A parallel path model forNecturus proximal tubule

Summary A parallel path model based on the principles of nonequilibrium thermodynamics was developed for theNecturus proximal tubule. The cellular path was represented as a luminal membrane followed by an irreversible active NaCl transport system in the peritubular barrier. The shunt pathway was described as three coarse barriers in series: tight junction, lateral intercellular spaces, and basement membrane with connective tissue. Volume and solute flows were predicted by the model equations as a function of applied electric current. Variations of the model parameters revealed the quantitative importance of the shunt path properties and the relative insensitivity of epithelial transport to changes in most cell parameters. Circulation of electric current and solute within the epithelium were shown to significantly influence the bahavior of the tubule in the presence of an electric field. Values for all transport parameters of the shunt path and epithelium were calculated and compared with available experimental evidence. Volume flow and electric currents predicted by the model compared favorably with experimental observations.     

A kinetically defined Na+/H+ antiporter within a mathematical model of the rat proximal tubule

The luminal membrane antiporter of the proximal tubule has been represented using the kinetic formulation of E. Heinz (1978. Mechanics and Engergetics of Biological Transport. Springer-Verlag, Berlin) with the assumption of equilibrium binding and 1:1 stoichiometry. Competitive binding and transport of NH+4 is included within this model. Ion affinities and permeation velocities were selected in a least-squares fit to the kinetic parameters determined experimentally in renal membrane vesicles (Aronson, P.S., M.A. Suhm, and J. Nee. 1983. Journal of Biological Chemistry. 258:6767-6771). The modifier role of internal H+ to enhance transport beyond the expected kinetics (Aronson, P.S., J. Nee, and M. A. Suhm. 1982. Nature. 299:161-163) is represented as a velocity effect of H+ binding to a single site. This kinetic formulation of the Na+/H+ antiporter was incorporated within a model of the rat proximal tubule (Weinstein, A. M. 1994. American Journal of Physiology. 267:F237-F248) as a replacement for the representation by linear nonequilibrium thermodynamics (NET). The membrane density of the antiporter was selected to yield agreement with the rate of tubular Na+ reabsorption. Simulation of 0.5 cm of tubule predicts that the activity of the Na+/H+ antiporter is the most important force for active secretion of ammonia. Model calculations of metabolic acid-base disturbances are performed and comparison is made among antiporter representations (kinetic model, kinetic model without internal modifier, and NET formulation). It is found that the ability to sharply turn off Na+/H+ exchange in cellular alkalosis substantially eliminates the cell volume increase associated with high HCO3- conditions. In the tubule model, diminished Na+/H+ exchange in alkalosis blunts the axial decrease in luminal HCO3- and thus diminishes paracellular reabsorption of Cl-. In this way, the kinetics of the Na+/H+ antiporter could act to enhance distal delivery of Na+, Cl-, and HCO3- in acute metabolic alkalosis.     

A two-dimensional mathematical model of percutaneous drug absorption

Background  

When a drug is applied on the skin surface, the concentration of the drug accumulated in the skin and the amount of the drug eliminated into the blood vessel depend on the value of a parameter, r. The values of r depend on the amount of diffusion and the normalized skin-capillary clearence. It is defined as the ratio of the steady-state drug concentration at the skin-capillary boundary to that at the skin-surface in one-dimensional models. The present paper studies the effect of the parameter values, when the region of contact of the skin with the drug, is a line segment on the skin surface.     

Nonequilibrium thermodynamic model of the rat proximal tubule epithelium.

The rat proximal tubule epithelium is represented as well-stirred, compliant cellular and paracellular compartments bounded by mucosal and serosal bathing solutions. With a uniform pCO2 throughout the epithelium, the model variables include the concentrations of Na, K, Cl, HCO3, H2PO4, HPO4, and H, as well as hydrostatic pressure and electrical potential. Except for a metabolically driven Na-K exchanger at the basolateral cell membrane, all membrane transport within the epithelium is passive and is represented by the linear equations of nonequilibrium thermodynamics. In particular, this includes the cotransport of Na-Cl and Na-H2PO4 and countertransport of Na-H at the apical cell membrane. Experimental constraints on the choice of ionic conductivities are satisfied by allowing K-Cl cotransport at the basolateral membrane. The model equations include those for mass balance of the nonreacting species, as well as chemical equilibrium for the acidification reactions. Time-dependent terms are retained to permit the study of transient phenomena. In the steady state the energy dissipation is computed and verified equal to the sum of input from the Na-K exchanger plus the Gibbs free energy of mass addition to the system. The parameter dependence of coupled water transport is studied and shown to be consistent with the predictions of previous analytical models of the lateral intercellular space. Water transport in the presence of an end-proximal (HCO3-depleted) luminal solution is investigated. Here the lower permeability and higher reflection coefficient of HCO3 enhance net sodium and water transport. Due to enhanced flux across the tight junction, this process may permit proximal tubule Na transport to proceed with diminished energy dissipation.     

