channels, then, in general, PflPd > 1 , and the larger the channel radius, the larger thc ratio. This is because osmotic water transport occurs by laminar, or quasi-laminar flow (Mauro, 1957). whereas isotopic water transport is diffusional in nature. In fact, insofar as macroscopic hydrodynamic equations are still applicable at the molecular level, which is (surprisingly) often the case (Einstein, 1905: Finkelstein and Rosenberg, 19791, channel radii can be calculated from the value of P,.lPCl(Pappenheimer, 1953; Solomon, 1968). The exceptions to the dependence of PfIP,I on channel radius are those channels which are s o narrow that water molecules cannot pass one another: that is, single-file transport occurs. In those cases, P,/P,I = N , where N is the number of water molecules in single-file array (Levitt, 1974).This surprising result is a consequence of the unusual nature of the diffusion process (which determines P d ) ,in which a water molecule can traverse the channel only if all of the other water molecules ahead of it do so first (Finkelstein and Rosenberg, 1979). In summary, PflPd

=

1

solubility-diffusion trtinsport through hydrophobic phase

transport through channels of radius R > RHZO

single-file transport, where N = number of water molecules in single-file array.

(4a)

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ALAN FINKELSTEIN

II.

WATER PERMEABILITY OF PLANAR LIPID BI LAYER MEMBRANES

A. Unmodified Membrane

Molecules, including water, cross lipid bilayer membranes by a solubility-diffusion mechanism, and consequently, PfIPC1= 1 (Finkelstein and Cass, 1968). Of greater interest are the actual values of Pr (or P d )in these membranes. Depending on temperature, cholesterol content, chain length, and degree of saturation of fatty acid chains, water permeability coefficients span a 500-fold range from 2 X lop5 (Finkelstein, 1976a) to 1 x cmhecond (Huang and Thompson, 1966). These values encompass almost the entire range of values reported for plasma membranes, a point to which we shall return in our discussion of water movement across cell membranes. In the determinations of water permeability coefficients for nystatin and amphotericin B channels and for gramicidin A channels, discussed in the following sections, the background permeability of the membrane is always subtracted from the measured values. B. Modified Membranes 1. NYSTATIN A N D AMPHOTERICIN B

Nystatin and amphotericin B, which are polyene antibiotics (the former a tetraene, the latter a heptaene), have almost identical chemical structures (Fig. 1); their effects on lipid bilayer membranes are so similar that for purposes of this discussion I shall generally not distinguish between them. Membranes treated with these polyenes “sieve” nonelectrolytes; permeability coefficients decrease with increasing molecular radius for molecules up to the size of glucose (radius = 4 A),above which they are zero (Holz and Finkelstein, 1970). This fact, combined with molecular model building, leads to the belief that nystatin and amphotericin B form transmembrane channels of about 4 A in radius, with the polar interior of the channel lined by hydroxyl groups (Fig. 2) (Finkelstein and Holz, 1973; deKruijff and Demel, 1974). In fact, it appears that these polyenes can form either “single-length’’ or “double-length” channels, the latter being twice the length of the former (see legend to Fig. 21, and that because of flexibility in bilayer structure and thickness, both of these channels can completely span the bilayer (Marty and Finkelstein, 1975). Recent experiments have shown that the ratio of urea permeability to glycerol permeability is the same for single- and double-length channels, thus con-

299

WATER MOVEMENT THROUGH MEMBRANE CHANNELS OH

0

OH

OH

OH

OH

0

HOOC

0

OH

0

OH

OH

OH

OH

0

OH Arnphotericin B

FIG. I . The structural formulas of nystatin and amphotericin B. (After Medoff and Kobayashi, 1980.)

firming that they have essentially the same radius (Kleinberg and Finkelstein, 1984). As expected for water transport through a channel, PI > P d ; in fact (Holz and Finkelstein, 19701, P I I P ~= 3

(nysttitin and amphotericin B channel)

(5)

