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The electrical resistance of epithelia in the presence of osmotic and hydrostatic pressure gradients
J. tlreor. Biol. (1978) 72, 545-550
The Electrical Resistance of Epithelia in the Presence of Osmotic and Hydrostatic Pressure Gradients LYNDSAY G. M. GORDON Department
of Physiology, University Dune&n, New Zealancl
qf Otago,
(Received 1 September 1977, and in revised form 30 January 1978) The electrical resistance has been determined for aqueous channels through thick walls which separate electrolyte solutions of different concentrations under hydrostatic and osmotic pressure gradients. It is shown that the variation of the conductivity of epithelial layers under various constraints can be subjected to a similar analysis. Although the treatment is quantitative, concomitant morphological changes in the tissue could also take place which would introduce a non-predictive element. An awareness of both effects appears essential, when osmotic and/or hydrostatic pressure gradients are applied across epithelia.
1. Introduction Epithelia are found in a wide variety of tissues and play an important role in the maintenance of salt and water balance in animals. Although the arrangement of cells in epithelia can vary in complexity within tubular or planar structures, some are multilayered, e.g. frog skin, while others are unilayered, e.g. mammalian nephron, the cells can also vary widely in their geometry and membrane permeabilities. Furthermore, the intercellular spaces and limiting junctions show morphological variations between tissues. Functionally, epithelial cells, in addition to taking part in the maintaining of the internal environment of the animal by actively transporting ions across the tissue, also control concomitant fluxes of other substances, e.g. water, amino-acids, sugars. Initially, the attention of researchers was focussed on the asymmetry of the cells which have outer and inner membranes differing in structure and permeability (Koefoed-Johnsen & Ussing, 1958). More recently, greater emphasis has been placed on the role of the intercellular junctions which can give rise to an additional variation in the nature of transepithelial fluxes (for review see Diamond, 1974). Although the width of the intercellular spaces can be altered by osmotic and hydrostatic pressure gradients (Ussing, Erlij OO22-5193/‘78/0606-0545
SOl.OO/O
(2 1978 Academic
Press Inc. (London)
Ltd.
546
L.
G.
M.
GORDON
& Lassen, 1974), the average ratio of the junctional to cellular conductance is possibly an intrinsic property of the tissue which can differ widely throughout the range of epithelia (Fromter & Diamond, 1972). It is necessary to know the relationship between the ionic concentrations ot the bathing media and the conductance of the tissue, because the xpecitic conductance of a particular epithelium can be used as a criterion, both of its normality (increased conductivity above the norm may indicate the presence of damaged tissue), and as a parameter in investigating various ionic pathways through the epithelium. An excellent review of the theoretical treatments of ion transport across membranes can be found in the monograph 1~) Lakshminarayanaiah (1969). In vivo, epithelia often separate two phases having different osmotic and hydrostatic pressures and in vitro studies have also involved these variables (Stackelburg, 1969; Lindley, Hoshiko & Leb, 1964). They have been found to affect the conductivity of epithelia, particularly the intercellular pathways (for review see Ussing et al., 1974), and although in some cases (mucosal hypertonicity) the morphology of the tissue changes, there is the possibihty that with concentration-gradients of electrolytes across the epithelin, ion distributions within the pathways play a considerable role in determining theit conductances i.e. changes in the paracellular (or shunt) conductances of epithelia during exposure to hydrostatic or osmotic pressure gradients can result from (i) changes of the conductivity of the solution(s) in, or (ii) changes in the geometry of these pathways and the puspose of this work is to analyze the contribution of (i) to the changes observed in the paracellular (shunt) resistance in the presence of such gradients. 2. Calculation of Junctional Resistance
The electrolyte concentration within the inter-cellular space, i;, can be related to the corresponding concentrations in the bathing media, C, by the distribution coefficient, K, i.e. K = F/C. (1) Under the conditions of zero hydrostatic and osmotic pressures and assuming that the mean diffusion coefficient, 4, of the electrolyte is independent of i;, the solute efflux is given by: JD = -DKA(c,-C,)/d (2) where d is the length of the pathway between the epithelial cells, A is the cross-sectional area and the subscripts o and i represent respectively the outside and inside of the epithelium. (To achieve a zero osmotic pressure gradient when Ci # COit is necessary to balance the osmolality with a non-
