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Feedback-mediated dynamics in two coupled nephrons.

E Bruce Pitman1, Roman M Zaritski, Kevin J Kesseler

  • 1Department of Mathematics, State University of New York, Buffalo, NY 14260-2900, USA. pitman@buffalo.edu

Bulletin of Mathematical Biology
|November 4, 2004
PubMed
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Coupling two kidney nephrons enhances the likelihood of stable limit-cycle oscillations (LCO) in fluid flow and chloride concentration, especially when nephrons are similar. This occurs at lower feedback gains or shorter delays than in single nephrons.

Area of Science:

  • Renal physiology and biophysics
  • Mathematical modeling of biological systems
  • Nephron dynamics and tubuloglomerular feedback

Background:

  • Previous development of a dynamic model for the tubuloglomerular feedback (TGF) system in a single mammalian kidney nephron.
  • The single-nephron model utilized a hyperbolic partial differential equation to describe chloride transport in the thick ascending limb (TAL) and incorporated a time delay for glomerular filtration rate regulation.
  • Analysis of the single-nephron model revealed conditions for stable limit-cycle oscillations (LCO) in nephron fluid flow and chloride concentration.

Purpose of the Study:

  • To extend the single-nephron TGF model to a system of two coupled nephrons.
  • To investigate the conditions under which stable LCO emerge in coupled nephrons.
  • To determine how nephron coupling affects the emergence of LCO compared to uncoupled nephrons.

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Main Methods:

  • Extension of a previously developed dynamic model of the tubuloglomerular feedback (TGF) system from one to two coupled nephrons.
  • Mathematical analysis to derive explicit analytical conditions for bifurcation loci in two special cases: differing gains with identical delays, and differing delays with identical gains.
  • Comparison of LCO emergence conditions in the coupled two-nephron system versus the single-nephron model.

Main Results:

  • Stable limit-cycle oscillations (LCO) can emerge in the coupled two-nephron system under conditions of sufficiently large feedback gains and time delays.
  • The emergence of LCO in coupled nephrons can occur at lower feedback gain magnitudes or shorter time delays compared to a single, uncoupled nephron.
  • The likelihood of LCO is increased when the delays in coupled nephrons are sufficiently close.

Conclusions:

  • Coupling between nephrons can significantly influence the dynamics of the tubuloglomerular feedback system.
  • The study suggests that in vivo, coupling between sufficiently similar nephrons promotes the occurrence of stable limit-cycle oscillations.
  • These findings highlight the importance of considering inter-nephron interactions in understanding renal physiological regulation.