The calculated single-channel permeability coefficients for urea are 23 X 10-16 and 3.6 x cm3/second for single- and double-length nystatin channels, respectively (Kleinberg and Finkelstein, 1984).' Since Pfis 42 times greater than Pd (urea) for nystatin channels (Holz and Finkelstein, I Nonelectrolyte and water permeability determinations are, by necessity, made on membranes containing many channels (- lo9channels/cm2),as water flow or isotope flux through fewer channels is experimentally unmeasurable. On the other hand, because of the exquisite sensitivity of electrical measurements, conductances of individual channels are measured on membranes containing one or a few channels. Single-channel permeability coefficients to water and nonelectrolytes are calculated by dividing the measured permeability coefficients by the number of channels in the membrane. The latter is computed by dividing the membrane conductance by the single-channel conductance. on the assumption that the singlechannel conductance in membranes containing lo9 channelskm? is the same as that in a membrane containing one or a few channels. Electrostatic interactions among neighboring channels in close proximity may modify single-channel conductances and hence cause errors in the estimations of the number of channels in the membrane. This, in turn, will cause errors in the calculations of single-chbnnel permeability coefficients. This caveat pertains to all single-channel permeability coefficients discussed in this article.

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ALAN FINKELSTEIN

300

4 \

4

FIG.2. Diagram of a single-length nystatin or amphotericin B channel. Each nystatin (or amphotericin B) molecule is schematized as a plane with a protuberance and a solid dot. The shaded portion of each plane represents the hydroxyl face of the hydroxyl-containing chain, the protuberance represents the amino sugar, and the solid dot represents the single hydroxyl group at the nonpolar end of the molecule. The interior of the pore is polar. whereas the exterior is completely nonpolar. Note that the ring of hydroxyl groups at the top of the figure can hydrogen bond in the middle of the membrane with an identical structure from the other side to form a double-length channel. (From Finkelstein and Holz, 1973.)

1970), we calculate that pf is 9.7 x and 1.5 x cm3/second for single- and double-length nystatin channels, respectively.

2. GRAMKIDINA This pentadecapeptide (Fig. 3) is believed to form channels that are about 2 A in radius. This belief is based both upon molecular model building (Urry, 1972) and upon observations that gramicidin A-treated membranes are permeable to water but not to urea or other small nonelectrolytes (Rosenberg and Finkelstein, 1978b). For the gramicidin A channel (Rosenberg and Finkelstein, 1978b) P f / P d= 5

(gramicidin A channel)

(6)

301

WATER MOVEMENT THROUGH MEMBRANE CHANNELS

CHO

-

L-Val - G l v - L-Alo - 0-Leu

L-Alo - 0-Val - L-Val

L-Trp

-

D-Leu

-

-

D-Val

- L-Trp - D-Leu

L-Trp - D-Leu - L-Trp

-

NHCH2CH20H

FIG. 3. Structure of valine-gramicidin A. Each horizontal row of amino acids corresponds to approximately one helical turn of Urry’s &-helical model (Urry, 1972). The two diagonal lines represent peptide bonds connecting the three helical turns. (After Finkelstein and Andersen, 1981.)

In such a narrow channel, single-file transport of ions and water must occur. The number of water molecules N in single-file array can be determined either from the ratio of PFto P,’ [Eq. (4c)l or from streaming potential measurements. [For the theory behind the latter method for determining N, see Levitt ct d., (1978). Levitt (this volume), or Finkelstein and Rosenberg (1979).] Streaming potential measurements yield values of about 6-7 (Rosenberg and Finkelstein, 1978a) or 8-9 (Dani and Levitt, 1981b) for N . The reasonablc agreement between these values for Nand that determined from P~IP,I[ Eq. ( 6 ) ] provides additional cvidence for single-file transport through the gramicidin A channel. The osmotic water permeability coefficient ( p r ) for this channel has been calculated to be - I x cm3/second by Finkelstein and Rosenberg (1979) and -6 x cm7/secondby Dani and Levitt (1981a). (For a possible cause of the sixfold difference in values, see Footnote I . ) I t is noteworthy that the rate of movement for an ion such as Nat from one end of the channel to the other is the same as that for a water molecule (Finkelstein and Andersen, 1981; Dani and Levitt, 1981b). Both require the movement of N water molecules in single-file array; the equality of the two rates means that the movement of these N water molecules is the major barrier to ion transport. In other words, ion-wall interactions and electrostatic energy barriers are minor impediments to ion movement through the channel. There is an additional barrier, however, for ion transport at the end of the channel (the exit step), and this makes the transport rate of ions across the entire channel (as opposed to the transport rate from end to end) less than that for water. This raises the interesting possibility that the water permeability of a gramicidin A channel could be salt dependent; that is, the water permeability of a channel occupied by an ion could be considerably less than that of an unoccupied one (Finkelstein and Rosenberg, 1979). In essence the ion can block the channel to water flow. Dani and Levitt (1981b) report such an effect with Lit, K’,