OSMOTIC
PRESSURE-DEPENDENT
RESISTANCE
547
electrolyte with an identical reflection coefficient.) JD is a pure diffusion flux and is obtained simply by assuming that the total impedance to flow is within the junctional complex and not at the entrances and that the system is in a steady state, i.e. JD = - DA dc,ldx is independent of time. In tight epithelia, n may be considered to be the length of the tight junction as a first approximation. If the system is made more complex by the addition of osmotic or hydrostatic forces across the epithelium then the steady-state condition in the intercellular space will no longer be represented by equation (3). These forces will have vectorial components in the same direction as JD and depending on the amount of coupling between the flows of solute and solvent, the value of J, is modified accordingly. Descriptions of interacting fluxes can be seen in the treatments based on irreversible thermodynamics (Johnson et al., 1966; Spiegler & Kedem, 1966). These superimposed forces can be considered to add a component to the diffusion flux, so that the net flux of solute, JD.F, in the steady-state under these conditions is given by J,,,
= - DA (di;,y/ds) + kc,
(4)
where k .is a parameter independent of N. The concentration-profile of the electrolyte across the junction can be obtained by the integration of equation (4) F, = (JD, F/lc)+[KCi-(Jo,
F/k)] exp (“-yI
(AD)’
(5)
(A linear relationship between i;, and .Yis obtained when k = 0 [integration of equation (3)l.j The electrical resistance of the inter-cellular space, R, is a function of the concentration-profile and the molar conductivity (A,,,) of the electrolyte. If we assume that A,,, is independent of concentration (see Conway, 1952) then the specific conductivity, X,V, at s is proportional to Fs. i.e. It follows that
i.e.
R
I [kd-ADln D’ ’ = AA,,,J,>, F
(:)I
:
(Ci # C,).
548
L.
G.
M.
Using equation (5) and substituting
GORDON
x = d, the solute flux is given by
kK(C,
- CJ J D’ F = 1 - exp (kd/Afl = kKC;
’
c* # ci
(8a)
(C” = Ci = C)
@b)
which can be seen to revert to equation (2) when kd/Ai3 is small. Utilizing equations (7) and (8a) and re-arranging R
ev CWY~~I - 1 D’F = AA,kK(Ci-
Ci # c,*
C,)
(9)
In the absence of fluxes caused by osmotic and hydrostatic pressure gradients across the epithelia (k = 0), the resistance of the junctional pathways reduces to d ci RD
=
zi\,K(c,-c,)
In
c,
and when Ci = C,, = C R=--------
d
A&KC
(11)
which holds even in the presence of the superimposed forces. For the case where kd/AD is small R D,F __ zz R
&!+ -1 I* 5 AD(Ci- C,) Ci- C, C,
= l(Ci = C,).
(124
Wb) Since the second term of the R.H.S. of equation (12a) approaches C-l as C, approaches Ci the ratio k/(C, - C,) must have a value of zero at the same limit. This conclusion suggests that k is porportional to (Ci-C,)” where n > 1. The plot RD, //R VS. (In Ci/C,)(Ci-C,)-’ using data from toad urinary bladder (Reuss & Finn, 1975) where the R’s are the shunt Cparacellular) resistances (Fig. l), shows deviations from the theoretical line (dashed) in which k is taken as zero. With hypertonic mucosal solutions the graph curves rapidly downwards and this has been interpreted as being due to morphological changes (Reuss & Finn, 1975). This argument is supported by the fact that mucosal hyperosmolality produced by non-electrolytes has a similar effect on the transepithelial resistance and the morphology of the tissue (“blisters” occur in the tight junctions) (DiBona & Civan, 1973; Wade, Revel & DiScala, 1973). In hypotonic solutions the gradual increasing difference between the observed and theoretical values of R,,,/R is possibly explained by the osmotic term in equation (I 2a).
OSMOTIC
PRESSURE-DEPENDENT
RESISTANCE
549
FIG. 1. Changes of shunt resistance R D. F as a function of the electrolyte concentrations of the mucosal (C,) and serosal (C, = 115 mmol l- I) solutions. Results are normalized to the value of R with Ringer’s solution bathing both sides of the tissue. (Data from Fig. 6, Reuss & Finn, 1975).
0 0
x X I.4 X 0
X
033 0
X
X 0.6
-
0 1.35
235 Osmolal~ty
Ftc. 2. Effect on the resistance of bullfrog skin of exposure of outside surface to thiourea (u) and mannitol (x) at various osmolalities (mosmol)/Kg H,O. The electrolyte concentrations were held constant (C, # C,). (Data from Table 1, Lindley et al., 1964).
