A numerical model of the renal distal tubule.

A numerical model of the rat distal tubule was developed to simulate water and solute transport in this nephron segment. This model incorporates the following: 1) Na-Cl cotransporter, K-Cl cotransporter, Na channel, K channel, and Cl channel in the luminal membrane; 2) Na-K-ATPase, K channel, and Cl channel in the basolateral membrane; and 3) conductances for Na, K, and Cl in the paracellular pathway. Transport rates were calculated using kinetic equations. Axial heterogeneity was represented by partitioning the model into two subsegments with different sets of model parameters. Model equations derived from the principles of mass conservation and electrical neutrality were solved numerically. Values of the model parameters were adjusted to minimize a penalty function that was devised to quantify the difference between model predictions and experimental results. The developed model could simulate the water and solute transport of the distal tubule in the normal state, as well as in conditions including thiazide or amiloride application and various levels of sodium load and tubular flow rate.

[1]  F. S. Wright,et al.  Thiazide-sensitive sodium chloride cotransport in early distal tubule. , 1987, The American journal of physiology.

[2]  R. Kunau,et al.  Clarification of the site of action of chlorothiazide in the rat nephron. , 1975, The Journal of clinical investigation.

[3]  B. Brenner,et al.  Primary structure and functional expression of a cDNA encoding the thiazide-sensitive, electroneutral sodium-chloride cotransporter. , 1993, Proceedings of the National Academy of Sciences of the United States of America.

[4]  F. S. Wright,et al.  Mutual dependence of sodium and chloride absorption by renal distal tubule. , 1984, The American journal of physiology.

[5]  F. S. Wright,et al.  Increasing magnitude of electrical potential along the renal distal tubule. , 1971, The American journal of physiology.

[6]  S. Gullans,et al.  Localization of the thiazide sensitive Na-Cl cotransporter, rTSC1 in the rat kidney. , 1996, Kidney international.

[7]  G. Capasso,et al.  Acidification in mammalian cortical distal tubule. , 1994, Kidney international.

[8]  R. Kunau,et al.  Characteristics of the relationship between the flow rate of tubular fluid and potassium transport in the distal tubule of the rat. , 1974, Journal of Clinical Investigation.

[9]  G. G. Allen,et al.  Origin of positive transepithelial potential difference in early distal segments of rat kidney. , 1985, Kidney international.

[10]  G. Giebisch,et al.  Effect of amiloride, ouabain, and furosemide on distal tubular function in the rat. , 1971, The American journal of physiology.

[11]  Hao Zhou,et al.  Primary structure and functional properties of an epithelial K channel. , 1994, The American journal of physiology.

[12]  D. E. Goldman POTENTIAL, IMPEDANCE, AND RECTIFICATION IN MEMBRANES , 1943, The Journal of general physiology.

[13]  R. R. Robinson,et al.  Osmolality of distal tubular fluid in the dog. , 1966, The Journal of clinical investigation.

[14]  G. Giebisch,et al.  Micropuncture study of distal tubular potassium and sodium transport in rat nephron. , 1966, The American journal of physiology.

[15]  A. Weinstein,et al.  Mathematical models of tubular transport. , 1994, Annual review of physiology.

[16]  G. Giebisch,et al.  Renal potassium channels: an overview. , 1995, Kidney international.

[17]  W. Jonathan Lederer,et al.  Cloning and expression of an inwardly rectifying ATP-regulated potassium channel , 1993, Nature.

[18]  F. S. Wright,et al.  Luminal influences on potassium secretion: sodium concentration and fluid flow rate. , 1979, The American journal of physiology.

[19]  E. Bruce Pitman,et al.  A dynamic numerical method for models of renal tubules , 1994 .

[20]  K. Tabei,et al.  Profiles of water and solute transport along long-loop descending limb: analysis by mathematical model. , 1987, The American journal of physiology.

[21]  G. Giebisch,et al.  A mathematical model of the rabbit cortical collecting tubule. , 1992, The American journal of physiology.

[22]  Bjarne Stroustrup,et al.  C++ Programming Language , 1986, IEEE Softw..

[23]  G. Giebisch,et al.  Structural and functional study of the rat distal nephron: effects of potassium adaptation and depletion. , 1981, Kidney international.

[24]  F. S. Wright,et al.  Luminal influences on potassium secretion: transepithelial voltage. , 1980, The American journal of physiology.

[25]  Tianxin Yang,et al.  Localization of bumetanide- and thiazide-sensitive Na-K-Cl cotransporters along the rat nephron. , 1996, The American journal of physiology.

[26]  L. Costanzo Localization of diuretic action in microperfused rat distal tubules: Ca and Na transport. , 1985, The American journal of physiology.

[27]  C. Tisher,et al.  Structural-functional relationships along the distal nephron. , 1986, The American journal of physiology.

[28]  G. G. Allen,et al.  Effect of aldosterone on the transepithelial potential difference of the rat distal tubule. , 1981, Kidney international.

[29]  S. Agulian,et al.  Electrochemical potentials of chloride in distal renal tubule of the rat. , 1974, The American journal of physiology.

[30]  F. Rector,et al.  Transepithelial potential difference profile of the distal tubule of the rat kidney. , 1975, Kidney international.

[31]  Bjarne Stroustrup,et al.  The C++ programming language (3. ed.) , 1997 .

