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Heterodyning in Tubuloglomerular Feedback Induced Oscillations in Coupled Model Nephrons

In each nephron of the mammalian kidney, a negative feedback mechanism, tubuloglomerular feedback (TGF), participates in the regulation of the glomerular filtration rate. In a previous study, we used a mathematical model to predict the effects of coupling between the TGF systems of two short‐looped rat nephrons (Bull. Math. Biol. 66(6): 1463–1492, 2004). That study predicted parameter regions in which a perturbation of a time‐independent steady state results in a transition to sustained and stable oscillations in the glomerular filtration rate and thus oscillations in nephron tubular flow. These oscillations were predicted to arise for sufficiently large TGF gains and for sufficiently long time delays in TGF response. In the present study, we have used the same two nephron model to investigate how the oscillations are affected by varying time delays in TGF response. We found that when the TGF gains are equal and the TGF delays are sufficiently close, the oscillations in the two model nephrons synchronize: they have identical fundamental frequencies and they oscillate in phase. However, when the delays differ sufficiently, the oscillations in the two model nephrons have differing fundamental frequencies and may exhibit complex behaviors. Power spectra computed from time series generated by the model reveal both harmonic and heterodyne frequencies. These model results may help explain power spectra obtained in experimental studies of rat kidneys: in both normotensive rats and spontaneously hypertensive rats the power spectra frequently exhibit power at non‐fundamental frequencies.