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Electrical conductivity and ion permeation in planar lipid membranes
ELSEVIER
Bioelectrochemistry
and Bioenergetics
41 (1996)
197-200
Short communication
Electrical conductivity and ion permeation in planar lipid membranes F. Bordi avc,C. Cametti b7c**,F. Natali b a Sezione di Fish ’ Istituto
Medicu, Dipurtimmto di Medicina Interna, Uniuersitu’ di Roma “Tar Vergata”. Rome. ltuly b Dipartimento di Fisica, Uniuersita’ di Rome “La Supienza”, Rome. Italy Nuzicmule di Fisica della Materia, Uniuersitu’ di Romrr “La Sapienza”, Rome, Italy Received
Keywords:
Planar membranes;
Ion permeation;
Patch-clamp;
31 January
1996; revised
Membrane
resistance
1. Introduction Phospholipid bilayer membranes represent useful model systems for the investigation of the basic aspects of the lipid bilayer components of biological cell membranes and, in particular, ionic transport processes. Although the electrical properties of these structures, which are of fundamental importance in many areas of biology, have been characterized in detail by a variety of experimental techniques [ 1I, the basic mechanism of ion translocation or ion permeation across the hydrophobic region of the lipid bilayer is not completely understood. In the simplest model of ion transport across a membrane, the ion must diffuse to the membrane interface, adsorb, cross the lipid core, desorb and finally diffuse away on the other side. This process should require an energy of the order of 100-150 k.I mol- ‘, when estimated for a monovalent ion diffusing from an aqueous phase to the hydrocarbon region of the lipid bilayer [2]. Since the measured ionic flux of monovalent ions is larger than that calculated from the Born energy, it follows that non-specific conductance pathways must appear in the membrane structure, i.e. substantial facilitated ion diffusion occurs through aqueous pores which are an intrinsic part of the bilayer structure. As pointed out by Smith et al. [2], these pores may be formed as a result of fluctuations in lipid organization, but their density, of the order of lo”--10’ pores cm-*, is sufficiently small to have no effect on the basic structure of the hydrophobic region of the lipid bilayer. To gain further insight into the ionic conductance across lipid bilayers, the electrical conductivity across a planar
* Corresponding
author
0302.4598/96/$15.00 Copyright PII SO302-45YX(96)05OY4-5
0 1996 Elsevier
18 March
1996
lipid membrane, separating bath solutions of different potassium chloride concentration in the range 0.1-l mol I-‘, was measured using a patch-clamp pipette technique. The results are discussed in terms of a channel conduction model based on the statistical rate theory recently proposed by Skinner et al. [3]. The results indicate that the ionic transport process in these systems can be described as a first-order chemical reaction with appropriate values of the equilibrium exchange rate constant and partition coefficients.
2. Experimental
details
Phospholipid bilayers were formed at the tip of a patch-clamp pipette using the dipping technique described by Coronado and Latorre [4,5]. After immersion of the pipette within the electrolyte solution (0.1 mol 1-l KCl, 10e2 mol l- ’ Hepes Tris, pH 7.5) contained in the measuring cell, an appropriate amount of lipid dissolved in chloroform (10 ml at a concentration of 10 mg ml-’ ) was spread on the aqueous surface to form a monolayer. After evaporation of the solvent from the surface of the solution and the formation of a high-resistance seal between the glass pipette and the polar head groups of the lipid, the bilayer was formed by moving the pipette into the air and then back into the solution. The formation of seals giving rise to a bilayer structure was ascertained from the change in the electrical resistance during the movement of the pipette. The lipids used (dipalmitoylphosphatidylethanolamine (DPPE) and dimyristoylphosphatidylethanolamine (DMPE)) were obtained from Sigma Chemical Company and were used without further purification. All measurements were carried out at a temperature of 25°C within
Science S.A. All rights reserved.
