PARTI. MECHANISM OF ACTION IN MEMBRANES
OF
CARRIERS AND CHANNELS
FUNCTIONS OF THE LIPID IN BILAYER ION PERMEABILITY D. A. Haydon Physiological Laboratory University of Cambridge Cambridge, England
INTRODUCTION The extensive studies over the past few years of the mechanisms of ion transport across artificial lipid membranes have revealed a great deal both about the ionophores themselves and about the properties which the lipid membranes must have in order that the ionophores should function efficiently. For a carrier molecule, for example, it is of little value that it may have a high ion selectivity if it will not combine with the membrane or, if it does combine, it will not move or bind ions in the membrane. For pore-forming molecules, binding to different membranes may be very similar, but the efficiency of the transport process may depend critically on the state of ionization of the lipid or on the membrane thickness. In this introductory paper it is proposed to review the various properties of lipid membranes which we now know to have special relevance to ion transport by polypeptides and other small macromolecules, and to illustrate the discussion with detailed descriptions of selected topics. It is thus hoped to emphasize the considerable range of factors which contribute to the success or otherwise of attempts to incorporate biological membrane components in artificial lipid bilayers. Since most of the findings described in this paper are for “black” lipid membranes, i.e., those formed using a hydrocarbon solvent, it is perhaps pertinent to summarize at the outset current knowledge of the interrelationship between these membranes and those of the lamellar phase of lecithin and the planar solventless membranes studied by Montal and Mueller.’, ’ As seen in TABLE 1, the thickness, as deduced from x-ray data, of the hydrocarbon region of a leaflet of the fully hydrated lamellar phase is not significantly different from the thickness deduced from the specific capacitance of a planar
THICKNESSES OF
TABLE 1 ARTIFICIAL LIPIDBILAYERSFORMED FROM EGG LECITHIN
System
Specific Capacitance (rF/cma)
Lecithin-hexadecane (black film)* Lecithin (no so1vent)t Lecithin (liquid crystal)$
0.603 -0.76 -
* From Fettiplace et ul.’ t From Fettiplace‘ and Fettiplace et d.
$ From Lecuyer et af.,6 Reiss-Husson,’ and Small.’
2
Hydrocarbon Region Thickness (A) 31 ( ~ ~ 2 . 1 4 ) -25 ( E = 2.14) -26 (x-ray)
Haydon:
Lipid Function in Bilayer Ion Permeability
3
solventless membrane, assuming a dielectric constant of 2.14. Although the data of Fettiplace'. ' cannot be claimed as definitive, the close agreement of the two thicknesses helps greatly to establish the validity of using a bulk dielectric constant for aliphatic hydrocarbon in the interpretation of the capacitance data. The somewhat smaller capacitance and larger thickness of the lecithin-hexadecane black film can be attributed to the retention of some solvent, although just how much is difficult to say. It may be that a small amount of solvent has a large effect on the capacitance (and hence on the thickness) or it may be that the area per molecule given previously3 is about 10% too low. The above check on the validity of membrane thicknesses calculated from specific capacitances places on a firmer basis the earlier findings that black films formed from shorter chain alkanes such as decane are indeed of greater thickness than the solventless structures, and that this is because they retain considerable amounts of ~ o l v e n t . ~lo~ The various roles that the lipid may play in bilayer ion permeability may be conveniently considered under the broad headings of (1) combination of the ionophore with the membrane and (2) functioning of the ionophore in the membrane. Under ( l ) , the potential relevance of studies such as those of GulikKrzywicki et al." concerning the combination of proteins with phospholipid liposomes is obvious, although the importance of the sign of the charged groups, which was brought out in this work, has not so far seemed of comparable importance for the known ion transporting molecules. It may turn out to be generally unimportant owing, perhaps, to the necessarily lipophilic character of an ionophore and also to the screening of any ionic groups in the relatively high electrolyte concentrations often employed. The nature of the nonpolar part of the membrane is, by contrast, known to have a considerable influence on the uptake of certain ionophores. The necessity for cholesterol in the case of the polyenes (e.g., nystatin and amphotericin B)", and the adverse effects of cholesterol on the uptake of valinomycin" are well documented. The state of the hydrocarbon region of the bilayer, i.e., liquid or solid, might also be expected to influence the binding of ionophores. The experiments of Krasne et aZ.15 are of special interest in this respect. Cooling the bilayer to the point where it appeared solid rather than liquid eliminated conduction by nonactin but not by gramicidin A. Obviously the solidification of the membrane did not cause the desorption of the gramicidin, but whether the nonactin conduction ceased because it could no longer diffuse across the hydrocarbon region or whether it ceased because it was simply not taken up by the membrane is not clear." The result for gramicidin prompts the question of whether or not the polypeptide induces conduction when placed in the presence of an already solidified membrane. If it does not, it has to be concluded that the freezing of the membrane may trap pore-forming molecules, at least for long periods, in a functioning but nonequilibrium state. The binding of an ionophore by a membrane is clearly a necessary, but not sufficient condition for ion transport. Conditions in the membrane may well prevent the ionophore from functioning as efficiently or normally as in a biological system. Thus, under heading (2), factors such as membrane fluidity, surface potential, membrane thickness and specific lipid-polypeptide interactions are known to be important. The significance of membrane fluidity
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Annals New York Academy of Sciences
for the functioning of carriers is obvious; the surface potential affects the uptake of ions by the ionophores in the membrane and this in turn determines selectivity between ions of different valence and sign; membrane thickness can greatly influence the conduction efficiency of an assembly of pore-forming molecules; and specific interactions may completely change the response of a pore-forming molecule to applied potential, The effects of membrane fluidity have been well described in a number of place^.^'^ '' Ways in which the other factors may operate are illustrated in the remainder of this paper.
SURFACE POTENTIAL The relationship of the ion permeability of a lipid membrane to the change in the electrostatic potential across its surface has been discussed by several la-= In earlier work, only the diffuse and Stern layer potentials were considered, but it is now recognized that the potential change arising from the oriented dipoles of the polar head groups may be of similar or even greater " This is clear for carrier transport from the fact that either the ion or the ion-carrier complex must pass through all of the potential changes due to the presence of the polar groups (FIGURE1). For the classical pore where, as far as the permeating ions are concerned, the lipid polar groups are considered to be shunted, the position is less obvious. 3' '
aqueous
double layer
hydrocarbon
dipoles
FIGURE1. A simple representation of the variation of electrostatic potential across a lipid bilayer. The lipids are assumed to be negatively charged while the oriented dipoles of the polar groups are taken to be positive inwards.
Haydon:
Lipid Function in Bilayer Ion Permeability
5
The Debye-Huckel reciprocal length parameter is likely to be sufficiently large that diffuse layer potentials will affect the ion concentrations over the entrance to a pore. However, the range of influence of the lipid polar group dipoles is much less, and the permeating ions could be unaffected by their presence. While the importance of the surface potential (or, at least, the diffuse layer part of it) for the functioning of biological membranes has long been appreciated, attempts at quantitative tests of the hypothesis have been made only recently, and these so far only with artificial membranes. If consideration is restricted to carrier systems, elementary theory suggests that for constant electrolyte concentration, carrier concentration in the membrane and mobility of ion-carrier complex, the membrane conductance G(0) in the limit of zero applied potential is given byl6
where z is the valence of the ion and lUris the total potential difference between the aqueous phase and the interior of the membrane, as indicated in FIGURE 1. 41/w may be split into the ionic double layer (4i)and dipole (4d) contributions. Thus
4lh
=
4,
+4d
(2)
It has been amply demonstrated that changes in G(0) for a given ion-carrier system may be accurately accounted for in terms of the changes in qh / w measured for monolayers of the appropriate lipids at air or hydrocarbon/water interfaces.24 Moreover, in certain systems, when q5d is assumed constant and specific adsorption of ions is minimal, + i appears to be given fairly accurately by the Gouy-Chapman theory.21. Within the above theoretical framework it is thus possible to understand variations in the conductance for a given ion, and the selectivity of the bilayer as between cations and anions, in terms of the average surface dipole moment and degree of ionization of the membrane lipids. Surface or compensation potentials, AVl I w , for some lipids and lipid mixtures 2. These values are not equal to $J~ / w but are the changes which are shown in TABLE occur in c # J ~ / , ~when the lipid monolayer is spread on a clean aqueous solution surface.26 Therefore AVi / w = 41/ w - 4 a / w (3) where is numerically equal to the so-called X-potential of water (or of the appropriate aqueous solution). Differences in AVl /w, all other factors being equal, should therefore reflect the relative intrinsic permeabilities of different lipid membranes to cations and anions, iz.,the permeabilities that would be found if the cation and the anion were identical except for the sign of their charge. That this is accurately so for the permeability of egg phosphatidyl choline and monoolein bilayers to K+-nonactin has been shown. Thus, the difference in AVl1,"for the two lipids is -120 mV, whereas the difference in the conductance corresponds to -115 mV.2K(It should be noted, however, that the introduction of cholesterol destroys this agreement, presumably owing either to its tendency to reduce the solubility of the nonactin in the membrane or to its effect on the fluidity, and hence on the mobility of the ion-carrier complex.) For the phosphatidyl serine and phosphatidyl inositol given in TABLE 2, the ionic double layer potentials are likely to be in the region of -12.5 mV. The dipole potentials for all the phospholipids, and the cholesterol, shown 2 are therefore very similar and, apart from the relatively small in TABLE
6
Annals New York Academy of Sciences TABLE 2 SURFACE POTENTIALS OF LIPIDMONOLAYERS AT AREASPER SIMILAR TO THOSE IN T H E &LAYER
MOLECULE
Lipid ~~~
~
Phosphatidyl choline (egg) Phosphatidyl ethanolamine(egg) Phosphatidyl serine Phosphatidyl inositol Cholesterol Phosphatidyl choline + cholesterol (-3: 1) Glyceryl monooleate Monooleyl glyceryl ether
441t 420$ 320$
300$ 390 5 420t 321t 411t
* The sign of the potential is for the air (or hydrocarbon) relative to the aqueous phase. t Substrate 0.1 M NaC1, pH 6.
