The electrophysiological analysis of tubular transport

Kidney International, Vol. 30 (1986), PP. 216—228

The electrophysiological analysis of tubular transport EBERHARD FROMTER Depariment of Physiology, Johann Wolfgang Goethe University, 6000 Frankfurt am Main 70, Federal Republic of Germany

Although as early as 1935 Wilbrandt [1] made a first attempt must be observed. For a more fundamental introduction into to measure transepithelial potentials in Necturus kidney prox- the theory of electrophysiological measurements the reader is imal tubule, the electrophysiological analysis of tubular trans- referred to [10].

port began only in the late fifties, and it was not before the

Analysis of ion transport properties I.) By measuring the potential change in response to current

mid-seventies that well—defined information on the electrical phenomena associated with tubular transport became available.

The reason for this slow development has been in part the

(I) applied from external electrodes we can determine the

methodological problems inherent in the technique which initially were only poorly understood. After these problems had been solved 121, however, the method has become an increasingly important tool in the hands of renal physiologists, and has contributed considerably to our present understanding of tubular transport phenomena and will undoubtedly continue to do so in the coming years. Much of this power is owed to the recent development of new methodological concepts such as ion—selective microlectrode techniques [3—7] and patch—clamp techniques [8, 91, which enable us not only to look into the tubular cell and follow changes in ion—activities, but also to directly observe single channel currents in cell membranes. I think it is fair to say that, with the exception of some optical measurements such as micro-fluorescence or cell volume measurements, there is presently no alternative approach available for studying ion transport events in normally functioning cells with comparable space and time resolution.

membrane conductance (g), which is the sum over the conductances of all individual ions (g1). in terms of the phenomenologic theory of membrane transport it can be defined as

g=

gj

= J1=coostnt

=

k

(i

I

k)

k

zF i:,=1

z1FL13

(1.1)

j=1

where the subscripts i andj denote individual ions (i, J = I z and F are valency and Faraday constant and the L1 are phenomenologic coefficients as observed in the linear range of

the membrane system [10, in Jact is the rate of active ion is the chemical potential difference, p' — transport and

,/', between the external phases (' and ") with x representing either ions (i), permeable non-electrolytes (n) or water (w). The

Measurement of electrical potential differences

side conditions under which this measurement must be perMembrane potentials may result from a great number of formed will be further considered below. 2.) By measuring potential changes in response to concendiverse transport phenomena. They may be generated by current flow (either imposed external currents or intrinsic, tration changes of non-permeating non-electrolytes which escircular currents), by solvent drag of ions, by ionic diffusion, by ion—nonelectrolyte flux coupling and/or by active ion transport. It is evident, therefore, that steady—state measurements of cell

sentially represent changes in the chemical potential difference

of water ()

and

hence changes in water flow, we can

measure streaming potentials:

membrane potentials or transepithelial potential differences

alone do not provide much insight into the ion transport processes of a given membrane. The situation is different, however, if we determine potential changes in response to well—defined changes of external fluid composition (uni- or bilateral changes in ion or non-electrolyte concentration) or in response to changes in current or waterflow, or if we apply inhibitors, which in other membranes have proven to selectively block individual transport events, in the following paragraphs I critically review which information can

J.actCanstant (i= I

where

© 1986 by the International Society of Nephrology

— — zFL1 g

(xcn)

(1.2)

k)

L is the phenomenologic coefficient describing the

interaction of ion and water flow. As shown in References 10 and 11, these measurements may be interpreted in terms of single ion reflection coefficients (uj) since the right hand side of this equation may be replaced by

be obtained from such measurements and what precautions Received for publication March 4, 1986

=

1=0

— —

where , and

z1F (1 — oj)

(w), respectively, and coefficient of water transport. 216

c

g1_1 are mean concentrations of ions (i) and water

is the phenomenologic straight

217

Electrophysiological analysis of transport

As described in equation 1.2, the streaming potential com- which implies a "doublc—Nernstian" slope for the cation (122 prises always the ion—water interaction of all ions simulta- mV per tenfold change in c ) and a negative Nernstian slope neously. Hence, in order to estimate a single ion reflection (anomalous Nernst response) for the anion. Alternatively, in h

coefficient (a1) we measure the streaming potential twice, first in

the presence of i and second, after complete or partial substitution of i by a non-penetrating ion r of the same valency. To our knowledge this concept has not yet been applied to biological or artificial membranes. 3.) By measuring potential changes in response to ion con-

case

az=

—2

(as in cotransport of I Na with 3

HCO3 [13]), we find t+ = —0.5 and t_ = + 1.5. 4.) By measuring potential changes in response to changing non-electrolyte concentrations, but constant osmotic driving centration changes we determine the membrane diffusion potential force, it is possible to observe non-electrolyte transport potentials, if ion and non-electrolyte flows are coupled (I.j,, # 0) k

=—

(At)

—

g 1=1

A5,0 (x=n,w) 5—i

-

zFj=i L

(1.3)

1k

I

g 1=1

nk+I

=—--E z1F

(A40i-s 1t'x=s (x—,,w) 5=1

(1.6)

k)

from which transference numbers (t1) can be derived, which may be defined as

where n denotes individual non-electrolytes which are indexed

tj' z1FL

5.) Active transport potentials can be measured if one dimmates all passive driving forces' across the membrane:

z1F k

z1FJ I

(1.4)

g

and may be inserted into the right hand side of equation I .3 to yield 1

asn=k+I

L

(i4°t) 5t,—5 (x=i,n,w)

=—— zF j1act g '=1

(1.7)

k

Since it is virtually impossible to eliminate all passive driving forces across the membrane of a living cell, equation 1.7 is

1=1

useful only if J13CI can be changed, as for example by application

=--—A/Lj

if we want to determine the transference number of a single of specific blockers. On the other hand, the concept can be used ion, the electroneutrality condition forces us again to replace to measure lransepithelial active transport potentials or, rethe ion (i) by a non-penetrating ion r Or = 0) of identical valence. spectively, the short circuit current l0], although it should be Otherwise, one can change a salt concentration to obtain the kept in mind that we cannot distinguish between primary and difference between transference numbers of cation and anion, secondary active transport [Ill in such experiments. which in case no other salt was present allows the individual t÷ Side condilions fbr measurements on epahelia and t_ to be determined (single—salt gradient potentials), since In the theoretical formulation of the individual measurements k described above, we have always selected one passive driving t, = (1.5)

1.

