- Email: [email protected]
Experimental evidence of specific electrical contribution of a membrane system
Bioelectrochemistry and Bioe.nergetics 7 (1980) 2 o 9 - 2 I 7 J. Electroanal. Chem. 116 (t98o) 2 o 9 - 2 1 7 E l s e v i e r S e q u o i a S.A., L a u s a n n e - P r i n t e d in I t a l y
302 - Experimental Evidence of Specific Electrical Contribution of a Membrane S y s t e m * by A. R~JOU-MICltF~L, M. DELMOTTE and M. VILLARDI L a b o r a t o i r e de T h e r m o d y n a m i q u e des M i l i e u x I o n i q u e s et B i o l o g i q u e s - T o u r 33-43 - E 2 - U n i v e r s i t 6 P a r i s V I I - 75221 P a r i s C e d e x 05, F r a n c e E q u i p e d e R e c h e r c h e Associ6e au C . N . R . S . E R A n ° 37 ° R e v i s e d m a n u s c r i p t r e c e i v e d N o v e m b e r 2 9 t h 1979
Summary A technical device, designed to measure directly the membrane permeability in non-equilibrium steady state, has been developed for the s t u d y of membrane potential differences. It is shown t h a t the membrane potential does not depend on membrane nature and bulk concentrations only, but also on local concentrations on membrane walls due to experimental mixing conditions. This observation leads us to define a specific contribution of membrane A(Dsm :
AOmb = AO~i q- AO,~ where AqSmbis the measured membrane potential and AOlj is the liquid junction potential. AO,m includes two t e r m s : - - a diffusion term depending on concentration ratio, and - - a charge term depending also on the concentration level. From theoretical and experimental treatment, we can show t h a t our artificial albumin membranes are negatively charged. We can also determine local ionic transference numbers inside the membrane phasis. The studied electrolytes are NaC1 or CaC12. We observe t h a t the relative mobility of Ca 2+ decreases inside membrane phase whereas the relative mobility of Na + increases with respect to the relative mobility of CI-.
* P r e s e n t e d at t h e 5th I n t e r n a t i o n a l S y m p o s i u m on t3ioelectrochemistry, 3 - 8 S e p t e m b e r 1979, "Weimar ( D . D . R . ) .
o3o2-4958/8o/o2o9-o217
© E l s e v i e r S e q u o i a S.A.
21o
R6jou-Michel, Delmotte and ViUardi
Introduction Experimental devices have been designed to s t u d y the permeabilities of chemico-active membranes, clamped under non-equilibrium conditions [I~. These devices have been designed since 1976 for the measurement of membrane potential differences, under the same conditions. In the first section of this paper, it is shown t h a t any membrane, put under one and the same ionic concentration constraint, exhibits several membrane potential difference values. However, these values characterize the experimental conditions. This observation leads us to define a membrane system which plays the part of the membrane itself as far as permeabilities and electrical properties are concerned. Then, we present experimental results regarding the electrical COlltribution due to such a membrane system. The concentration constraints are the concentration differences of NaC1 or CaC12, in a phosphate or adenosinetriphosphate buffer. In conclusion, theoretical descriptions [21 applied to such systems are justified and allow us to calculate ionic intramembrane mobility.
