Skip to main content
SpringerLink
Log in

Role of UTB Urea Transporters in the Urine Concentrating Mechanism of the Rat Kidney

  • Original Article
  • Published:
Bulletin of Mathematical Biology Aims and scope Submit manuscript

Abstract

A mathematical model of the renal medulla of the rat kidney was used to investigate urine concentrating mechanism function in animals lacking the UTB urea transporter. The UTB transporter is believed to mediate countercurrent urea exchange between descending vasa recta (DVR) and ascending vasa recta (AVR) by facilitating urea transport across DVR endothelia. The model represents the outer medulla (OM) and inner medulla (IM), with the actions of the cortex incorporated via boundary conditions. Blood flow in the model vasculature is divided into plasma and red blood cell compartments. In the base-case model configuration tubular dimensions and transport parameters are based on, or estimated from, experimental measurements or immunohistochemical evidence in wild-type rats. The base-case model configuration generated an osmolality gradient along the cortico-medullary axis that is consistent with measurements from rats in a moderately antidiuretic state. When expression of UTB was eliminated in the model, model results indicated that, relative to wild-type, the OM cortico-medullary osmolality gradient and the net urea flow through the OM were little affected by absence of UTB transporter. However, because urea transfer from AVR to DVR was much reduced, urea trapping by countercurrent exchange was significantly compromised. Consequently, urine urea concentration and osmolality were decreased by 12% and 8.9% from base case, respectively, with most of the reduction attributable to the impaired IM concentrating mechanism. These results indicate that the in vivo urine concentrating defect in knockout mouse, reported by Yang et al. (J Biol Chem 277(12), 10633–10637, 2002), is not attributable to an OM concentrating mechanism defect, but that reduced urea trapping by long vasa recta plays a significant role in compromising the concentrating mechanism of the IM. Moreover, model results are in general agreement with the explanation of knockout renal function proposed by Yang et al.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • Akizuki, N., Uchida, S., Sasaki, S., Marumo, F., 2001. Impaired solute accumulation in inner medulla of Clcnk1-/- mice kidney. Am. J. Physiol. Renal. Physiol. 280, F79–F87.

    Google Scholar 

  • Armsen, T., Reinhardt, H.W., 1971. Transtubular movement of urea at different degrees of water diuresis. Pflügers Arch. 326, 270–280.

    Article  Google Scholar 

  • Atherton, J.C., Hai, M.A., Thomas, S., 1968. The time course of changes in renal tissue composition during water diuresis in the rat. J. Physiol. 197, 429–443.

    Google Scholar 

  • Atherton, J.C., Hai, M.A., Thomas, S., 1969. Acute effects of lysine vasopressin injection (single and continuous) on urinary composition in the conscious water diuretic rat. Pflügers Arch. 310, 281–296.

    Article  Google Scholar 

  • Bankir, L., de Rouffignac, C., 1985. Urinary concentrating ability: Insights from comparative anatomy. Am. J. Physiol. (Regulatory Integrative Comp Physiol 18) 249, R643–R666.

    Google Scholar 

  • Bankr, L., Chen, K., Yang, B., 2004. Lack of UT-B in vasa recta and red blood cells prevents urea-induced improvement of urine concentrating ability. Am. J. Physiol. Renal. Physiol. 286, F144–F151.

    Article  Google Scholar 

  • Beauchat, C. A., 1996. Structure and concentrating ability of the mammalian kidney: Correlations with habitat. Am. J. Physiol. (Regulatory Integrative Comp Physiol 40) 271, R157–R179.

    Google Scholar 

  • Chou, C.-L., Knepper, M.A., 1992. In vitro perfusion of chinchilla thin limb segments: Segmentation and osmotic water permeability. Am. J. Physiol. (Renal Fluid Electrolyte Physiol 32) 263, F417–F426.

    Google Scholar 

  • Colton, C.K., Smith, K.A., Merrill, E.W., Reece, J.M., 1970. Diffusion of organic solutes in stagnant plasma and red cell suspension. Chem. Eng. Prog. Symp. Ser. 66, 85–100.

    Google Scholar 

  • de Rouffignac, C., Bouvalet, J.P., 1970. Étude chez le rat des variations du débit individuel de filtration glomérulaire des néphron superficiels et profonds en fonction de l’apport sodé. Pflügers Arch. 317, 141–156.

    Article  Google Scholar 

  • Edwards, A., Delong, M.J., Pallone, T.L., 2000. Interstitial water and solute recovery by inner medullary vasa recta. Am. J. Physiol. Renal. Physiol. 278, F257–F269.