1=1

force and have set all others to zero. To achieve this in an

experiment, however, is often difficult or impossible. Alterna-

If a membrane is permeable only to one ion (i), measurements according to equation 1 .3 yield the Nernstian relationship with

tively, provided the system is in its linear range, the same

a slope of 61 mV per tenfold change of concentration for a univalent ion at 37°C. If obligatory ion flux coupling exists between ions i = I . . . h, their transference numbers may assume surprising values. To illustrate this we consider in the following some membranes which are thought to contain only h but one coupled transport mechanism for ions i = I nothing else and we denote the stoichiometry of flux coupling by a:

keep all others constant. This imposes a number of side

...

h

z, =

(i) if

0, coupled transport of these ions is not

associated with net charge transfer, and we obtain t1 h) (obligatory electroneutral salt transport).

0 (i

a1 z

0, t+ or t_ may assume negative values or

steady—state which yields a measurable response. Even this precaution, however, does not necessarily warrant that the observations are unambiguously and quantitatively interpretable. in fact, it appears that under control conditions in most cells,

may he so far displaced from equilibrium that quantitative analyses based on linear equations yield only a crude approximative view of the true events. Attempts to use non-linear

equations based on the constant field assumption [14] or,

+ I (as in cotransport of 2 Nab with

/1=1'!

glutamate [12]), and if there is no other ion transport mechanism present in the membrane, we find t÷ = 2 and t_ —1 I

from equilibrium or the least possible disturbance of the

respectively, on the rate theory of Eyring [1511 have, of course,

become even greater I.

For example, if v1z1

conditions which complicate the electrophysiological analysis of epithelia. Linear range. Regarding the restriction to the linear range, it is always advisable to work with the least possible deviation

the electrochemical potential differences of the principal ions 1

ii

(ii) If

information can be obtained if we vary one driving force and

The constant field assumption and the rate theory yield essentially identical mathematical formulae tor ionic currents across phase boundaries.

218

Frömter

been made and the applicability of this complex matter has been

neatly discussed by Helman and Thompson recently [16]. It appears, however, that its practicality is still rather limited, since the Goldman—type rectification is not the only possible source of macroscopic non-linearity. Thus, we know from patch clamp studies that open—close kinetics may be voltage— dependent, imposing for example "anomalous" rectification on macroscopic partial ion conductances, even when single chan-

a potential change even if the transference number ofi was zero at the beginning and remained zero. This may be the case, for example, if cell membranes hyperpolarize during replacement

of Na by non-penetrating cations: Ca INa countertransport may reverse, causing intracellular Ca concentration to increase near the membrane, which in turn may affect cell membrane K or Cl permeability. 3.) If t1 = 0, but tj 0 and if the membrane contains an electroneutral exchange mechanism for i and j, external replacement of i may lead to transient accumulation of j (in

nel conductances exhibit typical Goldman rectification. Such restrictions, however, do not apply to transepithelial measurements in leaky epithelia, In such epithelia, transepithelial trans- exchange of i) inside the cell, which then alters the membrane ference numbers can be accurately measured and properly diffusion potential. 4.) Replacement of an ion i may alter active rheogenic ion interpreted as passive properties of the paraccllular pathway

(tight junction) provided the high preponderance of the transport so that in addition to the change in membrane paracellular conductance is ascertained under the experimental conditions.2 Time limitation. Since epithelia consist of serial and parallel

diffusion potential, the active transport potential changes. This seems to happen regularly if one changes extracellular K to

determine tK of cell membranes, since the rate of active

arrays of membranes with various cellular and intercellular rheogenic Na/K transport is a function of extracellular K compartments interposed, it is mandatory that all measure- concentration [19, 20]. 5.) All potential measurements described above are defined at ments are completed before the ionic composition of those compartments changes, which means that parameters are to be I = 0 (so—called zero current potentials). In leaky epithelia, changed and measurements are to be performed as fast as however, a circular current may continuously flow in a closed possible. On the other hand, before the measurements can be loop from one cell membrane across the paracellular shunt and taken, it is necessary that the cell membranes proper have through the other cell membrane back into the cell: reached a steady—state with regard to redistribution of electrical

charge and with regard to water and solute fluxes (including chemical reactions which they may involve). The time required

—

C—

l'a

—

+

Ra+Rh+Rs

(1.8)

for charge redistribution can be estimated from membrane resistances and capacitances. It varies somewhat but falls where the i/i° are zero current potentials and the R are usually between 50 and 200 msec, a time that should also suffice resistances of both cell membranes (a and b) and of the shunt for reaching new steady—state flows across cell membranes. (s). Since this current can neither be eliminated nor kept The point in time when intra-epithelial ion concentrations start constant, it can happen that a potential change, for example to change depends on overall permeabilities, cell volume, and on membrane surface area, and hence may vary considerably from preparation to preparation. In mammalian proximal tubule the relaxation time of the cellular compartment may be as short as 2 to 3 seconds [17, 181. Hence, special perfusion techniques have been devised to produce concentration changes in the luminal or peritubular compartments in the time range of 0.2 to I sec. If the change is too slow, the potential will pass through a series of steady—states, which reflect both the effect of the known parameter changes in the external solutions and of the unknown changes in the intra-epithelial compartments.

across membrane a in response to a change in external solution, does not reflect a change in qJ° but exclusively or additionally a resistance change (for example in R) and hence, a change in

