A multiscale model of the thick ascending limb
by Nieves-Gonzalez, Aniel, Ph.D., STATE UNIVERSITY OF NEW YORK AT STONY BROOK, 2010, 132 pages; 3444166

Abstract:

A multiscale, cell-based mathematical model of the thick ascending limb (TAL) was implemented and used to estimate the efficiency of Na+ transport along the TAL, to examine what 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 transport pathways. The model equations are based on mass conservation and electroneutrality constraints. Empirical descriptions of cell volume regulation (CVR), pH control, and tubuloglomerular feedback (TGF) system are implemented in the model. Transport efficiency was calculated as the ratio of total net Na+ transport to transcellular Na+ transport. The results show that: (1) Because the function of the TAL segment is to generate dilute tubular fluid, the transepithelial [Na+] gradient that is created substantially reduces transport efficiency. This factor calls into question the widely-held notion that a substantial fraction of TAL Na+ reabsorption occurs by passive paracellular diffusion secondary to apical membrane K+ cycling. (2) CVR responses in individual autonomous TAL cells limits Na+ transport by each cell such that the workload distribution along the TAL segment is sufficiently uniform to result in more efficient transport. In essence, a self-organization process that raises transport efficiency emerges from the CVR responses in the ensemble of TAL cells. (3) At the segmental level, the TGF system acts synergistically with the CVR mechanism to increase transport efficiency by regulating tubular fluid inflow such that the outflow Na + and Cl concentrations are maintained well above the limiting static-head values where there is no net transport and zero efficiency. Further, TGF restrains tubular fluid inflow to levels that are consistent with the reabsorptive capacity of the TAL, thereby ensuring that the effluent is adequately dilute for the operation of the urine concentrating mechanism. (4) Together, the CVR responses and the regulation of TAL flow by TGF result in a quasi-uniform distribution of NaCl transport and an axial [Cl] gradient sufficiently steep to yield a TGF system gain consistent with experimental data. This suggests that TGF is a self-optimizing feedback system, in that it drives the TAL towards a state that ensures a high feedback gain. (5) The apical membrane cycling of [special characters omitted] through K+ channels, the NKCC2 transporter, and the NHE exchanger prevents luminal potassium depletion and substantially increases Na+ uptake into the TAL cells. Without [special characters omitted] cycling, the TAL model 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 a characteristic harmonic structure that reflects the establishment of standing waves of Na+ and Cl in the lumen of the TAL. This finding is consistent with both earlier modeling efforts and experimental data. In addition, the TAL cells themselves are predicted to act as multi-input/multi-output nonlinear filters. (7) When the TGF system is active and its gain exceeds a critical value, limit cycle oscillations in tubular fluid flow emerge, a behavior that is consistent with experimental observations.

 
AdvisersLeon C. Moore; David Green
SchoolSTATE UNIVERSITY OF NEW YORK AT STONY BROOK
SourceDAI/B 72-05, p. , Mar 2011
Source TypeDissertation
SubjectsApplied mathematics; Physiology
Publication Number3444166
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