A M . ZOOLOGIST, 10:355-364 (1970).
Fluxes across Epithelia
Barry D. Lindley
Department of Physiology, School of Medicine, Case Western Reserve
University, Cleveland, Ohio 44106
SYNOPSIS. Epithelial membranes are useful and convenient tissues in which to study
fundamental processes of ionic transport. They devote a substantial fraction of their
total energy resources to transport, they serve as a convenient model for plasmalemmal
transport, and they have interesting properties related to hormonal regulation. The
frog's skin, in particular, has been fruitful in generating concepts relating to the properties of serial membrane systems and to the use of isotopic tracers in the study of
transport mechanisms.
In previous papers of this Symposium,
we have seen how one approaches the
physical and mathematical description of
the movement of simple substances across
simple membranes and how these descriptions can be applied to the study of physiological problems involving the plasmalemma—particularly insofar as the asymmetric
distribution of ions is concerned. We are
now going to consider the movement of
simple substances across complicated membranes—epithelia.
After outlining some of the milestones
in the development of our current notions
about one particular transporting epithelium, frog skin, chosen because it has played
a key role in the major generalizations
about epithelial transport, I shall discuss
briefly three of our major conceptual heirlooms from the last two decades:
1. the use of isotopes and the flux-ratio
equation for determining active transport,
2. the composition of simple membranes
into composite membranes with interesting new properties,
3. the short-circuit current as a tool for
investigating active transport.
EPITHELIA AS TISSUES IN WHICH TO STUDY
TRANSPORT
Every living cell has an array of transThe author holds a Lederle Medical Faculty
Award. Research related to the topics discussed
here has been supported by Grants GB-5197 and
7668 from the National Science Foundation.
port processes across its plasma membrane,
serving to regulate cellular volume, nutrition, excretion, communication along the
surface of the cell, and communication between the inside and the outside of the
cell. This "membrane-theory" might be
called a modular concept for the structure
of the cellular systems in biology, i.e., relatively independent modules coupled in a
simple way are exploited to carry out the
functions of the cell. This point of view is
sometimes disputed by those who take too
literally Goethe's maxim that nature has
neither core nor crust. Nonetheless, that
the multicellular higher organism is built
in this way cannot be disputed. Certain
tissues and organs are specialized to carry
on functions on behalf of the entire organism, and the interdependence of these
modules can be described in fairly simple
terms of distribution kinetics and formally
simple if largely unknown controlling
mechanisms. Most of the overall transport
functions of organisms are carried out by
epithelial tissues which couple structural
specializations, such as geographical differentiation of the cell surface and tight junctions for the knitting of cells into tough
membranes, with differentiation and emphasis of the properties of cellular transport.
These epithelia function to line spaces
or cavities and (1) afford protection as a
barrier to permeability, in which mucous
secretion may assist, (2) secrete products
derived from the blood to assist in diges-
355
356
BARRYD. LINDLEY
tion, lubrication, and regulation of temperature, (3) absorb nutrients and selectively retain "desirable" substances during
processes of filtration, and (4) regulate the
composition of body fluid compartments
through facultative absorptive and secretory processes.
Whereas permeability is, in general, a
trace property of the plasmalemma, we
find that many epithelial membranes are
designed to enhance permeability through
increased surface area produced by wrinkles and folds and other devices. Thus, in
the morphology of epithelia we find a
whole new world of biological tools. A very
thorough review has just appeared concerning both structure and function in a
wide variety of epithelia (Keynes, 1969).
Epithelia have served as models for the
functions of the plasmalemma. The
clearest and most direct evidence for the
ability of biological systems to create spatial concentration gradients from stores of
metabolic energy comes from epithelia.
Few other demonstrations in physiology
have the directness and finality of Carl
Ludwig's proof that salivary secretion was
not nitration because saliva could be produced against a hydrostatic pressure exceeding the perfusion pressure for the
gland, or the observation by Heidcnhain
that the intestine can diminish the volume
of serum instilled into its lumen — net
transfer in the absence of any concentration gradients.