550
I..
G.
M.
GORDON
Figure 2 illustrates the variation of the epithelial resistance of frog skin under changing osmotic gradients with (C;- CO) at ;I constant non-zero value. R,,,/R is plotted against the osmolality of the neutral solutes. it can he seen that raising the osniolality of the hypotonic mucosal solution decrcasch the value of R,,f, as would be expected from the model. However it is not possible to judge from the graphs of Fig . 2 the role played by morphological changes in the tissue which could b,: important at high hypertonicity. Also in this work the changes in R,),,, may he associated with pathways othrl than simple diffusional ones. In summary we should like to make clear that the resistance changes which occur in the presence of gradients of electrolytes across tissues, and caused by hydrostatic or osmotic pressures, do not necessarily imply that morphological changes have taken place. The quantitative heparation of the two efl‘ects discussed above require:, greater knowledge of the osmotic factor. /;, for rhc particular tissue. However, as shown by Fig. I a large portion of‘ the resistance changes can result from conductivity changes alone. This work was supported
COSWAY,
DIAMOND, DIBONA, FROMTER, JOHI\SON,
by
the Medical Research Council of New Zealand.
REFERENCES (1952). Elec/,c)c/rc,/llicrrl D~trr, Ch. 4. J. M. (1974). Fed. PYOC.33, X20. D. R. & CIVAN, M. M. (1973). J. mm Bid. B. E.
E. & DIAMOND, J. S., DRESNER,
J. M. (1972). L. & KRAIIS,
Spiegler, ed.), p. 345. New
York
KOEFOED-JOHNSEN, V. & Ussrw, LAKSFIMINARAYANAIAH, N. (1969).
Amsterdam: 12,
tlscvier
Pub.
Co.
101.
A’orrw~. hew Biol. 235, Y. K. A. (1966). In f’rincipk.t
o/
fA~.tn/im/io~~
(K.
S.
London
:
: Academic Press. H. H. (1958). Actn P/IJ,.Go/. Scu&. Tw/q~o/.t Plwrrowr~rr i/r Mmzh~nrres.
42, ‘98. NW
York,
Academic Press. LINDLEY, B. D., HOSHII
The Electrical Resistance of Epithelia in the Presence of Osmotic and Hydrostatic Pressure Gradients LYNDSAY G. M. GORDON Department
of Physiology, University Dune&n, New Zealancl
qf Otago,
(Received 1 September 1977, and in revised form 30 January 1978) The electrical resistance has been determined for aqueous channels through thick walls which separate electrolyte solutions of different concentrations under hydrostatic and osmotic pressure gradients. It is shown that the variation of the conductivity of epithelial layers under various constraints can be subjected to a similar analysis. Although the treatment is quantitative, concomitant morphological changes in the tissue could also take place which would introduce a non-predictive element. An awareness of both effects appears essential, when osmotic and/or hydrostatic pressure gradients are applied across epithelia.
1. Introduction Epithelia are found in a wide variety of tissues and play an important role in the maintenance of salt and water balance in animals. Although the arrangement of cells in epithelia can vary in complexity within tubular or planar structures, some are multilayered, e.g. frog skin, while others are unilayered, e.g. mammalian nephron, the cells can also vary widely in their geometry and membrane permeabilities. Furthermore, the intercellular spaces and limiting junctions show morphological variations between tissues. Functionally, epithelial cells, in addition to taking part in the maintaining of the internal environment of the animal by actively transporting ions across the tissue, also control concomitant fluxes of other substances, e.g. water, amino-acids, sugars. Initially, the attention of researchers was focussed on the asymmetry of the cells which have outer and inner membranes differing in structure and permeability (Koefoed-Johnsen & Ussing, 1958). More recently, greater emphasis has been placed on the role of the intercellular junctions which can give rise to an additional variation in the nature of transepithelial fluxes (for review see Diamond, 1974). Although the width of the intercellular spaces can be altered by osmotic and hydrostatic pressure gradients (Ussing, Erlij OO22-5193/‘78/0606-0545
SOl.OO/O
(2 1978 Academic
Press Inc. (London)
Ltd.
546
L.
G.
M.
