Electrophysiological Analysis of Transepithelial Transport

In this chapter we discuss electrophysiological approaches to the study of renal function. The purpose is to provide an overview of the available techniques, with particular emphasis on what can be learned using the latest methods. However, the chapter is neither a technical manual nor a comprehensive review of the literature. For this, we refer the reader to other sections of the book which deal with specific nephron segments and transport mechanisms. Finally, we will not derive mathematical equations from first principles. Those equations that are essential to the text are provided in the main body of the chapter, while the more detailed formulae are described in the appendices.

Introduction

We have arbitrarily divided the field of epithelial electrophysiology into three major sections. The first describes measurements of transepithelial electrical properties. The second section focuses on the use of intracellular microelectrodes to discriminate apical and basolateral membrane properties. The final section deals with the technique of patch clamping to investigate the functional characteristics of individual ion channels, and in some cases their molecular identification.

The interpretation of electrical signals from epithelia is complicated by the geometry of the tissues. At least three structures within an epithelium contribute to its electrical properties: the apical plasma membrane; the basolateral plasma membrane; and the paracellular pathway. The individual cell membrane properties will, in turn, be determined by various conductive pathways, including those of passive or dissipative pathways, through which ions flow driven by their own electrochemical potential differences, and active transport, which can use metabolic energy to drive ions against these potential differences. The paracellular pathway, in turn, consists of the tight junctions connecting the epithelial cells and the lateral interspaces between the cells.

The electrical properties of this complex structure can be most easily understood in terms of equivalent circuits. A comprehensive equivalent circuit of a generic reabsorbing epithelium is illustrated in Figure 7.1 . Electrolyte diffusion across the apical membrane can be separated into its constituent ionic pathways, as shown by the expanded view of the apical membrane in Figure 7.1 . Each ionic pathway is associated with an electromotive force (EMF) or battery representing the chemical potential for each ion. Electrogenic carriers such as the Na-glucose co-transporter can also be represented by an additional resistor (R _glu ) and EMF (E _glu ) in parallel with the diffusional elements. All of the batteries and resistors can be lumped respectively into a single apical EMF (E _ap ) and a single resistance R _ap as shown in the center diagram. The basal membrane has a similar set of elements: R _b and E _b which represent a dissipative ion pathway in parallel with an active transport pathway, represented by a resistor (R _ap ) and an EMF (E _p ). Thus:

E_{x} = − \frac{R T}{z_{i} F} L n \frac{[X_{1}]}{[X_{2}]}

$E_{x} = − \frac{R T}{z_{i} F} L n \frac{[X_{1}]}{[X_{2}]}$

where [ X ₁ ] and [ X ₂ ] are the concentrations of ion X on the two sides of the membrane, and z _i is the charge on the ion. The weighting factor for each ion is the transference number, t _x , which expresses the fraction of membrane conductance that is attributable to that particular ion:

t_{x} = \frac{g_{x}}{g_{t o t}}

$t_{x} = \frac{g_{x}}{g_{t o t}}$

where g represents the conductance of the individual ion pathways and g _tot is the total ionic conductance of the membrane. In most cases g _tot will simply be the sum of the Na, K, and Cl conductances of the barrier. Hence, the total EMF can be generally expressed by the equation:

\begin{matrix} E & = t_{N a} E_{N a} + t_{K} E_{K} + t_{C l} E_{C l} \\ = - \frac{R T}{F} \sum_{x = N a, K, C l} \frac{t_{x}}{z_{x}} L n \frac{[X_{1}]}{[X_{2}]} \end{matrix}

$\begin{matrix} E & = t_{N a} E_{N a} + t_{K} E_{K} + t_{C l} E_{C l} \\ = - \frac{R T}{F} \sum_{x = N a, K, C l} \frac{t_{x}}{z_{x}} L n \frac{[X_{1}]}{[X_{2}]} \end{matrix}$

Figure 7.1, Electrical equivalent circuit for a general epithelium.

The overall goal of classical electrophysiology, described in the first two sections of this chapter, is to evaluate the different elements of this equivalent circuit, to quantify the various resistances and EMFs, and to describe the extent to which they change during regulation. To this end, it has often been desirable to use reductions of the main equivalent circuit of Figure 7.1 , and to work under conditions in which these reduced circuits are applicable. Such simplifications are discussed in more detail in the sections entitled, “Transepithelial Measurements” and “Intracellular Measurements.” Finally, the section entitled, “Measurements of Individual Ion Channels” describes application of the patch clamp technique to epithelia, and permits a description of ion transport in more molecular terms.