Transport of chlorine in the proximal tubule. Its effects on water-electrolyte absorption

Several studies in rat kidney have established that an appreciable fraction of proximal absorption is passive in nature and occurs across the highly conductive paracellular pathway. Passive absorption is generally ascribed to the transepithelial Cl- distribution, luminal Cl- activity (alpha lCl) being higher than plasma Cl- activity (alpha pCl). The inequality alpha lCl greater than alpha pCl generates a transepithelial diffusion potential, lumen positive, which taken together with the chemical potential differences of Cl- and Na+ across the epithelium gives rise to transepithelial electrochemical potential differences for Cl- and Na+ favoring their absorption. The alpha lCl greater than alpha pCl distribution is traditionally ascribed to preferential bicarbonate absorption. We argue that HCO3- absorption alone cannot generate a non equilibrium transepithelial Cl- distribution. Other mechanisms are necessary. Our measurements in amphibian proximal tubule demonstrate that the intracellular Cl- activity, alpha cCl, is higher than the theoretical value predicted for equilibrium. This distribution is the result of two basolateral coupled transport processes (Cl-/HCO3- exchange and Cl-/Na+ cotransport). It contributes to the exit of Cl- from cell to lumen (by passive diffusion and K+/Cl- cotransport), yielding alpha lCl values higher than the theoretical value for equilibrium with regard to plasma. Thus, a small transcellular flux of Cl- (without solvent) proceeds from interstitium to lumen. It compensates the dissipative tendency of a much higher paracellular Cl- absorptive flux (in association with water) on the transepithelial Cl- gradient. The result is a steady-state luminal Cl- distribution above equilibrium, along the major part of the proximal tubule.     

Effect of cAMP and calmodulin inhibitors on water absorption in rat proximal tubule

The possible role of calmodulin in solute transport was examined in the kidney of the rat. Utilizing a radioimmunoassay, calmodulin was identified and quantitated in homogenates of the cortex of the kidney. The physiologic significance of these findings was examined utilizing in vivo microperfusion techniques applied to the proximal convoluted tubule of the thyroparathyroidectomized rat. The addition of dibutyryl cyclic adenosine monophosphate (cAMP) to the luminal perfusion solution resulted in a lower rate of water absorption of 1.67 +/- 0.09 nl min-1 mm-1 as compared to 2.46 +/- 0.11 in controls. The addition of either of two compounds with affinity for calmodulin, trifluoperazine (TFP) or W-13, reversed the cAMP-induced inhibition of water absorption. In the absence of cAMP, neither agent affected water absorption. Analogs of TFP and W-13 with lower binding affinities for calmodulin had no effect on water absorption and did not reverse the cAMP effect. None of the above experimental maneuvers affected the absorption of phosphate. These results demonstrate the presence of calmodulin in the kidney of the rat and suggest that calmodulin may be involved in cAMP-associated inhibition of water and electrolyte transport in the proximal tubule of the rat.     

A two-dimensional mathematical model of non-linear dual-sorption of percutaneous drug absorption

Background  

Certain drugs, for example scopolamine and timolol, show non-linear kinetic behavior during permeation process. This non-linear kinetic behavior is due to two mechanisms; the first mechanism being a simple dissolution producing mobile and freely diffusible molecules and the second being an adsorption process producing non-mobile molecules that do not participate in the diffusion process. When such a drug is applied on the skin surface, the concentration of the drug accumulated in the skin and the amount of the drug eliminated into the blood vessel depend on the value of a parameter, C, the donor concentration. The present paper studies the effect of the parameter value, C, when the region of the contact of the skin with drug, is a line segment on the skin surface. To confirm that dual-sorption process gives an explanation to non-linear kinetic behavior, the characteristic features that are used in one-dimensional models are (1) prolongation of half-life if the plot of flux versus time are straight lines soon after the vehicle removal, (2) the decrease in half-life with increase in donor concentration. This paper introduces another feature as a characteristic to confirm that dual-sorption model gives an explanation to the non-linear kinetic behavior of the drug. This new feature is "the prolongation of half-life is not a necessary feature if the plots of drug flux versus time is a non-linear curve, soon after the vehicle removal".     