198
F. Bordi
et al./
Bioelectrochemistry
1°C. Movement of the pipette was obtained in a reproducible manner using a coarse micromanipulator. Pipettes were filled with KC1 electrolyte solution at different molarities between 0.1 and 1 mol I-‘. To measure the electrical currents produced by the KC1 gradients under the influence of an external electrical field, the bilayers were formed with both the aqueous phases at identical concentrations; the electrolyte concentration in the electrode pipette compartment was then varied by the addition of more concentrated salt solution. The voltage was applied to the electrode inside the pipette, and the external electrode was grounded through the current amplifier. Pipettes, made of hard glass capillaries (KG 331, were prepared immediately before use by a vertical pipette puller (model PP-83, Narishige Science Instruments Laboratory) using the standard two-pull method. The heater current was adjusted to produce pipettes with a tip diameter in the range l-2 km.
3. Review
of the permeation
model
Recently, on the basis of the statistical rate approach proposed by Ward [6] and Ward et al. [7], Skinner et al. [3] derived an expression to describe the ionic transport across a membrane considering the whole process as a chemical reaction. A brief summary of the model proposed by Skinner et al. [3] is given and the most relevant relationships are reviewed using the same symbols as in Ref. [3]. The permeation model underlying this approach consists of three independent steps, each giving rise to an ionic flux, from the external medium to the membrane pore, across the membrane pore and from the membrane pore to the inner medium. For each step, the current density can be written, following Skinner et al. [3], as pj[ XliexpgQi X,ci = zxFKi,ci
I
7
and
Biomergetics
F
jce.e = z.JKce.,
7 I7
QCe ,J
where [Xii, [C,],, [C, I, and [Xl, are the concentrations of ion x in the bulk inner medium, the membrane pore at the interface with the inner medium, the membrane pore at the interface with the external medium and the bulk external medium respectively. In this context, the inner and external media indicate conventionally the two media separated by the presence of the double layer (the membrane). In the above expressions, @ is the electrical potential and the superscripts and subscripts refer, as above, to the inner medium (i), the outer medium (e>, the inner side of the membrane pore (Ci> and the external side of the membrane pore (Ce). Finally, z, is the valence, R is the gas constant, F is the Faraday constant (F = 96 485 Coulomb mol- ’ 1, T is the absolute temperature, Ki,ci, Kci,c- and Kce,e are the equilibrium exchange rates across the unit area of the interface in the three different transport processes and p\ and p’, are the partition coefficients on the inner interface and outer interface respectively. Fig. 1 shows a sketch of the membrane separating two different media; the symbols refer to the different quantities involved in the different regions of the system. In the steady state condition, the current densities must be equal, i.e. j3ji,ci
=jCi,Ce
=.k,,
This yields, taking the reference potential as that of the external medium, @” = 0, the following expressions Y =A Ki ci x Kc,,ce
\ _.- 77 r\
p[ Xliexpg
8:[Xliexp~E X
X
-
,ce =
ZX
FKCi
.Ce
@I[ XliexpzE
Qi J
i
7
1
l-7
[C,l,expsQc’
where
ZXF#ci
x = [ C,li exp=
[C,],expg -
ace \ -
[C,liexpsQci
lT
)
J
I
.7 L‘
[C,V]iexpg@ci jci
QCe
i
[ C,],expz
[C,]iexp$iPc’
-
197-200
[C.,],expg
x --Y
[C,]iexps@Ci
41 (19961
y= [C,],expg@”
)
J
F. Bordi
et ul./Bioelectrochemistry
md Bioenergetics
41 11996) 197-200
199
3000 2500 2000 1500 1000 500 Fio0’ 1. Schematic diagram of the media. The symbols used for the different regions of the system are those used by Skinner et al. [3] in
membrane separating two different different quantities involved in the shown. The symbols are the same as their statistical rate theory approach.
The solution of the above system cally only in particular cases, i.e. at the interfaces or when for the rium exchange rates are equal. current density is given by
can be obtained analytiwhen equilibrium exists three fluxes the equilibIn this latter case, the l/3
pj[ Xliexp$E j = 2, FKci .ce
( P3 x lY3
(1) This equation depends on two parameters: the equilibrium exchange rate Kci,ce and the ratio of the partition coefficients ( pj/p,“).