-
$ From Papahadjopo~los.~~ Substrate 0.145 M NaCl, pH 6.
0 From Adam
Substrate 0.02 M HCI.
ionic double layer potentials, the intrinsic relative permeabilities of the corresponding bilayers should also be very similar. The absolute magnitude of these relative permeabilities to cations and anions may be estimated. The direct approach is simply to measure the membrane conductance in the presence of equal concentrations of permeating, oppositely charged, but otherwise identical ions. This has been attempted using lecithin-cholesterol membranes with tetraphenyl boride and tetraphenylphosphonium ions." The specific conductance for the negative boride was some 10'-fold larger than for the positive tetraphenylphosphonium ion, from which may ba calculated to be 115 mV. or the X-potential of An alternative method is based on a knowledge of water. The most recent and probably best estimate of this is 40 k 100 mV.z*Bearing in mind that a different sign convention is used for present purposes, and taking AV1.,,( as 420 mV, 4l for lecithin: cholesterol (-3 :1 mole ratio) may be calculated from Equation 3 to be between 280 and 480 mV. This result reinforces the idea that the lipid bilayer has a strong intrinsic selectivity for anions over cations. The quantitative discrepancy between the two estimates of / w given above is not surprising, but also is not readily explicable. Despite first appearances, there may be significant differences between tetraphenyl boride and tetraphenylphosphonium ions or their interactions with the bilayer which invalidate their use for present purposes. On the other hand, estimates of the X-potential for water have, in the past, been so widely varied that complete confidence in the most recent result may not be fully justified. In addition to affecting the conductance and the selectivity, the dipole potential of either the natural lipids, or a change in this quantity produced by the adsorption of dipolar molecules, may act in much the same way as an ionic double layer potential in changing the polarization or depolarization required to stimulate conduction in a voltage-dependent system such as a 2. Provided the effect is asymnerve axon. This point is illustrated in FIGURE metrical, both an increased negative ionic double layer potential, or an increased negative dipole potential tend to increase the field in the membrane and, although the resting potential is not changed, a larger than normal depolarization could be needed to produce an action potential. N
Haydon:
Lipid Function in Bilayer Ion Permeability
7
(0
FIGURE2. An illustration of the way in which surface potentials might influence the stimulation of an action potential in a nerve axon. (a) A normal axon having a resting potential of -63 mV which is stimulated by depolarization to -43 mV. A small negative surface charge density is assumed to be present on the inner surface of the membrane. (b) The resting potential is the same but ion adsorption on the inner surface is assumed to increase the negative charge. In order to restore the field in the membrane to that which produced stimulation in the normal axon, a larger depolarization is now required. (c) This is analogous to (b) except that the field in the membrane is assumed to be enhanced in the resting state by the adsorption of dipolar molecules on the inside. MEMBRANETHICKNESS The thickness of artificial membranes increases with the chain length of the lipid', and, in the case of black films, tends to vary inversely with the chain length of the solvent.'* Together, these two effects make it possible for artificial bilayers formed from Cle to C?z lipids to have hydrocarbon thicknesses ranging from approximately 26 to 53 A. In such membranes the ion transferring characteristics of polypeptides and macrocyclic molecules are known to vary considerably. Thus, in phosphatidyl choline decane membranes the conductance per mole of the carrier molecule valinomycin in the system decreases with increasing membrane thickness. For fatty acid chain lengths from CH to CZ2(corresponding to a thickness increase of about 10 A) the conductance has been found to decrease by about an order of magnitude?' When the membrane conductance arises from pore formation by gramicidin, the effect of thickness appears to be rather larger. Accurate data supporting this statement are not easy to obtain, as there is no reliable means of making a succession of membranes of different thickness such that they each contain the same amount of the polypeptide" and, furthermore, there is as yet no way of monitoring the concentration of gramicidin in the membranes once they are formed. Results for a limited range of thickness may, however, be deduced from a comparison of the current-voltage curves for compressible and incompressible membranes. Two such membranes are glyceryl monooleate decane and glyceryl monooleate hexadecane. The current-voltage curves for these membranes containing gramicidin, in 0.5 M NaCI, have been shown,
+
+
+
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Annals New York Academy of Sciences
normalized at low applied potential, by Haydon and Hladky.Ia For the incompressible membrane, the current-voltage curve is nearly linear and, in this respect, resembles the corresponding curve for the single channel~.~' The curve for the compressible membrane is strongly nonlinear, the conductance increasing with applied potential, in contrast to the single channel current-voltage relationship, which is ohmic and identical to that for the incompressible membrane. It is inferred that the rise in the conductance in the compressible membrane reflects chiefly the formation of additional channels from the inactive gramicidin known to be present." Since the variation of the membrane thickness with the applied potential has been determined,' it is possible to deduce how, for a membrane containing a constant amount of gramicidin, the conductance 3. As can be seen, the rate varies with thickness. This is shown in FIGURE of change of the conductance ratio corresponds to an increase of nearly two orders of magnitude for a thickness decrease of 10 A, and, for the range 47 to 31 A, which can readily occur in black films, to over three orders of magnitude. Over the latter range, the rate constant for closure of the channels has been measured. From this data and the extrapolated conductance ratio, the variation of the channel opening rate constant may be inferred (TABLE 3). The equilibrium constant (which is proportional to the conductance ratio) is thus seen to increase with decreasing membrane thickness partly because the closure rate constant decreases but mainly because the opening rate constant increases. (The proportionality constant, which is identical for the equilibrium and opening rate constants, arises because, although Bamberg and Lauger3* have determined them for one thickness of a lecithin-decane system, no absolute measurements of these quantities have yet been made in glyceryl monooleate membranes.) The long extrapolation indicated in FIGURE 3 as necessary to obtain the data of TABLE 3 leaves some doubt
FIGURE 3. The dependence on thickness of the conductance of a monoolein black film containing gramicidin. The ordinate is the logarithm of the ratio of the conductance at a given thickness to that at a thickness of 48 A.
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Lipid Function in Bilayer Ion Permeability
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TABLE3 GRAMICIDIN CONDUCTANCE PARAMETERS AS A FUNCTION OF MEMBRANE THICKNESS FOR MONOOLEIN BLACKFILMS Hydrocarbon Solvent ndecane n-tetradecane n-hexadecane
Hydrocarbon Region Thickness Constant X k* (A) (mol-'sec-') 47 40 31
2.5 12.8 335
kt (sec-I)
Constant X K$ (mol-I)
2.5 0.11 0.45
16.6 131
1
* k = channel opening rate constant.
t k = channel closing rate constant.