I. It is evident, therefore, that any quantitative analysis of

potential changes in leaky epithelia needs appropriate corrections. To overcome these problems a series of strategies based on extra measurements may be chosen. For example, case I can be solved by testing different substituting ions. Cases 2 and 3 may be largely excluded if only fast concentration step experiments are performed: even if exchange mechanisms were present and were working at extremely high rates, they should operate with Problems of interpretation some delay which might be recognized. In addition, it should be Since potential differences may have so many different mentioned that the dependence of a potential change on the sources of origin it is not surprising that often the interpretation logarithm of ion concentration may help to positively identify remains'mbiguous and further experiments are required. Es- conductive ion transport mechanisms. Case 5 might be solved by simultaneously determining all circuit resistances and their sentially the following problems may arise: I.) When replacing an ion i by a non-permeating ion r, it is possible changes immediately before and after the imposition of necessary to ascertain that t is indeed zero, or in other words the membrane perturbation, although this is technically quite that r does not penetrate the membrane. This is important for all demanding. A proper solution for case 4, however, is not yet available, at least as far as a quantitative correction for changes quantitative considerations. 2.) Replacement of an ion i may alter the membrane, thus in active electrogenic Na/K transport during step changes of changing the permeability or transference number of other ions K in the interstitial fluid compartment is concerned. As a j. If ionj is not distributed in equilibrium, one may then observe consequence, one may conclude that virtually all calculations of' transference numbers or partial conductances of cell membranes for K are at best crude estimates. In view of these difficulties, it is fortunate that we have a 2 Problems may arise if leaky epithelia are bathcd in high K solutions which lead to a drastic fall of cell membrane resistances. number of highly specific inhibitors available today which are

219

Electroplivstological analysis of transport

Table I. Ton transport inhibitors in epithelial cell membranes Substance Active ion pumps onabain vanadate

Inhibitory side effects

Transport mechanism

Comments

Dio-9 DCCD*

HtATPase [23, 24]

— intracell. ATPases intracell. ATPases

omeprazol

H/K-ATPase of stomach 125]

—

metabolite more potent

Kt channels [26]

KCI-symport (7) [27] HD: tight junction 129] HD: NaIl-I exchange [31] HD: tight junction [32]

not all Kt channels inhibitable [281

Nat channel

low affinity

NaJK-ATPase [21] NaIK-ATPase [22]

low affinity in rat acts from cytoplasmic surface (uncouplers)

Channels

amiloride

Nat channel [30]

anthraccne-9-COOH DPC** and analogues

Cl— channel [33, 34]

Passive co- or countertransport mechanisms amiloride NaJH antiport [31, 36] guanochlor furosemide NaKCI2 symport [37] SITS, DIDS*** Cl/HCO exchange [38] Nat (HCO3 )-symport [39] phlorizin Nat.glucosesymport

not all C1 channels inhibitable [35]

(see above) HD: carbonic anhydrase, NaIK-ATPase low affinity

—

Abbreviations are: * DCCD, dicyclohcxylcarbodiimide; DPC, diphenylamine-2-carboxylatc; 2.2'-disulfonic acid; DIDS, 4.4'-diisothiocyanostilbene-2.2'-disulfonic acid; liD, high dose effects.

SITS, 4-acetamido-4'-isothiocyanostilbene-

known to selectively block individual transport mechanisms

1.) The problem of leaky impalements has troubled electrophysiologists ever since the beginning, but thus far no direct test is available to tell whether a given impalement is leaky or blockers are applied under the above discussed precautions leakfree. This problem is particularly severe if one punctures (fast application, proper corrections for circular current small cells of mammalian epithelia. Thus far, the only orientachanges, etc.), there is no doubt that simple potential measure- tion available was (i) the stability of the record (preferably it 2 ments can yield very detailed and most valuable information on mV for at least 2 mm, and (ii) a comparison of individual measurements with the distribution of a greater number of ion transport mechanisms. observations, which in case of varying leaks usually show significant skewing towards zero 47]. Both criteria, however, Comments on specific technical problems left open doubts' dnd uncertainties. Recently, when measuring

(Table 1), They can be used to identify transport mechanisms in membranes about which only little is known thus far. If these

Although this article is not thought to serve as a cookbook for eleetrophysiologists, it might be appropriate to briefly consider some purely technical problems. Transepithelial measurements. Previous problems with tip potential artifacts of Ling—Gerard—typc electrodes and uncertainties of tip localization have been solved by using bevelled tip microelectrodes [2]. Today, a series of very simple bevelling techniques' are available [40—43]. A problem which persists and

intracellular Na F activity with fast responding double—barrelled

microlectrodes, we found a new criterion: if the inipalement is tight, one may expect that the intracellular Nat activity is low

and remains stable; in case of a leak, however, one may anticipate that intracellular Nat is low at the beginning but rises then to a new elevated level which may or may not he stable.

Hence, by considering the time course of cell Na activity in the first ten seconds after the impalement, we can distinguish has to be reconsidered in every individual application is the tight from leaky punctures [48]. proper choice of the electrode filling solution and the proper 2.) Contamination of the cell with electrode fluid may present correction for liquid junction potentials. Ultimate care must be a problem with relatively large tip, low resistance electrodes (10 observed here, particularly if the expected potential values are to 20 MU) if they are filled with highly concentrated KCI low. A number of efficient technical approaches has been solution, and particularly if the electrodes are tightly screwed described to solve this prohlcni [2, 44—46]. into holders so that the fluid is under pressure. It leads to cell Cell potential measurements. Here the following problems swelling with subsequent rejection of the eel! from the epithelial exist: cell assembly. This problem has been quantitatively studied by

I.) Impalement artifacts due to imperfect sealing of the a number of laboratories who suggest various alternative electrode in the cell membrane; 2.) Spilling of cytoplasm with electrode solution; and 3.) Liquid junction potentials between cytoplasm and electrode fluid or generally speaking changes of tip potentials.

isotonic filling solutions [49—SI]. In work on mammalian kidney tubules, the problem does not seem to be of importance because

(i) the cells are always under microscopic control which would allow the recognition of cell swelling, and (ii) because one must

220

Frömter

use very fine tip electrodes (50 to 80 M) which do not lose significant amounts of KCI even if they are filled with saturated solution. 3.) Although the technique of the self—filling internal fiber glass microelectrodes has greatly reduced the occurrence and magnitude of tip potentials (as compared to the previously used methanol and negative pressure techniques), the problem of tip potential changes has not disappeared. Our personal experience is that tip potentials can be reduced towards zero when the inner glass surface of the capillary glass tubing is rinsed and well hydrated immediately before pulling, with only a short interruption for drying purposes of the order of two to three mm. An interesting alternative suggested by Thomas and Cohen circumvents tip potentials by filling the electrodes with a cation exchanger which does not discriminate between Na and K [52]. Provided the sum over both cation concentrations is equal in the extra— and intracellular compartment, this electrode should indicate the membrane potential properly and should not cause tip potential artifacts nor alter the composition of the cytoplasm. A disadvantage may be that the resistance of such electrodes is considerably higher than that of conventional electrodes of identical tip diameter.

