A Multiscale Model of the Thick Ascending Limb

Abstract

A multiscale, cell-based mathematical model of the thick ascending limb (TAL) was implementedand used to estimate the efficiency of Na<super>+</super> transport along the TAL, to examinewhat determines transport efficiency, and to study the dynamical properties of the TAL.The TAL model consists of epithelial cell models that represent all major solutes and transportpathways. The model equations are based on mass conservation and electroneutralityconstraints. Empirical descriptions of cell volume regulation (CVR), pH control, and tubuloglomerularfeedback (TGF) system are implemented in the model. Transport efficiencywas calculated as the ratio of total net Na<super>+<\super> transport to transcellular Na<super>+<\super> transport. The results show that: 1) Because the function of the TAL segment is to generate dilute tubularfluid, the transepithelial [Na<super>+<\super>] gradient that is created substantially reduces transportefficiency. This factor calls into question the widely-held notion that a substantial fractionof TAL Na<super>+<\super> reabsorption occurs by passive paracellular diffusion secondary to apicalmembrane K<super>+<\super> cycling. 2) CVR responses in individual autonomous TAL cells limitsNa<super>+<\super> transport by each cell such that the workload distribution along the TAL segment issufficiently uniform to result in more efficient transport. In essence, a self-organizationprocess that raises transport efficiency emerges from the CVR responses in the ensembleof TAL cells. 3) At the segmental level, the TGF system acts synergistically with the CVRmechanism to increase transport efficiency by regulating tubular fluid inflow such that theoutflow Na<super>+<\super> and Cl<super>-<\super> concentrations are maintained well above the limiting static-head values where there is no net transport and zero efficiency. Further, TGF restrains tubularfluid inflow to levels that are consistent with the reabsorptive capacity of the TAL, therebyensuring that the effluent is adequately dilute for the operation of the urine concentratingmechanism. 4) Together, the CVR responses and the regulation of TAL flow by TGF resultin a quasi-uniform distribution of NaCl transport and an axial [Cl] gradient sufficientlysteep to yield a TGF system gain consistent with experimental data. This suggests thatTGF is a self-optimizing feedback system, in that it drives the TAL towards a state that ensuresa high feedback gain. 5) The apical membrane cycling of NH+4 through K<super>+<\super> channels,the NKCC2 transporter, and the NHE exchanger prevents luminal potassium depletion andsubstantially increases Na+ uptake into the TAL cells. Without NH+4 cycling, the TALmodel predicts that the dilutional capacity of the TAL will be severely compromised. 6)When TAL inflow oscillates, the TAL segment acts as a nonlinear low-pass filter with acharacteristic harmonic structure that reflects the establishment of standing waves of Na<super>+<\super>and Cl<super>-<\super> in the lumen of the TAL. This finding is consistent with both earlier modelingefforts and experimental data. In addition, the TAL cells themselves are predicted to act asmulti-input/multi-output nonlinear filters. 7) When the TGF system is active and its gainexceeds a critical value, limit cycle oscillations in tubular fluid flow emerge, a behavior thatis consistent with experimental observations.