$ K = channel opening rate constant/channel closing rate constant.
as to whether or not the thickness effect is as large as has been concluded from the analysis. For what it is worth, the magnitude of the effect is confirmed very roughly by the substantially smaller stoichiometric concentrations of gramicidin in the bulk phases needed to produce similar levels of conductance in glyceryl monooleate hexadecane as compared with glyceryl monooleate decane membranes." Membranes containing alamethicin, which is also well established as a pore-forming molecule, might also be expected to show a strong dependence of conductance on thickness. As with gramicidin, however, there are technical difficulties in demonstrating the effect directly. A 1,000-fold change in conductance in a membrane containing alamethicin may arise from either a twofold change in the concentration of the adsorbed polypeptide or from a change of some 27 mV in the applied potential. Although experimental conditions should be controllable to within these limits, the margin for error is small and convincing data would not be readily obtained. Certainly, no clear evidence has yet been presented. The reason for the relative instability of gramicidin channels in the thicker membranes is not known for certain. However, one obvious explanation, that energy is required to deform or dimple the lipid so as to expose the entrances to the pores, happens to account semiquantitatively for the observations. If it is accepted that the gramicidin channel is approximately 28 A in length,", 34-3' it is clear that when the hydrocarbon region of the membrane is 48 A thick, dimples 10 A deep on each side are required to expose the pore (FIGURE 4). If the mean diameter of the dimple is 7 A and if tile effective tension in the surface of the dimple is 5 dyne/cm, the free energy of their formation erg. This is sufficient to reduce the channel opening rate constant is 2.2 x by some 200-fold. Together with the observed increase in the closure rate constant of about 5x, this accounts for the change in the equilibrium constant.
+
+
AND VOLTAGE-DEPENDENT PERMEABILITY LIPID COMPOSITION
The means by which the lipid may influence the voltage dependence of permeability through its ionic double layer and dipole potentials has been
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Annals New York Academy of Sciences
I
8- 5 dym d l
FIGURE4. An illustration of the dimpling that a lipid membrane may have to undergo in order that gramicidin pores may form. For the influence of this phenomenon on the channel opening rate constant, see text. mentioned briefly in an earlier section. Specific interactions between lipid and polypeptide may also affect the voltage dependence of permeability. In the experiments described by Bean3*on EIM it is probable that all these effects played some part. The behavior of alamethicin too is sensitive, in some respects, to the nature of the membrane lipid. This system, while still complex, has the merit that it is somewhat simpler than those involving EIM, and the et al.," Gordon and Haydon", in which specific interactions seem important. When alamethicin is introduced to one side of some lipid bilayers, a conductance increase may be obtained by applying either positive or negative potentials (though of different magnitude) to the polypeptide side of the membrane (FIGURE5 ) . Eisenberg et al. reported, however, that with certain phosphatidyl ethanolamine membranes no response was obtained when the alamethicin side was negative. This finding has been subsequently confirmed by Dr. Gordon in our laboratory. Two possible explanations immediately offer themselves. The first is that the alamethicin is able to diffuse across some membranes, but not those formed from phosphatidyl ethanolamine, and that it is the material which has done so that responds when the compartment to which the polypeptide was originally added is made negative. In this mechanism, therefore, the alamethicin is supposed to respond to one sign only of the membrane field and, in phosphatidyl ethanolamine membranes, the absence of polypeptide on one side restricts the stimulation of permeability to one direction of the field. Assuming this explanation to be correct, the nature of the lipid determines whether or not the polypeptide may penetrate to the far side of the membrane. The second explanation reveals the lipid in another role but, before this can be advanced, it is necessary to examine the evidence concerning the interaction of the alamethicin with the applied field. There is general agreement'that conduction is stimulated when the alamethicin side of the membrane becomes more positive, and it has been proposed by several authors that this is because the polypeptide binds inorganic cations. Thus Mueller and Rudin," Eisenberg et al.38 and others have found that the membrane conductance is proportional to a high power of the inorganic electrolyte concentration. While this is consistent with the binding of ions, it has been shown by Gordon and Haydon" that the effect appears to originate from the dependence of the adsorption of the alamethicin at the membrane surface on approximately the square root of the electrolyte concentration,
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Lipid Function in Bilayer Ion Permeability
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FIGURE 5. The current-voltage relationship for a membrane formed from monoolein cholesterol in hexadecane, in 2 M KCI. Alamethicin (lo-' M ) was added to only one of the two aqueous compartments. The sign of the potential is given for the alamethicin side of the membrane. (T = 20" C ) .
+
and does not necessarily imply any ion binding. P r e s ~ m a nfound '~ that alamethicin extracted alkali metal ions into nonpolar media, and concluded that this resulted from a binding of the ions by the polypeptide. Unless a nonspecific binding by the glutamyl carboxyl is invoked an alternative explanation for this data is less easy to see. It is significant, however, that no clearly defined complexes with alkali metal ions (such as are known for the actins, valinomycin, and other ionophores) have yet been reported. More direct evidence against ion binding comes from the observation that the membrane conductances show the same potential dependence for a number of quite different electrolytes including sodium, potassium, calcium,* tetramethylammonium and tris chlorides, and do so over a range of electrolyte c~ncentrations.~~ The implication of these observations is that, if ion binding occurs, it must, under all these varied circumstances, remain constant and at a high level. The improbability that this would occur, however, seems such that the ion binding hypothesis must be discounted. In the absence of substantial evidence that the alamethicin may carry a net positive charge, it would appear that the polypeptide or, at least, its * It has not been found possible to reproduce the effects of di- and trivalent cations on the slope of the current-voltage curve," as reported by Cherry ei uLu
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Annals New York Academy of Sciences
aggregates, must respond to the applied field through the possession of a dipole moment. If the whole membrane potential were to fall across a dipole of length 5 A, the current-voltage data require that the moment per alamethicin molecule should be about 17 Debye units. For a polypeptide of the size of alamethicin such a dipole moment is, in general, quite feasible, and surface potential studies of alamethicin monolayers at air/water interface^^^ show that in these conditions the molecule has a moment, normal to the surface, of the required order of magnitude. If it is accepted that the alamethicin molecule, or its aggregate, reacts to applied potentials because it is dipolar rather than because it carries a net charge, several features of the membrane conductance are more readily accounted for. Thus, it is no longer necessary to postulate that the molecules must diffuse through the bilayer and establish themselves on the far side in order that conduction may occur when the direction of the field is reversed. Instead, the molecules need merely to orient themselves in the membrane in the opposite sense. If this occurred, however, it is unlikely that the threshold 5 ) would be the same for potential for the onset of conduction (FIGURE the two field directions since the interactions of the alamethicin molecule with the membrane would almost certainly favor one orientation rather than the other. Moreover, the difference between the threshold potentials for the two field directions should depend on the nature of the lipid. Thus, the finding of Eisenberg et al." that for bacterial phosphatidyl ethanolamine membranes no conduction occurs when the polypeptide side of the membrane is negative, may be regarded as simply an extreme instance in which the interaction of the alamethicin with the lipid is so much stronger in one orientation than the other that it is not significantly affected by any field that the membrane will tolerate. The difference in the interaction free energies for the two orientations needed to account for this observation does not have to be greater than about 10 kcal for the whole conducting aggregate, and hence is relatively trivial in comparison to the hydrogen and lipophilic bonding capacity for the eight or nine molecule assembly. A mathematical analysis of the conduction mechanism for a dipole model of alamethicin has been given by Gordon and Haydon.'' A further consequence of the dipole mechanism, and the different interaction free energies of the conducting aggregate in its two orientations with respect to the lipid, is that the properties of the aggregate might vary according to which direction of the field produced the conduction. For membranes of glycerol monooleate cholesterol this appears to be so (FIGURE 6 ) . Although the levels of conduction exhibited by a single complex are the same for the two field directions, the probability of their occurrence is quite different and, in fact, more levels are detectable when the alamethicin side of the membrane is negative than when it is positive. These observations appear to constitute strong evidence that the conduction which occurs when the polypeptide side of the membrane is negative does not originate from alamethicin which has penetrated the bilayer and is responding as it would have done on the side from whence it came. Although not directly connected with the potential-dependence of alamethicin conductance, it is also of interest that the rate constants for transition between the levels of a single current burst are very sensitive to the nature of the membrane lipid. An extreme example is a comparison of results for cholesphosphatidyl ethanolamine on the one hand and glyceryl monooleate
+
+
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1 I I l l 1 1 (D
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O
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Lipid Function in Bilayer Ion Permeability
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Annals New York Academy of Sciences
terol on the other. In the glyceride membranes the transitions, both upward and downward, occur about 100 times more frequently than in the phospholipid membranes. However, both rate constants are affected simlarly by the change of lipid so that the overall level probability is unchanged.“ Although, in the example given, the membrane thicknesses are not the same, it has been shown that it is through its chemical constitution, rather than through its effect on membrane thickness that the lipid chiefly acts.“ As with the switching on of the conductance, therefore, the specific interaction of the lipid with the polypeptide seems to be important. The main purpose of the foregoing discussion of conduction by alamethicin is to illustrate the point that, for a potential-dependent permeability, the nature of the lipid may seriously affect the extent of the membrane polarization or depolarization necessary to open the channels. Indeed, if the dipole mechanism is correct, there is at least one lipid, phosphatidyl ethanolamine, for which inaccessibly large depolarizations are required. This finding, and those discussed in earlier sections, combine to emphasize the importance of working with appropriate lipids in biological membrane reconstitution studies. Not only may the natural transport proteins fail to function in foreign lipids but, more confusingly, they may function quite abnormally. In addition, membrane components, which in the natural state are not involved in ion transport, may become so in association with different lipids.