Experimental description The so-called membrane potential is measured by means of two double-junctioI1 flowing reference electrodes. These electrodes dip in two ionic aqueous solutions of different concentrations Ch and cl (with ch > cl). An artificial membrane is horizontally set between the two compartments of a diffusion-reaction cell E3~ which contains both solutions. The more concentrated solutions is always in the bottom compartment. Both solutions can be mixed or not and the concentrations are artificially kept time-constant by means of an inlet or an outlet of matter. Moreover, t h e y are thermostated at 2o.oo ~ o.oo5 °C. During the first stage of each experiment, which lasts three to six hours, the mixing is realized by two special magnet-driven mixers and is adjustable and regulated at a chosen value. Consequently, the average thickness of the hydrodynamic boundary layers is kept constant on both sides of the membrane. Under these conditions, both concentrations are inclined to quickly evolve to a common value by diffusion through the membrane. To counterbalance this evolution and to clamp both concentrations, we measure the concentrations and we introduce counterbalance solutions by means of servomechanisms. The measurement of the concentration (not time-dependent) is performed in the middle part of the compartments by a "specific electrode - reference electrode" couple, far away from the hydrodynamic layers. The membrane potential is permanently measured; the two flowing electrodes are also far away from the hydrodynamic boundary layers [41. The second measurement stage begins with the cessation of mixing. At the technical level, it becomes impossible to keep the concentrations automatically constant because of the absence of mixing of the counter-
Electrical
Contribution
of a 1 V [ e m b r a n e S y s t e m
21I
balance solution. Nevertheless, we observe through concentration measurement t h a t these concentrations, in the surroundings of the detectors, stay quasi-steady for about 4 8 hours. This has been verified by delayed titrations of the solutions contained inside the compartments. Throughout this stage, we measure the membrane potential. During these two steps, the membrane system is set in a n o n equilibrium state, imposed by the same Ch-Cl concentration constraint. In spite of this, the membrane potential presents two very different values. The second stage's value is always close to the liquid junction potential difference E5]. Membrane potential characteristics
The liquid junction potential difference is usually measured without any membrane, between two ionic solutions of different concentrations connected by a capillary tube [61. This parameter is characteristic of the ionic species and their concentrations only, as we can see in the usual formula [7] : II
=
.
--
grad ~i dx
(I)
I
tl, zl and ~i are the transference number, the electrovalence and the chemical potential of the ionic species i respectively, and x is the integration coordinate from I to II. The second period of our experiments shows t h a t there are experimental conditions under which the membrane potential is strictly n o n membrane-dependent. Consequently, the potential difference measured during experiments is more dependent on the membrane system characteristics than on the membrane itself. On the other hand, the first stage shows t h a t the membrane potential is a function of - - the mixing conditions of both media in contact with the membrane walls, - - the nature and the permeability of the membrane itself, - - the nature and the bulk concentrations of the ionic species, - - the nature and the concentration of the used pH-buffer. The membrane potential is measured by two flgwing KC1 electrodes so t h a t their contributions are strictly null E2].
Experimental results
The ionic solutions studied are either CaC12 solution (I to 5 ° mM) in an equimolar N a 3 H A T P - N a ~ A T P buffer (pH 6.8, total ATP-concentrations I to 5 m M ) , or NaCl solutiort (5 to 12o mM). In this case
212
R6jou-Michel,
Delmotte
and
Villardi
we use the same ATP buffer or a phosphate buffer (pH 7.o, total concentration I raM). In either case (NaC1 or CaC12) we measure the cationic concentration by C1- titration. Because of these measurements, we never observed complexation between ATP and the cation. The membranes are made of albumin reticulated by glutaraldehyde [8I. They call contain I to 2 °/o of rhodopsin. Their thickness is about 7 ° to 9 ° ~m. We measure the total permeability P,m [9] and the different electrical parameters oi1 these membranes. Previously, we showed [2] t h a t we can express the membrane potential A~,,b as a function of the liquid junction potential AOli and of a contribution AO,m especially due to the membrane system : A ~ b = Aq)l~ + AO,~ (2) II1 figures I and 2, we present the albumin membrane contribution AO,m in CaC12 or NaC1 solutions and several buffers (ATP buffer or phosphate buffer). It clearly appears t h a t the specific contribution and consequently the membrane potential do not depend only on the ratio Ch/Cl, whereas the liquid junction potential does. It was shown already t h a t such results can be explained by means of a diffusion potential and the DONNAN potential description:
/~l~sm
-
I(At.,b- At) c, in --
-
+
Ce
(I - -
Et,.b) i n
CEc,,mbECe)] [CI]i [Cl]e ,~b
,
,
(3)
d
2O *15
E
IO 0.5
1.% Ln (c~/~)
l
i
/
X \
\
b
j
v
\
\
\
• \
-5 Fig. I. P l o t s of t h e Aft*sin v u l u e s for a l b u m i n m e m b r a n e b e t w e e n t w o CaCI~ s o l u t i o n s a g M n s t t h e r a t i o Ch/C I. (a) W h e n Chic I ~ 2 . 9 2 ; t h e (Ch+ cl)/2 v a l u e s are i n d i c a t e d in m m o l e / l ( O ) . (b) W h e n c I ~ 5 m m o l e / l (V). (c) W h e n c l = 5 m m o l e / / w i t h a less p e r m e a b l e m e m b r a n e (IF).
