A mathematical model of the urine concentrating mechanism in the rat renal medulla. II. Functional implications of three-dimensional architecture.
In a companion study [Layton AT. A mathematical model of the urine concentrating mechanism in the rat renal medulla. I. Formulation and base-case results. Am J Physiol Renal Physiol. (First published November 10, 2010). 10.1152/ajprenal.00203.2010] a region-based mathematical model was formulated for the urine concentrating mechanism in the renal medulla of the rat kidney. In the present study, we investigated model sensitivity to some of the fundamental structural assumptions. An unexpected finding is that the concentrating capability of this region-based model falls short of the capability of models that have radially homogeneous interstitial fluid at each level of only the inner medulla (IM) or of both the outer medulla and IM, but are otherwise analogous to the region-based model. Nonetheless, model results reveal the functional significance of several aspects of tubular segmentation and heterogeneity: 1) the exclusion of ascending thin limbs that reach into the deep IM from the collecting duct clusters in the upper IM promotes urea cycling within the IM; 2) the high urea permeability of the lower IM thin limb segments allows their tubular fluid urea content to equilibrate with the surrounding interstitium; 3) the aquaporin-1-null terminal descending limb segments prevent water entry and maintain the transepithelial NaCl concentration gradient; 4) a higher thick ascending limb Na(+) active transport rate in the inner stripe augments concentrating capability without a corresponding increase in energy expenditure for transport; 5) active Na(+) reabsorption from the collecting duct elevates its tubular fluid urea concentration. Model calculations predict that these aspects of tubular segmentation and heterogeneity promote effective urine concentrating functions.
Department of Mathematics, Duke University, Durham, NC 27708-0320, USA. alayton@math.duke.edu
Anita T
AT
Layton
D000818:Animals; D051398:Aquaporin 1 / Q000032:analysis / Q000378:metabolism; D001693:Biological Transport, Active / Q000502:physiology; D003198:Computer Simulation; D007671:Kidney Concentrating Ability / Q000502:physiology*; D007679:Kidney Medulla / Q000033:anatomy & histology* / Q000502:physiology*; D008138:Loop of Henle / Q000502:physiology; D008954:Models, Biological; D009994:Osmolar Concentration; D051381:Rats; D012965:Sodium Chloride / Q000378:metabolism; D014508:Urea / Q000378:metabolism
C496022:Aqp1 protein, rat; D051398:Aquaporin 1; D012965:Sodium Chloride; D014508:Urea