The rationale for representing the pump by a resistance and an EMF is discussed further in the section entitled “Intracellular Measurements.” Briefly, the E _p represents the maximum amount of energy that the pump derives from splitting ATP or, alternatively, the maximum electrochemical potential difference against which the pump can operate. The pump pathway must also include a non-zero internal resistance. The magnitude of this internal resistance is determined by the actual current–voltage relation for the membrane bound Na-K-ATPase. To maintain generality, all membrane resistances are shown as variable resistors to include the possibility of intrinsic or extrinsic regulation of ion channels.

Although the paracellular pathway is not a membrane barrier, it can also be modeled by resistive (R _tj ) and electromotive elements (E _par ). A lateral network (indicated to the right of the main circuit) is also included in the model. This network takes into consideration the finite resistance of fluid in the lateral spaces. This aspect of the circuit becomes important for calculation of individual membrane resistances from voltage deflection experiments (see Section entitled “Intracellular Measurements”).

Transepithelial Measurements

Measurements of transepithelial electrical properties are by far the simplest to perform, and the most difficult to interpret. They are easy to carry out because they are non-invasive; only extracellular electrodes are employed. They are difficult to interpret because the parameters which can be measured reflect, in most cases, a combination of many of the circuit elements shown in Figure 7.1 . In this chapter we will describe how transepithelial techniques are used to measure three basic parameters that characterize an epithelium: transepithelial voltage; transepithelial resistance; and short-circuit current. We will then discuss a number of special extracellular approaches which have been employed to gain additional insights into epithelial properties.

Measurement of Transepithelial Voltage

Methods of measuring transepithelial voltage (V _te ) are conceptually simple. In principle, the potential difference between two electrodes placed on either side of the epithelium is simply determined with an appropriate electrometer. With flat epithelia that can be mounted in Ussing chambers, the transepithelial electrodes are placed in the two bathing compartments. In cylindrical epithelia such as the renal nephron, classical measurements of transepithelial potential have been performed in vivo using micropuncture techniques. In this technique, a pipette filled with electrolyte is introduced into the lumen of the tubule, and voltage is measured relative to another electrode placed in a capillary. Here, the presumption is that the voltage reflects the properties of the impaled tubule, and is not greatly influenced by those of neighboring segments. Under most conditions this should be a reasonable assumption. For a lumen of 10 μm diameter and an isoosmotic saline solution with a resistivity of around 60 Ω•cm, the axial resistance of the tubule will be about 8×10 ⁷ Ω/cm. This is much larger than the value of the transepithelial resistance of around 100 Ω•cm ² ( Table 7.1 ), which for the same 10 μm lumen is equivalent to 3×10 ⁴ Ω/cm. Thus, each part of the nephron will be effectively electrically isolated from other parts of the high resistance of the luminal pathway. If the nephron segment can be isolated and perfused in vitro , the perfusion and/or collection pipette can be used to monitor the intraluminal voltage with respect to the bath potential. This is illustrated in Figure 7.2 .

Table 7.1

Transepithelial Properties of Renal Epithelia

Tissue	V _te (mV)	R _te (Ωcm ² )	R _par (Ωcm ² )	P _Na /P _Cl
Amphibians
Proximal tubule ( Ambystoma )	−10	70	70	0.25
Diluting segment ( Amphiuma , frog)	+10	290	306	4 to 5
Collecting duct ( Amphiuma )	−24	160	200	0.84
Urinary bladder (Toad)	−94	8,900	50,000	–
Mammals
Proximal tubule (rabbit)	−2 to +2	5	5
TALH ^a (rabbit)	+3 to +10	10 to 35	10 to 50	2 to 4
CCD ^a (rabbit)	0 to −60	110	160	0.8
OMCD ^a (rabbit)	−2 to −11	233
IMCD ^a (rabbit)	−2 to 0	73
Urinary bladder (rabbit)	−20 to −75	13,000 to 23,000	>78,000	–

a TALH, thick ascending limb of Henle’s loop; CCD, cortical collecting duct; OMCD, outer medullary collecting duct; IMCD, inner medullary collecting duct.

Figure 7.2, Experimental apparatus for determining electrophysiological properties of renal epithelia.

