Sodium and Chloride Transport: Proximal Nephron

The principal function of the proximal tubule is the reabsorption of some two-thirds to three-quarters of the glomerular filtrate. This means, primarily, reabsorption of Na + , Cl , HCO 3 , and in smaller quantities potassium, phosphate, and various filtered organic compounds. In view of the copious glomerular filtrate, proximal reabsorption plays a crucial role in the maintenance of fluid and electrolyte balance of the body. In particular, modern hypertension research has considered it essential to identify proximal tubule Na + transporters, and understand the signals and second messengers that regulate these transporters. Proximal tubular transport is energized by the metabolic reactions within the proximal tubular epithelium, either directly by ATP-driven “ion pumps” (primary active transport) or indirectly by the coupling of solute fluxes to Na-transport (secondary active transport). The workload to this epithelium is prescribed by the glomerular filtration rate (GFR), which can vary several-fold within the course of a day, so that the ensemble of epithelial transport systems are also asked to modulate their function responsively, and in a coordinated manner.


The principal function of the proximal tubule is the reabsorption of some two-thirds to three-quarters of the glomerular filtrate. This means, primarily, reabsorption of Na + , Cl , HCO 3 , and in smaller quantities potassium, phosphate, and various filtered organic compounds. In view of the copious glomerular filtrate, proximal reabsorption plays a crucial role in the maintenance of fluid and electrolyte balance of the body. In particular, modern hypertension research has considered it essential to identify proximal tubule Na + transporters, and understand the signals and second messengers that regulate these transporters. Proximal tubular transport is energized by the metabolic reactions within the proximal tubular epithelium, either directly by ATP-driven “ion pumps” (primary active transport) or indirectly by the coupling of solute fluxes to Na-transport (secondary active transport). The workload to this epithelium is prescribed by the glomerular filtration rate (GFR), which can vary several-fold within the course of a day, so that the ensemble of epithelial transport systems are also asked to modulate their function responsively, and in a coordinated manner.

All segments of isolated proximal tubules are capable of reabsorbing the same solutes when perfused in vitro . Quantitatively, however, marked differences exist along the tubule; reabsorption of sodium, water, glucose, and bicarbonate in the early proximal tubule is about three-fold greater than that in the mid-portion of the convoluted proximal tubule, and nearly ten times that of the straight segment of the tubule. Furthermore, in vivo , the transtubular concentration gradients of the luminal solutes, as well as the electrical potential of the lumen, change as one moves from early- to late-proximal tubule. In the earliest part of the proximal tubule, preferential reabsorption of organic solutes (glucose and amino acids, etc.) and of sodium bicarbonate, lactate, acetate, phosphate, and citrate occurs. Consequently, the luminal concentration of these solutes is reduced in the remaining portion of the proximal tubule. Alterations in solute reabsorption have been inferred in a number of disorders of proximal tubule, and have been of particular interest to workers seeking to understand how changes in urine composition alter the propensity to kidney stone formation.

Historically, in vivo micropuncture and microperfusion was the experimental method that delineated proximal tubule transport properties, namely transepithelial fluxes and permeabilities. The next investigative focus was identification of specific transporters within luminal and peritubular cell membranes, and the experimental techniques have been diverse. Assessment of the cellular compartment was first done electrophysiologically, using conventional and ion-selective microelectrodes, and subsequently with pH- or cation-sensitive fluorescent dyes. More direct information about the membrane transporters derived from vesicle preparations enriched in fractions from luminal (brush border) or peritubular cell membranes. Patch-clamp techniques (whole-cell or excised patch) allowed the study of single membrane ion channels, but have had limited application to proximal tubule. A major advance came with molecular identification of the transporters, expressing these transporters in cells that are convenient for study, developing antibodies for location and quantification within tubular cell membranes, and examination of tubules from mice in which the transporter has been knocked-out.

