Mathematical Modeling of Renal Function: Fluid dilution and efficiency of Na+ transport in a mathematical model of a thick ascending limb cell

摘要

Thick ascending limb (TAL) cells are capable of reducing tubular fluid Na⁺ concentration to as low as ∼25 mM, and yet they are thought to transport Na⁺ efficiently owing to passive paracellular Na⁺ absorption. Transport efficiency in the TAL is of particular importance in the outer medulla where O2 availability is limited by low blood flow. We used a mathematical model of a TAL cell to estimate the efficiency of Na⁺ transport and to examine how tubular dilution and cell volume regulation influence transport efficiency. The TAL cell model represents 13 major solutes and the associated transporters and channels; model equations are based on mass conservation and electroneutrality constraints. We analyzed TAL transport in cells with conditions relevant to the inner stripe of the outer medulla, the cortico-medullary junction, and the distal cortical TAL. At each location Na⁺ transport efficiency was computed as functions of changes in luminal NaCl concentration ([NaCl]), [K⁺], [NH4⁺], junctional Na⁺ permeability, and apical K⁺ permeability. Na⁺ transport efficiency was calculated as the ratio of total net Na⁺ transport to transcellular Na⁺ transport. Transport efficiency is predicted to be highest at the cortico-medullary boundary where the transepithelial Na⁺ gradient is the smallest. Transport efficiency is lowest in the cortex where luminal [NaCl] approaches static head.