[32]  H. G. Ferreira,et al.  A mathematical model of rabbit cortical thick ascending limb of the Henle's loop. , 1991, Biochimica et biophysica acta.

[33]  R. Zahler,et al.  Sodium Kinetics of Na,K-ATPase α Isoforms in Intact Transfected HeLa Cells , 1997, The Journal of general physiology.

[34]  A. Hodgkin,et al.  The effect of temperature on the electrical activity of the giant axon of the squid , 1949, The Journal of physiology.

[35]  G. Giebisch,et al.  MICROPUNCTURE STUDY OF RENAL POTASSIUM EXCRETION IN THE RAT. , 1964, The American journal of physiology.

[36]  B. Rossier,et al.  Epithelial sodium channel related to proteins involved in neurodegeneration , 1993, Nature.

[37]  T. Ohhashi,et al.  Effect of microvibration on activity of ureteral and portal smooth muscles. , 1979, The American journal of physiology.

[38]  G. Giebisch,et al.  Kinetics of potassium transport across single distal tubules of rat kidney , 1973, The Journal of physiology.

[39]  B. Brenner,et al.  ROMK inwardly rectifying ATP-sensitive K+ channel. II. Cloning and distribution of alternative forms. , 1995, The American journal of physiology.

[40]  F. S. Wright,et al.  Luminal influences on potassium secretion: low sodium concentration. , 1984, The American journal of physiology.

[41]  P. B. Woodhall,et al.  Response of the distal tubule and cortical collecting duct to vasopressin in the rat. , 1973, The Journal of clinical investigation.

[42]  K. Ullrich,et al.  [WATER PERMEABILITY AND TRANSTUBULAR WATER FLOW OF CORTICAL NEPHRON SECTIONS IN DIFFERENT STATES OF DIURESIS]. , 1964, Pflugers Archiv fur die gesamte Physiologie des Menschen und der Tiere.

[43]  J. A. Payne,et al.  Molecular Cloning and Functional Expression of the K-Cl Cotransporter from Rabbit, Rat, and Human , 1996, The Journal of Biological Chemistry.

[44]  G. Giebisch,et al.  Factors influencing transepithelial potential difference in mammalian distal tubule. , 1978, The American journal of physiology.

[45]  F. S. Wright,et al.  Chloride-dependent potassium secretion in early and late renal distal tubules. , 1987, The American journal of physiology.

[46]  H. Choe,et al.  Is the secretory K channel in the rat CCT ROMK? , 1997, The American journal of physiology.

[47]  B. Hille Ionic channels of excitable membranes , 2001 .

[48]  R Reilly,et al.  Expression of the thiazide-sensitive Na-Cl cotransporter in rat and human kidney. , 1995, The American journal of physiology.

[49]  L. Schild,et al.  Amiloride-sensitive epithelial Na+ channel is made of three homologous subunits , 1994, Nature.

[50]  M. Lazdunski,et al.  Expression cloning of an epithelial amiloride‐sensitive Na+ channel , 1993, FEBS letters.

[51]  W. Stein Intrinsic, apparent, and effective affinities of co- and countertransport systems. , 1986, The American journal of physiology.

[52]  Edward L Cussler,et al.  Diffusion: Mass Transfer in Fluid Systems , 1984 .

[53]  F. Morel,et al.  Na-K-ATPase activity along the rabbit, rat, and mouse nephron. , 1979, The American journal of physiology.

[54]  F. S. Wright,et al.  Stimulation of distal potassium secretion by low lumen chloride in the presence of barium. , 1985, The American journal of physiology.

[55]  Y. Hirata,et al.  Cloning and expression of apical membrane water channel of rat kidney collecting tubule , 1993, Nature.

[56]  A. Weinstein A mathematical model of the rat proximal tubule. , 1986, The American journal of physiology.

[57]  E. Windhager,et al.  Calcium and sodium transport by the distal convoluted tubule of the rat. , 1978, The American journal of physiology.

[58]  G. Giebisch,et al.  Effect of ionic substitutions on distal potential differences in rat kidney. , 1966, The American journal of physiology.

[59]  A. Verkman,et al.  Kinetic transport model for cellular regulation of pH and solute concentration in the renal proximal tubule. , 1987, Biophysical journal.

[60]  H. Sullivan Ionic Channels of Excitable Membranes, 2nd Ed. , 1992, Neurology.

[61]  F. S. Wright,et al.  Effects of diuretic drugs on Na, Cl, and K transport by rat renal distal tubule. , 1986, The American journal of physiology.

[62]  N. Farman,et al.  Cell-specific expression of epithelial sodium channel alpha, beta, and gamma subunits in aldosterone-responsive epithelia from the rat: localization by in situ hybridization and immunocytochemistry , 1994, The Journal of cell biology.

[63]  G. Giebisch,et al.  Some electrical properties of distal tubular epithelium in the rat. , 1972, The American journal of physiology.

[64]  C. W. Gottschalk,et al.  Micropuncture study of composition of proximal and distal tubular fluid in rat kidney. , 1963, The American journal of physiology.

[65]  J. H. Stein,et al.  Potassium transport in the distal tubule and collecting duct of the rat. , 1975, The American journal of physiology.

[66]  R. Kunau,et al.  Characteristics of sodium reabsorption in the loop of Henle and distal tubule. , 1974, The American journal of physiology.