GORDON
& Lassen, 1974), the average ratio of the junctional to cellular conductance is possibly an intrinsic property of the tissue which can differ widely throughout the range of epithelia (Fromter & Diamond, 1972). It is necessary to know the relationship between the ionic concentrations ot the bathing media and the conductance of the tissue, because the xpecitic conductance of a particular epithelium can be used as a criterion, both of its normality (increased conductivity above the norm may indicate the presence of damaged tissue), and as a parameter in investigating various ionic pathways through the epithelium. An excellent review of the theoretical treatments of ion transport across membranes can be found in the monograph 1~) Lakshminarayanaiah (1969). In vivo, epithelia often separate two phases having different osmotic and hydrostatic pressures and in vitro studies have also involved these variables (Stackelburg, 1969; Lindley, Hoshiko & Leb, 1964). They have been found to affect the conductivity of epithelia, particularly the intercellular pathways (for review see Ussing et al., 1974), and although in some cases (mucosal hypertonicity) the morphology of the tissue changes, there is the possibihty that with concentration-gradients of electrolytes across the epithelin, ion distributions within the pathways play a considerable role in determining theit conductances i.e. changes in the paracellular (or shunt) conductances of epithelia during exposure to hydrostatic or osmotic pressure gradients can result from (i) changes of the conductivity of the solution(s) in, or (ii) changes in the geometry of these pathways and the puspose of this work is to analyze the contribution of (i) to the changes observed in the paracellular (shunt) resistance in the presence of such gradients. 2. Calculation of Junctional Resistance
The electrolyte concentration within the inter-cellular space, i;, can be related to the corresponding concentrations in the bathing media, C, by the distribution coefficient, K, i.e. K = F/C. (1) Under the conditions of zero hydrostatic and osmotic pressures and assuming that the mean diffusion coefficient, 4, of the electrolyte is independent of i;, the solute efflux is given by: JD = -DKA(c,-C,)/d (2) where d is the length of the pathway between the epithelial cells, A is the cross-sectional area and the subscripts o and i represent respectively the outside and inside of the epithelium. (To achieve a zero osmotic pressure gradient when Ci # COit is necessary to balance the osmolality with a non-
OSMOTIC
PRESSURE-DEPENDENT
RESISTANCE
547
electrolyte with an identical reflection coefficient.) JD is a pure diffusion flux and is obtained simply by assuming that the total impedance to flow is within the junctional complex and not at the entrances and that the system is in a steady state, i.e. JD = - DA dc,ldx is independent of time. In tight epithelia, n may be considered to be the length of the tight junction as a first approximation. If the system is made more complex by the addition of osmotic or hydrostatic forces across the epithelium then the steady-state condition in the intercellular space will no longer be represented by equation (3). These forces will have vectorial components in the same direction as JD and depending on the amount of coupling between the flows of solute and solvent, the value of J, is modified accordingly. Descriptions of interacting fluxes can be seen in the treatments based on irreversible thermodynamics (Johnson et al., 1966; Spiegler & Kedem, 1966). These superimposed forces can be considered to add a component to the diffusion flux, so that the net flux of solute, JD.F, in the steady-state under these conditions is given by J,,,
= - DA (di;,y/ds) + kc,
(4)
where k .is a parameter independent of N. The concentration-profile of the electrolyte across the junction can be obtained by the integration of equation (4) F, = (JD, F/lc)+[KCi-(Jo,
F/k)] exp (“-yI
(AD)’
(5)
(A linear relationship between i;, and .Yis obtained when k = 0 [integration of equation (3)l.j The electrical resistance of the inter-cellular space, R, is a function of the concentration-profile and the molar conductivity (A,,,) of the electrolyte. If we assume that A,,, is independent of concentration (see Conway, 1952) then the specific conductivity, X,V, at s is proportional to Fs. i.e. It follows that
i.e.
R
I [kd-ADln D’ ’ = AA,,,J,>, F
(:)I
:
(Ci # C,).
548
L.
G.
M.
Using equation (5) and substituting
GORDON
x = d, the solute flux is given by
kK(C,
- CJ J D’ F = 1 - exp (kd/Afl = kKC;
’
c* # ci
(8a)
(C” = Ci = C)
@b)
which can be seen to revert to equation (2) when kd/Ai3 is small. Utilizing equations (7) and (8a) and re-arranging R
ev CWY~~I - 1 D’F = AA,kK(Ci-
Ci # c,*
C,)
(9)
In the absence of fluxes caused by osmotic and hydrostatic pressure gradients across the epithelia (k = 0), the resistance of the junctional pathways reduces to d ci RD
=
zi\,K(c,-c,)
In
c,
and when Ci = C,, = C R=--------
d
A&KC
(11)
which holds even in the presence of the superimposed forces. For the case where kd/AD is small R D,F __ zz R
&!+ -1 I* 5 AD(Ci- C,) Ci- C, C,
= l(Ci = C,).