4. Results The formation of a stable close-packed planar bilayer at the end of the pipette, consisting of a bimolecular struc-
0
0
20
30
40
50
60
Electrical potential E /mV Fig. 3. I-E relationship of DPPE membrane for different concentrations of KCI: A, 0.1 mol I-‘; 0, 0.2 mol I-‘; 0, 0.6 mol I-‘; 0, I mol I-‘. The concentration of the electrolyte solution of the external bath is maintained constant at a value of 0.1 mol 1-l KCI. The full lines represent the calculated values according to Eq. (I) with the parameters shown in Fig. 5.
ture, was ascertained by measuring the electrical capacitance derived from the decay of the current signal towards the steady state value after an electrical potential step was applied. For the phospholipid investigated, all values were in the range 0.45-0.55 FLF cm-‘, remaining approximately constant over the whole membrane lifetime. The bilayer thickness derived from the specific capacitance, assuming for the dielectric constant a value of F = 2.1 (the average permittivity of long-chain hydrocarbon media), varied approximately from 3.4 to 4.2 nm, covering the values generally found for these systems. The resistances of the two different phospholipid membranes, calculated from the regression of the current-voltage curves (Z-E curves), are shown in Fig. 2. The I-E relationships for various values of the ionic concentration in the external bath are shown in Fig. 3 and Fig. 4 for both bilayers; the full lines are calculated on the basis of eq. (1) of Skinner’s model.
3500 I
c:
180
5
160
!x
140
2500 ;
8 t:3
120
2000
100
‘Z2
80
1500 i 1000 I 500 ;
r
2oi,, 0.0
10
3000 b
, 0.2
0.4
,
O;L
, 0.6
0.8
1.0
Ionic concentration c /mol 1.’ Fig. 2. Resistance of the membrane formed using two different phospholipids as a function of the salt concentration (KC]) at one side of the membrane (inner medium). The concentration of the electrolyte solution on the other side (external medium) is maintained constant at a value of 0.1 mol I- ’ KCl: 0, DMPE; A, DPPE.
10
20
Electrical
30 potential
40
50
60
E / mV
Fig. 4. I-E relationship of DMPE membrane for different concentrations ofKC1: a,O.Imoll~‘; q ,0.2mol1-‘;0,0.6molI~‘;0,1mol1~‘. The concentration of the electrolyte solution of the external bath is maintained constant at a value of 0.1 mol 1-l KCI. The full lines represent the calculated values according to Eq. (1) with the parameters shown in Fig. 5.
200
F. Bordi
OL,,,’ 0.0
0.2
,,I
0.4
,,I,d,/’ 0.6
Ionic concentration
et al./ Biorlectrochemistry
,”
0.8
1.0
ro
c / mol 1.’
Fig. 5. Equilibrium exchange rate Kci,c, and partition coefficient ( pi / 0:) of the DMPE and DPPE membranes as a function of the ionic concentration in the inner bath, derived from the fitting of Eq. (1) to the measured I- E curves.
The occurrence of a non-linear current-voltage relationship, which indicates that the use of common membrane equations based on Ohm’s law is inadequate, can be taken into account with good agreement by Eq. (1). Deviation from linearity is more marked as the ion concentration gradient increases. This effect can be well accounted for by Skinner’s model by varying appropriately the equilibrium exchange rate. A non-linear, least-squares fitting procedure was used to find the values of the two parameters Kci.c, and ( /3,:/p,‘> which best fit the data to the functional form of Eq. (1). The results are shown in Fig. 5 where the equilibrium exchange rate and the ratio of the partition coefficients are plotted as a function of the ionic concentration in the external medium. The values of the conductance per unit surface G,,, derived from the Z-E curves allow the density of the aqueous pathways in the bilayer structure to be evaluated. This quantity is given, to a first approximation, by G,,,=NpGp(na2)
+G,(l
-N&W’))
where Gp and G, are the conductance per unit surface of the aqueous pore and hydrophobic region respectively, N, is the pore density and a is the pore radius. Each water pore of thickness d contributes with a surface conductance given by G,=n-
and Bioenergetics
41 (1996)
197-200
thickness of the bilayer of the order of 4.0 nm, the pore density Np varies from 9 X 10” to 3 X 10” pores mm2 for DPPE and from 3 X 10” to 2 X 10” pores m-2 for DMPE as the ion concentration in the external bath is varied from 0.1 to 1 mol 1-l. These values, although sufficiently small to have no effect on the basic structure of the bilayer, occupying only about 2 X 10m6 of the bilayer surface, completely justify the observed behaviour of ionic conduction. It should be noted that the pore density is only slightly different for the two systems investigated, although the hydrophobic region differs by two CH, groups. These results indicate that the hydrophobic region of the lipid bilayer does not behave as a uniform non-conductive bulk phase where, on the basis of the simple application of Born energy considerations, the ionic conductance should be negligible. In contrast, transient fluctuations in the bilayer structure, as suggested by computer simulation [9], may give rise to a set of pore pathways in which facilitated ion transport may occur. The results reported here show that, for both lipids investigated, the exchange rate constants increase with increasing ionic concentration, indicating that the corresponding chemical reaction depends on the bulk ion content. Moreover, at the ionic concentration employed, for both phospholipids, the ratio of the partition coefficients ( P2P.3 is aPProximately the same with a value around unity, i.e. the solubility for the particular ionic species investigated, despite the different outer and inner ion concentrations, is about the same. In contrast, different extracellular and intracellular compositions in membranes of biological cells yield different solubilities and in turn different partition coefficients. This result may suggest that, in the ionic transport process within a simple bilayer, without the specific components organized in the cell membrane system, the interface between the aqueous phase and the hydrophilic layer is not strongly influenced by the head group chemical composition and behaves, to a first approximation, independently of the ionic concentration.