    Google Scholar 

  • Edwards, A., Pallone, T.L., 1997. Faciliated transport in vasa recta: Theoretical effects on solute exchange in the medullary microcirculation. Am. J. Physiol. Renal. Physiol. 272, F505–F514.

    Google Scholar 

  • Greger, R., Velázquez, H., 1987. The cortical thick ascending limb and early distal convoluted tubule in the concentrating mechanism. Kidney Int. 31, 590–596.

    Article  Google Scholar 

  • Hai, M.A., Thomas, S., 1969. The time-course of changes in renal tissue composition during lysine vasopressin infusion in the rat. Pflügers Arch. 310, 297–319.

    Article  Google Scholar 

  • Han, J.S., Thompson, K.A., Chou, C.-L., Knepper, M.A., 1992. Experimental tests of three-dimensional model of urinary concentrating mechanism. J. Am. Soc. Nephrol. 2, 1677–1688.

    Google Scholar 

  • Hervy, S., Thomas, S.R., 2003. Inner medullary lactate production and urine-concentrating mechanism: A flat medullary model. Am. J. Physiol. Renal. Physiol. 284, F65–F81.

    Google Scholar 

  • Jamison, R.L., Kriz, W., 1982. Urinary Concentrating Mechanism: Structure and Function. Oxford University Press, New York.

    Google Scholar 

  • Kato, A., Naruse, M., Knepper, M.A., Sands, J.M., 1998. Long-term regulation of inner medullary collecting duct urea transport in rat. J. Am. Soc. Nephrol. 9, 737–745.

    Google Scholar 

  • Kellogg, R.B., 1987. Some singular perturbation problems in renal models. J. Math. Anal. Appl. 128, 214–240.

    Article  MATH  MathSciNet  Google Scholar 

  • Knepper, MA., 1982. Measurement of osmolality in kidney slices using vapor pressure osmometry. Kidney Int. 21, 653–655.

    Article  Google Scholar 

  • Knepper, M.A., Danielson, R.A., Saidel, G.M., Post, R.S., 1977. Quantitative analysis of renal medullary anatomy in rats and rabbits. Kidney Int. 12, 313–323.

    Article  Google Scholar 

  • Koepsell, H., Nicholson, W.A.P., Kriz, W., Höhling, H.J., 1974. Measurements of exponential gradients of sodium and chloride in the rat kidney medulla using the electron microprobe. Pflügers Arch. 350, 167–184.

    Article  Google Scholar 

  • Kokko, J.P., Rector, F.C., 1972. Countercurrent multiplication system without active transport in the inner medulla. Kidney Int. 2, 214–223.

    Article  Google Scholar 

  • Kriz, W., 1967. Der architektonische and funktionelle Aufbau der Rattenniere. Z. Zellforsch. 82.

  • Kriz, W., 1981. Structural organization of the renal medulla: Comparative and functional aspects. Am. J. Physiol. (Regulatory Integrative Comp Physiol 10) 241, R3–R16.

    Google Scholar 

  • Kriz, W., Kaissling, B., 2000. Structural organization of the mammalian kidney. In: The Kidney: Physiology and Pathophysiology, Lippincott Williams & Wilkins, Philadelphia, pp. 587–654.

  • Kriz, W., Koepsell, H., 1974. The structural organization of the mouse kidney. Z. Anat. Entwickl-Gesch. 144, 137–163.

    Article  Google Scholar 

  • Kriz, W., Schnermann, J., Koepsell, H., 1972. The position of short and long loops of Henle in the rat kidney. Z. Anat. Entwickl-Gesch. 138, 301–319.

    Article  Google Scholar 

  • Layton, A.T., Layton, H.E., 2002a. An efficient numerical method for distributed-loop models of the urine concentrating mechanism. Math. Biosci. 181(2), 111–132.

    Article  MathSciNet  Google Scholar 

  • Layton, A.T., Layton, H.E., 2002b. A numerical method for renal tubules with abrupt changes in membrane properties.J. Math. Biol. 45(6), 549–567.

    Article  MATH  MathSciNet  Google Scholar 

  • Layton, A.T., Layton, H.E., 2003a. A region-based mathematical model of the urine concentrating mechanism in the rat outer medulla: I. Formulation and base-case results. Am. J. Physiol. Renal. Physiol. submitted.

  • Layton, A.T., Layton, H.E., 2003b. A region-based mathematical model of the urine concentrating mechanism in the rat outer medulla: II. Parameter sensitivity and tubular inhomogeneity. Am. J. Physiol. Renal. Physiol. submitted.

  • Layton, A.T., Layton, H.E., 2003c. A region-based model framework for the rat urine concentrating mechanism. Bull. Math. Biol. 65(5), 859–901.