REFERENCES 1. 2. 3.
MONTAL, M. & P. MUELLER. 1972. Proc. Nat. Acad. Sci. U.S.A. 69: 3561-3566. MONTAL, M. 1973. Biochim. Biophys. Acta 298: 750-754. FETTIPLACE, R., D. M. ANDREWS & D. A. HAYDON. 1971. J. Membrane Biol.
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FETTIPLACE, R. 1974. Ph.D. dissertation. FEITIPLACE, R., L. G. M. GORDON, S. B. HLADKY, J. REQUENA, H. P. ZINGSHEIM & D. A. HAYDON. 1975. Techniques in the formation and examination of “black” lipid bilayer membranes. In Methods in Membrane Biology. E. D. Korn, Ed. Vol. 4: Plenum Press. New York, N.Y. LECUYER, H. & D. G. DERVICHIAN. 1969. J. Mol. Biol. 45: 39-57. REISS-HUSSON, F. 1967. J. Mol. Biol. 25: 363-382. SMALL, D. M. 1967. J. Lipid Res. 8: 551-557. ANDREWS, D. M., E. D. MANEV & D. A. HAYDON. 1970. Spec. Discuss. Faraday SOC.1: 46-56. & J. TAYLOR. 1964. Proc. Roy. SOC.,Ser. A 281: HANAI,T., D. A. HAYDON
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GULIK-KRZYWICKI, T., E. SCHTECTER, V. LUZZATI & M. FAURE. 1969. Nature
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NORMAN, A. W.,R. A. DEMEL,B. de KRUYFF,W. S. M. GEURTS van KESSELL & L. L. M. van DEENEN.1972. Biochim. Biophys. Acta 290: 1-14. FINKELSTEIN, A. & R. HOLZ. 1973. Aqueous pores created in thin lipid membranes by the polyene antibiotics nystatin and amphotericin B. In Membranes. G. Eisenman, Ed. Vol. 2: 377-408. Marcel Dekker, Inc. New York. N.Y. HUNTER,M. J. 1974. The use of lipid bilayers as cell membrane models: An experimental test using the ionophore, valinomycin. In Drugs and Transport Processes. B. A. Callingham, Ed.: 227-240. Macmillan. London. England. KRASNE, S., G. EISENMAN & G. SZABO. 1971. Science 174: 412-415. HAYDON, D. A. & S. B. HLADKY. 1972. Q. Rev. Biophys. 5: 187-282. SZABO, G., G. EISENMAN, R. LAPRADE, S. M. CUNI & S. KRASNE. 1973. Experi-
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Lipid Function in Bilayer Ion Permeability
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mentally observed effects of carriers on the electrical properties of bilayer membranes-equilibrium domain. In Membranes. G. Eisenman, Ed. Vol. 2: 179-328. Marcel Dekker, Inc. New York, N.Y. W. K., A. L. HODGKIN & H. MEVES.1965. J. Physiol. 1 8 0 821-836. CHANDLER, GILBERT,D. L. & G. EHRENSTEIN. 1969. Biophys. J. 9 447-463. NEUMCKE,B. 1970. Biophysik 6 23 1-240. MCLAUGHLIN, S. G. A., G. SUBO, G. EISENMAN& S. M. CIANI. 1970. Proc. Nat. Acad. Sci. U S A . 67: 1268-1275. MCLAUGHLIN, S. G. A., G. SZABO& G. EISENMAN.1971. J. Gen. Physiol. 58: 667-687. MULLER,R. U. & A. 'FINKELSTEIN. 1972. J. Gen. Physiol. 60: 285-306. HAYDON, D. A. & V. B. MYERS.1973. Biochim. Biophys. Acta 307: 429-443. HLADKY, S. B. & D. A. HAYDON. 1973. Biochim. Biophys. Acta 318: 464-468. AVEYARD, R. & D. A. HAYDON. 1973. An Introduction to the Principles of Surface Chemistry. Cambridge University Press. Cambridge, England. 0. H. JR. 1970. TPMAs. Abstracts of Biophysical Society. 14th Annual LEBLANC, Meeting. Baltimore, Maryland. The Biophysical Society. NEDERMEIJER-DENESSEN, H. J. M. & C. L. DE LIGNY.1974. J. Electroanal. Chem. 57: 265-266. TAYLOR, J. & D. A. HAYDON. 1966. Discuss. Faraday SOC.42: 51-59. STARK,G., R. BENZ, G. W. POHL& K. JANKO.1972. Biochim. Biophys. Acta 2 6 6 603-612. J. & D. A. HAYDON. Proc. Roy. SOC.London, Ser. A. In press. REQUENA, S. B. & D. A. HAYDON.1972. Biochim. Biophys. Acta 274: 294-312. HLADKY, BAMBERG, E. & P. LAUGER.1973. J. Membrane Biol. 11: 177-194. URRY,D. W., M. C. GOODALL, J. D. GLICKSON & D. F. MAYERS.1971. Proc. Nat. Acad. Sci. U S A . 6 8 1907-1911. VEATCH,W. R., E. T. FOSSEL & E. R. BLOUT.1974. Biochemistry 13: 5249-5256. VEATCH,W. R. & E. R. BLOUT.1974. Biochemistry 13: 5257-5264. FOSSEL,E. T., W. R. VEATCH,Y. A. OVCHINNIKOV & E. R. BLOUT.1974. Biochemistry 13: 5264-5275. BEAN,R. C. 1973. Protein-mediated mechanisms of variable ion conductance in thin lipid membranes. In Membranes. G . Eisenman, Ed. Vol. 2: 409-477. Marcel Dekker, Inc. New York. N.Y. EISENBERG, M., J. E. HALL& C. A. MEAD.1973. J. Membrane Biol. 14: 143-176. GORDON, L. G. M.& D. A. HAYDON. 1975. Phil. Trans. Roy. Soc. London, Ser. B. 210: 433-447. To be published. GORDON,L. G. M. & D. A. HAYDON. MUELLER, R. & D. 0. RUDIN.1968. Nature 217: 398-404. PRESSMAN, B. C. 1968. Fed. Proc. 27: 1283-1288. CHERRY,R. J., D. CHAPMAN & D. E. GRAHAM.1972. J. Membrane Biol. 7: 325-344. PAPAHADJOPOULOS, D. 1968. Biochim. Biophys. Acta 163: 240-254. ADAM,N. K., F. A. ASKEW& J. F. DANIELLI.1935. Biochem. J. 29: 1786-1801. HLADKY, S. B. Private communication. GORDON, L. G. M. Private communication. GORDON, L. G. M. & D. A. HAYDON. Unpublished results.
DISCUSSION DR. TOSTESON: Do you have any evidence on the ion-selectivity of the alamethicin channels opened by the opposite signs of potential?
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Annals New York Academy of Sciences
DR. HAYDON:The alamethicin channel is remarkably unselective, apart from surface charge effects, and I don’t think that the opening from opposite sides makes any difference to that state of affairs. Both are nonselective. The conductances of the channels themselves are exactly the same; it’s only the probabilities of the different levels that seem changed. DR. S. MCLAUGHLIN (State University of N e w Y o r k , Stony Brook, L.I., N . Y . ) : Dr. Haydon, what is the origin of the dipole potential that seems to occur somewhere at the surface of glycerol monooleate and phospholipids? DR. HAYDON: We thought of trying to pin this down at one stage, but it is incredibly difficult to devise experiments to do this. Since such a wide variety of lipids seem to give a similar sort of dipole potential and these lipids include, for example, cholesterol, which has a fairly simple polar group, I can only think that it must arise from the carbon-oxygen bonds between the hydrocarbon chains and the inside boundary of the head group. This bond is the one thing that all the lipids seem to have in common, and they all seem to have the same sign of potential. DR. S. CHAN(California Institute of Technology, Pasadena, C a l i f . ): We have studied the aggregation properties of alamethicin in solution as a function of ionic strength and we have found that the aggregation does go up as you increase the ionic strength of the solution, which is consistent with your idea. Secondly, by analyzing this aggregation data, we were able to show that the equilibrium concentration of the decamer varies as the ninth power of the alamethicin concentration under the experimental conditions of Hall and Eisenberg. DR. HAYDON: That’s very comforting.