Central to its role in body fluid homeostasis is the responsiveness of proximal tubule sodium transport to changes in GFR, as well as to neural and hormonal signals. In large measure, changes in sodium reabsorption that accompany changes in GFR may be understood in terms of transepithelial oncotic and hydrodynamic forces which impact on the tubule cells or on the paracellular pathway. Neurohumoral regulation of proximal tubule transport begins with a cellular signal, followed by transduction steps, which ultimately produce changes in transporter densities or kinetics within the cell membranes. The signaling pathways for the important neurohumoral regulators have been an object of intense investigation, although the insights have come slowly. This research program has had to contend with a number of cellular second messenger molecules, with a number of kinases and phosphatases, with identification of anchoring proteins that secure the local action of a signal, and with the cytoskeletal elements responsible for transporter traffic. Although much information is available, a facile description of the path from neurohumoral signal to transporter flux is not yet at hand.

The organization of this chapter starts with the description of whole tubule function: fluxes and the associated driving forces; and tubule permeabilities. Historically, this is the section with the oldest data, and the section that has undergone the least revision from earlier chapter versions. The next two sections are devoted to the description of the epithelial components: luminal and peritubular cell membrane transporters; the tight junction; and the lateral intercellular space. In view of the copious transepithelial solute fluxes, special attention will be given to the problem of matching luminal and peritubular transport fluxes, in order to avoid catastrophic perturbation of cell volume and composition. The last section describes the regulation of proximal transport, with emphasis on physical factors, and on the action of the two key regulatory molecules, angiotensin and dopamine.

Epithelial Function

Net Fluxes

The filtered load of a solute to the proximal tubule is the product of the single nephron glomerular filtration rate (SNGFR) and the ultrafilterable concentration of the solute. For small nonelectrolyte species the ultrafilterable concentration is that in plasma water. For electrolytes, negatively-charged serum proteins produce a Donnan potential, which acts to decrease ultrafilterable Na + and increase Cl concentration with respect to that of plasma water. In amphibian and mammalian proximal tubules, the net effect of proximal tubule transport is the reabsorption of the luminal solution, resulting in a diminished axial flow rate as one proceeds along the tubules. The systemic infusion of a substance, such as inulin, which is filtered at the glomerulus, not reabsorbed (or secreted) by the proximal tubule, and which may be assayed in aliquots of tubular fluid, permits the calculation of the net volume reabsorption by the tubule from the glomerulus to the point of sampling. Thus, in the rat superficial cortical nephrons, the tubular fluid (TF) inulin concentration at the end of the convoluted proximal tubules is twice that of plasma (P), indicating that half of the filtrate is reabsorbed proximally. In the amphibian, Necturus , the TF/P ratio suggests that about one-third of the filtrate is reabsorbed by the proximal tubule, and in certain fish, the net effect of proximal tubule transport is secretion of fluid into the lumen ; however, in view of translational considerations, only the mammalian kidney is considered in this chapter.

With micropuncture sampling of fluid from the proximal tubule, if a complete collection of tubule fluid is made, then the absolute transport rate by the nephron segment is known and can be expressed as a flux per unit area of epithelium ( Table 33.1 ). Alternatively, one may perfuse dissected segments of tubule to directly establish the epithelial fluxes under well-defined luminal and peritubular conditions. One must then obtain an independent measure of SNGFR to estimate the fractional reabsorption. The advantage of this approach is that proximal nephron segments not accessible to micropuncture may be examined. For the data from the perfused proximal convoluted tubule of the rabbit shown in Table 33.1 , the measured sodium flux, referred to a 5.4 mm segment of tubule, implies sodium reabsorption of 1.2 nEq/min. With a SNGFR of 20 nl/min, the filtered load of sodium is 2.9 nEq/min, so that the fractional reabsorption is predicted to be about 40%. In the instances of successful micropuncture of rabbit proximal tubule, the observed fractional reabsorption of sodium has been 50 and 45%. This type of comparison is particularly important, in that it suggests a reasonably well-maintained transport capacity for tubules examined in vitro . When examined carefully, however, conditions in vitro can produce subtle differences from the tubule in vivo . As might be expected, dissection conditions of isolated rabbit proximal tubules can decrease the peritubular membrane electrical potential and increase cytosolic Na + concentration; however, they can also engender a peritubular membrane K + channel, not seen in vivo , and change the Na + :HCO 3 stoichiometry of the peritubular membrane co-transporter from 3:1 to 2:1.