Measurement of Transepithelial Resistance

For measurements of transepithelial resistance ( R _te ), current must be injected across the epithelium to perturb V _te . This is most easily accomplished when the epithelium can be mounted in Ussing chambers, where current flow and voltage changes are assumed to be uniform in the plane of the tissue. Resistance can then be computed from Ohms law as the ratio of the change in V _te to the amount of current passed:

R_{t e} = \frac{Δ V_{t e}}{Δ I}

$R_{t e} = \frac{Δ V_{t e}}{Δ I}$

Epithelia can be studied in open-circuited or voltage-clamped conditions. In open circuit the tissue is allowed to maintain its spontaneous transepithelial voltage. In this case the resistance is determined from the change in voltage produced by passing a known amount of current. Under voltage-clamp conditions a current is passed across the epithelium to maintain the transepithelial voltage at a predetermined level. In the case where this level is zero, so that the transepithelial voltage is abolished, it is called the “short-circuited” state. If the epithelium is voltage-clamped, resistance is determined from the change in current produced by a controlled voltage step. In open-circuited tubular epithelia, transepithelial current flow is not constant along the length of the tubule. In this case, cable analysis must be used to estimate the transepithelial resistance (see below).

Measurement of Transepithelial Resistance in Open Circuited Renal Tubules

The measurement of overall transepithelial resistance, R _te , in renal tubules under open circuit conditions is best carried out with a double-barreled perfusion pipette system similar to the one illustrated in Figure 7.2 . In this technique, the tubule is cannulated at both the perfusion and collection ends. The double-barreled perfusion pipette, fabricated from theta glass creates separate pathways for current flow and voltage recording. An alternative technique uses the same single-barreled pipette for both current injection and voltage measurement. This is not nearly as accurate as the double-barreled technique, because the voltage deflection arising from the internal resistance of the perfusion pipette must be nulled with a bridge circuit. The microelectrodes in Figure 7.2 are for evaluation of individual cell membrane resistances. This will be discussed in the section entitled, “Intracellular Measurements.”

A thin fluid-exchange tubing (not shown) can be inserted into one barrel of the perfusion pipette of Figure 7.2 to permit rapid exchange of the perfusion solution while measuring the transepithelial potential V _te ( x=0 ). Current is passed from a chlorided silver wire glued into the other barrel of the pipette. The transepithelial length constant of the tubule λ _te is determined from the voltage deflections at the perfusion, ΔV _te ( x=0 ), and collection, ΔV _te ( x=L ), sides of the tubule, resulting from a transepithelial current pulse, I _te , through the current side of the perfusion pipette. For a doubly cannulated, isolated tubule of length L , λ _te is given by Eq. (7.5) from Sackin and Boulpaep :

\frac{L}{λ_{t e}} = \cosh^{- 1} [\frac{Δ V_{t e} (x = 0)}{Δ V_{t e} (x = L)}]

$\frac{L}{λ_{t e}} = \cosh^{- 1} [\frac{Δ V_{t e} (x = 0)}{Δ V_{t e} (x = L)}]$

The transepithelial resistance R _te in Ωcm ² is given by Eq. (7.6) :

R_{t e} = 2 \sqrt{π λ_{t e}^{3} R_{i n} R_{i}} \sqrt{t a n h (L / λ_{t e})}

$R_{t e} = 2 \sqrt{π λ_{t e}^{3} R_{i n} R_{i}} \sqrt{t a n h (L / λ_{t e})}$

In the above equation, R _in is the input resistance measured in ohms (Ω). It is operationally defined as the voltage deflection at the perfusion end ΔV _te ( x=0 ) divided by the total injected current I _te . Typical injected currents for proximal tubules are 100 nA pulses of 1 to 5 seconds duration. Ideally, none of the current injected into the lumen from the perfusion pipette enters the compressed region of tubule within the holding pipette, which presumably acts like an electrical insulator when compared to the relatively low resistance of the tubule. However, artifacts may still arise from current leaks at either the perfusion or collection ends of the tubule. These can be detected by a “mismatch” between the calculated electrical radius ( r _e ) of the tubule and its measured optical radius ( r _o ).

r_{e} = \frac{2 R_{i} λ_{t e}^{2}}{R_{t e}}

$r_{e} = \frac{2 R_{i} λ_{t e}^{2}}{R_{t e}}$

Use of a double-barreled perfusion pipette ( Figure 7.2 ) eliminates much of the uncertainty in R _in . Double-barreled perfusion pipettes have the additional advantage that R _te can be measured during changes in the perfusion solution. This is practically impossible with a single-barreled perfusion pipette, because the bridge circuit is unstable during solution changes. Finally, the term R _i (Ω•cm) is the volume resistivity of the perfusion solution, as measured with a standard conductivity meter.