References
ze2D K,Td
[l]
where n is the ion concentration, ze is the electrical charge of the ion and D is the diffusion coefficient. Assuming that the electrostatic energy difference for ion transport is about AU = 20 kJ mol-’ [8], the ion concentration n in the aqueous pore can be obtained from the concentration c of the external bath through the relation n=cexp Assuming
AE
i 1 --
[2] [3] [4] [5] [6] [7]
RT
G, =O, D = 10e9 m* s-‘,
a = 1.0 nm and a
[8] [9]
B.B. Bhowmik and P. Nandy, Chem. Phys. Lipids, 34 (1983) IOl106. J.R. Smith, D.R. Laver and H.G.L. Caster, Chem. Phys. Lipids, 34 (1984) 227-235. F.K. Skinner, CA. Ward and B.L. Bardakjian, Biophys. J.. 65 (1993) 618-629. R. Coronado and R. Latorre, Biophys. J.. 43 (1983) 231-236. R. Coronado, Biophys. J., 47 (1985) 851-857. C.A. Ward, J. Chem. Phys., 67 (1977) 229-235. C.A. Ward, R.D. Findlay and M. Rizk, J. Chem. Phys., 76 (1982) 5599-5605. A. Parsegian, Nature, 221 (1969) 844-847. B. Owenson and L.R. Pratt, J. Phys. Chem., 88 (1984) 6048-6058.
Bioelectrochemistry
and Bioenergetics
41 (1996)
197-200
Short communication
Electrical conductivity and ion permeation in planar lipid membranes F. Bordi avc,C. Cametti b7c**,F. Natali b a Sezione di Fish ’ Istituto
Medicu, Dipurtimmto di Medicina Interna, Uniuersitu’ di Roma “Tar Vergata”. Rome. ltuly b Dipartimento di Fisica, Uniuersita’ di Rome “La Supienza”, Rome. Italy Nuzicmule di Fisica della Materia, Uniuersitu’ di Romrr “La Sapienza”, Rome, Italy Received
Keywords:
Planar membranes;
Ion permeation;
Patch-clamp;
31 January
1996; revised
Membrane
resistance
1. Introduction Phospholipid bilayer membranes represent useful model systems for the investigation of the basic aspects of the lipid bilayer components of biological cell membranes and, in particular, ionic transport processes. Although the electrical properties of these structures, which are of fundamental importance in many areas of biology, have been characterized in detail by a variety of experimental techniques [ 1I, the basic mechanism of ion translocation or ion permeation across the hydrophobic region of the lipid bilayer is not completely understood. In the simplest model of ion transport across a membrane, the ion must diffuse to the membrane interface, adsorb, cross the lipid core, desorb and finally diffuse away on the other side. This process should require an energy of the order of 100-150 k.I mol- ‘, when estimated for a monovalent ion diffusing from an aqueous phase to the hydrocarbon region of the lipid bilayer [2]. Since the measured ionic flux of monovalent ions is larger than that calculated from the Born energy, it follows that non-specific conductance pathways must appear in the membrane structure, i.e. substantial facilitated ion diffusion occurs through aqueous pores which are an intrinsic part of the bilayer structure. As pointed out by Smith et al. [2], these pores may be formed as a result of fluctuations in lipid organization, but their density, of the order of lo”--10’ pores cm-*, is sufficiently small to have no effect on the basic structure of the hydrophobic region of the lipid bilayer. To gain further insight into the ionic conductance across lipid bilayers, the electrical conductivity across a planar
* Corresponding
author
0302.4598/96/$15.00 Copyright PII SO302-45YX(96)05OY4-5
0 1996 Elsevier
18 March
1996
lipid membrane, separating bath solutions of different potassium chloride concentration in the range 0.1-l mol I-‘, was measured using a patch-clamp pipette technique. The results are discussed in terms of a channel conduction model based on the statistical rate theory recently proposed by Skinner et al. [3]. The results indicate that the ionic transport process in these systems can be described as a first-order chemical reaction with appropriate values of the equilibrium exchange rate constant and partition coefficients.