Electrical
Contribution 1
0.5
j
I
~n
of a Membrane
1.5
2
l
I
(cjc)
System
213
-10
-2C
* ~
o
]a
-30
-40
-50
Fig. 2. Plots of t h e A ~ s m values for a l b u m i n m e m b r a n e s b e t w e e n t w o NaCI solutions a g a i n s t t h e ratio Ch/CI. (a) W h e n Ch/C1 = 3.o5 ; t h e (Ch+ @ / 2 values are s a m p l e d b e t w e e n 2o a n d 80 m m o l e / / (O). (b) W h e n c I ~ 25 m m o l e / / (@) or w h e n ch ~ 4 ° m m o l e / l (V). I n this case, t h e two plots are similar b e c a u s e A ~ s m ,char is m u c h smaller t h a n A ~ s m ,difJ.
At is the difference between anionic and cationic transference numbers in aqueous solutions and Atmb the same difference in the membrane phase, Y'tmb is the sum of the transference numbers of the ions concerned by the gradient, ci and ce are the local electrolyte concentrations on the membrane walls; [C1]i,mb and EC1]e,mb are the chloride concentrations inside the charged membrane close to the membrane walls. Equation (3) can be briefly w r i t t e n :
(4)
/k~)sm = AOPsm, diK @ /k(D . . . . bar
If the volumic charge concentration M is much smaller than the ionic concentrations, we obtain by approximations:
RT A ¢ ~
c,o.
""
-
o~
M z(z @ i) ci
(ci (~
--
:Ct..b)
-
Ce
) ~
(5)
214
R6jou-lKichel,
Delmotte
and
Villardi
where z is the electrovalence of the cation when the anion is mollovaleltt. h i the case of a negatively charged membrane, equation (4) becomes (6)
AaPsm = A~sm, d i ~ - - A~sm, char
AO,m, aa, directly shows the relationship between the concentration level and the membrane potential. If ci and Ce are derived from Ch and cl [51 :
L
)! P.m(Ch )i
Ci = Ch I -~- - ~ d
Ch
Ce z
Cl
Cl I @ - ~ d
(7)
I
(8)
A(I)sm, char becomes
RT Al~Jsm, char =
M
--"
(I - -
5:~[mb) K
(9)
z(z + I) Ch
where K is a function of the permeabilities P,m and Pa (Pd is the apparent permeability of diffusion boundary layers) and of the ratio Ch/Cl only
(
1--2
.
P.m) ch(ch ) .
.
Pd
.
I
.
ci
cl
K =
(~o) - -
Cl
Jr-
I .
~
.
.
Pd
.
.
I
cl
So, if Ch/Cl is constant, we see that AO,m, char, Al~sm and Aq~m~ are linear functions of I/Ch. In figure 3, we have plotted AO),~ against I/Ch for CaC12 experiments (Ch/q ~ 2,92) and for NaC1 experiments (Ch/Cl ---- 3.O5). When I/Ch moves down to o, the extrapolated value allows us to determine immediately AO,~, dly and the AGb. The values of At differences with respect to different experimental conditions are gathered in the following table :
At in buffer free solution
At in experimental buffer
Atmb
NaC1
o.216
o.188
-0.642
CaCI 2
0.357
0.339
0.673
~v~
Electrical
Contribution
of a Membrane
System
215
10
50
v ~
100
li1%(l/MO{) XZ
-5 /
-2o
t0 .
.
.
.
.
~
.
.
.
.
20 1
30 r I/Ch ([/fvlo()
-30
b
Fig. 3AO)sm a g a i n s t I/C h when Chic1 is c o n s t a n t . lutions (V).
(a) F o r CaCI 2 solutions (V).
