A mathematical model of the rabbit cortical collecting tubule. 1992

J Strieter, and J L Stephenson, and G Giebisch, and A M Weinstein
Department of Physiology and Biophysics, Cornell University Medical College, New York, New York 10021.

The epithelium of the cortical collecting tubule of the rabbit is represented as four well-stirred compliant compartments corresponding to principal cell, alpha- and beta-intercalated cells, and lateral interspace. Model variables include the concentrations of Na, K, Cl, and HCO3, pH, cell volume, and electrical potential. The model equations specify mass conservation and chemical equilibrium for buffer reactions. Ionic conductance is represented by the Goldman constant-field equation. For the intercalated cells, phenomenological expressions describing the proton pumps are structured to agree with data of O. S. Andersen, J. E. N. Silveira, and P. R. Steinmetz (J. Gen. Physiol. 86: 215-234, 1985) in the turtle bladder. Coupled transport via Na/H and Cl/HCO3 exchangers is represented according to the formalism of linear nonequilibrium thermodynamics. To construct the tubule model, the flat epithelium is wrapped into a cylinder, creating a luminal compartment. Luminal variables include volume flow, hydrostatic pressure, electrical potential, and ionic concentrations. A specific aim of this investigation was to simulate the capability of the epithelium to maintain Na reabsorption in the presence of low luminal salt concentration. In this regard, critical features of the model include tight junctional conductance and the apical Na permeability of the principal cell. In particular, we examine a principal cell apical Na permeability inversely dependent on luminal and intracellular Na concentrations (M. M. Civan and R. J. Bookman. J. Membr. Biol. 65: 63-80, 1982). This concentration-dependent permeability together with a low junctional conductance produces three results congruent with experimental data: 1) dilution of luminal Na and maintenance of reabsorptive Na transport despite a steep transtubular gradient, 2) a relatively constant level of K secretion over a wide range of luminal Na concentrations, and 3) a relatively constant transepithelial potential over this range of luminal Na.

UI MeSH Term Description Entries
D007672 Kidney Cortex The outer zone of the KIDNEY, beneath the capsule, consisting of KIDNEY GLOMERULUS; KIDNEY TUBULES, DISTAL; and KIDNEY TUBULES, PROXIMAL. Cortex, Kidney
D007685 Kidney Tubules, Collecting Straight tubes commencing in the radiate part of the kidney cortex where they receive the curved ends of the distal convoluted tubules. In the medulla the collecting tubules of each pyramid converge to join a central tube (duct of Bellini) which opens on the summit of the papilla. Kidney Collecting Ducts,Kidney Collecting Duct,Collecting Duct, Kidney,Collecting Ducts, Kidney
D008954 Models, Biological Theoretical representations that simulate the behavior or activity of biological processes or diseases. For disease models in living animals, DISEASE MODELS, ANIMAL is available. Biological models include the use of mathematical equations, computers, and other electronic equipment. Biological Model,Biological Models,Model, Biological,Models, Biologic,Biologic Model,Biologic Models,Model, Biologic
D011677 Punctures Incision of tissues for injection of medication or for other diagnostic or therapeutic procedures. Punctures of the skin, for example may be used for diagnostic drainage; of blood vessels for diagnostic imaging procedures. Micropunctures,Micropuncture,Puncture
D011817 Rabbits A burrowing plant-eating mammal with hind limbs that are longer than its fore limbs. It belongs to the family Leporidae of the order Lagomorpha, and in contrast to hares, possesses 22 instead of 24 pairs of chromosomes. Belgian Hare,New Zealand Rabbit,New Zealand Rabbits,New Zealand White Rabbit,Rabbit,Rabbit, Domestic,Chinchilla Rabbits,NZW Rabbits,New Zealand White Rabbits,Oryctolagus cuniculus,Chinchilla Rabbit,Domestic Rabbit,Domestic Rabbits,Hare, Belgian,NZW Rabbit,Rabbit, Chinchilla,Rabbit, NZW,Rabbit, New Zealand,Rabbits, Chinchilla,Rabbits, Domestic,Rabbits, NZW,Rabbits, New Zealand,Zealand Rabbit, New,Zealand Rabbits, New,cuniculus, Oryctolagus
D002463 Cell Membrane Permeability A quality of cell membranes which permits the passage of solvents and solutes into and out of cells. Permeability, Cell Membrane
D004594 Electrophysiology The study of the generation and behavior of electrical charges in living organisms particularly the nervous system and the effects of electricity on living organisms.
D000042 Absorption The physical or physiological processes by which substances, tissue, cells, etc. take up or take in other substances or energy.
D000818 Animals Unicellular or multicellular, heterotrophic organisms, that have sensation and the power of voluntary movement. Under the older five kingdom paradigm, Animalia was one of the kingdoms. Under the modern three domain model, Animalia represents one of the many groups in the domain EUKARYOTA. Animal,Metazoa,Animalia
D012964 Sodium A member of the alkali group of metals. It has the atomic symbol Na, atomic number 11, and atomic weight 23. Sodium Ion Level,Sodium-23,Ion Level, Sodium,Level, Sodium Ion,Sodium 23

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