Math @ Duke

Publications [#287313] of Harold Layton
Papers Published
 Bruce Pitman, E; Zaritski, RM; Kesseler, KJ; Moore, LC; Layton, HE, Feedbackmediated dynamics in two coupled nephrons.,
Bulletin of Mathematical Biology, vol. 66 no. 6
,
pp. 14631492 [doi]
(last updated on 2019/06/17)
Abstract: Previously, we developed a dynamic model for the tubuloglomerular feedback (TGF) system in a single, shortlooped nephron of the mammalian kidney. In that model, a semilinear 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 limitcycle oscillations (LCO) in nephron fluid flow and chloride concentration can emerge for sufficiently large feedback gain magnitude and time delay. In this study, the singlenephron 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.


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