Measurement of Transepithelial Resistance in Voltage Clamped Renal Tubules

There have been a number of early attempts to elucidate the electrical properties of renal tubules using voltage clamp techniques similar to those originally developed for flat epithelia. The basis of these methods is to isolate a segment of tubule (usually with oil droplets) that is short enough to permit a uniform current distribution across the epithelium. To accomplish this, metallic axial electrodes are directly inserted into the lumen of the tubule. These axial electrodes can also be used for AC impedance analysis. However, one important problem with metal electrodes is the release of ions into a restricted space during continuous current flow.

An alternative technique employs segments of isolated, perfused tubules that have been shortened to such an extent that the current distribution within the lumen is virtually homogeneous. In this case R _te is essentially determined from the input resistance according to Eq. (7.8) :

R_{t e} = 2 π r_{o} L \cdot R_{i}

$R_{t e} = 2 π r_{o} L \cdot R_{i}$

where r _o is the optical radius, and R _te has units of Ω•cm ² .

Typical Results

Measurements of V _te and R _te in some representative epithelia are shown in Table 7.1 . The range of both these parameters is large, with values of V _te ranging from ±2 mV in the proximal tubule to as much as −60 to −80 mV in the CCT. R _te values vary from less than 10 Ωcm ² in proximal tubule to more than 5000 Ωcm ² in urinary bladder. Despite the range of values observed, the transepithelial voltages in all cases reflect two factors: the conductance of the epithelium to the major ions and the active transport of ions. In general, a high value of V _te indicates that active transport is taking place across a high resistance epithelium, whereas low values of V _te can reflect either a low R _te or a low rate of active transport.

Traditionally, epithelia have been divided into the categories “tight” and “leaky,” according to their transepithelial resistances. In leaky epithelia the low value of R _te is thought to largely reflect the low resistance of the tight junctions which constitute the major electrical resistance of the paracellular pathway between the epithelial cells. In tight epithelia the tight junctional resistance, and therefore the transepithelial resistance, is much higher. However, the resistance above which an epithelium is considered “tight” is not precisely defined. Even though the amphibian proximal tubule and the mammalian collecting duct have similar absolute values of paracellular resistance, the proximal tubule is considered a leaky epithelium, whereas the collecting duct is usually referred to as “tight.” Thus, a better definition of a leaky epithelium is one in which the paracellular resistance is low relative to that of the cell membranes. For example, in Table 7.1 it can be seen that in leaky proximal tubules R _te is virtually equal to R _par , which is small compared to the parallel transcellular resistance R _c . In tight epithelia R _par is significantly larger than R _te . This implies that R _par is of the same order of magnitude as R _c or even much larger in the case of the urinary bladder. Another feature of a tight epithelium is its ability to separate two fluid compartments with very different ion compositions. High resistance tight junctions slow the “backleak” of ions and other solutes down their concentration gradients. Thus, in a tight epithelium it is harder to dissipate the ion gradients established by active transport processes.

Interpretation of Measurements of V _te and R _te

As discussed above, transepithelial measurements of voltage and resistance are difficult to interpret because they lump together information from many different electrical pathways arranged in parallel. To analyze such data, it is often useful to use a simplified equivalent electrical circuit.

The terms R _c and E _c represent the resistance and electromotive forces across the transcellular pathway, whereas R _ti and E _par are respectively the resistance and electromotive forces across the paracellular pathway. If the potential differences V _te , E _c , and E _par are all defined with respect to the bath or serosal side, the overall measured transepithelial values R _te and V _te are related to this circuit by Eqs (7.9) and (7.10) :

R_{t e} = \frac{R_{t j} R_{c}}{R_{t j} + R_{c}}

$R_{t e} = \frac{R_{t j} R_{c}}{R_{t j} + R_{c}}$

V_{t e} = \frac{E_{c} R_{t j} + E_{p a r} R_{c}}{R_{t j} + R_{c}}

$V_{t e} = \frac{E_{c} R_{t j} + E_{p a r} R_{c}}{R_{t j} + R_{c}}$

The dissection of the measured parameters into the appropriate contributions from cellular and paracellular pathways can sometimes be accomplished by using maneuvers that affect only one of the pathways or cause one pathway to dominate the other. Some of these perturbations and special conditions will be discussed below.