2. Experimental
details
Phospholipid bilayers were formed at the tip of a patch-clamp pipette using the dipping technique described by Coronado and Latorre [4,5]. After immersion of the pipette within the electrolyte solution (0.1 mol 1-l KCl, 10e2 mol l- ’ Hepes Tris, pH 7.5) contained in the measuring cell, an appropriate amount of lipid dissolved in chloroform (10 ml at a concentration of 10 mg ml-’ ) was spread on the aqueous surface to form a monolayer. After evaporation of the solvent from the surface of the solution and the formation of a high-resistance seal between the glass pipette and the polar head groups of the lipid, the bilayer was formed by moving the pipette into the air and then back into the solution. The formation of seals giving rise to a bilayer structure was ascertained from the change in the electrical resistance during the movement of the pipette. The lipids used (dipalmitoylphosphatidylethanolamine (DPPE) and dimyristoylphosphatidylethanolamine (DMPE)) were obtained from Sigma Chemical Company and were used without further purification. All measurements were carried out at a temperature of 25°C within
Science S.A. All rights reserved.
198
F. Bordi
et al./
Bioelectrochemistry
1°C. Movement of the pipette was obtained in a reproducible manner using a coarse micromanipulator. Pipettes were filled with KC1 electrolyte solution at different molarities between 0.1 and 1 mol I-‘. To measure the electrical currents produced by the KC1 gradients under the influence of an external electrical field, the bilayers were formed with both the aqueous phases at identical concentrations; the electrolyte concentration in the electrode pipette compartment was then varied by the addition of more concentrated salt solution. The voltage was applied to the electrode inside the pipette, and the external electrode was grounded through the current amplifier. Pipettes, made of hard glass capillaries (KG 331, were prepared immediately before use by a vertical pipette puller (model PP-83, Narishige Science Instruments Laboratory) using the standard two-pull method. The heater current was adjusted to produce pipettes with a tip diameter in the range l-2 km.
3. Review
of the permeation
model
Recently, on the basis of the statistical rate approach proposed by Ward [6] and Ward et al. [7], Skinner et al. [3] derived an expression to describe the ionic transport across a membrane considering the whole process as a chemical reaction. A brief summary of the model proposed by Skinner et al. [3] is given and the most relevant relationships are reviewed using the same symbols as in Ref. [3]. The permeation model underlying this approach consists of three independent steps, each giving rise to an ionic flux, from the external medium to the membrane pore, across the membrane pore and from the membrane pore to the inner medium. For each step, the current density can be written, following Skinner et al. [3], as pj[ XliexpgQi X,ci = zxFKi,ci
I
7
and
Biomergetics
F
jce.e = z.JKce.,
7 I7
QCe ,J
where [Xii, [C,],, [C, I, and [Xl, are the concentrations of ion x in the bulk inner medium, the membrane pore at the interface with the inner medium, the membrane pore at the interface with the external medium and the bulk external medium respectively. In this context, the inner and external media indicate conventionally the two media separated by the presence of the double layer (the membrane). In the above expressions, @ is the electrical potential and the superscripts and subscripts refer, as above, to the inner medium (i), the outer medium (e>, the inner side of the membrane pore (Ci> and the external side of the membrane pore (Ce). Finally, z, is the valence, R is the gas constant, F is the Faraday constant (F = 96 485 Coulomb mol- ’ 1, T is the absolute temperature, Ki,ci, Kci,c- and Kce,e are the equilibrium exchange rates across the unit area of the interface in the three different transport processes and p\ and p’, are the partition coefficients on the inner interface and outer interface respectively. Fig. 1 shows a sketch of the membrane separating two different media; the symbols refer to the different quantities involved in the different regions of the system. In the steady state condition, the current densities must be equal, i.e. j3ji,ci