OF
CARRIERS AND CHANNELS
FUNCTIONS OF THE LIPID IN BILAYER ION PERMEABILITY D. A. Haydon Physiological Laboratory University of Cambridge Cambridge, England
INTRODUCTION The extensive studies over the past few years of the mechanisms of ion transport across artificial lipid membranes have revealed a great deal both about the ionophores themselves and about the properties which the lipid membranes must have in order that the ionophores should function efficiently. For a carrier molecule, for example, it is of little value that it may have a high ion selectivity if it will not combine with the membrane or, if it does combine, it will not move or bind ions in the membrane. For pore-forming molecules, binding to different membranes may be very similar, but the efficiency of the transport process may depend critically on the state of ionization of the lipid or on the membrane thickness. In this introductory paper it is proposed to review the various properties of lipid membranes which we now know to have special relevance to ion transport by polypeptides and other small macromolecules, and to illustrate the discussion with detailed descriptions of selected topics. It is thus hoped to emphasize the considerable range of factors which contribute to the success or otherwise of attempts to incorporate biological membrane components in artificial lipid bilayers. Since most of the findings described in this paper are for “black” lipid membranes, i.e., those formed using a hydrocarbon solvent, it is perhaps pertinent to summarize at the outset current knowledge of the interrelationship between these membranes and those of the lamellar phase of lecithin and the planar solventless membranes studied by Montal and Mueller.’, ’ As seen in TABLE 1, the thickness, as deduced from x-ray data, of the hydrocarbon region of a leaflet of the fully hydrated lamellar phase is not significantly different from the thickness deduced from the specific capacitance of a planar
THICKNESSES OF
TABLE 1 ARTIFICIAL LIPIDBILAYERSFORMED FROM EGG LECITHIN
System
Specific Capacitance (rF/cma)
Lecithin-hexadecane (black film)* Lecithin (no so1vent)t Lecithin (liquid crystal)$
0.603 -0.76 -
* From Fettiplace et ul.’ t From Fettiplace‘ and Fettiplace et d.
$ From Lecuyer et af.,6 Reiss-Husson,’ and Small.’
2
Hydrocarbon Region Thickness (A) 31 ( ~ ~ 2 . 1 4 ) -25 ( E = 2.14) -26 (x-ray)
Haydon:
Lipid Function in Bilayer Ion Permeability
3
solventless membrane, assuming a dielectric constant of 2.14. Although the data of Fettiplace'. ' cannot be claimed as definitive, the close agreement of the two thicknesses helps greatly to establish the validity of using a bulk dielectric constant for aliphatic hydrocarbon in the interpretation of the capacitance data. The somewhat smaller capacitance and larger thickness of the lecithin-hexadecane black film can be attributed to the retention of some solvent, although just how much is difficult to say. It may be that a small amount of solvent has a large effect on the capacitance (and hence on the thickness) or it may be that the area per molecule given previously3 is about 10% too low. The above check on the validity of membrane thicknesses calculated from specific capacitances places on a firmer basis the earlier findings that black films formed from shorter chain alkanes such as decane are indeed of greater thickness than the solventless structures, and that this is because they retain considerable amounts of ~ o l v e n t . ~lo~ The various roles that the lipid may play in bilayer ion permeability may be conveniently considered under the broad headings of (1) combination of the ionophore with the membrane and (2) functioning of the ionophore in the membrane. Under ( l ) , the potential relevance of studies such as those of GulikKrzywicki et al." concerning the combination of proteins with phospholipid liposomes is obvious, although the importance of the sign of the charged groups, which was brought out in this work, has not so far seemed of comparable importance for the known ion transporting molecules. It may turn out to be generally unimportant owing, perhaps, to the necessarily lipophilic character of an ionophore and also to the screening of any ionic groups in the relatively high electrolyte concentrations often employed. The nature of the nonpolar part of the membrane is, by contrast, known to have a considerable influence on the uptake of certain ionophores. The necessity for cholesterol in the case of the polyenes (e.g., nystatin and amphotericin B)", and the adverse effects of cholesterol on the uptake of valinomycin" are well documented. The state of the hydrocarbon region of the bilayer, i.e., liquid or solid, might also be expected to influence the binding of ionophores. The experiments of Krasne et aZ.15 are of special interest in this respect. Cooling the bilayer to the point where it appeared solid rather than liquid eliminated conduction by nonactin but not by gramicidin A. Obviously the solidification of the membrane did not cause the desorption of the gramicidin, but whether the nonactin conduction ceased because it could no longer diffuse across the hydrocarbon region or whether it ceased because it was simply not taken up by the membrane is not clear." The result for gramicidin prompts the question of whether or not the polypeptide induces conduction when placed in the presence of an already solidified membrane. If it does not, it has to be concluded that the freezing of the membrane may trap pore-forming molecules, at least for long periods, in a functioning but nonequilibrium state. The binding of an ionophore by a membrane is clearly a necessary, but not sufficient condition for ion transport. Conditions in the membrane may well prevent the ionophore from functioning as efficiently or normally as in a biological system. Thus, under heading (2), factors such as membrane fluidity, surface potential, membrane thickness and specific lipid-polypeptide interactions are known to be important. The significance of membrane fluidity
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Annals New York Academy of Sciences
for the functioning of carriers is obvious; the surface potential affects the uptake of ions by the ionophores in the membrane and this in turn determines selectivity between ions of different valence and sign; membrane thickness can greatly influence the conduction efficiency of an assembly of pore-forming molecules; and specific interactions may completely change the response of a pore-forming molecule to applied potential, The effects of membrane fluidity have been well described in a number of place^.^'^ '' Ways in which the other factors may operate are illustrated in the remainder of this paper.
SURFACE POTENTIAL The relationship of the ion permeability of a lipid membrane to the change in the electrostatic potential across its surface has been discussed by several la-= In earlier work, only the diffuse and Stern layer potentials were considered, but it is now recognized that the potential change arising from the oriented dipoles of the polar head groups may be of similar or even greater " This is clear for carrier transport from the fact that either the ion or the ion-carrier complex must pass through all of the potential changes due to the presence of the polar groups (FIGURE1). For the classical pore where, as far as the permeating ions are concerned, the lipid polar groups are considered to be shunted, the position is less obvious. 3' '
aqueous
double layer
hydrocarbon
dipoles
FIGURE1. A simple representation of the variation of electrostatic potential across a lipid bilayer. The lipids are assumed to be negatively charged while the oriented dipoles of the polar groups are taken to be positive inwards.
Haydon:
Lipid Function in Bilayer Ion Permeability
5
The Debye-Huckel reciprocal length parameter is likely to be sufficiently large that diffuse layer potentials will affect the ion concentrations over the entrance to a pore. However, the range of influence of the lipid polar group dipoles is much less, and the permeating ions could be unaffected by their presence. While the importance of the surface potential (or, at least, the diffuse layer part of it) for the functioning of biological membranes has long been appreciated, attempts at quantitative tests of the hypothesis have been made only recently, and these so far only with artificial membranes. If consideration is restricted to carrier systems, elementary theory suggests that for constant electrolyte concentration, carrier concentration in the membrane and mobility of ion-carrier complex, the membrane conductance G(0) in the limit of zero applied potential is given byl6
where z is the valence of the ion and lUris the total potential difference between the aqueous phase and the interior of the membrane, as indicated in FIGURE 1. 41/w may be split into the ionic double layer (4i)and dipole (4d) contributions. Thus
4lh
=
4,
+4d
(2)
It has been amply demonstrated that changes in G(0) for a given ion-carrier system may be accurately accounted for in terms of the changes in qh / w measured for monolayers of the appropriate lipids at air or hydrocarbon/water interfaces.24 Moreover, in certain systems, when q5d is assumed constant and specific adsorption of ions is minimal, + i appears to be given fairly accurately by the Gouy-Chapman theory.21. Within the above theoretical framework it is thus possible to understand variations in the conductance for a given ion, and the selectivity of the bilayer as between cations and anions, in terms of the average surface dipole moment and degree of ionization of the membrane lipids. Surface or compensation potentials, AVl I w , for some lipids and lipid mixtures 2. These values are not equal to $J~ / w but are the changes which are shown in TABLE occur in c # J ~ / , ~when the lipid monolayer is spread on a clean aqueous solution surface.26 Therefore AVi / w = 41/ w - 4 a / w (3) where is numerically equal to the so-called X-potential of water (or of the appropriate aqueous solution). Differences in AVl /w, all other factors being equal, should therefore reflect the relative intrinsic permeabilities of different lipid membranes to cations and anions, iz.,the permeabilities that would be found if the cation and the anion were identical except for the sign of their charge. That this is accurately so for the permeability of egg phosphatidyl choline and monoolein bilayers to K+-nonactin has been shown. Thus, the difference in AVl1,"for the two lipids is -120 mV, whereas the difference in the conductance corresponds to -115 mV.2K(It should be noted, however, that the introduction of cholesterol destroys this agreement, presumably owing either to its tendency to reduce the solubility of the nonactin in the membrane or to its effect on the fluidity, and hence on the mobility of the ion-carrier complex.) For the phosphatidyl serine and phosphatidyl inositol given in TABLE 2, the ionic double layer potentials are likely to be in the region of -12.5 mV. The dipole potentials for all the phospholipids, and the cholesterol, shown 2 are therefore very similar and, apart from the relatively small in TABLE
6
Annals New York Academy of Sciences TABLE 2 SURFACE POTENTIALS OF LIPIDMONOLAYERS AT AREASPER SIMILAR TO THOSE IN T H E &LAYER
MOLECULE
Lipid ~~~
~
Phosphatidyl choline (egg) Phosphatidyl ethanolamine(egg) Phosphatidyl serine Phosphatidyl inositol Cholesterol Phosphatidyl choline + cholesterol (-3: 1) Glyceryl monooleate Monooleyl glyceryl ether
441t 420$ 320$
300$ 390 5 420t 321t 411t
* The sign of the potential is for the air (or hydrocarbon) relative to the aqueous phase. t Substrate 0.1 M NaC1, pH 6.