R=

4 X2 —a--— =ir2d3R02 ______ = \/8i-pX3R0

d

p

= 2iidXR0

(2.3)

The consistency of the measurements can be tested by calculating the diameter from the electrical measurements according

to d=

(2.4)

TR0

comparing it with the microscopic diameter. Since deviations have been noticed, it is always preferable to determine the length constant rather than only the input resistance. Isolated microperfused tubules are usually short and may be considered as finite cables which are terminated at both ends by infinite resistors. If both ends are tightly sealed [541, the voltage attenuation is expected to obey the equation and

L-x

cosh ______

V, =

V0

L

(2.5)

cosh —

x

where L is the exposed tubular length. In isolated tubules it is usually not feasible to measure the length constant of voltage

Resistance measurements

The membrane conductance indicates the ease with which attenuation along the lumen directly. It may be calculated, however, from the current induced voltage signals V0 and VL electrical field. Even though a given membrane may possess recorded at both ends of the preparation obligatorily coupled electroneutral co- or counter—transport V0 mechanisms which allow ions to migrate but do not contribute X = L cosh — (2.6) to the electrical conductance, there is no question that the VL membrane conductance or its reciprocal: the membrane resistance, (Ri) is an interesting property to characterize a mem- and the transepithelial resistance can be calculated from brane. In addition, it has the advantage that it is usually easily L measurable. The latter, unfortunately, is not true for tubular R = iid X R0tanh — (2.7) epithelia, where resistance measurements require the use of cable theory [531. with R0 as defined above. From these measurements we derive the tubular diameter as Transepithelial resistance ions can be driven across a membrane under the influence of an

In first approximation the tubular lumen may be considered

as the

core and the cell layer as the wall of an infinite electrical cable. Injecting current from a point source within the lumen (at x = t)) into the surrounding medium and observing the voltage

L /4pX d= \f—cotgh— X

(2.8)

irR0

Under specific experimental conditions, a number of alterna-

tive formulations or extensions of the cable equations have

(V) along the luminal axis (x) this model predicts a simple been used, such as equations for branched cables describing the exponential voltage attenuation in both directions along the situation in the papillary collecting duct [551.

Although simple cable analysis describes transepithelial measurements in tubular epithelia generally quite well, in reality it

lumen

V V0e'

(2.1)

represents only a simplification of the voltage attenuation

problem that is based on a number of neglections and approximations, the critical importance of which is sometimes difficult where V0 is related to the total current, 10, by to assess. One simplification is the assumption that the peritubular surface consists of a homogeneous volume conductor of V0 = R010 (2.2) infinite conductivity. This problem has not been treated quanFrom combinations of the following variables: the input resist- titatively thus far. It may cause errors particularly in measureance, R0 (fl), the length constant, A (cm), the resistivity of the ments on low resistance epithelia in situ. Another problem is lumen fluid, p (fl - cm), or the luminal diameter, d (cm), we can the phenomenon of origin distortion [56], which is particularly calculate the wall resistance which represents the specific important if current is injected from a point source into the transepithelial resistance, R (U cm2) according to one of the tubular lumen where it initially generates radial voltage gradifollowing formulae

ents. In addition to these problems, simple cable analysis

221

Llectrophysiological analysis of transport vi - —

— —Lumen

vc — —

— —Cell

and A and A represent the length constants of the luminal and cellular cable respectively, which could he measured if both cables were isolated from each other: I i 71 l'\ fi l\ —=rI—+—land—=rl—+—I (2.11) x2 X2

\r

r.J

\ja

r5J

Note that a has the same values in the lumen and in the cell ——

— —Interstitium

layer and the same is true for [3. From the boundary conditions appropriate to luminal current injection one finds

Fig. 1. Equivalent circuit element of infinite double cable representing a tubular epithelium with luminal, cellular and perituhular fluid compartment. The resistances r are defined per unit length. They repre-

A

—

r 10a3(X12 — [32)

2 X2(a2 — /32)

sent: r and r,, luminal and basofateral cell membrane; r, paiacellular

shunt; r,, lumen fluid; and r, cytoplasm (including cell to cell coupling).

V, and V, are the luminal and cellular voltage with reference to interstitium.

neglects current flow from cell to cell which in reality may also contribute to axial voltage attenuation. The latter problem will be considered in detail in the following pages which deal with the determination of cell membrane resistances.

B

r_________________ 10/33(X12 /32)

—

2 X2(tx2 — —

rr I a3/32 2 ra (a2

D =

The cell membrane resistances and the resistance of the paracellular shunt

/32)

—

/32)

rr I a2/33 2 ra (a2 —

(2.12)

/32)

where I is the total injected current. From equation 2.10, it Even if we are able to measure the "input" resistance by follows that a < /3, and further considerations indicate a A1, passing current into a cell and measuring the voltage response

/3. Using this sequence one finds that the coefficients A, B

in the same cell (with two separate electrodes, or with a and D are always positive while C is always negative. This double—barrelled electrode, or less reliably with a single—bar- indicates that voltage attenuation along the lumen follows the relled electrode using specific compensation techniques), such measurements do not allow us to calculate the cell membrane resistances because cell—to--cell—coupling via gap junctions diverts too much of the injected current into neighboring cells.