Table 33.1

Net Fluxes across Proximal Tubules

Rat PCT References Rabbit PCT References Rabbit PST References
SNGFR (nl/min) 30 (a) 20 (c)
PT diameter (μm) 20 (a) 26 (d) 22 (g)
Length (mm) 5.5 (a) 5.4 (c) 3.3 (h)
J v (nl/s/cm 2 ) 65 (b) 30 (e) 9.8 (g)
J Na (nEq/s/cm 2 ) 9.4 (b) 4.5 (e) 1.5 (g)
J Cl 5.1 (b) 1.3 (g)
J HCO3 2.7 (b) 1.7 (f) 0.2 (g)

(a) ; (b) ; (c) ; (d) ; (e) ; (f) ; (g) ; (h) .

Unfortunately, attempts to present a concise tabulation of proximal transport ( Table 33.1 ) must be tempered by an appreciation of internephron heterogeneity, and the structural changes along the individual tubule. In broad terms, two nephron populations have been identified: those with superficial cortical glomeruli, whose short loops of Henle turn at the outer–inner medullary border (about ⅔ of rat nephrons); and those with juxtamedullary glomeruli, whose long loops of Henle penetrate the inner medulla to variable extents. In many mammalian species, the juxtamedullary glomeruli are larger and have a greater SNGFR than the mid-cortical or superficial cortical nephrons. In the rat, the filtration rate of juxtamedullary glomeruli has been measured by micropuncture collection of Henle limb fluid, and found to be about 1.5- to 2-fold that of superficial glomeruli. In the rabbit, an indirect technique has given estimates confirming the disparity between superficial and juxtamedullary nephrons (e.g., 43 and 66 nl/min, ; 23 and 29 nl/min ). Comparisons of transport properties of superficial cortical and juxtamedullary proximal tubules are available. Corresponding to the greater SNGFR of the juxtamedullary nephrons, there is a greater overall rate of volume and sodium reabsorption. Perfused tubule data from rabbit has indicated a relative magnitude of juxtamedullary-to-superficial Na + fluxes from 1.2- to 2-fold larger; the relative magnitude of HCO 3 fluxes is 2-fold larger. Beyond this quantitative distinction, the relative importance of specific transport mechanisms may also differ between the two nephron populations.

The capacity for volume transport gradually diminishes as one proceeds along the mammalian proximal nephron. This occurs in association with morphologic changes at the electron-microscopic level that have prompted the division of mammalian proximal tubule into three segments ( Figure 33.1 ). The early proximal convoluted tubule, S1, is characterized by tall, densely-packed apical microvilli, numerous mitochondria, and an intricate pattern of folding and interdigitation of the lateral cell membranes. There is a gradual transition to the S2 segment, which comprises the remainder of the proximal convoluted tubule and the very beginning of the proximal straight tubule. Here, there are fewer mitochondria and less amplification of membrane area. Finally, the proximal straight tubule, S3, shows a more cuboidal cell with fewer mitochondria and rare interdigitations. Welling and Welling have compared the cell membrane areas in the S1 and S3 segments of rabbit proximal tubule, and found that for each segment, the apical and basolateral areas are nearly equal. In S1, however, the absorptive area of the cell is increased by membrane folding to 36 cm 2 /cm 2 epithelium, whereas in S3 this value is 15 cm 2 /cm 2 epithelium. The transport of solutes and water has been measured in dissected perfused segments of rabbit proximal tubule, and the spontaneous transport rate was substantially less in the proximal straight tubule than in convoluted segments ( Table 33.1 ). In the rat, microperfusion of proximal tubule segments in vivo (with comparable flow rates and luminal fluid composition) has demonstrated a lower volume reabsorption rate for segments more than 1–2 mm from the glomerulus. Serial micropuncture along a single proximal tubule with filtered fluid flowing freely confirmed the sharp decline in reabsorptive flux of volume (sodium) and anions after the first 1–2 mm of tubule ( Figure 33.2 ). Comparison of Na + transport by perfused proximal straight tubules from superficial and juxtamedullary rabbit nephrons has demonstrated comparable reabsorptive rates. The respective convoluted tubule fluxes are two- and four-fold greater for Na + , with a similar proportionality for HCO 3 . Proximal convoluted tubule fluxes of glucose may be six-fold greater, and of phosphate three-fold greater than those of proximal straight tubule.