=jCi,Ce
=.k,,
This yields, taking the reference potential as that of the external medium, @” = 0, the following expressions Y =A Ki ci x Kc,,ce
\ _.- 77 r\
p[ Xliexpg
8:[Xliexp~E X
X
-
,ce =
ZX
FKCi
.Ce
@I[ XliexpzE
Qi J
i
7
1
l-7
[C,l,expsQc’
where
ZXF#ci
x = [ C,li exp=
[C,],expg -
ace \ -
[C,liexpsQci
lT
)
J
I
.7 L‘
[C,V]iexpg@ci jci
QCe
i
[ C,],expz
[C,]iexp$iPc’
-
197-200
[C.,],expg
x --Y
[C,]iexps@Ci
41 (19961
y= [C,],expg@”
)
J
F. Bordi
et ul./Bioelectrochemistry
md Bioenergetics
41 11996) 197-200
199
3000 2500 2000 1500 1000 500 Fio0’ 1. Schematic diagram of the media. The symbols used for the different regions of the system are those used by Skinner et al. [3] in
membrane separating two different different quantities involved in the shown. The symbols are the same as their statistical rate theory approach.
The solution of the above system cally only in particular cases, i.e. at the interfaces or when for the rium exchange rates are equal. current density is given by
can be obtained analytiwhen equilibrium exists three fluxes the equilibIn this latter case, the l/3
pj[ Xliexp$E j = 2, FKci .ce
( P3 x lY3
(1) This equation depends on two parameters: the equilibrium exchange rate Kci,ce and the ratio of the partition coefficients ( pj/p,“).
4. Results The formation of a stable close-packed planar bilayer at the end of the pipette, consisting of a bimolecular struc-
0
0
20
30
40
50
60
Electrical potential E /mV Fig. 3. I-E relationship of DPPE membrane for different concentrations of KCI: A, 0.1 mol I-‘; 0, 0.2 mol I-‘; 0, 0.6 mol I-‘; 0, I mol I-‘. The concentration of the electrolyte solution of the external bath is maintained constant at a value of 0.1 mol 1-l KCI. The full lines represent the calculated values according to Eq. (I) with the parameters shown in Fig. 5.
ture, was ascertained by measuring the electrical capacitance derived from the decay of the current signal towards the steady state value after an electrical potential step was applied. For the phospholipid investigated, all values were in the range 0.45-0.55 FLF cm-‘, remaining approximately constant over the whole membrane lifetime. The bilayer thickness derived from the specific capacitance, assuming for the dielectric constant a value of F = 2.1 (the average permittivity of long-chain hydrocarbon media), varied approximately from 3.4 to 4.2 nm, covering the values generally found for these systems. The resistances of the two different phospholipid membranes, calculated from the regression of the current-voltage curves (Z-E curves), are shown in Fig. 2. The I-E relationships for various values of the ionic concentration in the external bath are shown in Fig. 3 and Fig. 4 for both bilayers; the full lines are calculated on the basis of eq. (1) of Skinner’s model.
3500 I
c:
180
5
160
!x
140
2500 ;
8 t:3
120
2000
100
‘Z2
80
1500 i 1000 I 500 ;
r
2oi,, 0.0
10
3000 b
, 0.2
0.4
,
O;L
, 0.6
0.8
1.0
Ionic concentration c /mol 1.’ Fig. 2. Resistance of the membrane formed using two different phospholipids as a function of the salt concentration (KC]) at one side of the membrane (inner medium). The concentration of the electrolyte solution on the other side (external medium) is maintained constant at a value of 0.1 mol I- ’ KCl: 0, DMPE; A, DPPE.