    Article  Google Scholar 

  • Layton, A.T., Pannabecker, T.L., Dantzler, W.H., Layton, H.E., 2004. Two modes for concentrating urine in the rat inner medulla. Am. J. Physiol. Renal. Physiol. 287, F816–F839.

    Article  Google Scholar 

  • Layton, H.E., 1986. Distribution of Henle’s loops may enhance urine concentrating capability. Biophys. J. 49, 1033–1040.

    Article  Google Scholar 

  • Layton, H.E., 2002. Mathematical models of the mammalian urine concentrating mechanism. In: Membrane Transport and Renal Physiology, The IMA Volumes in Mathematics and Its Applications, vol. 129, Springer, New York, pp. 233–272.

  • Layton, H.E., Knepper, M.A., Chou, C.-L., 1996. Permeability criteria for effective function of passive countercurrent multiplier. Am. J. Physiol. (Renal Fluid Electrolyte Physiol 39) 270, F9–F20.

    Google Scholar 

  • Layton, H.E., Pitman, E.B., 1994. A dynamic numerical method for models of renal tubules. Bull. Math. Biol. 56(3), 547–565.

    MATH  Google Scholar 

  • Lemley, K.V., Kriz, W., 1987. Cycles and separations: The histotopography of urinary concentrating process. Kidney Int. 31, 538–548.

    Article  Google Scholar 

  • Moores, R.R., Stohlman, F., Brecher, G., 1963. Humoral regulation of erythropoiesis. XI. The pattern of response to specific therapy in iron deficiency anemia. Blood 22, 286–294.

    Google Scholar 

  • Pallone, T.L., 1994. Characterization of the urea transporter in outer medullary descending vasa recta. Am. J. Physiol. Regul. Integr. Comp. Physiol. 267, R260–R267.

    Google Scholar 

  • Pallone, T.L., Morgenthaler, T.I., Deen, W.M., 1984. Analysis of microvascular water and solute exchanges in the renal medulla. Am. J. Physiol. Renal. Fluid. Electrolyte. Physiol. 247.

  • Pallone, T.L., Robertson, C.R., Jamison, R.L., 1990. Renal medullary microcirculation. Physiol. Rev. 70, 885–920.

    Google Scholar 

  • Pallone, T.L., Turner, M.R., Edwards, A., Jamison, R.L., 2003. Countercurrent exchange in the renal medulla. Am. J. Physiol. Renal. Integr. Comp. Physiol. 284, R113–R1175.

    Google Scholar 

  • Pallone, T.L., Work, J., Myers, R., Jamison, R.L., 1994. Transport of sodium and urea in outer medullary vascular bundles. J. Clin. Invest. 93, 212–222.

    Article  Google Scholar 

  • Pallone, T.L., Yagil, Y., Jamison, R.L., 1989. Effect of small-solute gradients on transcapillary fluid movement in renal inner medulla. Am. J. Physiol. Renal. Fluid Electrolyte Physiol. (26) 257, F547–F553.

    Google Scholar 

  • Pannabecker, T.L., Abbott, D.E., Dantzler, W.H., 2004. Three-dimensional functional reconstruction of inner medullary thin limbs of Henle’s loop. Am. J. Physiol. Renal. Physiol. 286, F38–F45.

    Article  Google Scholar 

  • Pannabecker, T.L., Dahlmann, A., Brokl, O.H., Dantzler, W.H., 2000. Mixed descending- and ascending-type thin limbs of Henle’s loop in mammalian renal inner medulla. Am. J. Physiol. Renal. Physiol. 278, F202–F208.

    Google Scholar 

  • Pannabecker, T.L., Dantzler, W.H., 2004. Three-dimensional lateral and vertical relationship of inner medullary loops of henle and collecting duct. Am. J. Physiol. Renal. Physiol. 287, F767–F774.

    Article  Google Scholar 

  • Pennell, J.P., Lacy, F.B., Jamison, R.L., 1974. An in vivo study of the concentrating process in the descending limb of Henle’s loop. Kidney Int. 5, 337–347.

    Article  Google Scholar 

  • Pfaller, W., 1982. Structure Function Correlation on Rat Kidney: Quantitative Correlation of Structure and Function in the Normal and Injured Rat Kidney. Springer-Verlag, New York.

  • Rytand, D.A., 1938. The number and size of mammalian glomeruli as related to kidney and to body weight, with methods for their enumeration and measurement. Am. J. Anat. 62, 507–520.