(b) F o r NaC1 so-
The description from the approximated formula (7) does not allow us to calculate M values and the (I-Xtmb) factor. Nevertheless, the latter canltot be null as Fig. 3 shows it. This observation suggests t h a t ions other than Ca 2+ and C1- or Na + and Ct- have non-negligible mobilities and play a part in the membrane system behaviour.
Interpretation For the "Ch/Ci group" experiments, we deduce from the evolution of AO,m against In Ch/Cl t h a t taking into account a negative immobilized charge, the description can only agree. As a matter of fact, albumin membranes are made of proteins and are charged if the pH of their buffer solutions is different from the isoelectric pH. In the isoelectric case, there is neutralization between -COO- charges and -NHa + charges. The albumins are considered to be acid proteins; in our experimental situations (pH 6.8), the basic form N H 2 - R - C O 0 - plays a leading part [IO]. We point out here special variations of the relative mobilities of Ca ~+ and Na + with respect to C1- mobility. In the CaC12 case, Atmb is larger than At value, so that inside the membranes pores, Ca 2+ interac-
216
R6jou-Michel, Delmotte and Villardi
tions are more important and consequently, the Atmb difference increases. On the other hand, in the NaC1 case, Atmb is much smaller than At and even negative due to relative mobility inversion. The Na + ion is much more mobile in the membrane phase than the C1- ion. This experimental and theoretical treatment allows us to obtain microscopic parameters characteristic to the membrane phase alone although the membrane cannot be analysed without its two diffusion boundary layers. The intrinsic parameters are deduced from various measured potential differences which always concern the whole membrane system and the media in contact with the membrane system. The link between these two analysis levels is induced by the notion of local concentration. The local concentrations are the concentrations effectively present on the membrane walls. During the first period of the manipulation, the local concentrations ci and ce are quasi-equal to the extreme clamped concentrations Ch and cl (cl ~- 0.90 ch for CaCI~, ci ~- 0.98 Ch for NaC1) ; thus the concentration gradient applied to the properly so-called membrane is practically the gradient realized by the Ca and cl concentrations. During the second period, the diffusion boundary layers spread out progressively and the local concentrations ci and Ce tend towards one another. When ci and Ce are equal, the experimental situation is exactly t h a t of liquid junction potential difference measurement. In the first period, the concentration gradient is applied to a medium characterized by Atmb difference whereas in the second period, the same gradient is applied to a free aqueous medium characterized by the At difference. Ill the latter case, the membrane plays a negligible part in the middle of the gradient zone. Our basic theoretical description consists in analysing the membrane potential difference as a succession of elementary potential differences along the concentration profile. We can suppose t h a t a local surconcentration on tile membrane wall i or e introduces two equal electrical contributions of opposite sign. Under such an assumption, the membrane potential cannot be distinguished from the liquid junction potential difference in each case. In fact, the effects of such a surconcentration are asymmetric because the diffusion conditions are different inside the membrane itself and inside the diffusion layers.
References