The determination of cell membrane resistances is rather difficult therefore, and thus far a simple and accurate method is

sum of two positive exponentials, while that along the cell layer follows the difference of two exponentials (the first exponential with the shorter length constant a is subtracted from the second exponential with the longer length constant /3, which leads to a depression of the curve near the origin Fig. 2A). If cellular and luminal voltage attenuation has been measured (Fig. 2B), it is now possible by computer, least square fitting of equation 2.9 to

not available. All approaches that have been devised rely on estimate the resistances of the cell membranes ra, r and the approximations or unproven assumptions, which implies that resistance of the shuntpath r (as well as re), which are then the limits of their applicability must be carefully discussed in usually converted to obtain specific resistances R, Rh, and ft. each experiment. cm2 related to apparent luminal surface area: Double—cable analysis with current injection into the tubtilar lumen. In this approach 157—601, current is injected through a R = dra; Rh lrdrh, R. = (2.13) point source into the tubular lumen and the voltage attenuation It should he noticed, however, that even this rather complex along the tubule is measured in the lumen and in the cell layer. The theoretical analysis of this problem as obtained from the approach involves important simpl ifications and approximadouble—cable equivalent circuit of Figure 1 predicts that both tions in as much as the double cable model lumps the the voltage response in the lumen (V1) and in the cell layer suhcornponents of the paracellular shunt resistance: the resist(V) exhibit double—exponential attenuation as described by ance of the tight junction, R, and that of the lateral intercellular space, Rik, into a single value: R. This simplification may lead the equations: to overestimation of Rh. In planar epithelia, we have succeeded = A e" + B

dr

=

+De

C

(2.9)

where the length constants a and /3 arc defined as

1 11 1/i 1 \2+ 4rjrclu/2 =—++ll———l X2 r2 1

a2

1

/32

1

2

1 Ii

i

[\).2 [71

2 X2 2 [\Xj2

X2J

1\ x2 ,j

4r.r,li2l ra j J

in separating R1 and R11 by means of impedance measurements [61, 62]. Whether this technique can be successfully transferred

to renal tubules is uncertain at present. Double cable analysis with current injection into a cell. This problem leads to the same solution as presented in equation 2.9 with only the coefficients assuming different values. For better distinction we use the primes:

=

= C'e"

+ Be_x -I-

D'e'

(2.14)

222

PrO inter

A

luminal current injection (Fig. 2A). The reverse, however, does

log V

not hold since C' A and D'

B. As a consequence it may be that luminal voltage attenuation (during luminal current injecI), but tion) follows virtually a single exponential (A/B cellular voltage attenuation (during cellular current injection) does not because C'/D' differs from A/B (except if A, = A0):

VI

AK

C'

(X02 — —

D'

—

(X2 —

p2)(X2 — a2) a2)(X12

A

—

(2.16)

This implies that single—exponential fits to cellular voltage

attenuation curves (obtained from cellular current injection

x

x=

0 (as assumed in the double cable equations), we obtain

some tent—like distortion of the voltage profile towards the cell into which the current is injected. This effect may then obscure

B

40

a double exponential voltage attenuation. In wider tubules, it maybe of advantage to consider the cable wall as a planar sheet

30

1591 and to apply the 2-D cable analysis which has been derived for planar epithelia [631. In leaky epithelia [64—661, it has been assumed that the lumen may be considered in good approximation as iso-potential with

20

E

studies) may be in error. An additional problem is presented by circumferential current flow. Since current is injected only into one cell, rather than into all cells which form the cable wall at

10

the peritubular space so that simple cable equations can he applied to determine R.d, Rb, and R0 from cellular voltage attenuation (observed during current injection into a cell) and

a,

>6 0

from voltage divider measurements AVa/AVb (obtained during current injection into the lumen). As long as no further information is available to estimate the possible error, this approach cannot be recommended.

4

2 0

0.2

0.4

0.6

0.8

1.0

1.2

Distance, mm

Fig. 2. A. Voltage attenuation along double cable model during luminal

current injection as predicted by equations 2.9. Abscissa is axial distance from current source, and ordinate is voltage in logarithmic

scale. V1 and V are as defined in Figure 1. B. Voltage attenuation along renal proximal tubule of Triturus during luminal current injection (from Ref 58 with permission). Symbols are: 0, control conditions; X. luminal perfusion with Ringer solution containing alanine (20 mmol/liter). Lines represent computer fits of equation 2.9. Note, coefficient A of Figure 2A is neghgibly small in Figure 2B. This finding has implications for the use of the voltage divider ratio in resistance analyses [601.

and find

A'=C; B'=D;

i —

n2

kc

passing current across the epithelium and measuring the voltage response across the apical (AVa) or basal (Vh) cell membrane to calculate AVa/Vh. If the paracellular shunt is negligible, this

ratio immediately yields the fractional and (after combining with R) the absolute resistances of the cell membranes. Side conditions are that the measurements are performed in the proper time domain [101, and that appropriate corrections are applied for the I/V drop across sub-epithelial connective tissue layers. If the paracellular shunt is not negligible, as in leaky epithelia, such measurements can still be used to calculate Ra, Rh and R, hut in that case a = AVa/AVb = R0/Rb and R must be measured before and after (a', Ri') a resistance change has been effected in one of the cell membranes 167, 68]. Ra, Rh, R md Ra' can then be calculated as follows: Ra =

- a3, 2 — n2 r0 p — C' — 2X02(a2—/32) 2

Measurements based on voltage divider ratios. In planar epithelia, the voltage divider ratio can he easily measured by

Rb

n2

215

2X02(a2—/32)

Since a A1, A0 J3 remains valid, A' is negative and B', C', and D' are positive. Since A' = C and B' = D, we can conclude that luminal voltage attenuation (during cellular current injection) follows exactly the same pattern as cellular voltage attenuation during

a(a — a')

RR'

(1 + a)(l + a')(R — Ri') (a — a')

RR'

(1 + a)(l + a')(R — Ri')

(a—a')RR,'

(l+a)R'—(1+a')R, Ra' =

a'(a — a')

R, R'

(1 + a)(l + a')(R — Ri')

(2.17)

223

Electroj,lzvsiological analytic of transport

In case we measure thc change in Vt and in Vh following the membranes (r4 + rh)/rb. Near the current source at x = 0 we = R/Rh, we can use the obtain alteration of R1 and define b = following equations:

r4 + rb

R5

a(I + a + b)

