Bulletin of Mathematical Biology

, Volume 66, Issue 6, pp 1463–1492 | Cite as

Feedback-mediated dynamics in two coupled nephrons

  • E. Bruce Pitman
  • Roman M. Zaritski
  • Kevin J. Kesseler
  • Leon C. Moore
  • Harold E. Layton
Article

Abstract

Previously, we developed a dynamic model for the tubuloglomerular feedback (TGF) system in a single, short-looped nephron of the mammalian kidney. In that model, a semi-linear hyperbolic partial differential equation was used to represent two fundamental processes of solute transport in the nephron’s thick ascending limb (TAL): chloride advection by fluid flow along the TAL lumen and transepithelial chloride transport from the lumen to the interstitium. An empirical function and a time delay were used to relate glomerular filtration rate to the chloride concentration at the macula densa of the TAL. Analysis of the model equations indicated that stable limit-cycle oscillations (LCO) in nephron fluid flow and chloride concentration can emerge for sufficiently large feedback gain magnitude and time delay. In this study, the single-nephron model was extended to two nephrons, which were coupled through their filtration rates. Explicit analytical conditions were obtained for bifurcation loci corresponding to two special cases: (1) identical time delays but differing feedback gains, and (2) identical gains but differing delays. Similar to the case of a single nephron, our analysis indicates that stable LCO can emerge in coupled nephrons for sufficiently large gains and delays. However, these LCO may emerge at lower values of the feedback gain, relative to a single (i.e., uncoupled) nephron, or at shorter delays, provided the delays are sufficiently close. These results suggest that, in vivo, if two nephrons are sufficiently similar, then coupling will tend to increase the likelihood of LCO.

Keywords

Sustained Oscillation Bifurcation Locus Thick Ascend Limb Tubuloglomerular Feedback Macula Densa 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Society for Mathematical Biology 2004

Authors and Affiliations

  • E. Bruce Pitman
    • 1
  • Roman M. Zaritski
    • 1
  • Kevin J. Kesseler
    • 2
  • Leon C. Moore
    • 3
  • Harold E. Layton
    • 2
  1. 1.Department of MathematicsState University of New YorkBuffaloUSA
  2. 2.Department of MathematicsDuke UniversityDurhamUSA
  3. 3.Department of Physiology and BiophysicsState University of New YorkStony BrookUSA

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