Contribution of Active Transport to V _te

The major effect of the pump is to establish transmembrane ionic gradients, i.e., to keep cell Na low and cell K high. As was first pointed out by Koefoed-Johnsen and Ussing in their classic paper of 1958, the permeability properties of the apical and basolateral membranes of the frog skin are quite different. Since the apical membrane is selectively permeable to Na, and the driving force for this ion is inward, the entry of Na will tend to make the cell voltage positive with respect to the mucosal solution. Conversely, the basolateral membrane is selectively permeable to K. This ion will tend to flow out of the cell, making the cell voltage negative with respect to that of the serosal fluid. The EMFs E _ap (= RT / F Δln[Na]) and E _bl (= RT / F Δln[K]) will be in the same direction with respect to the epithelium and the transepithelial EMF, and hence V _te , will reflect their sum ( Figure 7.4 ).

Figure 7.4, Contribution of transcellular potentials to the transepithelial potential.

Although the Na-K-ATPase is ultimately responsible for the transepithelial potential in many Na-reabsorptive epithelia, the magnitude of V _te does not correlate with the magnitude of active transport when different tissues are compared. In general, the effect of active ion transport will be shunted by the paracellular resistance. This shunting is least in the tight epithelia such as frog skin and toad urinary bladder, where V _te can be over 100 mV. In leaky epithelia such as the proximal tubule the shunting is considerable, and the values of V _te are much lower.

In leaky epithelia, E _par will be much smaller than E _c ( Figure 7.3 ), since ion gradients across the tight junction are relatively small. In tight epithelia where ion gradients can be significant, R _tj >R _c so that the term E _par R _c will be small compared to E _c R _tj , and Eq. (7.10) becomes:

V_{t e} = \frac{E_{c}}{1 + R_{c} / R_{t j}}

$V_{t e} = \frac{E_{c}}{1 + R_{c} / R_{t j}}$

Figure 7.3, Simplified equivalent electrical circuit for an epithelium.

The implication of Eq. (7.11) is that if R _tj >>R _c , V _te will approach E _c , a quantity which is limited by the EMF of the Na-pump. In general, V _te will be reduced according to the ratio R _c /R _tj . The contribution of active transport to cell membrane potential is discussed in the section entitled, “Estimation of renal Na,K pump current and electrogenic potential.”

The mammalian TALH, and its amphibian counterpart the diluting segment, have lumen-positive V _te despite the fact that they are also Na-reabsorbing epithelia ( Table 7.1 , Figure 7.4 ). This turns out to be the exception that proves the rule. As discussed in detail by Greger, Na does not enter the TALH cell through a conductive mechanism, as in the frog skin and other epithelia, but through an electrically neutral co-transport system along with K and Cl. Thus, Na entry does not contribute to a lumen-negative voltage, and in fact the membrane is more permeable to K than to Na. Furthermore, the basolateral membrane has a rather high permeability to Cl. This makes the lumped EMF E _ap less negative than E _bl , and the potential difference between the cell and the blood side is less negative than the potential difference between the cell and the lumen. Hence, the mechanism for the lumen-positive potential in the TALH is accounted for by the different permeability properties of the two membranes, just as in the frog skin.

Contribution of Diffusion Potentials to V _te

Paracellular diffusion potentials can contribute significantly to the overall transepithelial potential, especially when V _te is small. For example, in the mammalian proximal tubule the early portion of the segment has a lumen-negative V _te in vivo , which is thought to reflect active Na reabsorption. Farther down the nephron, however, the lumen becomes positive with respect to the blood. Preferential luminal reabsorption of HCO ₃ ⁻ relative to Cl ⁻ establishes opposing gradients for Cl ⁻ and HCO ₃ ⁻ across the tight junction ( Figure 7.5 ). This results in a lumen-positive potential since Cl ⁻ diffuses more rapidly across the junctions than HCO ₃ ⁻ .

Figure 7.5, Contribution of paracellular potentials to the transepithelial potential.