Rb=

(I+a)b

1+a+b (I + a)b

+

rh

raJ3

(2.22)

which always overestimates the resistance ratio of the cell membranes. The point x at which changes from overestimate to underestimate (and hence is a correct measure of the resistance ratio (r4 -- rb)/rh) falls somewhere between x o and x = [3. Further analysis has indicated that in all double cables which exhibit single exponential voltage attenuation

R

l+a+b R

(2.18)

1+a

along the lumen (as ascertained with an error of <5%) equals (ra + rh)/rb within an error of at most 8.8%,

Alternatively, one can derive the same information from a and that this error reduces even further to 6.4% if the measureseries of resistance changes [69] by determining slope and ments are not taken at x [3but at x = 0.87 f3. From this we intercept in a plot of l/R versus (I + a)1 according to the conclude that voltage divider measurements in tubular epithelia should be performed at a point which is 87% of the luminal equation: length constant away from the point of current injection.4 In 1 1 1 — =— + (2.19) case measuring conditions permit, it is preferable, of course, to

R R5 Rb (1 + a)

All these measurements, however, require that (I) the resistance

measure the voltage divider ratio not only at a single point but to perform a complete double cable analysis or to determine the

change is completed before intracellular ion concentrations length dependence of V1/V, at least in the region of x = start to change, (ii) the voltage responses V4, Vh and/or vt 0.5 [3to x = I. If the voltage divider ratio is constant in this are measured immediately after redistribution of electrical region, one can conclude with great security that it is an accurate charge on the membrane capacitors is completed but before any intracellular ion concentrations change, and (iii) the resistance change is restricted to one cell membrane only (such as, that R,

estimate of the ratio of the cell membrane resistances and hence that it can be used for determination of R, Rh and R [601.

is changed, but Rh and R remain constant). Whether or not

Other methods

these preconditions are fulfilled in a given experiment is usually difficult to assess.3 The concept of voltage divider measurements has also been

In large tubular structures, such as Necturus renal proximal tubules, the basal cell membrane resistance has been measured using simple cable analysis when the lumen was filled with oil [57, 64, 65]. II care is taken to analyze the voltage attenuation

applied to tubular epithelia, although initially the theoretical implications were not clear [17, 70—74]. The problem here is that

a part of the axial current flow proceeds inside the cell layer so that the current entering a cell from the lumen must not equal that which leaves across the basal cell membrane, as would be required for proper determination of R4/Rh. This problem has recently been studied in detail [601 and will be discussed here only briefly, For mathematical simplicity, rather than V/Vb we eonsider now an alternative formulation of the voltage divider ratio: V1/V which equals (V4 + AVh)/Vh. The length dependence of this ratio is described by the following equation: — —

r

Xr

a3(X2 — p2)

e — p3(X2

2) e

(vi) —=.

r5

-F r

r

(ra + rb) Xc2 2

rbp

origin—this method should give accurate estimates of Rh. The method is restricted, though, to studies of changes of Rh under non-physiological conditions. In mammalian proximal tubules, to our knowledge thus far nobody has succeeded in puncturing the cells of oil-filled tubules.

Finally, we want to mention at least briefly that in larger tubules, such as proximal tubule of Necturus, resistance measurements may also be performed with an axial wire electrode which is advanced inside the lumen and isolated between oil droplets 175].

a3p2eih — a2p3eil At x = we obtain as limiting value =

far enough from the point of current injection—in order to exclude the region of circumferential current flow near the

Measurements of ion activities with microelectrodes

The development of ion selective microelectrodes has greatly advanced the efficacy of electrophysiological measurements. (2.21)

which always underestimates the resistance ratio of the cell Thus far amiloride, D-glucose, or L-amino acids, as well as Bail have been used to bring about sudden resistance changes in R4 or H5. While alt substances lead to changes in cell membrane potentials, which may affect membrane resistances on the contralateral surface, in high concentrations amiloride and Bail may in addition affect the resistance of the tight junctions (Table I).

Although the recalculation of some data from the literature in Figure

2 of our recent publication [60] may suggest that errors in voltage divider measurements on leaky epithelia arc always negligible, this cannot be taken for granted. Based on recently communicated corrected data of Hoshi and collaborators (personal communication) we calculate now 1.821 while (r. + r5)/r5 from computer simulation yields 1.986, that is. an error of 8.3%. The same result (—8%) is found if we calculate the p and q values from the best fit computer estimates of r,, rh, r, r and r according to equations 24 of 160] and search for the error in the p,q-planc (Fig. 4 of [60]).

Fromter

224 Table 2. lon-ligands or ion-exchangers used in ion-specific

(from so—called theta—glass or from fused glass tubing of equal

microelectrodes

or unequal diameter). Construction and handling of such electrodes is usually more difficult but—provided the tip is fine enough and does not damage the cell—the information obtained (particularly on ion concentration changes) is also more reliable since E, and tfi are measured simultaneously.

Ion

H Na K

Principal interfering ions with K1 and references

Ligand

virtually none [79]

Li

Tridodecylamine ETH 227 Corning Nr.477317 ETH 149

Ca

ETH 1001

Mg

ETH 1117

Na:105; K:1054; Mgl049 [82]

Cl

Corning Nr.477913

HCO :0.08 [841, sensitive to many anionic drugs, including

HC01

WPI Nr.1E310*

C1:0.02 [86]

K:0.02; Ca:1.6—0.2 [80] Na:0.02; Ca:'0.002 [51 Na4 :0.05; K:0.005, Ca:0.25 [811

Na:0.08; K':0.004; Ca':12,5 [83]

dyes [851

ion—selective microelectrodes may be used to measure steady—state ion activities or, if time resolution permits, to measure transient changes in response to sudden changes of external solution or current. As in case of simple potential measurements the information content of the latter measurements is greater, since they allow ion fluxes to be calculated if the volume of the compartment remains constant. Steady—state measurements, however, allow also significant information to

be obtained since they enable us to decide whether an ion is

Symbol is: * 3:1:6 mixture of tri-n-octylpropylammonium chloride: octanol: trifluoroacetyl-p-butylbenzene.

