LETTERS TO THE EDITOR

A Comment on the Water Permeability through Planar Lipid Bilayers Dear Sir: In a recent article, Finkelstein (1976) has shown that the m e a s u r e d water permeability t h r o u g h a lecithin-decane planar bilayer m e m b r a n e is similar to the calculated permeability t h r o u g h a sheet o f n - h e x a d e c a n e 50 ,~ thick. T h a t is, the m e a s u r e d water permeability, Pa, was f o u n d equal to DKhc/AX, where D is the diffusion constant o f water in water, Khe is the w a t e r m - h e x a d e c a n e partition coefficient, and AX is the thickness o f the h y d r o c a r b o n " m e m b r a n e . " We suggest that t h e r e are a n u m b e r o f internal factors in the above calculation that may c o m p e n s a t e for one a n o t h e r so as to give a g r e e m e n t with e x p e r i m e n t . At the heart o f the problem is the question: can the interior o f the bilayer be treated as an isotropic, three-dimensional liquid? T h e r e is m o u n t i n g evidence that it cannot (White, 1976; Evans and Simon, 1975). In his calculations, Finkelstein has used the diffusion constant o f water and nonelectrolytes in water as a model for the diffusion constant o f these molecules in the m e m b r a n e interior. As the diffusion constant is inversely p r o p o r t i o n a l to the viscosity, f r o m the Stokes-Einstein equation one would p r e s u m e the bilayer interior to be about lcP. T h e viscosities o f water and n - h e x a d e c a n e at 20°C are 1.002 and 3.34 cP, respectively ( H a n d b o o k o f Chemistry and Physics, 55th edition), whereas the microviscosity o f lipid bilayers and plasma m e m b r a n e s , as d e t e r m i n e d by fluorescent probes (Azzi, 1975) and spin labels (Edidin, 1974), is the o r d e r o f m a g n i t u d e o f 1P. In particular, V a n d e r k o o i a n d Callis (1974) have f o u n d that at 20°C egg lecithin bilayers have a microviscosity o f 57.2 cP. T h u s if the permeability t h r o u g h a h e x a d e c a n e " m e m b r a n e " and a planar lipid bilayer are the same, and the viscosity o f the bilayer is two orders o f m a g n i t u d e h i g h e r than that o f n - h e x a d e c a n e , then the diffusion constant o f water in a bilayer should be about two o r d e r s o f m a g n i t u d e lower in a bilayer than n-hexadecane. Should this be the case, then either the partition coefficient for water in planar lipid bilayers is m u c h h i g h e r than for n - h e x a d e c a n e , or the presence o f the h y d r o c a r b o n solvent, n-decane, in the m e m b r a n e r e d u c e d the viscosity o f the bilayer. We suggest that both these effects may be important. I f the m e m b r a n e thickness is 50 ,~ and the diffusion constant is r e d u c e d by, at most, a factor o f 100, then the partition coefficient o f water in the bilayer must be 100 times greater than that o f an organic liquid to maintain the same permeability. This factor may be accounted for in a n u m b e r o f ways. First, the partition coefficient between the bilayer interior and water for molecules with either a net THE JOURNAL

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charge or a p e r m a n e n t dipole m o m e n t d e p e n d s directly on the e n e r g y barrier for transfer o f a molecule ingoing f r o m water (dielectric constant = 80) to the bilayer interior (dielectric constant -~2). This e n e r g y b a r r i e r is lower for the t r a n s f e r into the bilayer than the p e a k B o r n e n e r g y o f t r a n s f e r into bulk h y d r o c a r b o n . Consequently, we expect the partition coefficient to be higher. T h e reasons for the lower e n e r g y b a r r i e r has been discussed in the literature (Parsegian, 1969; H a y d o n a n d Hladky, 1972; A n d e r s e n a n d Fuchs, 1975). A reduction in the b a r r i e r height o f 2.8 kcal could account for the o b s e r v e d c h a n g e . Second, the presence o f double bonds could contribute to the larger partition coefficient o f water in e g g lecithin than n-hexadecane. T h e i r presence in bilayers has been shown to increase water permeability a n d , in organic liquids, water solubility (DeGier et al., 1968; G r a h a m and Lea, 1972; H i l d e b r a n d a n d Scott, 1964). Finally, we would like to point out that t h e r e is a significant d i f f e r e n c e in activation e n e r g y for water p e r m e a t i o n t h r o u g h egg lecithin vesicles ~LEa = 8.258.6 kcal/mol, (Cohen, 1975) a n d n - h e x a d e c a n e ~ = 11-12 kcal/mol ( H a y d o n , 1969), implying that t h e r e may be differences between vesicles, p l a n a r bilayers with organic solvents, a n d organic liquids r e g a r d i n g water permeability. The author cheerfully acknowledges many stimulating conversations with Dr. E. Evans. This work is supported by National Institutes of Health Grant HL-12157 and Office of Naval Research contract N00014-67-0251-0022. S. A. SIMON Department of Physiology and Anesthesiology Duke University Medical Center Durham, North Carolina 27710 Received for publication 6 December 1976. REFERENCES