Figure 33.1

Proximal tubule cells within the: (a) S1; (b) S2; and (c) S3 segments of the rabbit nephron.

(From , with permission.)

Figure 33.2

Reabsorption of water, bicarbonate, and chloride along the rat proximal convoluted tubule.

(From .)

In rat and rabbit kidneys, the Na + concentration, and hence the total osmolality, remain relatively constant along the proximal tubule. This constancy of tubule fluid osmolality implies “isotonic transport,” and poses a special problem for rationalizing the forces at work in water reabsorption ( vide infra ). The fates of chloride and bicarbonate in the mammalian proximal tubule differ, however, in that the chloride rapidly rises to a level above that of the glomerular filtrate and the bicarbonate falls. This shift in anion composition occurs early in the proximal tubule, that is to say, within the S1 segment. This is referred to as “preferential bicarbonate reabsorption,” and has received much attention as a clue to transport activity at the cellular level. The key features of the compositional changes in tubular fluid during its passage through the mammalian proximal tubule are illustrated in Figure 33.3 . The tubular fluid/plasma (TF/P) concentration ratio of several solutes is plotted as a function of proximal tubular length. TF/P inulin rises to approximately 2.0, indicating water reabsorption. Glucose and amino acids are rapidly reabsorbed so that at 25% proximal tubular length their concentrations decline to some 10% of the filtrate concentration. Preferential bicarbonate reabsorption lowers the bicarbonate concentration of tubular fluid to approximately 5–8 mM. Along the initial portion of the proximal tubule, the chloride concentration is increased by reabsorption of water. In the initial segment, the transepithelial voltage is lumen negative, due to the electrogenic nature of co-transport of sodium with glucose or amino acids. As the concentration of these solutes declines and that of chloride rises, the polarity of the transepithelial electrical potential difference changes to lumen positive values. This voltage is, at least in part, a diffusion potential, generated by the chloride and bicarbonate concentration gradients, and the greater permeability of the tubular wall to chloride than to bicarbonate.

Figure 33.3

Compositional changes in proximal tubule fluid along the mammalian nephron.

(From , with permission.)

Transport Forces

To attribute mechanisms to epithelial transport, fluxes must be resolved in terms of responsible driving forces, specifically hydrostatic or osmotic pressure, solute concentration gradients, electrical potential or metabolic energy. The transepithelial volume flow, J v (ml/s·cm 2 epithelium), is a function of hydrostatic and osmotic driving forces:

<SPAN role=presentation tabIndex=0 id=MathJax-Element-1-Frame class=MathJax style="POSITION: relative" data-mathml='Jv=Lp[Δp−RT∑1nσiΔci]=(RTLp)[ΔpRT−∑1nσiΔci]=v¯wPf[ΔpRT−∑1nσiΔci]’>??=??[?????1?????]=(????)[?????1?????]=????[?????1?????]Jv=Lp[Δp−RT∑1nσiΔci]=(RTLp)[ΔpRT−∑1nσiΔci]=v¯wPf[ΔpRT−∑1nσiΔci]
J v = L p [ Δ p − R T ∑ 1 n σ i Δ c i ] = ( R T L p ) [ Δ p R T − ∑ 1 n σ i Δ c i ] = v ¯ w P f [ Δ p R T − ∑ 1 n σ i Δ c i ]