Experimental convenience has favored
the use of epithelia for studies of transport. The membranes are often quite sturdy and readily available. Both sides of the
membrane are directly accessible, so that
the forces promoting transport can be controlled and the resulting flows measured.
Finally, there are happy and peculiar simplicities of epithlia —one with which we
shall be much concerned is the equivalence
of sodium transport and short-circuit current in the isolated frogskin.
Figure 1 shows one type of apparatus
used for the study of epithelial transport — commonly called an Ussing-type
chamber or some similar name. Note the
^"{o sal'J calomel ekdrode
FIG. 1. Ussing's chamber for the study of isolated
frogskin.
bubble lifts for mixing and aerating the
bathing solutions, and the inlets in each
half of the chamber for salt bridges from
electrodes used to monitor the difference
in electrical potential. These bridges are
placed as close to the skin as possible in
order to minimize errors from IR drops
during current flow between salt bridges
used to pass current through the skin; the
latter bridges enter the chambers at the
rear. In such chambers 2-7 cm2 of skin can
be maintained in a healthy transporting
condition for many hours.
Tissues specialized for transport are believed to devote a rather large fraction of
their total energy resources to transport.
Thus, such tissues have served for the metabolic study of transport, either directly as
in Zerahn's (1956) study of O2-consumption by the frog skin and Leaf, Page, and
Anderson's (1959) study of the toad bladder, or indirectly as in the use of kidney as
a source of ATPase (Post, et ah, 1965).
A third reason for the use of epithelial
membranes by those concerned with the
general physiology of cellular transport is
that the cells in epithelial membranes have
interesting properties. I have mentioned
FLUXES ACROSS EPITHELIA
357
the regulatory role of epithelial transport;
a number of epithelial membranes are
hormonally controlled, and cellular mechanisms of action of hormones such as
vasopressin (Leaf, 1962) and aldosterone
(Edelman, et al., 1963) have been studied
in epithelial preparations. Another example of an interesting property is the sensitivity of the frog skin potential to the concentration of sodium in the bathing solution (Lindley and Hoshiko, 1964). A stable
sodium selectivity is a rare thing in biology, and the frog skin has been suggested
for comparison with systems transiently selective for sodium, such as the nerve membrane.
THE FROG SKIN AS A MODEL EPITHELIUM
At the last International Congress of
Physiology, Professor Karger demonstrated
the production of energy by the frog's
skin (see Karger, 1968). Large silver-silver
chloride electrodes were used, one slipped
through an opening in the skin of the
anesthetized frog and the other in the solution outside the frog. A DC motor was
powered by the frog and turned a vane
attached to its shaft. In addition to its
directness, this method of study allows one
to determine the actual power delivery of
which the skin is capable when operating
as a passive engine without being driven
by external sources. As we discuss the skin
further we shall be concerned, on the contrary, with the use of external sources in
order to drive the skin to thermodynamic
limits.
When Professor Karger visited Cleveland recently, Richard Recknagel was fired
with enthusiam and suggested to our
bioengineering group the attractive prospect shown in Figure 2.
The last two decades have found in the
amphibian skin a union of electrophysiology and radiotracer methodology. The skin
has been a classical object of study, from
Mateucci's electrical observations in the
first half of the nineteenth century, Bayliss'
and Bradford's investigation of the alterations produced by nervous stimulation,
FIG. 2. One use for electrical energy generated by
epithelia. After a personal communication from
Richard Recknagel, with respects to Professor Karger.
and Reid's studies of irreciprocal permeability through to the demonstration of net
salt transport by Huf, studies of the effects
of an extraordinary variety of inorganic
salts by Hashida and Motokawa, and the
early applications of tracers by Krogh and
co-workers. Inded, the skin was the origin
of the problem of the relationship between
isotope exchange and net flow — involved
in the perennial question "Do tracers
trace?" — and of the problem of the relationship between osmotic and diffusive
permeabilities, P{ and Pa. The early literature on the skin is covered in Ussing's
(1960) monograph.