-
$ From Papahadjopo~los.~~ Substrate 0.145 M NaCl, pH 6.
0 From Adam
Substrate 0.02 M HCI.
ionic double layer potentials, the intrinsic relative permeabilities of the corresponding bilayers should also be very similar. The absolute magnitude of these relative permeabilities to cations and anions may be estimated. The direct approach is simply to measure the membrane conductance in the presence of equal concentrations of permeating, oppositely charged, but otherwise identical ions. This has been attempted using lecithin-cholesterol membranes with tetraphenyl boride and tetraphenylphosphonium ions." The specific conductance for the negative boride was some 10'-fold larger than for the positive tetraphenylphosphonium ion, from which may ba calculated to be 115 mV. or the X-potential of An alternative method is based on a knowledge of water. The most recent and probably best estimate of this is 40 k 100 mV.z*Bearing in mind that a different sign convention is used for present purposes, and taking AV1.,,( as 420 mV, 4l for lecithin: cholesterol (-3 :1 mole ratio) may be calculated from Equation 3 to be between 280 and 480 mV. This result reinforces the idea that the lipid bilayer has a strong intrinsic selectivity for anions over cations. The quantitative discrepancy between the two estimates of / w given above is not surprising, but also is not readily explicable. Despite first appearances, there may be significant differences between tetraphenyl boride and tetraphenylphosphonium ions or their interactions with the bilayer which invalidate their use for present purposes. On the other hand, estimates of the X-potential for water have, in the past, been so widely varied that complete confidence in the most recent result may not be fully justified. In addition to affecting the conductance and the selectivity, the dipole potential of either the natural lipids, or a change in this quantity produced by the adsorption of dipolar molecules, may act in much the same way as an ionic double layer potential in changing the polarization or depolarization required to stimulate conduction in a voltage-dependent system such as a 2. Provided the effect is asymnerve axon. This point is illustrated in FIGURE metrical, both an increased negative ionic double layer potential, or an increased negative dipole potential tend to increase the field in the membrane and, although the resting potential is not changed, a larger than normal depolarization could be needed to produce an action potential. N
Haydon:
Lipid Function in Bilayer Ion Permeability
7
(0
FIGURE2. An illustration of the way in which surface potentials might influence the stimulation of an action potential in a nerve axon. (a) A normal axon having a resting potential of -63 mV which is stimulated by depolarization to -43 mV. A small negative surface charge density is assumed to be present on the inner surface of the membrane. (b) The resting potential is the same but ion adsorption on the inner surface is assumed to increase the negative charge. In order to restore the field in the membrane to that which produced stimulation in the normal axon, a larger depolarization is now required. (c) This is analogous to (b) except that the field in the membrane is assumed to be enhanced in the resting state by the adsorption of dipolar molecules on the inside. MEMBRANETHICKNESS The thickness of artificial membranes increases with the chain length of the lipid', and, in the case of black films, tends to vary inversely with the chain length of the solvent.'* Together, these two effects make it possible for artificial bilayers formed from Cle to C?z lipids to have hydrocarbon thicknesses ranging from approximately 26 to 53 A. In such membranes the ion transferring characteristics of polypeptides and macrocyclic molecules are known to vary considerably. Thus, in phosphatidyl choline decane membranes the conductance per mole of the carrier molecule valinomycin in the system decreases with increasing membrane thickness. For fatty acid chain lengths from CH to CZ2(corresponding to a thickness increase of about 10 A) the conductance has been found to decrease by about an order of magnitude?' When the membrane conductance arises from pore formation by gramicidin, the effect of thickness appears to be rather larger. Accurate data supporting this statement are not easy to obtain, as there is no reliable means of making a succession of membranes of different thickness such that they each contain the same amount of the polypeptide" and, furthermore, there is as yet no way of monitoring the concentration of gramicidin in the membranes once they are formed. Results for a limited range of thickness may, however, be deduced from a comparison of the current-voltage curves for compressible and incompressible membranes. Two such membranes are glyceryl monooleate decane and glyceryl monooleate hexadecane. The current-voltage curves for these membranes containing gramicidin, in 0.5 M NaCI, have been shown,
+
+
+
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Annals New York Academy of Sciences
normalized at low applied potential, by Haydon and Hladky.Ia For the incompressible membrane, the current-voltage curve is nearly linear and, in this respect, resembles the corresponding curve for the single channel~.~' The curve for the compressible membrane is strongly nonlinear, the conductance increasing with applied potential, in contrast to the single channel current-voltage relationship, which is ohmic and identical to that for the incompressible membrane. It is inferred that the rise in the conductance in the compressible membrane reflects chiefly the formation of additional channels from the inactive gramicidin known to be present." Since the variation of the membrane thickness with the applied potential has been determined,' it is possible to deduce how, for a membrane containing a constant amount of gramicidin, the conductance 3. As can be seen, the rate varies with thickness. This is shown in FIGURE of change of the conductance ratio corresponds to an increase of nearly two orders of magnitude for a thickness decrease of 10 A, and, for the range 47 to 31 A, which can readily occur in black films, to over three orders of magnitude. Over the latter range, the rate constant for closure of the channels has been measured. From this data and the extrapolated conductance ratio, the variation of the channel opening rate constant may be inferred (TABLE 3). The equilibrium constant (which is proportional to the conductance ratio) is thus seen to increase with decreasing membrane thickness partly because the closure rate constant decreases but mainly because the opening rate constant increases. (The proportionality constant, which is identical for the equilibrium and opening rate constants, arises because, although Bamberg and Lauger3* have determined them for one thickness of a lecithin-decane system, no absolute measurements of these quantities have yet been made in glyceryl monooleate membranes.) The long extrapolation indicated in FIGURE 3 as necessary to obtain the data of TABLE 3 leaves some doubt
FIGURE 3. The dependence on thickness of the conductance of a monoolein black film containing gramicidin. The ordinate is the logarithm of the ratio of the conductance at a given thickness to that at a thickness of 48 A.
Haydon:
Lipid Function in Bilayer Ion Permeability
9
TABLE3 GRAMICIDIN CONDUCTANCE PARAMETERS AS A FUNCTION OF MEMBRANE THICKNESS FOR MONOOLEIN BLACKFILMS Hydrocarbon Solvent ndecane n-tetradecane n-hexadecane
Hydrocarbon Region Thickness Constant X k* (A) (mol-'sec-') 47 40 31
2.5 12.8 335
kt (sec-I)
Constant X K$ (mol-I)
2.5 0.11 0.45
16.6 131
1
* k = channel opening rate constant.
t k = channel closing rate constant.