Compared to the many problems with interpretation which arise with simple potential and resistance measurements, the information that can he collected with ion—selective electrodes is much more direct. Thus, ion—selective microelectrodes allow even electroneutral ion transport to be analyzed, which is not possible with the classical electrophysiological techniques.

distributed in equilibrium across a membrane or not, and hence whether active transport mechanisms are involved in the transport of this ion, even though such measurements cannot distinguish between primary and secondary active transport [II]. Besides some periods of mischief and failures in electrode

construction which every laboratory seems to undergo from

time to time, the major problems with this technique are incomplete selectivity (interference) and uncertainties about intracellular ionic activity coefficients. Interference problem. An empirical treatment of the interference problem is provided by the Nicolsky [76] equation

At present, microelectrodes for H, Nat, Lit, K, Ca,

and Mg, and for C1 and HC03 are available. Among the various electrode designs, such as spear—type [3, 41, or

E1 =

nRT

In (a1 + k1a) + C

(3.2)

z1F

recess—tip glass microelectrodes [7], and liquid ion—exchanger where E denotes the voltage recorded by the non-ideal elecmicroelectrodes [5, 61, today the latter are most frequently trode, the factor n corrects for non-ideal electrode slope in pure used, after a number of high affinity ligands (Table 2) have been solutions of i, a and aj are the activities of the ion under

synthesized in the laboratory of R. Simon at the ETH Zurich and have been made commercially available through Fluka AG,

investigation (i) and of the interfering ion (j), respectively. k is

a selectivity coefficient and C is an additive constant which sums up all constant phase boundary potentials of the measurmade hydrophobic with silane or silicone oil, and the electrode ing circuit. If < 1 the electrode is more sensitive to i than to is then filled with a hydrophobic solution of an ion—selective In the case of interference, instead of equation 3.1 the j. ligand, or with an ion—exchanger either through the tip or from following equation must be used to calculate a,, the unknown Buchs, Switzerland. The inside of the microelectrode tip is

the back. In our laboratory, treatment is by exposing the inside activity of i of the pipettes to dichioro-dimethyl-silane vapour from the back [76]. If the electrodes are not fully responsive, their perform1 = (a1" + kija") expl[z.F (E1 — 3i — a1' k1a' (3.3) ance may be improved by bevelling (breaking) the ultimate tip [IIRT in a suspension of Al203 powder agitated by magnetic stirring If a1' is unknown, one can (under special conditions such as [43].

j

Theoretically the measurement is based on the following intracellular Cl measurements) try to remove all ions i from

equation: a1' =

[zF a1"

exPJ__ a(E1

—

(3 1)

the system, assuming that the remaining electrode signal represents the interfering ions only. The constancy of such interference, however, is, of course, not guaranteed. Different methods have been described to determine the k1 such as (i) the mixed

solution method at constant ionic strength, (ii) the separate a1' and a" are the ion activities of i in the unknown fluid solution method, and (iii) the constant addition method. The and in a reference fluid of known composition, respectively, results have been found to agree quite well [78]. Table 2 lists and 3(E — qi) is the change of the potential difference selectivity coefficients for a number of available liquid ion—exmeasured between the ion-selective electrode and a non-selec- changers or ion—specific ligands. It should be mentioned, howtive reference electrode when passing from one fluid into the ever, that the Nicolsky equation provides only an empirical other. The reference electrode is usually a calomel half cell solution of the interference problem, since in some electrodes it which is connected to the fluid via a saturated KC1 bridge in has been found that the selectivity constants may be concenorder to minimize liquid junction potentials. The fact that two tration dependent [87, 88]. As a consequence, it may be more electrodes are required for each measurement has led to the realistic to prepare calibration curves in solutions which resemconstruction of various types of double—barrelled electrodes ble the unknown fluid as close as possible and to perform only where

Electrophysiological analysis qf transporl

225

small variations of the unknown ion concentration in the appropriate range. The usefulness of some alternative electrode equations has been briefly discussed 188]. Activity coefficients. To calculate ion concentrations from activities or to calculate ion fluxes from changes of ion activities it is necessary to know activity coefficients of single ions. A rigorous definition and the experimental determination of single ion activities, however, is not possible [891. Even the meaning of salt activities in mixed aqueous solutions is already proble-

matic, and this is the more so if we consider the cellular cytoplasm which contains a great amount of poly-electrolytes. Neglecting the problem of the poly-electrolytes, we have tried to estimate activity coefficients of NaCl and KC1 [881 in mixed isotonic solutions of constant ionic strength, using Harned's rule by extrapolating isopiestic measurements of Robinson [901

which had been made at higher concentrations. For 160 mmollliter of mixed NaCI and KC1 solutions we have found that YNacI varies only between 0.7410 and 0.7485 and YKcI between

Fig. 3. I%lain recording configuration qt patch clump pipettec: a, cell attached; b, excized inside—out patch; (, whole ce/I recording; and d, excized outside—out patch.