The turning point in a realization of a
model for the skin based on cell physiology
came in Ussing's interest in uptake of isotopes in the axolotl (Jorgensen, Levi, and
Ussing, 1946). The study led him to inquire about rigorous criteria for distinguishing between active transport and passive movement. Ussing realized that, rather
than being merely a simple analytical aid,
isotopes represented a new way of looking at transport.
These questions, this prospect, coupled
with the fact that no one could consider
the frog skin as a simple membrane from
the point of view of structure, made it
difficult to apply equations such as those
358
BARRY D. LINDLEY
developed by Koch and Gutknecht. How
could one rationalize the properties of the
skin in terms of elementary structures and
processes? The realization of a minimal
model is still in progress, but we shall retrace some of the steps to an intermediate
stage.
This was a very "hot" issue around
1950-55. Teorell, Linderholm, and Ottoson
and Sjostrand, as well as others mentioned
above actively investigated mechanisms of
ionic transport across the frog's skin.
It is instructive to look once more briefly
at the milestones in the development of a
model for epithelial transport of ions and
water.
1. Net uptake of salt demonstrated
(Huf, 1935, Krogh, 1937).
2. Bidirectional movement of isotopes
(measurement of net flux requires
two isotopes; Ussing, 1948).
3. Equivalence of sodium flux and shortcircuit current (Ussing and Zerahn,
1951).
4. Reformulation of the electrical behavior.
5. Microelectrode profile (Engbaek and
Hoshiko, 1957).
6. Lag in appearance of isotope (Hoshiko and Ussing, 1960).
7. Koefoed-Johnsen—Ussing model (1958).
8. Stoichiometric relationship between
short circuit current and 02-consumption (Zerahn, 1956).
9. Effects of hormones.
In this development, a hidden thread
was the use of the flux-ratio equation and
attempts to distinguish clearly and rigorously between active and passive transports. The important features of the model, now widely known, were (a) the emphasis on serial juxtaposition of two membranes with different properties (functional polarity of epithelia), (b) diffusion potentials with electroneutral active transport (sodium/potassium pump-coupling),
and (c) the possibility of studying active
transport directly and simply by looking at
the short-circuit current. These features
were rapidly exploited, and modifications
of concepts and methods developed from
using the frog's skin were applied to many
tissues.
In the last decade, a number of problems with a strict interpretation of the
model of Koefoed-Johnsen and Ussing
have emerged (Ussing and Windhager,
1964, Klahr and Bricker, 1964). These
problems have included more complicated
microelectrode profiles, emphasis on subtleties of structure, unsatisfactory understanding of the role of potassium, and the
absence of a molecular picture of the
mechanisms involved. At the level of cellular physiology, it is still unclear what steps
are rate-limiting. Nonetheless, the problems should not be allowed to detract from
three major contributions about which I
wish to talk further: (1) Flux-ratio equation and criteria for active transport; (2)
Series membrane systems; and (3) Shortcircuit current as a convenient measure of
active transport.
ISOTOI'ES AND ACTIVE TRANSPORT: THE FLUXRATIO EQUATION
A number of different criteria for active
transport have been developed in the last
25 years, all based in some sense on deviations from expected passive behavior.
These criteria include the following:
(1) Saturation kinetics; (2) Sensitivity
to metabolic poisons; (3) High temperature coefficient; (4) Susceptibility to "specific transport poisons;" and (5) Net
transfer against a gradient of electrochemical potential. None of these properties actually requires the coupling of metabolic
expenditure to translocation. Even (5) can
be based on entrainment of one species by
another, as in solvent-drag.
If, instead of looking at properties of
known active transport systems, we attempt
to arrive at a priori definitions of active
transport we can distinguish at least three
a2ipropriate definitions:
(1) Deviation from expected passive behavior; (2) Conservative rather than dissipative; (3) Primary entrainment by metabolic flux (Hoshiko and Lindley, 1967).