Diffusion potentials may also contribute to the normal lumen-positive V _te in the mammalian TALH ( Table 7.1 ). In this segment NaCl is reabsorbed but water is not, leading to a dilution of the luminal fluid. Since the tight junctions of the mammalian TALH are cation-selective, Na diffuses back more rapidly than the Cl, contributing to a lumen-positive diffusion potential ( Figure 7.5 ).

Contribution of Circulating Current to V _te

The different equivalent EMFs at the apical and basolateral sides of the cell produce a circulating current ( I ) which traverses both cell membranes in series, and returns via the paracellular shunt ( Figure 7.1 ). The magnitude of this current depends on the relative resistances of paracellular versus cell pathways, as well as the active transport rate for the particular epithelium. For example, in renal proximal tubules, the low shunt resistance (compared to transcellular resistance) characterizes this nephron segment as a leaky epithelia with large circulating current. On the other hand, tight epithelia like the urinary bladder or the frog skin have shunt resistances comparable to or larger than the transcellular resistance, so that the circulating current is small in comparison with proximal tubule.

The effect of circulating current on renal transepithelial potentials can be understood qualitatively by considering the electrical profiles depicted in Figure 7.6 . In this figure, the serosal or blood side of the epithelium is considered at ground and the voltage at any point is displayed as a function of distance from mucosa to serosa. For the sake of simplicity, we have assumed that the apical membrane is primarily selective to sodium, the basolateral membrane is primarily selective to potassium, and the interior of the cell is isopotential. Therefore, in the absence of circulating current, there is a “staircase” voltage profile through the epithelium determined by the respective diffusion potentials across the mucosal (or apical) membrane and across the serosal (or basolateral) membrane ( Figure 7.6a ) . Under these conditions the measured V _te (mucosa minus serosa) would actually be more negative than the basolateral cell membrane potential ( E _K ).

Figure 7.6, Electrical potential profiles across a simple epithelium.

In most epithelia the diffusion potential steps of Figure 7.6a would be modified by the effect of circulating current ( I ) across the resistance of the mucosal and serosal barriers. Specifically, the mucosal to cell step will be raised by an amount: I•R _ap due to the circulating current crossing the mucosal membrane resistance ( Figure 7.6b ). The same current crossing the basolateral side of the cell will decrease the size of the cell-to-serosal step by I• $R_{b l}^{*}$ $R_{b l}^{*}$ , where $R_{b l}^{*}$ $R_{b l}^{*}$ is the effective basolateral resistance. The final values of V _te and V _bl can be calculated by considering the complete equivalent circuit (Appendix 7.1).

In most epithelia, the resistance of the apical membrane is larger than the resistance of the basolateral membrane, and the effect of the circulating current is to transform the staircase potential ( Figure 7.6a ) into a “well-type” potential ( Figure 7.6c ), where the intracellular region is the most negative space and V _te is directly dependent on the magnitude of the current and the tightness of the epithelial cell layer. In some tight epithelia ( Necturus urinary bladder) with high paracellular resistance and low circulating current, the “staircase” potential profile is still maintained despite “IR drops” at both membranes.

Short-Circuit Current

It is also possible to measure transepithelial currents while controlling the transepithelial voltage. A special case of this voltage-clamp approach is the short-circuit current technique in which V _te is maintained at zero. If the solutions on both sides of the epithelium are identical, there is no net movement of ions through the paracellular spaces, since both electrical and chemical driving forces are reduced to zero. The current across the tissue, which must also pass through the external circuit and can thus be readily measured, results only from active transport processes (defined as those which take place against an electrochemical activity gradient). Thus this current (called the short-circuit current), will equal the sum of all active ion transport processes.

The particular ion being actively transported can be identified rigorously by measuring net fluxes at the same time as the short circuit current. For some cases, such as the frog skin and toad bladder, the short-circuit current can be accounted for by the active transport of only one ion species, namely Na ( Table 7.2 ). In general, the short-circuit current will represent the sum of the net transport of Na, K, H, Cl, and HCO ₃ . Another way to identify actively transported ions is to eliminate them from the bathing media and measure the resulting effects on short-circuit current. This approach is often experimentally much simpler, but it is less rigorous since the apical and basolateral solutions will not be identical. Furthermore, changing the external environment of the tissue can lead to secondary changes in cell composition and volume. In any case, once the transported species have been identified, the technique becomes a very convenient way to analyze the regulation of the active transport systems.