0.7345 and 0.7400 (at 25°C). Regarding the scatter of electrophysiological measurements and the biological variation among tissues and cells, these data suggest that corrections for activity may resist even the most enduring efforts of the experimenter coefficients can in most cases be handled quite summarily. but in some cases surrender after enzymatic treatment (such as Patch clamp technique with collagenase). This method is the latest offspring of the classical electroThe patch clamp technique has opened a completely new physiological measuring technique. It was developed by Neher domain of research on membrane properties, in allowing us to and Sakman in the mid-seventies [81 and refined in the same study the performance of individual protein molecules which laboratory by the introduction of the giga Ohm seal in 1981 19]. serve as ionic conductance channels inside their natural enviit has since then precipitously spread out through electrophys- ronment. 'Ihis is only one aspect, however. Since the technique is relatively new, there is no question that further fields of iological laboratories all over the world. Rather than inserting a microelectrode through the cell mem- application will he showing up in the future. In renal epithelia, thus far patch clamp studies have been brane into the cell, a blunt tip electrode of approximately 1 m diameter is advanced onto the membrane until a seal forms performed on apical and hasolateral cell membranes of isolated between the rim of the electrode tip and the membrane surface, tubules which were either held in a microperfusion pipette [921 either spontaneously or with the help of negative pressure or ripped open and mounted in metal clips [931. In addition, cell applied to the electrode shank. With seals of the order of 5 to cultures of renal tubular epithelia have been successfully inves100 giga Ohms, it is possible to change the local membrane tigated [94]. Interest has mainly focused on the detection of ion potential and to record the resulting current flow into or out of conductance channels and on the description of their properties the electrode tip by means of an appropriate amplifier (on—cell such as ionic selectivity, inhibition, voltage dependence, open recording, a, Fig. 3). Alternatively, it is possible to break the and close kinetics. Since space does not permit to discuss the patch after sealing by a second short pulse of negative pressure, rationale of such measurements in detail, I want to summarize and thereby gain access to the cytoplasm in order to record cell only very briefly the major ideas behind this approach. membrane potentials or whole cell voltage clamp currents Since the experimenter cannot aim at a given channel, the (whole—cell recording, c, Fig, 3). As another alternative, it is presence of channels in a given membrane patch is arbitrary also possible to excise the patch from the cell and to study the (unless one works with membranes which have previously been isolated piece of membrane on the tip of the electrode by shown to possess only a single type of channel). The first task exposing it to arbitrary test solutions (inside out patch, b, Fig. therefore, is to identify which ionic species generates an ob3). In addition, it is also possible to exchange the fluid on the served channel current. This can be achieved by recording inside of the patch pipette [911 and it is possible to form excised current voltage curves and comparing them with known ionic outside out patches (d, Fig. 3) by starting from the position of concentrations on both sides of the patch. If ion concentration whole cell recording and gradually withdrawing the pipette until a piece of membrane is pulled out which collapses and fuses on gradients are present and their magnitude is known, the i-vcurve should intersect the zero—current line at potentials (rethe tip of the patch electrode. The crucial point of the technique is the formation of the giga versal potentials) which reflect the Nernst potentials of individseal, which is essentially a spontaneous process reflecting ual ions. In addition, typical deformations of the i-v-curve can hydrophobic interactions of the membrane surface with the be observed that may follow the pattern of Goldman—rectificaglass surface of the pipette tip. it is evident, therefore, that tion [15] from which the migrating ionic species can be identimembranes must have a specific surface structure to be ame- fied. If the results are ambiguous, ion concentrations should be nable to patch clamping. Cell membranes covered with mucous, varied or specific inhibitors applied (in excised patch preparasurface coats, or cornified or collagenous layers (basal lamina) tions), if the spectrum of channels which are present in a given

Frörn/er

226

membrane is known, channels may later be identified more rapidly by the size of their conductances.

shape of voltage attenuation along the tubular lumen, which

allows the error to be estimated quantitatively. Important

The ion selectivity of single channels can also be determined progress was made in recent years with the development of new from conductances if the same membrane patch is exposed to technical approaches such as the ion—selective microelectrode different solutions. A further important characteristic which can and the patch clamp technique, which are briefly discussed. be determined easily is the fractional mean open time of a Although these techniques have their own limitations, there is channel, which often changes with membrane potential and no doubt that they allow more direct information to be obtained may therefore determine the overall current voltage relation. It on membrane transport processes. Particularly the latter techis analyzed by measuring the duration of open and close states. nique may be expected to advance our knowledge precipiSimilarly, the rate constants of open and close kinetics can be tiously, because it allows the investigation of the properties of determined from histograms of open and close times or from the individual ion transport mechanisms in the cell membranes respective probability density functions. Alternatively, Fourier directly.

analyses may be used [95]. For a detailed introduction into specific questions of single channel analysis the reader is referred to the book of Sakmann and Neher [96]. Other advantages which the patch clamp technique offers

Acknowledgement 1 thank Mr. 6. Weber for checking some of the equations and Mrs. U. Merseburg and Mrs. G. Selbach for typing the manuscript.

have not yet been exploited by renal physiologists. Thus, it may Reprint request to Dr. Eherhard From/er, Zen truin der Physiologic, be expected that in the future the whole—cell recording technique may increasingly be used for potential and resistance Johann Wolfgang Goethe UniversitOl, Theodor Stern Kai 7, 6000 measurements in epithelia, because this technique allows much Frankfurt 70, Federal Republic qf Germany. better seals to be obtained with cell membranes than can he References achieved when impaling cells with conventional microelec-

trodes. In addition, the relatively large free access of the micropipette to the cytoplasm (during whole—cell recording) can be utilized for applying substances intracellularly, which other-

wise are difficult to transfer into cells. Recently, Neher and Marty succeeded in making high resolution capacitance measurements on single cells in the whole—cell recording configura-

tion, which allowed them to identify single exocytotic and endocytotic events from changes in cell membrane capacitance that reflect changes in membrane surface area [97]. This most fascinating technique may also help to further elucidate transport events in epithelial cell membranes. Conclusion

In the present paper I have discussed the possibilities and limitations of electrophysiological measurements on tubular epithelia. The first two sections deal with classical cellular and transepithelial potential and resistance measurements. Although such measurements have contributed significantly to our present understanding of tubular ion transport, their limitations become increasingly apparent today. This reflects the complex-

ity of tubular transport organization, which could only be conceived as knowledge gradually progressed. Thus, it is evident today that even apparently simple experiments, as for example measurements of the cell potential response to changing peritubular K concentration, can at best be interpreted in a qualitative sense. To obtain a reliable quantitative estimate of the K5 conductance of the peritubular cell membrane would require a knowledge of whether and how circular current flow changed and how the rate of active Na 1K5 transport changed. Reliable information on these parameters, however, cannot be obtained readily. In addition, it would require one to know details about the presumed nonlinearity of the membrane system in the range in which the measurements have been performed. As another example of the precautions which must be observed, I may cite the analysis of the resistance distribution in tubular epithelia by means of voltage divider measurements. The quantitative interpretation of such data may also be in error, unless additional information is obtained, such as on the

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