    Article  Google Scholar 

  • Sands, J.M., Layton, H.E., 2000. Urine concentrating mechanism and its regulation. In: Seldin, D.W., Giebisch, G. (Eds.), The Kidney: Physiology and Pathophysiology. Lippincott Williams & Wilkins, Philadelphia, pp. 1175–1216.

  • Sands, J.M., Nonoguchi, H., Knepper, M.A., 1987. Vasopressin effects on urea and H2O transport in inner medullary collecting duct subsegments. Am. J. Physiol. Renal. Physiol. 253, F823–F832.

    Google Scholar 

  • Stephenson, J.L., 1972. Central core model of the renal counterflow system. Kidney Int. 2, 85–94.

    Article  Google Scholar 

  • Thomas, S.R., 1998. Cycles and separations in a model of the renal medulla. Am. J. Physiol. (Renal Fluid Electrolyte Physiol 44), 275, F671–F690.

    Google Scholar 

  • Tsukaguchi, H., Shaykul, C., Berger, U.V., Tokui, T., Bown, D., Hediger, M.A., 1997. Cloning and characterization of the urea transporter ut3: Localization in the rat kidney and testis. J. Clin. Invest. 99, 1506–1515.

    Google Scholar 

  • Ullrich, K.J., Jarausch, K.H., 1956. Untersuchungen zum Problem der Harnkonzentrierung and Harnverdünnung Ueber der Verteilung von Electrolyten (Na, K, Ca, Mg, Cl, anorganischem Phosphat), Harnstoff, Aminosäuren and exorgenem Kreatinin in Rinde und Mark der Hundeniere bei verschiedenen Dieresezuständen. Arch. Ges. Physiol. 262, 537–550.

  • Wade, J.B., Lee, A.J., Ecelbarger, C.A., Mitchell, C., Bradford, A.D., Terris, J., Kim, G.-H., Knepper, M.A., 2000. UT-A2: A 55-kDa urea transporter in thin descending limb whose abundance is regulated by vasopressin. Am. J. Physiol. Renal. Physiol. 278, F52–F62.

    Google Scholar 

  • Wang, X., Wexler, AS., Marsh, D.J., 1994. The effect of solution non-ideality on membrane transport in three-dimensional models of the renal concentrating mechanism. Bull. Math. Biol. 56(3), 515–549.

    MATH  Google Scholar 

  • Weast, R.C. (ed.), 1974. CRC Handbook of Chemistry and Physics. 55 edition, CRC Press, Cleveland.

  • Wexler, A.S., Kalaba, R.E., Marsh, D.J., 1991. Three-dimensional anatomy and renal concentrating mechanism. I. Modeling results. Am. J. Physiol. (Renal Fluid Electrolyte Physiol 29) 260, F368–F383.

    Google Scholar 

  • Wirz, H., Hargitay, B., Kuhn, W., 1951. Lokalisation des Konzentrierungsprozesses in der Niere durch direkte Kryoskopie. Helv. Physiol. Pharmacol. Acta. 9, 196–207.

    Google Scholar 

  • Xu, Y., Oliver, B., Bailly, P., Fischer, E., Ripoche, P., Cartron, J.P., Rondeau, E., 1997. Endothelial cells of the kidney vasa recta express the urea transporter hUT11. Kidney Int. 51, 138–146.

    Article  Google Scholar 

  • Yang, B., Bankir, L., 2005. Urea and urine concentrating ability: New insights from studies in mice. Am. J. Physiol. Renal. Physiol. 288, 881–896.

    Article  Google Scholar 

  • Yang, B., Bankir, L., Gillespie, A., Epstein, C.J., Verkman, A.S., 2002. Urea-selective concentrating defect in transgenic mice lacking urea transporter UT-B. J. Biol. Chem. 277(12), 10633–10637.

    Article  Google Scholar 

  • Zhang, W., Edwards, A., 2001. Transport of plasma proteins across vasa recta in the renal medulla. Am. J. Physiol. Renal. Physiol. 281, F278–F492.

    Google Scholar 

  • Zhang, W., Edwards, A., 2003. Theoretical effects of UTB urea transporters in the renal medullary microcirculation. Am. J. Physiol. Renal. Physiol. 285, F731–F747.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, Duke University, Box 90320, Durham, NC, 27708-0320, USA

    Anita T. Layton

Authors
  1. Anita T. Layton
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Anita T. Layton.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Layton, A.T. Role of UTB Urea Transporters in the Urine Concentrating Mechanism of the Rat Kidney. Bull. Math. Biol. 69, 887–929 (2007). https://doi.org/10.1007/s11538-005-9030-3

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11538-005-9030-3

Keywords

Search

Navigation