[I] M. DELMOTTE and J. CHA.NU, Bioelectrochem. Bioenerg. 3 (1976) 474 [2] A. RI~JOU--IV[ICI-IEL,IV[.VILL~,RDIand M. DELMOTTE,Bioelectrochem. Bioenerg. 6 (1979) 289 [3] M. DELIVIOTTE, Th~se Universitd Paris VII, Paris (1975) [4] G. LEVlCH, Physieochemical Hydrodynamics, Prentice-Hall Inc., Englewood Cliffs (1962) [5] A. 1R_I~JOU--I~/[ICHEL,Th~se 3~me cycle, Universitd Paris V I I , Paris (1978)
Electrical C o n t r i b u t i o n of a Membrane system
217
[6] M. DELMOTTE and J. CHANU, Topics Bioeleetroehem. Bioenerg., G. MILA.ZZO (Editor), J. Wiley, Chichester (1979) Vol. 3, p. 307 [7] D.A. MAc INNES, The Principles of Electrochemistry, Reinhold Publishing Co., New York (1939) [8] A. NA.PARSTEK, D. THOMA.S and S.R. CA.PLA.N, Biochim. Biophys. Acta 323 (1973) 643 [9] A. R~JOU--]V]~ICHEL,q3/[.P. FONTAINE et M. DELMOTTE, C.R. Hebd. Seances Acad. Sci. Ser. B 287 (1978 ) 183 IO] G. $CHA.PIRA., Eldments de Biochimie Gdndrale, F l a m m a r i o n , Paris (1965)
302 - Experimental Evidence of Specific Electrical Contribution of a Membrane S y s t e m * by A. R~JOU-MICltF~L, M. DELMOTTE and M. VILLARDI L a b o r a t o i r e de T h e r m o d y n a m i q u e des M i l i e u x I o n i q u e s et B i o l o g i q u e s - T o u r 33-43 - E 2 - U n i v e r s i t 6 P a r i s V I I - 75221 P a r i s C e d e x 05, F r a n c e E q u i p e d e R e c h e r c h e Associ6e au C . N . R . S . E R A n ° 37 ° R e v i s e d m a n u s c r i p t r e c e i v e d N o v e m b e r 2 9 t h 1979
Summary A technical device, designed to measure directly the membrane permeability in non-equilibrium steady state, has been developed for the s t u d y of membrane potential differences. It is shown t h a t the membrane potential does not depend on membrane nature and bulk concentrations only, but also on local concentrations on membrane walls due to experimental mixing conditions. This observation leads us to define a specific contribution of membrane A(Dsm :
AOmb = AO~i q- AO,~ where AqSmbis the measured membrane potential and AOlj is the liquid junction potential. AO,m includes two t e r m s : - - a diffusion term depending on concentration ratio, and - - a charge term depending also on the concentration level. From theoretical and experimental treatment, we can show t h a t our artificial albumin membranes are negatively charged. We can also determine local ionic transference numbers inside the membrane phasis. The studied electrolytes are NaC1 or CaC12. We observe t h a t the relative mobility of Ca 2+ decreases inside membrane phase whereas the relative mobility of Na + increases with respect to the relative mobility of CI-.
* P r e s e n t e d at t h e 5th I n t e r n a t i o n a l S y m p o s i u m on t3ioelectrochemistry, 3 - 8 S e p t e m b e r 1979, "Weimar ( D . D . R . ) .
o3o2-4958/8o/o2o9-o217
© E l s e v i e r S e q u o i a S.A.
21o
R6jou-Michel, Delmotte and ViUardi
Introduction Experimental devices have been designed to s t u d y the permeabilities of chemico-active membranes, clamped under non-equilibrium conditions [I~. These devices have been designed since 1976 for the measurement of membrane potential differences, under the same conditions. In the first section of this paper, it is shown t h a t any membrane, put under one and the same ionic concentration constraint, exhibits several membrane potential difference values. However, these values characterize the experimental conditions. This observation leads us to define a membrane system which plays the part of the membrane itself as far as permeabilities and electrical properties are concerned. Then, we present experimental results regarding the electrical COlltribution due to such a membrane system. The concentration constraints are the concentration differences of NaC1 or CaC12, in a phosphate or adenosinetriphosphate buffer. In conclusion, theoretical descriptions [21 applied to such systems are justified and allow us to calculate ionic intramembrane mobility.