Here the water permeability of the epithelium is represented either by the coefficient L p (ml/s·cm 2 ·mmHg), by RTL p (ml/s·cm 2 ·Osm) or by P f (cm/s), where RT is the product of the gas constant and absolute temperature (1.93×10 4 mmHg/Osm at 37°C), and <SPAN role=presentation tabIndex=0 id=MathJax-Element-2-Frame class=MathJax style="POSITION: relative" data-mathml='v¯w’>??v¯w
v ¯ w
is the partial molar volume of water (0.018 ml/mmol). In Eq. (33.1) the osmotic effect of any species is incorporated in the reflection coefficient, σ i , (0.0≤ σ i ≤1.0). For σ i =1.0, the species exerts a full osmotic effect, and the epithelium is an ideal semipermeable membrane. When σ i =0.0, the species exerts no osmotic force. To determine the reflection coefficient for a specific solute, the change in the transepithelial volume flow produced by a transepithelial concentration gradient, Δ c i , is compared to the volume flow produced by an equal concentration gradient of an impermeant species. The ratio of these two volume flows is just the reflection coefficient, σ i .

To represent solute transport, J i (mmol/s·cm 2 ), the epithelial flux equation is of the form:

<SPAN role=presentation tabIndex=0 id=MathJax-Element-3-Frame class=MathJax style="POSITION: relative" data-mathml='Ji=Jv(1−σi)c¯i+∑j=1nLijΔμ¯jc=Jv(1−σi)c¯i+∑j=1nLij[RTΔln(cj)+zjFΔψ]’>??=??(1??)??+??=1???????=??(1??)??+??=1???[???ln(??)+?????]Ji=Jv(1−σi)c¯i+∑j=1nLijΔμ¯jc=Jv(1−σi)c¯i+∑j=1nLij[RTΔln(cj)+zjFΔψ]
J i = J v ( 1 − σ i ) c ¯ i + ∑ j = 1 n L i j Δ μ ¯ j c = J v ( 1 − σ i ) c ¯ i + ∑ j = 1 n L i j [ R T Δ ln ( c j ) + z j F Δ ψ ]
in which the first term is a convective flux in which a mean concentration appears:
<SPAN role=presentation tabIndex=0 id=MathJax-Element-4-Frame class=MathJax style="POSITION: relative" data-mathml='c¯i=ΔciΔln(ci)≈0.5·[ci(l)+ci(p)]’>??=????ln(??)0.5·[??(?)+??(?)]c¯i=ΔciΔln(ci)≈0.5·[ci(l)+ci(p)]
c ¯ i = Δ c i Δ ln ( c i ) ≈ 0.5 · [ c i ( l ) + c i ( p ) ]
in which c i (l) and c i (p) designate luminal and plasma concentrations. It is a consequence of thermodynamic theory (Onsager symmetry) that the reflection coefficient, σ i , from Eq. (33.1) also appears in Eq. (33.2) for convective solute drag. This formalizes the intuitive notion that the smaller solutes, which are least osmotically effective, are more likely to be entrained in the volume flow. The second term in Eq. (33.2) represents electrodiffusive solute flux, namely the flux of solute i as a function of the electrochemical potential differences, <SPAN role=presentation tabIndex=0 id=MathJax-Element-5-Frame class=MathJax style="POSITION: relative" data-mathml='Δμ¯jc’>????Δμ¯jc
Δ μ ¯ j c
, of all of the solutes under consideration. Expansion of this potential is shown in the right-most expression, in which RT is the product of gas constant and absolute temperature (2.57 J/mmol at 37°C), z i is the valence of solute j, F is the Faraday (96.5 C/mEq), and Δψ is the electrical potential difference across the epithelium. It is also a consequence of Onsager symmetry that the coefficients L ij = L ji (mmol 2 /J·s cm 2 ). When the coefficient L ij is positive (for i≠j), then a reabsorptive driving force on solute i will also promote reabsorption of solute j, so that this coefficient may be considered to represent co-transport of the two solutes. Such co-transport obviously arises when a common carrier transports the two species, but may also occur as a result of intraepithelial convective flows.