ANDERSEN, O. S., and M. Fucns. 1975. Potential energy barriers to ion transport within lipid bilayers. Biophys. J. 15:795-830. Azzl, A. t975. The application of fluorescent probes in membrane studies. Q. Rev. Biophys. 8:237-316. CoHeN, B. E. 1975. The permeability of liposomes to nonelectrolytes. I. Activation energies for permeation. J. Membr. Biol. 20:205-234. DEGIER, J., ]. G. MANDERSLOOT,and L. L. M. VAN DrENrN. 1968. Lipid composition and permeability of iiposomes. Biochim. Biophys. Acta. 150:666-675. Er)II)IN, M. 1974. Transport at the cellular level. Syrup. Soc. Exp. Biol. 28:1-14. EVANS, E. A., and S. SIMON. 1975. Mechanics of electrocompression of lipid bilayer membranes. Biophys. J. 15:850-852. FtNKELSTEXN, A. 1976. Water and nonelectrolyte permeability of lipid bilayer membranes. J. Gen. Physiol. 68:127-135. GRAHAM, D. E., and E. J. A. LEA. 1972. The effect of surface charge on the water permeability of phospholipid bilayers. Biochim. Biophys. Acta. 274:286-293. HAVDON, D. A. 1969. Some recent developments in the study of bimolecular lipid films. In The Molecular Basis of Membrane Function. D. C. Tosteson, editor. Prentice-Hall, Inc., Englewood Cliffs, N . J . 111-131.

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HAYDON, D. A., and S. B. HLADKY.1972. Ion transport across thin membranes: a critical discussion of mechanism in selected systems. Q. Rev. Biophys. 5:187-282. HILDEBRAND,J. H., and R. L. SCOTT. 1964. The solubility of nonelectrolytes. Dover Publications, Inc., New York. 266. PARSEGIAN,A. 1969. Energy of an ion crossing a low dielectric membranes: solutions to four relevant electrostatic problems. Nature (Lond.). 221:884-846. WHITE, S. H. 1976. The lipid bilayer as a "solvent" for small hydrophobic molecules. Nature (Lond. ). 262:421-422. VANDERKOOI,J. M., and J. B. CALLIS. 1974. Pyrene: a probe of lateral diffusion in the hydrophobic region of membranes. Biochemistry. 13:4000-4006.

RepLy to A Comment on the Water Permeability through Planar Lipid Bilayers Dear Sir: Simon (1977) notes f r o m a recent p a p e r o f mine (Finkelstein, 1976) that insofar as water permeability is c o n c e r n e d , an egg lecithin bilayer is equivalent to a 50-,~ thick sheet o f bulk h y d r o c a r b o n , a This he finds disturbing. Specifically, Simon points out that the microviscosity o f egg lecithin bilayers, as m e a s u r e d by fluorescent probes, is considerably h i g h e r than that o f bulk h y d r o c a r b o n (hexadecane), a n d he t h e r e f o r e feels that the diffusion constant o f H 2 0 in the bilayer interior should be c o r r e s p o n d i n g l y r e d u c e d . T h e a g r e e m e n t between Pa, the water permeability o f an e g g lecithin bilayer m e m b r a n e , a n d DKhc/AX is thus in Simon's view, f o r t u i t o u s - t h e result o f the c o m p e n s a t i o n o f "a n u m b e r o f internal factors", z Simon considers several possible c o m p e n s a t i n g factors. R a t h e r than taking these up, however, I wish to draw attention to what, I feel, is a fallacy in his basic premise. Namely, I believe, that the so-called microviscosity o f bilayers as m e a s u r e d by fluorescent probes (e.g., pyrene) is not relevant to the viscosity perceived by the m u c h smaller water molecule as it traverses the bilayer. I n d e e d , the diffusion constant o f o x y g e n in lecithin m e m b r a n e s is a b o u t two o r d e r s o f m a g n i t u d e larger than that o f p y r e n e (Fischkoff a n d V a n d e r k o o i , 1975. T h u s , the diffusion constant o f H 2 0 in a bilayer o f viscosity -~50 cP need not be substantially less than the diffusion constant o f H~O in water. We see this clearly in Table 1. Note that a l t h o u g h n - h e x a d e c a n e is three times m o r e viscous than water, the diffusion constant o f H 2 0 in h e x a d e c a n e is actually larger than in water. Even m o r e pertinent to this discussion are the data on i No particular point was made of this in the paper as it is an old observation (Hanai and Haydon, 1966; Finkelstein and Cass, 1968). Khe is the hexadecane:water partition coefficient of H20, D is the diffusion constant of HzO in water, and AX is the membrane thickness.