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ALAN FINKELSTEIN

and TI+, but Finkelstein (reported in Finkelstein and Andersen, 1981) saw no such effect with Na+. 3. COMPARISON OF NYSTATIN A N D AMPHOTERICIN B CHANNELS WITH GRAMICIDIN A CHANNELS It is instructive to compare the water permeability of the 4-A-radius nystatin and amphotericin B channels with that of the 2-A-radius gramicidin A channel, particularly since these are the only channels in lipid bilayer membranes, or plasma membranes, for which more or less complete information is available. Table I summarizes the results presented in the previous section, along with additional relevant information about these channels. I wish to draw the readers' attention to three points in that table: first, although the radius of the gramicidin A channel is smaller, by a factor of 2, than that of the nystatin and amphotericin B channels, the ratio of Pf to P,! for the gramicidin A channel ( - 5 ) is larger than that for the polyene channels (-3). This is contrary to the general trend for PflPd to decline with decreasing radius [Eq. (4b)], but is not unexpected given the unique nature of the diffusional process in single-file transport, as reflected in Eq. (4c). Second, the values of pr (the osmotic permeability coefficients per channel) differ by up to only an order of magnitude with those calculated from a naive application of Poiseuille's law to these channels of molecular dimension. As noted previously (Finkelstein and Rosenberg, 1979), macroscopic hydrodynamic equations, derived from a continuum theory of fluids, have a way of retaining validity at the molecular level. Third, the conductance of the 2-A-radius gramicidin A channel is COMPARISON

OF

TABLE I GHAMlClDlN A A N D NYSTATIN CHANNELS pr (crn'/second)

Radius

Length

(A)

Conductance in 100 mM

Poiseuille's

KCI ( S )

PSlP,,

Experimental ( x i 0 14)

in

5.3 (3)

1-6 ( 3 . 4 )

3

2.5 x lo-" (2)

-

9.7 (2)

50

in

3.3 (4)

1.5 (2)

25

Channel

(A)

Grarnicidin A Nystatin (single length) Nystatin (double length)

2

25-30

4

21-25

4

42-48

1.3 x

11

(1)"

13

(2)

law ( X I O 14)

~~

References: (I) Hladky and Haydon (1972); (2) Kleinberg and Finkelctein (1984); (3) Rwenberg and Finkelstein (l978b); (4) Dani and Levitt (1981a).

WATER MOVEMENT THROUGH MEMBRANE CHANNELS

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almost 100-fold greater than that of the 4-A-radius nystatin channel. Although this article is not directly concerned with ion permeation through channels, 1 feel it is appropriate to point out with this example that it is very risky to infer, as is often done, channel radius from channel conductance. It is obvious that charges associated with a channel can have enormous effects on ion permeability; it is particularly striking in the present examples, however, that a large anomalous conductance difference arises between channels lacking any charge groups. 111.