10
20
Electrical
30 potential
40
50
60
E / mV
Fig. 4. I-E relationship of DMPE membrane for different concentrations ofKC1: a,O.Imoll~‘; q ,0.2mol1-‘;0,0.6molI~‘;0,1mol1~‘. The concentration of the electrolyte solution of the external bath is maintained constant at a value of 0.1 mol 1-l KCI. The full lines represent the calculated values according to Eq. (1) with the parameters shown in Fig. 5.
200
F. Bordi
OL,,,’ 0.0
0.2
,,I
0.4
,,I,d,/’ 0.6
Ionic concentration
et al./ Biorlectrochemistry
,”
0.8
1.0
ro
c / mol 1.’
Fig. 5. Equilibrium exchange rate Kci,c, and partition coefficient ( pi / 0:) of the DMPE and DPPE membranes as a function of the ionic concentration in the inner bath, derived from the fitting of Eq. (1) to the measured I- E curves.
The occurrence of a non-linear current-voltage relationship, which indicates that the use of common membrane equations based on Ohm’s law is inadequate, can be taken into account with good agreement by Eq. (1). Deviation from linearity is more marked as the ion concentration gradient increases. This effect can be well accounted for by Skinner’s model by varying appropriately the equilibrium exchange rate. A non-linear, least-squares fitting procedure was used to find the values of the two parameters Kci.c, and ( /3,:/p,‘> which best fit the data to the functional form of Eq. (1). The results are shown in Fig. 5 where the equilibrium exchange rate and the ratio of the partition coefficients are plotted as a function of the ionic concentration in the external medium. The values of the conductance per unit surface G,,, derived from the Z-E curves allow the density of the aqueous pathways in the bilayer structure to be evaluated. This quantity is given, to a first approximation, by G,,,=NpGp(na2)
+G,(l
-N&W’))
where Gp and G, are the conductance per unit surface of the aqueous pore and hydrophobic region respectively, N, is the pore density and a is the pore radius. Each water pore of thickness d contributes with a surface conductance given by G,=n-
and Bioenergetics
41 (1996)
197-200
thickness of the bilayer of the order of 4.0 nm, the pore density Np varies from 9 X 10” to 3 X 10” pores mm2 for DPPE and from 3 X 10” to 2 X 10” pores m-2 for DMPE as the ion concentration in the external bath is varied from 0.1 to 1 mol 1-l. These values, although sufficiently small to have no effect on the basic structure of the bilayer, occupying only about 2 X 10m6 of the bilayer surface, completely justify the observed behaviour of ionic conduction. It should be noted that the pore density is only slightly different for the two systems investigated, although the hydrophobic region differs by two CH, groups. These results indicate that the hydrophobic region of the lipid bilayer does not behave as a uniform non-conductive bulk phase where, on the basis of the simple application of Born energy considerations, the ionic conductance should be negligible. In contrast, transient fluctuations in the bilayer structure, as suggested by computer simulation [9], may give rise to a set of pore pathways in which facilitated ion transport may occur. The results reported here show that, for both lipids investigated, the exchange rate constants increase with increasing ionic concentration, indicating that the corresponding chemical reaction depends on the bulk ion content. Moreover, at the ionic concentration employed, for both phospholipids, the ratio of the partition coefficients ( P2P.3 is aPProximately the same with a value around unity, i.e. the solubility for the particular ionic species investigated, despite the different outer and inner ion concentrations, is about the same. In contrast, different extracellular and intracellular compositions in membranes of biological cells yield different solubilities and in turn different partition coefficients. This result may suggest that, in the ionic transport process within a simple bilayer, without the specific components organized in the cell membrane system, the interface between the aqueous phase and the hydrophilic layer is not strongly influenced by the head group chemical composition and behaves, to a first approximation, independently of the ionic concentration.
References
ze2D K,Td
[l]
where n is the ion concentration, ze is the electrical charge of the ion and D is the diffusion coefficient. Assuming that the electrostatic energy difference for ion transport is about AU = 20 kJ mol-’ [8], the ion concentration n in the aqueous pore can be obtained from the concentration c of the external bath through the relation n=cexp Assuming
AE
i 1 --
[2] [3] [4] [5] [6] [7]
RT
G, =O, D = 10e9 m* s-‘,
a = 1.0 nm and a
[8] [9]
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