Under (1), passive behavior is defined as
FLUXES ACROSS EPITHELIA
obeying relations discussed by other authors in this symposium, such as Fick's law,
the Nernst-Planck equation, and the
Goldman equation; it is important to note
that certain dissipative processes can still
violate these relations.
However, even under a restrictive definition of passive behavior, testing for violations still requires assumptions, e.g., the
diffusion coefficient or mobility within the
membrane. This requirement is severe
enough for a simple single membrane and
absurd for a complicated epithelium where
D is a function of x.
Visscher, et al. (1944) and Ussing
(1949) introduced the notion (previously
used in a simpler way by Behn) of using
the ratio of fluxes of substances believed to
be kinetically indistinguishable with respect to processes occurring in the membrane. The values for mobility then
cancel, and it is not necessary to assume
parameters for the membrane in order to
test for conformity to the principles of dissipative transfer.
The flux-ratio equation is often expressed as a relation between the gradient
of electrochemical potential and the ratio
of two unidirectional fluxes. For the moment, let us look at it in strictly operational
terms. We refer to an experimental situation — say the frog skin in an Ussing chamber—in which in general we have differences in concentration, electrical potential,
and pressure across the membrane. Since
there are forces, there will also be some
flows occurring, unless the membrane be
quite impermeable. Some flows will occur
even in the absence of direct metabolic
contributions, but some may be dependent
on expenditure of energy. We now choose
two similar substances (we shall in a moment allow them to resemble each other as
closely as we like with respect to an operational criterion) and add one to each side
of the membrane. Following a period of
changing specific activity within the membrane, steady state flows of the two substances can be measured.
Now, under certain conditions, there is a
simple relation between the ratio of these
359
two flows and the gradient of electrochemical potential, written assuming the identity
of the two tracers as a single parent substance:
RT In f =r — A£
= — [RT In (C7C') + zFE-)-vAP]
Activity coefficients have been omitted, F is
the Faraday, v the partial molar volume,
E the potential difference, z the valence, R
the gas constant, and T the absolute temperature. In fact, the natural logarithm of
the flux ratio is equal to the dimensionless
electrochemical potential gradient under
the following conditions (Hoshiko and
Lindley, 1964, 1970; Kedem and Essig,
1965):
(1) Kinetic indistinguishability; (2)
Ideal isotope exchange; (3) No entrainment of either isotope by other substances
including the other isotope; (4) Correction of the flows to equal mean concentrations; (5) Applicability of irreversible
thermodynamics, including linear rate
laws, on a local basis; (6) Steady state for
isotope specific activity within the membrane — a subtle and important restriction — the equation cannot be expected to
hold during transient shifts to new steady
states, e.g., during the onset of the effects
of drugs.
This is the bad side — and not such a
bad one. However, there are very strong
features which also deserve some attention.
The relation is still valid, for example,
under the following circumstances: (1)
The substance takes part in a chemical
reaction within the membrane; (2) The
membrane is composed of a serial juxtaposition of an arbitrary number of elementary layers; (3) The membrane is characterized by parallel heterogeneity — a "mosaic character."
What happens if we relax some of the
restrictions? This is most simply seen from
a Schlogl plot (Kashgarian, et al., 1963).
The flux ratio in general depends not only
on the electrochemical potential gradient
for the species under investigation, but
also on entrainment by other flows. Thus,
we can plot the logarithm of the flux ratio
360
BARRY D. LINDLEY
face. In a real experiment one would more
likely plot sections of the surface. If entrainment is not explicitly acknowledged it
will then intrude as a lift of the plot
away from the origin, as in Figure 4. Finally, the presence of interactions such as
are implied in file diffusion (Ussing, 1948)
and exchange diffusion (Hodgkin and
Keynes, 1955) will alter the slope of the
plot, as in Figure 5. These considerations
FILE DIFFUSION
In I
SIMPLE
DRAG
SCHL'dOL PLOT
FIG. 3. Schlogl surface indicating the values assumed by the logarithm of the flux ratio for
various values of electrochemical potential difference and drag terms in a hypothetical system.
as a surface involving two independent
variables, the electrochemical potential
gradient for that species and an entrainment term. Furthermore, because of nonlinearities and interactions the surface is,
in general, curved. Figure 3 is a fanciful
representation of a portion of such a surENTRAPMENT
In f.