WATER PERMEABILITY OF PLASMA MEMBRANES

As remarked at the beginning of this article, ion transport through channels in plasma membranes is now well established, and undoubtedly water also passes through these same channels. In this section we will consider the significance of this pathway for water transport, as opposed to diffusion through the bilayer proper of plasma membranes. Because of the large variety of cells and channel types, and the limited data on water permeability through channels, it is not reasonable to expect a single, allembracing answer. What I hope to provide, however, is a general outlook and point of view that is useful in analyzing specific examples. It might be thought that an excellent criterion for the importance of channel pathways in water transport is the value of PtIP,; in particular, values significantly greater than I would clearly indicate that channels were a major contributor to water movement. Unfortunately, with the exception of erythrocyte data, unstirred layer problems cause the values of Pdto be so underestimated that the large values commonly reported for PflPd cannot be attributed to channels in the plasma membrane (Dainty, 1963). We must therefore invoke other arguments in deciding this tissue. The reported range of permeability values for plasma membranes2 extends over four orders of magnitude-from 1 X cmlsecond for Fundulirs eggs (Dunham et a/., 1970) to 2 x cmlsecond for erythrocml cytes (Side1 and Solomon, 1957); most values fall around 2 x second. As was noted in an earlier section, the water permeability coefficients determined for various unmodified lipid bilayers cover most of this range (from 2 x to I x lo-* cmIsecond), so that the magnitude of the water permeabilities of most cell membranes can be accounted for simply I shall not deal with the large water permeability coefficients of “leaky” epithelia, in which the major pathway for water transport may be intercellular (Levitt, 1981). Later in this section, however, 1 consider the large values of PI induced by antidiuretic hormone in the luminal plasma membranes of “tight” epithelia such as toad urinary bladder.

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ALAN FINKELSTEIN

from the properties of the bilayer backbone of the plasma membrane. The very low water permeabilities of plasma membranes such as that of Fundulus eggs presumably result from lipid bilayer compositions with even lower H2O partition and diffusion coefficients than those so far studied in the planar bilayer model membranes. It is worth noting at this point that from a physiological standpoint, most cells do not need or require high water permeabilities, and therefore one does not expect their plasma membranes to have evolved special channels for water t r a n ~ p o r t[Eggs .~ which develop in tidal pools, where osmolarity can vary over wide ranges, must be protected from the vicissitudes of tonicity changes. This they have apparently accomplished both by evolving a bilayer composition and structure that is very impermeant (perhaps because of a high phase transition temperature), and by having a small surface-to-volume ratio (i.e., by being large).] Thus, if a large fraction of the water movement across a cell membrane occurs through channels, this must be incidental to other functions of those channels (e.g., ion permeability) and is not their primary purpose. With this in mind, let us see how things stand with most cells. We may assume that the water permeability of plasma membrane channels will not be significantly greater (and probably in general will be less) than that of single-length nystatin channels. (I base this on the assumption that the ion-selective regions of plasma membrane channels are probably considerably narrower than the 4-A-radius nystatin channel, although these regions may be somewhat shorter than 25 A in length.) Therefore, to cm/second, a value around which most cell account for a Pfof 2 x membrane permeability coefficients lie, there must be approximately loio of these channels ( p f= cm3/second)per cm2 (-lo2 channels/pm2). Single-channel conductances for many channel types in a variety of cells have been measured, and their values tend to be around lo-” S (see, for example, other articles in this volume). On the other hand, the conductances of most cell membranes fall around S/cm2; in other words, they have about lo8 ion-conducting channels/cm2. The Pf attributable to these channels is therefore cm/second, or only about 1% that of the actual value for the cell. In short, there are too few ion-conducting channels in most cell membranes to uct as a sign$cant pathway for water movement; by implication, most of a membrane’s water permeability is attributable to its bilayer structure. The interested reader can apply the above general arguments to his favorite cell, if Pfand single-channel data are available. An exception is the luminal plasma membranes of “tight” epithelia, which are considered later in this section.

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An interesting exception to the above considerations is the erythrocyte membrane. The magnitude of P f ( - 2 x 10-I cm/second) (Side1 and Solomon, 1957), the nonunity value of P f l P d (-3) (Paganelli and Solomon, 1957), and the effects of chemical modifications of the cell membrane on water permeability (Macey and Farmer, 1970) provide convincing evidence that a significant fraction of the water movement into and out of the cell occurs through channels. Yet, the conductance of the erythrocyte membrane is very low,
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1979). [The channels responsible for the large water permeability of the erythrocyte membrane, presumably the chloride-bicarbonate “carriers,” also have a very small ion conductance (Hunter, 1977).] This is another illustration of my earlier remark that for a channel of a given radius there is an enormous latitude in its possible ion permeability. IV. SUMMARY

