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The TGF system is a key regulator of filtration rate and of
water and electrolyte delivery to the distal nephron.
In the 1980's, experiments in rats by Leyssac and colleagues
demonstrated that nephron flow and related variables
may exhibit regular oscillations with a period of ~30 s.
Mathematical models have indicated that these regular oscillations
are TGF-mediated and that they arise
from a bifurcation: if feedback-loop gain is sufficiently
large, and if the delay in TGF signal transmission at the
juxtaglomerular apparatus is sufficiently long,
then the stable state of the system
is a regular oscillation and not a time-independent steady state.
Previous modeling studies have indicated that two dimensionless parameters, \gamma and \tau, play a key role in determining the stable state of the TGF system. The feedback-loop gain \gamma is the product of two factors: (1) the slope of the TGF response curve, and (2) the magnitude of the luminal [Cl-] profile alongside the macula densa. The delay parameter \tau is the ratio of two delays: \tau = D/T, where D is the delay in TGF signal transmission across the juxtaglomerular apparatus and T is the steady-state transit time of fluid through the thick ascending limb. Analysis of the model leads to a characteristic equation and a bifurcation diagram, which predict stable and oscillatory solutions in different parameter regimes.
Using our model, we plan to explain the irregular oscillations exhibited by the TGF system in hypertensive rats. These oscillations appear to have characteristics of deterministic chaos. Already, our model has predicted that coupled nephrons (i.e., nephrons that have the capability to influence each other's glomerular filtration rate) having sufficiently different parameters can produce a variety of complex oscillatory waveforms. The waveforms and power spectra arising in our model of coupled nephrons are similar to complex waveforms and corresponding power spectra from hypertensive rats. Thus, we hypothesize that irregular oscillations in hypertensive rats are attributable, at least in part, to mixed-mode oscillations in coupled nephrons. |