Some of the most precise experimental measurements that can be made are those of electrical potentials and currents. In the absence of solute-solute interaction, the transepithelial solute flux is written:

<SPAN role=presentation tabIndex=0 id=MathJax-Element-6-Frame class=MathJax style="POSITION: relative" data-mathml='Ji=Jv(1−σi)c¯i+Lii[RTΔln(ci)+ziFΔψ]=Jv(1−σi)c¯i+Pi[Δci+ziFRTc¯iΔψ]’>??=??(1??)??+???[???ln(??)+?????]=??(1??)??+??[???+?????????]Ji=Jv(1−σi)c¯i+Lii[RTΔln(ci)+ziFΔψ]=Jv(1−σi)c¯i+Pi[Δci+ziFRTc¯iΔψ]
J i = J v ( 1 − σ i ) c ¯ i + L i i [ R T Δ ln ( c i ) + z i F Δ ψ ] = J v ( 1 − σ i ) c ¯ i + P i [ Δ c i + z i F R T c ¯ i Δ ψ ]
where <SPAN role=presentation tabIndex=0 id=MathJax-Element-7-Frame class=MathJax style="POSITION: relative" data-mathml='RTLii/c¯i=Pi’>RTLii/??=??RTLii/c¯i=Pi
RTL ii / c ¯ i = P i
(cm/s) is the conventional solute permeability. Equation (33.3) has generally been the starting point for the application of electrophysiology to characterize proximal tubule. For example, if luminal and peritubular solutions have equal ionic concentrations (Δ c i =0), and there is zero volume flow, then application of an electrical potential difference (Δψ) produces a change in ionic current:
<SPAN role=presentation tabIndex=0 id=MathJax-Element-8-Frame class=MathJax style="POSITION: relative" data-mathml='Ii=ziFJi=Pi(zi2F2RT)c¯iΔψ=giΔψ’>??=?????=??(?2??2??)????=????Ii=ziFJi=Pi(zi2F2RT)c¯iΔψ=giΔψ
I i = z i F J i = P i ( z i 2 F 2 R T ) c ¯ i Δ ψ = g i Δ ψ
in which g i (S/cm 2 ) is the partial ionic conductance of species i. The total epithelial electrical conductance, g g i , or the epithelial electrical resistance, R=1/g, thus provides a measure of the sum of the ionic permeabilities. When the luminal and peritubular solutions are unequal, the open-circuit potential, in the absence of net transepithelial volume flow ( J v =0), gives useful information about the relative ionic permeabilities. In this case, the sum of all ionic currents is zero (0=Σ I i ), so that the transepithelial electrical potential is:
<SPAN role=presentation tabIndex=0 id=MathJax-Element-9-Frame class=MathJax style="POSITION: relative" data-mathml='Δψ=−∑i=1ngigRTziFΔln(ci)’>??=??=1?????????ln(??)Δψ=−∑i=1ngigRTziFΔln(ci)
Δ ψ = − ∑ i = 1 n g i g R T z i F Δ ln ( c i )

If, for example, the only concentration differences across the epithelium are equal and opposite anion gradients (such as chloride and bicarbonate), Eq. 33.5 ) shows that the difference in ionic conductances determines the magnitude of the transepithelial “diffusion potential.”