Alpha and beta adrenergic agonists stimulate water absorption in the rat proximal tubule

Summary Simultaneous capillary and luminal microperfusion studies were performed in the rat proximal tubule to determine the effects of the beta agonist isoproterenol and the alpha agonist phenylephrine on water absorption. Capillary and luminal perfusion solutions were composed such that organic solutes were not present, no bicarbonate was present in the lumen, and no chloride gradient was imposed. Under such conditions, water absorption (Jv) averaged 0.36±0.11 nl·min^–1·mm^–1. The addition of isoproterenol to the capillary solution in concentrations of 10^–6 and 10^–4 m resulted in significantly higherJv's of 0.68±0.10 and 0.71±0.11 nl·min^–1·mm^–1, respectively. The enhancing effect of isoproterenol was inhibited by the beta blocker propranolol (10^–4 m), but not by the alpha blocker phentolamine (10^–7 m). The addition of phenylephrine (10^–6 m) to the capillary perfusion solution also resulted in a significantly higherJv of 0.84±0.14 nl·min^–1·mm^–1, an effect inhibited by phentolamine (10^–7 m), but not by propranolol (10^–4 m). Neither phentolamine nor propranolol alone in the concentrations indicated had an effect on water absorption. These experiments indicate that both alpha and beta agonists stimulate water absorption in the superficial proximal tubule of the rat. This effect appears to be relatively specific for each class of agonist, as demonstrated by the effects of the specific antagonists.     

Glucose transport in a model of the rat proximal tubule epithelium

A mathematical model of the rat proximal tubule epithelium has been extended to include terms for glucose-sodium cotransport, as well as the passive permeability properties of urea. Except for a metabolically driven Na⁺-K⁺ exchanger at the cell basolateral membrane, all membrane transport is represented by the relations of linear nonequilibrium thermodynamics. Use of this formalism permits the explicit calculation of the intracellular depolarization immediately following the luminal application of glucose, and shows the magnitude of this potential deflection proportional to the glucose chemical-potential change. The steady-state glucose transport by this model epithelium, like experimental data, is fitted remarkably well by a three-parameter pump-leak model of transport. In view of the nonsaturability of the cotransporter of the model epithelium, the goodness of fit to the three-parameter model is surprising and underscores the uncertainty in extracting individual membrane properties from whole epithelial data. Experiments are simulated in which hypertonic glucose placed in the bath induces cell swelling and K⁺ uptake; a hypertonic impermeant induces cell shrinkage and K⁺ loss. Although this parallels the observations in vivo, the large K⁺ shifts predicted by the model suggest the absence of important volume-regulatory mechanisms from the model scheme.     

Androgens stimulate proximal tubule transport

Background: Disrupting the enzyme cytochrome P4a14 in mice leads to hypertension, which is more severe in male than in female mice and appears to be due to androgen excess. Androgens are known to increase expression of angiotensinogen,but the effect of androgens on proximal tubule transport is unknown.Objective: These studies aimed to determine the effect of androgens on proximal tubule transport.Methods: Proximal tubules from knockout (KKO) and wild-ttype (WWT) (SSV/1129) mice were perfused in vitro. Volume resorption (JJ v ) was measured using 3 H-methoxy inulin as a volume marker. In separate experiments, male Sprague-Dawley rats were given dihydrotestosterone (DDHT) injections IP for 10 days. Proximal tubule transport was measured in this model using in vivo microperfusion. The renal expression of angiotensinogen was measured by Northern analysis, and brush border membrane protein abundance of the sodium-hhydrogen exchanger isoform 3 (NNHE3) was measured by Western blotting in the control and DHT-ttreated rats.Results: Mean (SSE) J_v was significantly elevated in proximal tubules from KO mice compared with WT mice (11.11 [0.006] vs 0.77 [0.112] nL/mm . mm, respectively; P<0.05). The mean proximal tubule J_v rate was significantly higher in DHT-ttreated rats than in control rats given vehicle injections (44.57 [0.331] vs 3.31 [0.223] nL/mm . min, respectively; P<0.01). Luminal perfusion with either enalaprilat or losartan decreased the proximal tubule J v rate in DHT-ttreated rats to a greater degree than in control rats. The DHT-treated rats had higher blood pressures and lower serum angiotensin II concentrations than did the control rats.Conclusion: Results suggest that androgens may directly upregulate the proximal tubule reninangiotensin system, increase the expression of NHE3, and increase the J_v rate, thereby increasing extracel-lular volume and blood pressure and secondarily decreasing serum angiotensin II concentrations.     