Experimental description The so-called membrane potential is measured by means of two double-junctioI1 flowing reference electrodes. These electrodes dip in two ionic aqueous solutions of different concentrations Ch and cl (with ch > cl). An artificial membrane is horizontally set between the two compartments of a diffusion-reaction cell E3~ which contains both solutions. The more concentrated solutions is always in the bottom compartment. Both solutions can be mixed or not and the concentrations are artificially kept time-constant by means of an inlet or an outlet of matter. Moreover, t h e y are thermostated at 2o.oo ~ o.oo5 °C. During the first stage of each experiment, which lasts three to six hours, the mixing is realized by two special magnet-driven mixers and is adjustable and regulated at a chosen value. Consequently, the average thickness of the hydrodynamic boundary layers is kept constant on both sides of the membrane. Under these conditions, both concentrations are inclined to quickly evolve to a common value by diffusion through the membrane. To counterbalance this evolution and to clamp both concentrations, we measure the concentrations and we introduce counterbalance solutions by means of servomechanisms. The measurement of the concentration (not time-dependent) is performed in the middle part of the compartments by a "specific electrode - reference electrode" couple, far away from the hydrodynamic layers. The membrane potential is permanently measured; the two flowing electrodes are also far away from the hydrodynamic boundary layers [41. The second measurement stage begins with the cessation of mixing. At the technical level, it becomes impossible to keep the concentrations automatically constant because of the absence of mixing of the counter-
Electrical
Contribution
of a 1 V [ e m b r a n e S y s t e m
21I
balance solution. Nevertheless, we observe through concentration measurement t h a t these concentrations, in the surroundings of the detectors, stay quasi-steady for about 4 8 hours. This has been verified by delayed titrations of the solutions contained inside the compartments. Throughout this stage, we measure the membrane potential. During these two steps, the membrane system is set in a n o n equilibrium state, imposed by the same Ch-Cl concentration constraint. In spite of this, the membrane potential presents two very different values. The second stage's value is always close to the liquid junction potential difference E5]. Membrane potential characteristics
The liquid junction potential difference is usually measured without any membrane, between two ionic solutions of different concentrations connected by a capillary tube [61. This parameter is characteristic of the ionic species and their concentrations only, as we can see in the usual formula [7] : II
=
.
--
grad ~i dx
(I)
I
tl, zl and ~i are the transference number, the electrovalence and the chemical potential of the ionic species i respectively, and x is the integration coordinate from I to II. The second period of our experiments shows t h a t there are experimental conditions under which the membrane potential is strictly n o n membrane-dependent. Consequently, the potential difference measured during experiments is more dependent on the membrane system characteristics than on the membrane itself. On the other hand, the first stage shows t h a t the membrane potential is a function of - - the mixing conditions of both media in contact with the membrane walls, - - the nature and the permeability of the membrane itself, - - the nature and the bulk concentrations of the ionic species, - - the nature and the concentration of the used pH-buffer. The membrane potential is measured by two flgwing KC1 electrodes so t h a t their contributions are strictly null E2].
Experimental results
The ionic solutions studied are either CaC12 solution (I to 5 ° mM) in an equimolar N a 3 H A T P - N a ~ A T P buffer (pH 6.8, total ATP-concentrations I to 5 m M ) , or NaCl solutiort (5 to 12o mM). In this case
212
R6jou-Michel,
Delmotte
and
Villardi
we use the same ATP buffer or a phosphate buffer (pH 7.o, total concentration I raM). In either case (NaC1 or CaC12) we measure the cationic concentration by C1- titration. Because of these measurements, we never observed complexation between ATP and the cation. The membranes are made of albumin reticulated by glutaraldehyde [8I. They call contain I to 2 °/o of rhodopsin. Their thickness is about 7 ° to 9 ° ~m. We measure the total permeability P,m [9] and the different electrical parameters oi1 these membranes. Previously, we showed [2] t h a t we can express the membrane potential A~,,b as a function of the liquid junction potential AOli and of a contribution AO,m especially due to the membrane system : A ~ b = Aq)l~ + AO,~ (2) II1 figures I and 2, we present the albumin membrane contribution AO,m in CaC12 or NaC1 solutions and several buffers (ATP buffer or phosphate buffer). It clearly appears t h a t the specific contribution and consequently the membrane potential do not depend only on the ratio Ch/Cl, whereas the liquid junction potential does. It was shown already t h a t such results can be explained by means of a diffusion potential and the DONNAN potential description:
/~l~sm
-
I(At.,b- At) c, in --
-
+
Ce
(I - -
Et,.b) i n
CEc,,mbECe)] [CI]i [Cl]e ,~b
,
,
(3)
d
2O *15
E
IO 0.5
1.% Ln (c~/~)
l
i
/
X \
\
b
j
v
\
\
\
• \
-5 Fig. I. P l o t s of t h e Aft*sin v u l u e s for a l b u m i n m e m b r a n e b e t w e e n t w o CaCI~ s o l u t i o n s a g M n s t t h e r a t i o Ch/C I. (a) W h e n Chic I ~ 2 . 9 2 ; t h e (Ch+ cl)/2 v a l u e s are i n d i c a t e d in m m o l e / l ( O ) . (b) W h e n c I ~ 5 m m o l e / l (V). (c) W h e n c l = 5 m m o l e / / w i t h a less p e r m e a b l e m e m b r a n e (IF).