$ K = channel opening rate constant/channel closing rate constant.
as to whether or not the thickness effect is as large as has been concluded from the analysis. For what it is worth, the magnitude of the effect is confirmed very roughly by the substantially smaller stoichiometric concentrations of gramicidin in the bulk phases needed to produce similar levels of conductance in glyceryl monooleate hexadecane as compared with glyceryl monooleate decane membranes." Membranes containing alamethicin, which is also well established as a pore-forming molecule, might also be expected to show a strong dependence of conductance on thickness. As with gramicidin, however, there are technical difficulties in demonstrating the effect directly. A 1,000-fold change in conductance in a membrane containing alamethicin may arise from either a twofold change in the concentration of the adsorbed polypeptide or from a change of some 27 mV in the applied potential. Although experimental conditions should be controllable to within these limits, the margin for error is small and convincing data would not be readily obtained. Certainly, no clear evidence has yet been presented. The reason for the relative instability of gramicidin channels in the thicker membranes is not known for certain. However, one obvious explanation, that energy is required to deform or dimple the lipid so as to expose the entrances to the pores, happens to account semiquantitatively for the observations. If it is accepted that the gramicidin channel is approximately 28 A in length,", 34-3' it is clear that when the hydrocarbon region of the membrane is 48 A thick, dimples 10 A deep on each side are required to expose the pore (FIGURE 4). If the mean diameter of the dimple is 7 A and if tile effective tension in the surface of the dimple is 5 dyne/cm, the free energy of their formation erg. This is sufficient to reduce the channel opening rate constant is 2.2 x by some 200-fold. Together with the observed increase in the closure rate constant of about 5x, this accounts for the change in the equilibrium constant.
+
+
AND VOLTAGE-DEPENDENT PERMEABILITY LIPID COMPOSITION
The means by which the lipid may influence the voltage dependence of permeability through its ionic double layer and dipole potentials has been
10
Annals New York Academy of Sciences
I
8- 5 dym d l
FIGURE4. An illustration of the dimpling that a lipid membrane may have to undergo in order that gramicidin pores may form. For the influence of this phenomenon on the channel opening rate constant, see text. mentioned briefly in an earlier section. Specific interactions between lipid and polypeptide may also affect the voltage dependence of permeability. In the experiments described by Bean3*on EIM it is probable that all these effects played some part. The behavior of alamethicin too is sensitive, in some respects, to the nature of the membrane lipid. This system, while still complex, has the merit that it is somewhat simpler than those involving EIM, and the et al.," Gordon and Haydon", in which specific interactions seem important. When alamethicin is introduced to one side of some lipid bilayers, a conductance increase may be obtained by applying either positive or negative potentials (though of different magnitude) to the polypeptide side of the membrane (FIGURE5 ) . Eisenberg et al. reported, however, that with certain phosphatidyl ethanolamine membranes no response was obtained when the alamethicin side was negative. This finding has been subsequently confirmed by Dr. Gordon in our laboratory. Two possible explanations immediately offer themselves. The first is that the alamethicin is able to diffuse across some membranes, but not those formed from phosphatidyl ethanolamine, and that it is the material which has done so that responds when the compartment to which the polypeptide was originally added is made negative. In this mechanism, therefore, the alamethicin is supposed to respond to one sign only of the membrane field and, in phosphatidyl ethanolamine membranes, the absence of polypeptide on one side restricts the stimulation of permeability to one direction of the field. Assuming this explanation to be correct, the nature of the lipid determines whether or not the polypeptide may penetrate to the far side of the membrane. The second explanation reveals the lipid in another role but, before this can be advanced, it is necessary to examine the evidence concerning the interaction of the alamethicin with the applied field. There is general agreement'that conduction is stimulated when the alamethicin side of the membrane becomes more positive, and it has been proposed by several authors that this is because the polypeptide binds inorganic cations. Thus Mueller and Rudin," Eisenberg et al.38 and others have found that the membrane conductance is proportional to a high power of the inorganic electrolyte concentration. While this is consistent with the binding of ions, it has been shown by Gordon and Haydon" that the effect appears to originate from the dependence of the adsorption of the alamethicin at the membrane surface on approximately the square root of the electrolyte concentration,
Haydon:
Lipid Function in Bilayer Ion Permeability
11
FIGURE 5. The current-voltage relationship for a membrane formed from monoolein cholesterol in hexadecane, in 2 M KCI. Alamethicin (lo-' M ) was added to only one of the two aqueous compartments. The sign of the potential is given for the alamethicin side of the membrane. (T = 20" C ) .
+
and does not necessarily imply any ion binding. P r e s ~ m a nfound '~ that alamethicin extracted alkali metal ions into nonpolar media, and concluded that this resulted from a binding of the ions by the polypeptide. Unless a nonspecific binding by the glutamyl carboxyl is invoked an alternative explanation for this data is less easy to see. It is significant, however, that no clearly defined complexes with alkali metal ions (such as are known for the actins, valinomycin, and other ionophores) have yet been reported. More direct evidence against ion binding comes from the observation that the membrane conductances show the same potential dependence for a number of quite different electrolytes including sodium, potassium, calcium,* tetramethylammonium and tris chlorides, and do so over a range of electrolyte c~ncentrations.~~ The implication of these observations is that, if ion binding occurs, it must, under all these varied circumstances, remain constant and at a high level. The improbability that this would occur, however, seems such that the ion binding hypothesis must be discounted. In the absence of substantial evidence that the alamethicin may carry a net positive charge, it would appear that the polypeptide or, at least, its * It has not been found possible to reproduce the effects of di- and trivalent cations on the slope of the current-voltage curve," as reported by Cherry ei uLu
12
Annals New York Academy of Sciences
aggregates, must respond to the applied field through the possession of a dipole moment. If the whole membrane potential were to fall across a dipole of length 5 A, the current-voltage data require that the moment per alamethicin molecule should be about 17 Debye units. For a polypeptide of the size of alamethicin such a dipole moment is, in general, quite feasible, and surface potential studies of alamethicin monolayers at air/water interface^^^ show that in these conditions the molecule has a moment, normal to the surface, of the required order of magnitude. If it is accepted that the alamethicin molecule, or its aggregate, reacts to applied potentials because it is dipolar rather than because it carries a net charge, several features of the membrane conductance are more readily accounted for. Thus, it is no longer necessary to postulate that the molecules must diffuse through the bilayer and establish themselves on the far side in order that conduction may occur when the direction of the field is reversed. Instead, the molecules need merely to orient themselves in the membrane in the opposite sense. If this occurred, however, it is unlikely that the threshold 5 ) would be the same for potential for the onset of conduction (FIGURE the two field directions since the interactions of the alamethicin molecule with the membrane would almost certainly favor one orientation rather than the other. Moreover, the difference between the threshold potentials for the two field directions should depend on the nature of the lipid. Thus, the finding of Eisenberg et al." that for bacterial phosphatidyl ethanolamine membranes no conduction occurs when the polypeptide side of the membrane is negative, may be regarded as simply an extreme instance in which the interaction of the alamethicin with the lipid is so much stronger in one orientation than the other that it is not significantly affected by any field that the membrane will tolerate. The difference in the interaction free energies for the two orientations needed to account for this observation does not have to be greater than about 10 kcal for the whole conducting aggregate, and hence is relatively trivial in comparison to the hydrogen and lipophilic bonding capacity for the eight or nine molecule assembly. A mathematical analysis of the conduction mechanism for a dipole model of alamethicin has been given by Gordon and Haydon.'' A further consequence of the dipole mechanism, and the different interaction free energies of the conducting aggregate in its two orientations with respect to the lipid, is that the properties of the aggregate might vary according to which direction of the field produced the conduction. For membranes of glycerol monooleate cholesterol this appears to be so (FIGURE 6 ) . Although the levels of conduction exhibited by a single complex are the same for the two field directions, the probability of their occurrence is quite different and, in fact, more levels are detectable when the alamethicin side of the membrane is negative than when it is positive. These observations appear to constitute strong evidence that the conduction which occurs when the polypeptide side of the membrane is negative does not originate from alamethicin which has penetrated the bilayer and is responding as it would have done on the side from whence it came. Although not directly connected with the potential-dependence of alamethicin conductance, it is also of interest that the rate constants for transition between the levels of a single current burst are very sensitive to the nature of the membrane lipid. An extreme example is a comparison of results for cholesphosphatidyl ethanolamine on the one hand and glyceryl monooleate
+
+
Haydon:
1 I I l l 1 1 (D
9
O
N
Lipid Function in Bilayer Ion Permeability
13
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Annals New York Academy of Sciences
terol on the other. In the glyceride membranes the transitions, both upward and downward, occur about 100 times more frequently than in the phospholipid membranes. However, both rate constants are affected simlarly by the change of lipid so that the overall level probability is unchanged.“ Although, in the example given, the membrane thicknesses are not the same, it has been shown that it is through its chemical constitution, rather than through its effect on membrane thickness that the lipid chiefly acts.“ As with the switching on of the conductance, therefore, the specific interaction of the lipid with the polypeptide seems to be important. The main purpose of the foregoing discussion of conduction by alamethicin is to illustrate the point that, for a potential-dependent permeability, the nature of the lipid may seriously affect the extent of the membrane polarization or depolarization necessary to open the channels. Indeed, if the dipole mechanism is correct, there is at least one lipid, phosphatidyl ethanolamine, for which inaccessibly large depolarizations are required. This finding, and those discussed in earlier sections, combine to emphasize the importance of working with appropriate lipids in biological membrane reconstitution studies. Not only may the natural transport proteins fail to function in foreign lipids but, more confusingly, they may function quite abnormally. In addition, membrane components, which in the natural state are not involved in ion transport, may become so in association with different lipids.