A novel vasopressin receptor in rat early proximal tubule

In order to evaluate the receptor subtypes of arginine vasopressin (AVP) in early proximal tubule (S1), outer medullary thick ascending limb of Henle's loop (MTAL) and collecting tubule (OMCT), the effect of AVP on intracellular free calcium ([Ca++]i) was determined using the fluorescence indicator Fura-2. Physiological concentration (greater than or equal to 10(-12) M) of AVP in MTAL and OMCT mobilized [Ca++]i in a dose-dependent manner, but relatively high concentration (greater than or equal to 10(-9) M) of AVP in S1 increased [Ca++]i. Moreover, pretreatment with both V1 and V2 antagonists in MTAL or OMCT completely inhibited the AVP-induced [Ca++]i transient, but in S1 partially blocked it. Using several AVP analogues, a relative distribution of AVP receptor subtypes was tentatively calculated in each nephron segment, indicating that although these nephron segments possess V1, its density was very low (about 10%). The majority (about 90%) of AVP receptor in MTAL and OMCT was V2, while that in S1 was a new subtype (named Vp) which is insensitive to V1 and V2 antagonists. To evaluate physiological significance of Vp receptor, AVP-mediated cellular ATP change was measured. Cellular ATP content in S1 was significantly increased by 10(-7) M AVP, but in MTAL it was significantly decreased by the same concentration of AVP. This study suggests that a novel AVP receptor exists in isolated rat S1, and its physiological significance may be the inhibition of ATP-consuming ion transport system.     

Serum-induced inhibition of isotonic fluid absorption by the kidney proximal tubule I. Mechanism of inhibition

Isotonic reabsorption by the rat kidney proximal tubule was drastically inhibited after less than 2 min intraluminal perfusion with fresh sera from rat (both homologous and autologous), cat, rabbit and human, but not with sera from mouse and guinea pig. The inhibitory factor in serum in a heat (56° C for 30 min) and storage (4°C for 2–5 days) labile macromolecule (mol. wt 50 000) and requires Ca²⁺ for its effect. The cellular electrical potential difference of the proximal tubular cells was irreversively destroyed and intraluminally perfused trypan blue dye incorporated into the tubular cells after the intraluminal perfusion with serum for 2 min. These observations suggest that lysis of the proximal tubular cells is the mechanism for serum-induced inhibition of proximal tubular isotonic reabsorption.     

Current-induced voltage transients inNecturus proximal tubule

Summary Transients in the potential difference spontaneously developed by theNecturus proximal tubule were characterized during and after voltage or current clamp commands. These voltage transients were adequately fitted by an exponential function similar to that describing the ionic charging of a leaky fluid capacitance and were slower during clamp periods (t 1/2=0.98 min) than after release of the clamp (t 1/2-0.46 min). Changes in luminal ionic composition and cellular membrane potential were ruled out as sources of generation of the voltage transients. The volume of the fluid compartment in which concentration changes occurred was calculated from the electrical data and it was concluded that the extracellular shunt path was the principal site of the concentration changes which resulted in voltage transients. A fall in transepithelial resistance to nearly one-half its original value occurred during hyperpolarizing commands while depolarizing commands did not significantly alter resistance. The resistance changes were interpreted as indicative of the degree of widening of the lateral intercellular spaces caused by fluid accumulation or depletion. The important role of the lateral space dimensions in determining epithelial permeability, electrical resistance and voltage transients was pointed out, and a new electrical analogue model of the shunt path was proposed.     

Ontogeny of rabbit proximal tubule urea permeability

Urea transport in the proximal tubule is passive and is dependent on the epithelial permeability. The present study examined the maturation of urea permeability (P(urea)) in in vitro perfused proximal convoluted tubules (PCT) and basolateral membrane vesicles (BLMV) from rabbit renal cortex. Urea transport was lower in neonatal than adult PCT at both 37 and 25 degrees C. The PCT P(urea) was also lower in the neonates than the adults (37 degrees C: 45.4 +/- 10.8 vs. 88.5 +/- 15.2 x 10(-6) cm/s, P < 0.05; 25 degrees C: 28.5 +/- 6.9 vs. 55.3 +/- 10.4 x 10(-6) cm/s; P < 0.05). The activation energy for PCT P(urea) was not different between the neonatal and adult groups. BLMV P(urea) was determined by measuring vesicle shrinkage, due to efflux of urea, using a stop-flow instrument. Neonatal BLMV P(urea) was not different from adult BLMV P(urea) at 37 degrees C [1.14 +/- 0.05 x 10(-6) vs. 1.25 +/- 0.05 x 10(-6) cm/s; P = not significant (NS)] or 25 degrees C (0.94 +/- 0.06 vs. 1.05 +/- 0.10 x 10(-6) cm/s; P = NS). There was no effect of 250 microM phloretin, an inhibitor of the urea transporter, on P(urea) in either adult or neonatal BLMV. The activation energy for urea diffusion was also identical in the neonatal and adult BLMV. These findings in the BLMV are in contrast to the brush-border membrane vesicles (BBMV) where we have previously demonstrated that urea transport is lower in the neonate than the adult. Urea transport is lower in the neonatal proximal tubule than the adult. This is due to a lower rate of apical membrane urea transport, whereas basolateral urea transport is the same in neonates and adults. The lower P(urea) in neonatal proximal tubules may play a role in overall urea excretion and in developing and maintaining a high medullary urea concentration and thus in the ability to concentrate the urine during renal maturation.