Electrical
Contribution 1
0.5
j
I
~n
of a Membrane
1.5
2
l
I
(cjc)
System
213
-10
-2C
* ~
o
]a
-30
-40
-50
Fig. 2. Plots of t h e A ~ s m values for a l b u m i n m e m b r a n e s b e t w e e n t w o NaCI solutions a g a i n s t t h e ratio Ch/CI. (a) W h e n Ch/C1 = 3.o5 ; t h e (Ch+ @ / 2 values are s a m p l e d b e t w e e n 2o a n d 80 m m o l e / / (O). (b) W h e n c I ~ 25 m m o l e / / (@) or w h e n ch ~ 4 ° m m o l e / l (V). I n this case, t h e two plots are similar b e c a u s e A ~ s m ,char is m u c h smaller t h a n A ~ s m ,difJ.
At is the difference between anionic and cationic transference numbers in aqueous solutions and Atmb the same difference in the membrane phase, Y'tmb is the sum of the transference numbers of the ions concerned by the gradient, ci and ce are the local electrolyte concentrations on the membrane walls; [C1]i,mb and EC1]e,mb are the chloride concentrations inside the charged membrane close to the membrane walls. Equation (3) can be briefly w r i t t e n :
(4)
/k~)sm = AOPsm, diK @ /k(D . . . . bar
If the volumic charge concentration M is much smaller than the ionic concentrations, we obtain by approximations:
RT A ¢ ~
c,o.
""
-
o~
M z(z @ i) ci
(ci (~
--
:Ct..b)
-
Ce
) ~
(5)
214
R6jou-lKichel,
Delmotte
and
Villardi
where z is the electrovalence of the cation when the anion is mollovaleltt. h i the case of a negatively charged membrane, equation (4) becomes (6)
AaPsm = A~sm, d i ~ - - A~sm, char
AO,m, aa, directly shows the relationship between the concentration level and the membrane potential. If ci and Ce are derived from Ch and cl [51 :
L
)! P.m(Ch )i
Ci = Ch I -~- - ~ d
Ch
Ce z
Cl
Cl I @ - ~ d
(7)
I
(8)
A(I)sm, char becomes
RT Al~Jsm, char =
M
--"
(I - -
5:~[mb) K
(9)
z(z + I) Ch
where K is a function of the permeabilities P,m and Pa (Pd is the apparent permeability of diffusion boundary layers) and of the ratio Ch/Cl only
(
1--2
.
P.m) ch(ch ) .
.
Pd
.
I
.
ci
cl
K =
(~o) - -
Cl
Jr-
I .
~
.
.
Pd
.
.
I
cl
So, if Ch/Cl is constant, we see that AO,m, char, Al~sm and Aq~m~ are linear functions of I/Ch. In figure 3, we have plotted AO),~ against I/Ch for CaC12 experiments (Ch/q ~ 2,92) and for NaC1 experiments (Ch/Cl ---- 3.O5). When I/Ch moves down to o, the extrapolated value allows us to determine immediately AO,~, dly and the AGb. The values of At differences with respect to different experimental conditions are gathered in the following table :
At in buffer free solution
At in experimental buffer
Atmb
NaC1
o.216
o.188
-0.642
CaCI 2
0.357
0.339
0.673
~v~
Electrical
Contribution
of a Membrane
System
215
10
50
v ~
100
li1%(l/MO{) XZ
-5 /
-2o
t0 .
.
.
.
.
~
.
.
.
.
20 1
30 r I/Ch ([/fvlo()
-30
b
Fig. 3AO)sm a g a i n s t I/C h when Chic1 is c o n s t a n t . lutions (V).
(a) F o r CaCI 2 solutions (V).
(b) F o r NaC1 so-
The description from the approximated formula (7) does not allow us to calculate M values and the (I-Xtmb) factor. Nevertheless, the latter canltot be null as Fig. 3 shows it. This observation suggests t h a t ions other than Ca 2+ and C1- or Na + and Ct- have non-negligible mobilities and play a part in the membrane system behaviour.