Table 7.2

Equivalence of Net Na+ Fluxes and Short-Circuit Current in Model Epithelia, Transepithelial fluxes (nEq/cm ² /min)

Type of Epithelium	Mucosal to Serosal	Serosal to Mucosal	Net	Short-circuit Current
Frog skin	24.6	1.5	23.1	23.6
Toad urinary bladder	35.7	9.5	26.2	26.8

Data are from for frog skin and from for toad bladder.

An important limitation of the short-circuit current technique is that it often requires unphysiological conditions. For example, short-circuiting high resistance epithelia like frog skin will reduce the normally large V _te to values near zero. This will necessarily affect the transmembrane voltage of one or both cell membranes, which may in turn affect the ionic conductances of those membranes.

The short-circuit technique also involves bathing the apical side of the tissue with a solution that has an electrolyte composition close to that of the blood. This is a highly unphysiological condition for many tight epithelia like the frog skin, which is normally in contact with pond water, and the toad bladder, which is normally in contact with dilute urine. Another important problem with short-circuit experiments is that short-circuited tissues do not have to maintain the electroneutrality of the transported species. For example, in Na-transporting epithelia, such as the frog skin, Na ions can be reabsorbed only if another cation (e.g., K, H) is secreted or if an anion (Cl) is also reabsorbed. Under physiological conditions these other ionic pathways can be rate-limiting for Na reabsorption.

Finally, the uniform current distribution required by the short-circuit technique has largely restricted its use to flat epithelia which can be mounted in Ussing chambers. However, in some cases it has been possible to voltage-clamp large-diameter amphibian tubules. Attempts have also been made to circumvent these technical problems by defining an “equivalent short-circuit current” for renal epithelia. In this method, the current at V _te =0 is estimated by dividing the spontaneous value of V _te by the transepithelial resistance R _te . This approach assumes that R _te is constant; i.e., that the current voltage relation of the epithelium is linear. Even when this condition is satisfied, it is not always possible to attribute the equivalent short-circuit current to specific ion species, since net fluxes of the ions must be measured under true short-circuited conditions.

Technical Problems

For epithelia that can be studied as flat sheets in vitro , the major technical problem with transepithelial measurements is avoiding edge damage to the tissues, particularly when these tissues are mounted in Ussing chambers. On the other hand, for renal micropuncture experiments performed in situ , the major technical problem is localization of the microelectrode tip within the tubular lumen.

The most important general problem in the measurement of transepithelial resistance is the choice of the magnitude and duration of the applied perturbations. Currents (or voltage changes) which are too large can result in changes in the electrical properties of the membranes due to voltage-dependent ion conductances. Perturbations which are either too large or too long can lead to redistribution of ions across the cell membranes, which can also alter electrical properties. For example, in toad urinary bladder modest changes in V _te in the order of 10 mV under voltage-clamp conditions can result in time-dependent changes in the tissue resistance. On the other hand, if perturbations are too small they are difficult to measure accurately, and if they are applied for too short a time the capacitative, as well as the resistive, properties of the epithelium will affect the response. There are no generally accepted rules for determining the size and duration of the perturbations.

Estimation of Membrane Parameters from Transepithelial Measurements

Measurement of transepithelial electrical properties does not, in general, give any direct, quantitative information about the circuit elements of greatest interest, namely the conductances of individual membranes to specific ions. As emphasized throughout this section, R _te is a lumped parameter determined by R _ap , R _b , R _tj , and in some cases R _lis (see Figure 7.1 ). V _te is determined by all the R _s and EMFs in the circuit. Clearly, measuring two parameters is insufficient to determine seven or eight unknowns.

However, in some cases it has been possible to either use conditions which simplify the equivalent circuit or to use experimental perturbations that selectively change only one electrical parameter. These methods have provided a good deal of information about epithelial properties from purely transepithelial measurements. Some examples are given below.

Paracellular Resistance and Selectivity

When the paracellular (tight junction) resistance is low compared to the transcellular resistance, the transepithelial resistance is dominated by the resistance of the paracellular pathway. This happens in a leaky epithelium like the proximal tubule. This condition can also be produced in some tight epithelia by blocking the major conductive pathways at the apical membrane. The most frequently used blockers are amiloride, for the Na conductance, and Ba, for the K conductance. In both of these cases the paracellular resistance can then be estimated from transepithelial measurements ( Table 7.1 ), although intracellular recordings are usually required to prove that the transcellular resistance is high.