SIMPLE
EXCHANGE DIFFUSION
FIG. 5. Schlogl plot indicating that the slope will
depart from unity when the substance interacts
with the membrane in certain ways (after
Kashgarian, et at, 1963).
all appear in a generalized form of the
flux-ratio equation.
RT In f =
(R x /R) (—A/*+ "entrainment term")
FIG. 4. Schlogl plot, section of surface as in Figure
3, indicating that active transport or other forms of
entrainment will cause a non-zero intercept for
a plot of the logarithm of the flux ratio as a
function of the difference in electrochemical potential.
Thus, we have from examination of the
flux ratio in a Schlogl plot a convenient
way to classify deviations from expected
passive behavior. The final step to detection of active transport is to bring the
system to a null point where the deviations
of the flux ratio are less restrictive. It can
be seen from the plot that at zero gradient
of electrochemical potential the distinction
between linear and nonlinear rate laws
vanishes. Further, if one abolishes external
gradients of all other substances, entrainment can be only metabolic. Thus, departure of the flux ratio from unity at zero
gradient ("short-circuit") in the absence
FLUXES ACROSS EIMTHELIA
of other flows is definitive evidence of primary active transport.
361
er point of view become interesting properties of functional significance. As one consequence of the juxtaposition, the membrane may present different resistances to
SERIES SYSTEM — RECTIFICATION, STATIONdiffusion for gradients in opposite direcARY COUPLING
tions. This circumstance of "irreciprocal
The chief problem in a membrane com- permeability" comes about in part because
posed of elementary layers, perhaps with the concentration in the intermediate
compartments in between, is determining compartment may be different in different
the influence on measured parameters of cases.
the properties of the component memThe best example of such a property
branes. Leaf (1958), for example, pointed
also
is related to transport of water. Durout that in the steady state the permeabilibin
(1960) and Curran (1960) pointed
ty coefficients of Fick's law were comout
that
a composite membrane with difpounded in a fashion analogous to resisfering
reflection
coefficients for the comtances in parallel (or conductances in
ponents
could
pump
water by means of a
scries):
primary solute pump. Elevation of the intracellular osmolality by accumulation of a
solute would cause differing effective os1 trai
motic pressures across the two components.
As a consequence there would be a net
where the a and J3 refer to the component flow of solution across the membrane
membranes. A change in either component toward the side with the leakier memcan cause a change in Ptrans- This expres- brane. Ogilvie, Mclntosh, and Curran
sion is, in general, an oversimplification; in (1963) built a model system that operated
the presence of coupling the coefficients on this basis, and Patlak, Goldstein, and
become more complex. Indeed, in general, Hoffman (1963) have published a quantiseveral different properties of the com- tative treatment. Transfer of fluids in the
ponent membranes will be involved in a gall gladder has been explained by Diasingle property of the composite mem- mond and Tormey (1966) by a model that
brane. This can be seen most simply if we is identical in an abstract formal sense to
refer back to the frog-skin model of Koe- the series membrane system, although they
foed-Johnsen and Ussing. Here the entry were able to exploit structural specializaof sodium into the cell is necessary for tion of the tissue in a very interesting way,
active transport across the membrane. using the interstitial spaces as a central
Thus, a change in the permeability of the distributed compartment.
outer membrane of sodium would alter the
A final such property is electrogenesis
pumping rate, or the apparent coefficient
with
a neutral pump. According to the
for active transport across the skin. Of
original
model of Koefoed-Johnsen and
course, any change in the pump itself
Ussing,
the
pump transferred no net
would influence the rate of pumping, and
charge;
however,
it created ionic concenchanges in potassium permeability of the
tration
gradients
which could deliver
inner membrane might also be of consequence. Indeed, it is this complex inter- charge in the course of dissipation. As a
twining that has made it difficult to deter- result, the frog skin is an electrogenic
mine the rate-limiting steps. Nonetheless, device, although one need never imagine
techniques exist for making estimates of an active transport mechanism carrying
elementary steps for kinetic models, and naked charge. Again, the phenomenologithis particular area should be one of the cal property of the composite membrane is
more fruitful ones for future investigation. out of register with the actual properties
The complexities looked at from anoth- of the components.
