SPECTRAL PROPERTIES OF THE TUBULOGLOMERULAR FEEDBACK-SYSTEM

A simple mathematical model was used to investigate the spectral prope rties of the tubuloglomerular feedback (TGF) system. A perturbation, c onsisting of small-amplitude broadband forcing, was applied to simulat ed thick ascending limb (TAL) flow, and the resulting spectral respons e of the TGF pathway was assessed by computing a power spectrum from r esulting TGF-regulated TAL flow. Power spectra were computed for both open-and closed-feedback-loop cases. Open-feedback-loop power spectra are consistent with a mathematical analysis that predicts a nodal patt ern in TAL frequency response, with nodes corresponding; to frequencie s where oscillatory flow has a TAL transit time that equals the steady -state fluid transit time. Closed-feedback-loop spectra are dominated by the open-loop spectral response, provided that gamma, the magnitude of feedback gain, is less than the critical value gamma(c) required f or emergence of a sustained TGF-mediated oscillation. For gamma exceed ing gamma(c), closed-loop spectra have peaks corresponding to the fund amental frequency of the TGF-mediated oscillation and its harmonics. T he harmonics, expressed in a nonsinusoidal waveform for tubular flow, are introduced by nonlinear elements of the TGF pathway, notably TAL t ransit time and the TGF response curve. The effect of transit time on the flow waveform leads to crests that are broader than troughs and to an asymmetry in the magnitudes of increasing and decreasing slopes. F or feedback gain magnitude that is sufficiently large, the TGF respons e curve tends to give a square waveshape to the waveform. Published wa veforms and power spectra of in vivo TGF oscillations have features co nsistent with the predictions of this analysis.