The ion selectivity of the paracellular pathway can also be evaluated under these circumstances. This involves measurement of the transference numbers for various ions across the tight junction (see Eq. (7.12) ). The most important ions in this case are Na and Cl, and their transference numbers can be estimated by reducing the concentration of NaCl on one side of the junction by diluting one of the bathing solutions. If the transcellular resistance is sufficiently high (i.e., R _ap >>R _tj , see Eq. (A2.3) in Appendix 2) and is unaffected by the dilution, the measured change in V _te will approximately reflect the change in E _par where:

Δ E_{p a r} = - \frac{R T}{F} (t_{N a} - t_{C l}) L n \frac{{[N a C l]}_{1}}{{[N a C l]}_{2}}

$Δ E_{p a r} = - \frac{R T}{F} (t_{N a} - t_{C l}) L n \frac{{[N a C l]}_{1}}{{[N a C l]}_{2}}$

If sodium and chloride are the only conducting ions in the external solutions, the absolute transference numbers can be calculated from Eq. (7.12) and the requirement that t _Na + t _Cl =1. Some measurements of paracellular selectivity in renal epithelia are listed in Table 7.1 . This parameter is of considerable physiological interest. The results range from a significant selectivity for anions (Cl) over cations (Na) in the amphibian proximal tubule, to a cation selectivity in the thick ascending limb of Henle’s loop or its counterpart, the diluting segment, in the amphibian kidney. If ions moved through the tight junctions as if they were in free solution, a permeability ratio P _Na /P _Cl of 0.8 would be expected. The variations in selectivity result from differences in the expression of specific members of the tight-junction proteins claudins.

Membrane Selectivity

If the paracellular or tight junction resistance is much greater than the transcellular resistance, it is possible to determine the ion selectivity of the individual cell membranes. Specifically, if R _tj is very large compared to R _ap + R _bl , there will be negligible current through either the paracellular pathway or the cell pathway under open-circuit conditions. Under these conditions, the circuit of Figure 7.1 predicts that changes in E _ap will parallel changes in V _ap which, in turn, can be estimated from the measured changes in transepithelial potential Δ V _te (see Equations (A1.8) and (A1.11)–(A1.13) of Appendix 7.1). Such a situation was studied by Koefoed-Johnsen and Ussing in their classic paper on the frog skin, where pre-treatment of the skins with low concentrations of Cu ⁺² produced very high values of R _te and V _te .

This permits evaluation of individual membrane selectivities from transepithelial measurements alone if the concentration of just one ion on one side of the epithelium is replaced with an impermeant species, and the conditions associated with Eq. (A1.13) (Appendix 7.1) are satisfied. If this is the case and Na is partially replaced on the apical side, then:

Δ V_{t e} = Δ E_{a p} = - \frac{R T}{F} t_{N a} L n \frac{{[N a]}_{a p}^{e x p}}{{[N a]}_{a p}^{c o n}} f o r R_{t j} > > R_{a p} + R_{b l}^{*}

$Δ V_{t e} = Δ E_{a p} = - \frac{R T}{F} t_{N a} L n \frac{{[N a]}_{a p}^{e x p}}{{[N a]}_{a p}^{c o n}} f o r R_{t j} > > R_{a p} + R_{b l}^{*}$

where the change in potential is measured as experimental minus control. [Na] ^exp and [Na] ^con represent the concentrations of Na under experimental and control conditions, i.e., after and before the solution change.

Koefoed-Johnsen and Ussing found that changes in mucosal Na produced changes in V _te close to those which would be expected if t _Na =1. From this they inferred that the apical membrane was primarily conductive to Na ions. Similarly, changes in serosal K concentration produced changes consistent with the idea that the basolateral membrane conducted only K. The elegant conclusions of this study depended upon the rather unusual conditions achieved, namely a very high paracellular resistance and the absence of other “leak” pathways due to other cell types. Except for the case of the urinary bladder, such conditions are difficult to achieve in renal epithelia where paracellular pathways are usually leakier than in the frog skin.

Selectivity of the epithelial basolateral membrane has also been studied by using pore-forming polyene antibiotics to reduce apical membrane resistance so that V _te becomes a reasonable estimate of the basolateral potential V _bl ( see Equation A1.16 of Appendix 7.1). For example, in the turtle colon, Germann et al. were able to characterize two different conductances for K across the basolateral membrane using the amphotericin-B permeabilized epithelium. This approach has also been used mostly in flat epithelia rather than renal tubules.

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