362
BARRY D. LINDLEY
important to view a true "short-circuit" as
perhaps involving identical solutions on
The significance of the short-circuit cur- both sides of the membrane as well as abrent extends beyond the early attempts to sence of an electrical gradient.
study delivery of power by the frog skin,
As has been shown recently by Rehm
beyond the use of voltage clamp to elimi(1968)
the technique may be in error in
nate capacitive currents in the axon, even
certain
situations in vivo, particularly
beyond the demonstration by Ussing and
where
there
is flow of blood to the tissue
Zerahn that it was equivalent to the net
under
consideration.
Another source of ersodium transport in the frog's skin. "Shortcircuit" and "current" can be most usefully ror for tissues of very low resistance is the
viewed as labels for the general situation presence of drops in voltage in llic solution
of "zero gradient of electrochemical poten- bathing the tissue (Schultz and Zalusky,
tial" and "net flux of a substance." From 1964).
Finally, the study of the electrical propthis point of view one is involved in a sort
erties
of tissues may be useful at a level
of null experiment, where all forces that
might promote the movement of a sub- removed from direct studies of the active
stance have been eliminated by the craft of transport of a single species. For example,
the experimenter and the power of his I have found short-circuit current and voldevices, so that any remaining detectable tage clamp useful ways to study some asflow can be ascribed to metabolic entrain- pects of the function of the frog's skin
ment — without worry about nonlinearities, glands (Lindley, 1969), although the
interactions, and the like. Put in other short-circuit current of the skin involves
terms, at short-circuit all varieties of pas- active transport of chloride as well as sodisive behavior coincide, and their contribu- um during secretion.
tion can be reliably assessed.
SUMMARY
However, the special attractiveness of
the short-circuit current for most investigaOn my way to this symposium, I bought
tors resides in the fact that it is an easy King, Queen, Knave by Vladimir Naway to study net sodium active transport in bokov, a book of some literary merit in
the isolated frog skin under many condi- spite of its cover. Early in the book a very
tions (Ussing, 1960, pp. 116 ff.), including near-sighted young man breaks his glasses
hormonal action (except epincphrine), re- just after arriving in a new city and is
placement of sodium by other cations, and afloat in a world of strange, vague shapes
a variety of pharmacological actions.
and colors, an exciting world, nonetheless.
This convenience has led to the use of At certain periods of development of a
the short-circuit current in studying the field of inquiry, or indeed of learning
effects of transport inhibitors, hormonal about an established field new to oneself,
regulation, and saturation kinetics of ac- the scientist finds himself in a similar pretive transport (Kirschner, 1955).
dicament. Concepts are spectacles for such a
The technique has been extended to scientist, and the study of epithelial transmany other tissues. In this respect it must port over the last 25 years is no less imporbe pointed out that in general the tant for the conceptual tools it has introshort-circuit current is not equivalent to duced than for its contributions to our
the net active transport of sodium. Even in knowledge of physiology. Among the most
some species of frogs (Zadunaisky, et al., important concepts have been those relat1963) the equivalence does not hold be- ing to the use of tracers for detecting accause of active transport of oilier ions. At tive transport, the view of epithelia as serizero difference of electrical potential but al membrane systems, and the short-circuit
finite concentration gradient, passive net current.
movement of ions may contribute; it is
I hope to have given you some glimpse
SHORT-CIRCUIT CURRENT
FH;XF.S ACROSS EPITHELIA
of these years and these ideas in order to
make your own studies of epithelia more
profitable. The view is not a finished one;
I have omitted in particular the signs
pointing to the future of transport physiology and membrane biophysics.
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