REFERENCES 1. 2. 3.
MONTAL, M. & P. MUELLER. 1972. Proc. Nat. Acad. Sci. U.S.A. 69: 3561-3566. MONTAL, M. 1973. Biochim. Biophys. Acta 298: 750-754. FETTIPLACE, R., D. M. ANDREWS & D. A. HAYDON. 1971. J. Membrane Biol.
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FETTIPLACE, R. 1974. Ph.D. dissertation. FEITIPLACE, R., L. G. M. GORDON, S. B. HLADKY, J. REQUENA, H. P. ZINGSHEIM & D. A. HAYDON. 1975. Techniques in the formation and examination of “black” lipid bilayer membranes. In Methods in Membrane Biology. E. D. Korn, Ed. Vol. 4: Plenum Press. New York, N.Y. LECUYER, H. & D. G. DERVICHIAN. 1969. J. Mol. Biol. 45: 39-57. REISS-HUSSON, F. 1967. J. Mol. Biol. 25: 363-382. SMALL, D. M. 1967. J. Lipid Res. 8: 551-557. ANDREWS, D. M., E. D. MANEV & D. A. HAYDON. 1970. Spec. Discuss. Faraday SOC.1: 46-56. & J. TAYLOR. 1964. Proc. Roy. SOC.,Ser. A 281: HANAI,T., D. A. HAYDON
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NORMAN, A. W.,R. A. DEMEL,B. de KRUYFF,W. S. M. GEURTS van KESSELL & L. L. M. van DEENEN.1972. Biochim. Biophys. Acta 290: 1-14. FINKELSTEIN, A. & R. HOLZ. 1973. Aqueous pores created in thin lipid membranes by the polyene antibiotics nystatin and amphotericin B. In Membranes. G. Eisenman, Ed. Vol. 2: 377-408. Marcel Dekker, Inc. New York. N.Y. HUNTER,M. J. 1974. The use of lipid bilayers as cell membrane models: An experimental test using the ionophore, valinomycin. In Drugs and Transport Processes. B. A. Callingham, Ed.: 227-240. Macmillan. London. England. KRASNE, S., G. EISENMAN & G. SZABO. 1971. Science 174: 412-415. HAYDON, D. A. & S. B. HLADKY. 1972. Q. Rev. Biophys. 5: 187-282. SZABO, G., G. EISENMAN, R. LAPRADE, S. M. CUNI & S. KRASNE. 1973. Experi-
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mentally observed effects of carriers on the electrical properties of bilayer membranes-equilibrium domain. In Membranes. G. Eisenman, Ed. Vol. 2: 179-328. Marcel Dekker, Inc. New York, N.Y. W. K., A. L. HODGKIN & H. MEVES.1965. J. Physiol. 1 8 0 821-836. CHANDLER, GILBERT,D. L. & G. EHRENSTEIN. 1969. Biophys. J. 9 447-463. NEUMCKE,B. 1970. Biophysik 6 23 1-240. MCLAUGHLIN, S. G. A., G. SUBO, G. EISENMAN& S. M. CIANI. 1970. Proc. Nat. Acad. Sci. U S A . 67: 1268-1275. MCLAUGHLIN, S. G. A., G. SZABO& G. EISENMAN.1971. J. Gen. Physiol. 58: 667-687. MULLER,R. U. & A. 'FINKELSTEIN. 1972. J. Gen. Physiol. 60: 285-306. HAYDON, D. A. & V. B. MYERS.1973. Biochim. Biophys. Acta 307: 429-443. HLADKY, S. B. & D. A. HAYDON. 1973. Biochim. Biophys. Acta 318: 464-468. AVEYARD, R. & D. A. HAYDON. 1973. An Introduction to the Principles of Surface Chemistry. Cambridge University Press. Cambridge, England. 0. H. JR. 1970. TPMAs. Abstracts of Biophysical Society. 14th Annual LEBLANC, Meeting. Baltimore, Maryland. The Biophysical Society. NEDERMEIJER-DENESSEN, H. J. M. & C. L. DE LIGNY.1974. J. Electroanal. Chem. 57: 265-266. TAYLOR, J. & D. A. HAYDON. 1966. Discuss. Faraday SOC.42: 51-59. STARK,G., R. BENZ, G. W. POHL& K. JANKO.1972. Biochim. Biophys. Acta 2 6 6 603-612. J. & D. A. HAYDON. Proc. Roy. SOC.London, Ser. A. In press. REQUENA, S. B. & D. A. HAYDON.1972. Biochim. Biophys. Acta 274: 294-312. HLADKY, BAMBERG, E. & P. LAUGER.1973. J. Membrane Biol. 11: 177-194. URRY,D. W., M. C. GOODALL, J. D. GLICKSON & D. F. MAYERS.1971. Proc. Nat. Acad. Sci. U S A . 6 8 1907-1911. VEATCH,W. R., E. T. FOSSEL & E. R. BLOUT.1974. Biochemistry 13: 5249-5256. VEATCH,W. R. & E. R. BLOUT.1974. Biochemistry 13: 5257-5264. FOSSEL,E. T., W. R. VEATCH,Y. A. OVCHINNIKOV & E. R. BLOUT.1974. Biochemistry 13: 5264-5275. BEAN,R. C. 1973. Protein-mediated mechanisms of variable ion conductance in thin lipid membranes. In Membranes. G . Eisenman, Ed. Vol. 2: 409-477. Marcel Dekker, Inc. New York. N.Y. EISENBERG, M., J. E. HALL& C. A. MEAD.1973. J. Membrane Biol. 14: 143-176. GORDON, L. G. M.& D. A. HAYDON. 1975. Phil. Trans. Roy. Soc. London, Ser. B. 210: 433-447. To be published. GORDON,L. G. M. & D. A. HAYDON. MUELLER, R. & D. 0. RUDIN.1968. Nature 217: 398-404. PRESSMAN, B. C. 1968. Fed. Proc. 27: 1283-1288. CHERRY,R. J., D. CHAPMAN & D. E. GRAHAM.1972. J. Membrane Biol. 7: 325-344. PAPAHADJOPOULOS, D. 1968. Biochim. Biophys. Acta 163: 240-254. ADAM,N. K., F. A. ASKEW& J. F. DANIELLI.1935. Biochem. J. 29: 1786-1801. HLADKY, S. B. Private communication. GORDON, L. G. M. Private communication. GORDON, L. G. M. & D. A. HAYDON. Unpublished results.
DISCUSSION DR. TOSTESON: Do you have any evidence on the ion-selectivity of the alamethicin channels opened by the opposite signs of potential?
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DR. HAYDON:The alamethicin channel is remarkably unselective, apart from surface charge effects, and I don’t think that the opening from opposite sides makes any difference to that state of affairs. Both are nonselective. The conductances of the channels themselves are exactly the same; it’s only the probabilities of the different levels that seem changed. DR. S. MCLAUGHLIN (State University of N e w Y o r k , Stony Brook, L.I., N . Y . ) : Dr. Haydon, what is the origin of the dipole potential that seems to occur somewhere at the surface of glycerol monooleate and phospholipids? DR. HAYDON: We thought of trying to pin this down at one stage, but it is incredibly difficult to devise experiments to do this. Since such a wide variety of lipids seem to give a similar sort of dipole potential and these lipids include, for example, cholesterol, which has a fairly simple polar group, I can only think that it must arise from the carbon-oxygen bonds between the hydrocarbon chains and the inside boundary of the head group. This bond is the one thing that all the lipids seem to have in common, and they all seem to have the same sign of potential. DR. S. CHAN(California Institute of Technology, Pasadena, C a l i f . ): We have studied the aggregation properties of alamethicin in solution as a function of ionic strength and we have found that the aggregation does go up as you increase the ionic strength of the solution, which is consistent with your idea. Secondly, by analyzing this aggregation data, we were able to show that the equilibrium concentration of the decamer varies as the ninth power of the alamethicin concentration under the experimental conditions of Hall and Eisenberg. DR. HAYDON: That’s very comforting.