Interpretation For the "Ch/Ci group" experiments, we deduce from the evolution of AO,m against In Ch/Cl t h a t taking into account a negative immobilized charge, the description can only agree. As a matter of fact, albumin membranes are made of proteins and are charged if the pH of their buffer solutions is different from the isoelectric pH. In the isoelectric case, there is neutralization between -COO- charges and -NHa + charges. The albumins are considered to be acid proteins; in our experimental situations (pH 6.8), the basic form N H 2 - R - C O 0 - plays a leading part [IO]. We point out here special variations of the relative mobilities of Ca ~+ and Na + with respect to C1- mobility. In the CaC12 case, Atmb is larger than At value, so that inside the membranes pores, Ca 2+ interac-
216
R6jou-Michel, Delmotte and Villardi
tions are more important and consequently, the Atmb difference increases. On the other hand, in the NaC1 case, Atmb is much smaller than At and even negative due to relative mobility inversion. The Na + ion is much more mobile in the membrane phase than the C1- ion. This experimental and theoretical treatment allows us to obtain microscopic parameters characteristic to the membrane phase alone although the membrane cannot be analysed without its two diffusion boundary layers. The intrinsic parameters are deduced from various measured potential differences which always concern the whole membrane system and the media in contact with the membrane system. The link between these two analysis levels is induced by the notion of local concentration. The local concentrations are the concentrations effectively present on the membrane walls. During the first period of the manipulation, the local concentrations ci and ce are quasi-equal to the extreme clamped concentrations Ch and cl (cl ~- 0.90 ch for CaCI~, ci ~- 0.98 Ch for NaC1) ; thus the concentration gradient applied to the properly so-called membrane is practically the gradient realized by the Ca and cl concentrations. During the second period, the diffusion boundary layers spread out progressively and the local concentrations ci and Ce tend towards one another. When ci and Ce are equal, the experimental situation is exactly t h a t of liquid junction potential difference measurement. In the first period, the concentration gradient is applied to a medium characterized by Atmb difference whereas in the second period, the same gradient is applied to a free aqueous medium characterized by the At difference. Ill the latter case, the membrane plays a negligible part in the middle of the gradient zone. Our basic theoretical description consists in analysing the membrane potential difference as a succession of elementary potential differences along the concentration profile. We can suppose t h a t a local surconcentration on tile membrane wall i or e introduces two equal electrical contributions of opposite sign. Under such an assumption, the membrane potential cannot be distinguished from the liquid junction potential difference in each case. In fact, the effects of such a surconcentration are asymmetric because the diffusion conditions are different inside the membrane itself and inside the diffusion layers.
References
[I] M. DELMOTTE and J. CHA.NU, Bioelectrochem. Bioenerg. 3 (1976) 474 [2] A. RI~JOU--IV[ICI-IEL,IV[.VILL~,RDIand M. DELMOTTE,Bioelectrochem. Bioenerg. 6 (1979) 289 [3] M. DELIVIOTTE, Th~se Universitd Paris VII, Paris (1975) [4] G. LEVlCH, Physieochemical Hydrodynamics, Prentice-Hall Inc., Englewood Cliffs (1962) [5] A. 1R_I~JOU--I~/[ICHEL,Th~se 3~me cycle, Universitd Paris V I I , Paris (1978)
Electrical C o n t r i b u t i o n of a Membrane system
217
[6] M. DELMOTTE and J. CHANU, Topics Bioeleetroehem. Bioenerg., G. MILA.ZZO (Editor), J. Wiley, Chichester (1979) Vol. 3, p. 307 [7] D.A. MAc INNES, The Principles of Electrochemistry, Reinhold Publishing Co., New York (1939) [8] A. NA.PARSTEK, D. THOMA.S and S.R. CA.PLA.N, Biochim. Biophys. Acta 323 (1973) 643 [9] A. R~JOU--]V]~ICHEL,q3/[.P. FONTAINE et M. DELMOTTE, C.R. Hebd. Seances Acad. Sci. Ser. B 287 (1978 ) 183 IO] G. $CHA.PIRA., Eldments de Biochimie Gdndrale, F l a m m a r i o n , Paris (1965)