(124
Wb) Since the second term of the R.H.S. of equation (12a) approaches C-l as C, approaches Ci the ratio k/(C, - C,) must have a value of zero at the same limit. This conclusion suggests that k is porportional to (Ci-C,)” where n > 1. The plot RD, //R VS. (In Ci/C,)(Ci-C,)-’ using data from toad urinary bladder (Reuss & Finn, 1975) where the R’s are the shunt Cparacellular) resistances (Fig. l), shows deviations from the theoretical line (dashed) in which k is taken as zero. With hypertonic mucosal solutions the graph curves rapidly downwards and this has been interpreted as being due to morphological changes (Reuss & Finn, 1975). This argument is supported by the fact that mucosal hyperosmolality produced by non-electrolytes has a similar effect on the transepithelial resistance and the morphology of the tissue (“blisters” occur in the tight junctions) (DiBona & Civan, 1973; Wade, Revel & DiScala, 1973). In hypotonic solutions the gradual increasing difference between the observed and theoretical values of R,,,/R is possibly explained by the osmotic term in equation (I 2a).
OSMOTIC
PRESSURE-DEPENDENT
RESISTANCE
549
FIG. 1. Changes of shunt resistance R D. F as a function of the electrolyte concentrations of the mucosal (C,) and serosal (C, = 115 mmol l- I) solutions. Results are normalized to the value of R with Ringer’s solution bathing both sides of the tissue. (Data from Fig. 6, Reuss & Finn, 1975).
0 0
x X I.4 X 0
X
033 0
X
X 0.6
-
0 1.35
235 Osmolal~ty
Ftc. 2. Effect on the resistance of bullfrog skin of exposure of outside surface to thiourea (u) and mannitol (x) at various osmolalities (mosmol)/Kg H,O. The electrolyte concentrations were held constant (C, # C,). (Data from Table 1, Lindley et al., 1964).
550
I..
G.
M.
GORDON
Figure 2 illustrates the variation of the epithelial resistance of frog skin under changing osmotic gradients with (C;- CO) at ;I constant non-zero value. R,,,/R is plotted against the osmolality of the neutral solutes. it can he seen that raising the osniolality of the hypotonic mucosal solution decrcasch the value of R,,f, as would be expected from the model. However it is not possible to judge from the graphs of Fig . 2 the role played by morphological changes in the tissue which could b,: important at high hypertonicity. Also in this work the changes in R,),,, may he associated with pathways othrl than simple diffusional ones. In summary we should like to make clear that the resistance changes which occur in the presence of gradients of electrolytes across tissues, and caused by hydrostatic or osmotic pressures, do not necessarily imply that morphological changes have taken place. The quantitative heparation of the two efl‘ects discussed above require:, greater knowledge of the osmotic factor. /;, for rhc particular tissue. However, as shown by Fig. I a large portion of‘ the resistance changes can result from conductivity changes alone. This work was supported
COSWAY,
DIAMOND, DIBONA, FROMTER, JOHI\SON,
by
the Medical Research Council of New Zealand.
REFERENCES (1952). Elec/,c)c/rc,/llicrrl D~trr, Ch. 4. J. M. (1974). Fed. PYOC.33, X20. D. R. & CIVAN, M. M. (1973). J. mm Bid. B. E.
E. & DIAMOND, J. S., DRESNER,
J. M. (1972). L. & KRAIIS,
Spiegler, ed.), p. 345. New
York
KOEFOED-JOHNSEN, V. & Ussrw, LAKSFIMINARAYANAIAH, N. (1969).
Amsterdam: 12,
tlscvier
Pub.
Co.
101.
A’orrw~. hew Biol. 235, Y. K. A. (1966). In f’rincipk.t
o/
fA~.tn/im/io~~
(K.
S.
London
:
: Academic Press. H. H. (1958). Actn P/IJ,.Go/. Scu&. Tw/q~o/.t Plwrrowr~rr i/r Mmzh~nrres.
42, ‘98. NW
York,
Academic Press. LINDLEY, B. D., HOSHII