Table 33.2 is a compilation of the permeability properties of the proximal tubules of rat and rabbit. Again, the inclination to present such tabulation must be tempered by acknowledgement of variation of the permeabilities along the nephron, and of differences between superficial and juxtamedullary nephrons. With respect to water permeability, it has been suggested that there is a decline in L p from the S1 to the S2 segment of the rat tubule. Nevertheless, the water permeability remains at least as large in the straight segment as in the convoluted segment. With respect to solute permeabilities, an increase in the electrical conductance of the rat proximal tubule has been observed as one moves from the earliest to the latest accessible segments. Experiments in perfused rabbit tubules suggest that the increase in total conductance is due to an increase in the chloride permeability. Comparison of tubule permeabilities indicates that juxtamedullary proximal convoluted tubules and proximal straight tubules are more cation selective than the superficial proximal tubule segments. Comparison of permeabilities of K + and of Cl , between rabbit juxtamedullary and superficial proximal straight tubules suggests that the increase in cation selectivity derives from an absolute increase in juxtamedullary nephron cation permeability, with little difference in anion permeability.

Table 33.2

Permeabilities of Proximal Tubules

Rat PCT References Rabbit PCT References Rabbit PST References
L p ×10 8 ml/s·cm 2 ·mmHg 22.6 (a) 32.6 48.5
P f cm/s 0.24 0.35 (b) 0.52 (e)
σ(Na) 0.7 (a) 0.9– 1.0 (b)
σ(Cl) 0.43 (a) 0.78– 0.95 (b)
σ(HCO 3 ) 1.0 (a) 0.97 (b)
P(Na)×10 5 cm/s 24.7 (a) 4.0– 11.9 (b) 2.3– 2.6 (b)
P(K) 27.1 (a)
P(Cl) 21.2 (a) 1.9– 6.5 (b) 5.6– 7.3 (b)
P(HCO 3 ) 6.7 (a) 1.3– 2.3 (c,d) 0.4– 2.0 (b)
Resistance ohm·cm 2 5 (a) 7.0 (b) 8.2 (b)

(a) ; (b) ; (c) ; (d) ; (e) .

There is no doubt that proximal tubule metabolism is required for transport to proceed at its normal rate. In the absence of ionic concentration gradients across the epithelium, reabsorption still proceeds and cooling or poisoning with metabolic inhibitors abolishes transport. A generally accepted treatment of active transport by the proximal tubule has been that of Frömter in which Eq. (33.2) is extended by inclusion of a term for metabolically driven transport, <SPAN role=presentation tabIndex=0 id=MathJax-Element-10-Frame class=MathJax style="POSITION: relative" data-mathml='Jia’>???Jia
J i a

<SPAN role=presentation tabIndex=0 id=MathJax-Element-11-Frame class=MathJax style="POSITION: relative" data-mathml='Ji=Jv(1−σi)c¯i+∑j=1nLijΔμ¯jc+Jia’>??=??(1??)??+??=1???????+???Ji=Jv(1−σi)c¯i+∑j=1nLijΔμ¯jc+Jia
J i = J v ( 1 − σ i ) c ¯ i + ∑ j = 1 n L i j Δ μ ¯ j c + J i a
or in the absence of coupled fluxes
<SPAN role=presentation tabIndex=0 id=MathJax-Element-12-Frame class=MathJax style="POSITION: relative" data-mathml='Ji=Jv(1−σi)c¯i+Pi[Δci+ziFRTc¯iΔψ]+Jia’>??=??(1??)??+??[???+?????????]+???Ji=Jv(1−σi)c¯i+Pi[Δci+ziFRTc¯iΔψ]+Jia
J i = J v ( 1 − σ i ) c ¯ i + P i [ Δ c i + z i F R T c ¯ i Δ ψ ] + J i a

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Jun 6, 2019 | Posted by in NEPHROLOGY | Comments Off on Sodium and Chloride Transport: Proximal Nephron

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