The only direct data on water transport through “biological-like” channels come from studies on the channels formed in planar lipid bilayer membranes by gramicidin A and the polyene antibiotics nystatin and amphotericin B. These data were reviewed along with water permeability measurements on unmodified lipid bilayer membranes. From the water permeability coefficients for single nystatin or gramicidin A channels, one can estimate the number of channels required in plasma membranes to account for their water permeability. The general conclusion is that there are too few channels in most plasma membranes to represent a significant pathway for water movement, and therefore, by implication, the major route for water transport across most plasma membranes is through their lipid bilayers. Two exceptions are noted: the erythrocyte membrane and the luminal membranes of certain “tight” epithelia. It appears that a major pathway for water permeation across the erythrocyte membrane is through the anion “carrier” protein. This water transport is incidental to the main function of the “carrier.” Indeed, it is pointed out that most cells do not require high water permeabilities, and therefore one does not expect to find in their plasma membranes channels specifically devoted to water movement. An exception are the luminal membranes of such “tight” epithelia as toad urinary bladder and cortical collecting tubule. The ADH-induced water permeability of these membranes is through specific channels that are permeable to water and very little else. Since the water permeability of these membranes is of great physiologic concern to the organism, it is not surprising to find channels in them especially devoted to water transport. ACKNOWLEDGMENT This work was supported by NIH Grant GM 29210-06. REFERENCES Brahm, J . (1982). Diffusional water permeability of human erythrocytes and their ghosts. J . Gen. Physiol. 79, 791-819.

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Cass, A. (1968). Water and ion permeability of thin lipid membranes. Doctoral Thesis, pp. 119-121. Rockefeller University, New York. Dainty, J. (1963). Water relations of plant cells. Adu. Bot. Res. I, 279-326. Dani, J. A., and Levitt, D. G . (1981a). Binding constants for Li’. K + , and TI’ in the gramicidin channel determined from water permeability measurements. Biophys. J . 35, 485-500. Dani, J . A., and Levitt, D. G . (198lb). Water transport and ion-water interaction in the gramicidin channel. Biophys. J . 35, 501-508. deKruijff, B . , and Dernel, R. A. (1974). Polyene antibiotic-sterol interactions in membranes of Acholeplusmu laidlawii cells and lecithin liposomes. Ill. Molecular structure of the polyene antibiotic cholesterol complexes. Biochim. Bioplrys. Acrci 339, 57-70. Dunham, P. B.. Cass, A., Trinkaus, J . P., and Bennett, M. V. L. (1970). Water permeability of Fi~nditluseggs. B i d . Bull. ( Woods Hole, Muss. ) 139, 420-421. Ehrenstein, G . , Lecar, H., and Nossal, R. (1970). The nature of the negative resistance in bimolecular lipid membranes containing excitability-inducing material. J . Gerr. Physiol. 55, 119-133. Einstein. A. (1905). On the movement of small particles suspended in a stationary liquid demanded by the molecular-kinetic theory of heat. [Translated from Atin. Phys. ( L e i p z i r ) [4] 17,549-560.1 In “Investigations on the Theory of the Brownian Movement by Albert Einstein” (R. Furth, ed.; transl. by A. D. Cowper), pp. 1-18. Dover, New York, 1956. Finkelstein, A. (1976a). Water and nonelectrolyte permeability of lipid bilayer membranes. J . Gen. Physiol. 68, 127-135. Finkelstein, A. (1976b). Nature of the water permeability increase induced by antidiuretic hormone (ADH) in toad urinary bladder and related tissues. J . Gen. Physiol. 68, 137143. Finkelstein, A., and Andersen, 0. S. (1981). The gramicidin A channel: A review of its permeability characteristics with special reference to the single-file aspects of transport. J . Membr. Biol. 59, 155-171. Finkelstein, A,. and Cass, A. (1968). Permeability and electrical properties of thin lipid membranes. J . Gen. Physiol. 52, 145s-172s. Finkelstein, A., and Holz, R. (19731. Aqueous pores created in thin lipid membranes by the polyene antibiotics nystatin and amphotericin B . I n “Membranes 2. Lipid Bilayers and Antibiotics” ( G . Eisenman, ed.), pp. 377-408. Dekker, New York. Finkelstein, A., and Rosenberg, P. A. (1979). Single-file transport: Implications for ion and water movement through gramicidin A channels. Membr. Trunsp. Proc,es.ses 3, 73-88. Hladky, S. B., and Haydon, D. A . (1972). Ion transfer across lipid membranes in the presence of gramicidin A. 1. Studies on the unit conductance channel. Biochim. Biophys. Acta 274, 294-3 12. Holz, R., and Finkelstein, A. (1970). The water and nonelectrolyte permeability induced in thin lipid membranes by the polyene antibiotics nystatin and amphotericin B. J . Gen. Physiol. 56, 125-145. Huang, C.. and Thompson, T. E. (1966). Properties of lipid bilayer membranes separating two aqueous phases: Water permeability. J . Mol. Biol. 15, 539-554. Hunter, M. J . (1977). Human erythrocyte anion permeabilities measured under conditions of net charge transfer. J . Physiol. (London) 268, 35-49. Jones, M . N., and Nickson, J. K. (1981). Monosaccharide transport proteins of the human erythrocyte membrane. Biochim. Biophvs. Actu 650, 1-20. Kleinberg, M. E., and Finkelstein, A. (1984). Single-length and double-length channels formed by nystatin in lipid bilayer membranes. J . Memhr. B i d . (in press).