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TABLE DIFFUSION

CONSTANT

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70 • 1977

I

(Dn,o) O F W A T E R I N D I F F E R E N T

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Water n-Hexadecane Perhydrosqualene

Vi.~cosity

Da~o

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o n 2 5-1

1.0 3.3 37

2.4 4.2 1.7

Viscosity is at 20°C; Dit2o is at 25°C. T h e viscosity of water and n-hexadecane are from the Hafidbook of Chemistry and Physics, 57th edition; the viscosity of perhydrosqualene (squalane) is from the Merck Index, 8th edition. Da,o in water is from Wang (1953); DH,o in n-hexadecane and perhydrosqualene (squalane) is from Schatzberg (1965).

p e r h y d r o s q u a l e n e (popularly known as 2,6,10,15,19,23-hexamethyltetracosane). Although its viscosity is 37 cP (which is c o m p a r a b l e to the 57 cP value obtained by V a n d e r k o o i and Callis (1974) for the microviscosity o f egg lecithin bilayers), DH2o in p e r h y d r o s q u a l e n e is virtually equal to that in water. I think that the explanation for these data is that an H 2 0 molecule sees methyl groups as it diffuses t h r o u g h h y d r o c a r b o n , and their"viscosity" is not a strong function o f h y d r o c a r b o n chain length and structure. (A fluorescent probe, on the o t h e r h a n d , sees m u c h m o r e o f the h y d r o c a r b o n molecule, and t h e r e f o r e senses a viscosity more comparable to macroscopic viscosity m e a s u r e m e n t s . I n d e e d , these probes are calibrated against bulk h y d r o c a r b o n viscosity values.) Regardless o f the explanation for the data, it is clear f r o m them that it is not unreasonable to assume that Dmo in the interior o f a lecithin bilayer is comparable to Dmo in water, despite the obvious intricacy and subtlety o f the bilayer's structure. ALAN FINKELSTEIN

Department of Physiology Albert Einstein College of Medicine Bronx, New York 10461 Received for publication 1 March 1977, REFERENCES

FINKELSTE1N, A. 1976. Water and nonelectrolyte permeability of lipid bilayer membranes. J. Gen. Physiol. 68:127-135. FINKELSTEIN, A., and A. CASS. 1968. Permeability and electrical properties of thin lipid membranes. ]. Gen. Physiol. 52:145s-172s. FISCHKOFt, S., and J. M. VANDERKOO1. 1975. Oxygen diffusion in biological and artificial membranes determined by the fluorochrome pyrene. J. Gen. Physiol. 65:663676. HANAI, T., and D. A. HAVDON. 1966. The permeability to water of bimolecular lipid membranes. J. Theor. Biol. 11:370-382. SCHATZBERG, P. 1965. Diffusion of water through hydrocarbon iiquids. J. Polym. Sci. 10 (Pt. C):87-92.

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S. A. 1977. A comment on the water permeability through planar lipid bilayers.J.

Gen. Physiol. 70:123-125. VANDERKOOI,J. M., and J. B. CALLIS. 1974. Pyrene: a probe of lateral diffusion in the hydrophobic region of membranes. Biochemistry. 13:4000-4006. WANG, J. H., C. V. ROBINSON, and I. S. EDELMAN. 1953. Self-diffusion and structure of liquid water. III. Measurement of the self-diffusion of liquid water with H 2, H 3, and O is as tracers. J. Am. Chem. Soc. 75:466-470.

A comment on the water permeability through planar lipid bilayers.

LETTERS TO THE EDITOR A Comment on the Water Permeability through Planar Lipid Bilayers Dear Sir: In a recent article, Finkelstein (1976) has shown t...
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