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Knauf, P. A. (1979). Erythrocyte anion exchange and the band 3 protein: Transport kinetics and molecular structure. Curr. Top. Mefnbr. Trump. 12, 249-363. Levitt, D. G. (1974). A new theory of transport for cell membrane pores. I. General theory and application to red cell. Biochim. Biophys. Acta 373, 115-131. Levitt, D. G. (1981). Routes of membrane water transport: Comparative physiology. Alfred Benzon Symp. 15, 248-257. Levitt, D. G . , Elias, S. R., and Hautman, J. M. (1978). Number of water molecules coupled to the transport of Na’, K’, and H+ via gramicidin, nonactin, or valinomycin. Biochim. Biophys. Acta 512, 436-451. Macey, R. I., and Farmer, R. E. L. (1970). Inhibition of water and solute permeability in human red cells. Biochim. Biophys. Actu 211, 104-106. Marty, A., and Finkelstein, A. (1975). Pores formed in lipid bilayer membranes by nystatin. Differences in its one-sided and two-sided action. J . Gen. Physiol. 65, 515-526. Mauro, A. (1957). Nature of solvent transfer in osmosis. Science 126, 252-253. Medoff, G., and Kobayashi, G. A. (1980). The polyenes. In “Antifungal Chemotherapy” (D. C . E. Speller, ed.), pp. 3-33. Wiley, New York. Paganelli, C. V., and Solomon, A. K. (1957). The rate of exchange of tritiated water across the human red cell membrane. J . Gen. Physiol. 41, 259-277. Pappenheimer, J. R. (1953). Passage of molecules through capillary walls. Physiol. Rev. 33, 387-423. Rosenberg, P. A., and Finkelstein, A. (1978a). Interaction of ions and water in gramicidin A channels. Streaming potentials across lipid bilayer membranes. J . Gen. Physiol. 72, 327-340. Rosenberg, P. A , , and Finkelstein, A. (1978b). Water permeability of gramicidin A-treated lipid bilayer membranes. J . Gen. Physiol. 72, 341-350. Sha’afi, R. I., and Feinstein, M. B. (1977). Membrane water channels and SH-groups. Adu. Exp. Med. Biol. 84, 67-83. Sidel, V. W., and Solomon, A. K. (1957). Entrance of water into human red cells under an osmotic pressure gradient. J . Gen. Physiol. 41, 243-257. Solomon, A. K. (1968). Characterization of biological membranes by equivalent pores. J . Gen. Physiol. 51, 335s-364s. Solomon, A. K., Chasan, B., Dix, J. A . , Lukacovic, M. F., Toon, M. R., and Verkman, A. S. (1983). The aqueous pore in the red cell membrane: Band 3 as a channel for anions, cations, nonelectrolytes and water. Ann. N . Y . Acad. Sci. 414, 97-124. Urry, D. W. (1972). Protein conformation in biomembranes: Optical rotation and absorption of membrane suspensions. Biochim. Biophys. Acta 265, 115-168.