Spectral properties of the tubuloglomerular feedback system

Abstract

A simple mathematical model was used to investigate the spectral properties of the tubuloglomerular feedback (TGF) system. A perturbation, consisting of small-amplitude broad-band forcing, was applied to simulated thick ascending limb (TAL) flow, and the resulting spectral response of the TGF pathway was assessed by computing a power spectrum from resulting 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 pattern in TAL frequency response, with nodes corresponding to frequencies 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 γ, the magnitude of feedback gain, is less than the critical value γc required for emergence of a sustained TGF-mediated oscillation. For γ exceeding γc, closed-loop spectra have peaks corresponding to the fundamental frequency of the TGF-mediated oscillation and its harmonics. The harmonics, expressed in a nonsinusoidal waveform for tubular flow, are introduced by nonlinear elements of the TGF pathway, notably TAL transit 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. For feedback gain magnitude that is sufficiently large, the TGF response curve tends to give a square waveshape to the waveform. Published waveforms and power spectra of in vivo TGF oscillations have features consistent with the predictions of this analysis.

Effect of sustained flow perturbations on stability and compensation of tubuloglomerular feedback

“…This characteristic equation generalizes previous versions (12,15) by including the effect of F op 1; previously, we assumed F op ϭ 1 so that F op did not appear. The method of derivation of the characteristic equation was explained previously (12,13,22).…”

“…Second, we do not know how PT transepithelial transport may be affected by TGF-mediated flow oscillations, which have short periods relative to the time intervals used in steady-state measurements. In contrast, both experimental and theoretical studies indicate that the TAL has a major influence on the dynamic behavior of the TGF loop in its action as a transducer of flow changes into concentration changes (6,15).…”

“…In our previous model investigations (12,13,15,22), F op was always set to the (nondimensional) base-case value of 1. Thus F op did not appear in the earlier versions of the characteristic equation, and the steadystate concentration profile S (which depends on F op ) was a fixed function.…”

“…Using this technique, Leyssac and collaborators (5,17,18) have demonstrated that LCO can be initiated or extinguished in halothane-anesthetized rats by insertion or removal of PT fluid, findings that indicate that PT fluid flow can have a substantial effect on the stability of the TGF system. Some insight into the basis of this phenomenon is provided by our previous investigations of the TGF-mediated LCO (12)(13)(14)(15)(16)22). These modeling studies indicate that LCO will emerge for sufficiently large feedback loop gain magnitude (12), that the parameter regime that supports LCO may overlap the parameter regime of normal TGF operation, that a gain magnitude near that needed for LCO will produce maximal feedback compensation (16), and that LCO may augment NaCl delivery to the distal nephron (16).…”

Oscillating Cortical Thick Ascending Limb Cells at the Juxtaglomerular Apparatus

“…5 In these studies, we found that activation of the calcium-sensing receptor produced increases in Ca Interestingly, the frequency of oscillations in perimacular cTAL cell [Ca 2ϩ ] i is remarkably close to that of TGF-dependent oscillations in tubular fluid flow and renal blood flow in anesthetized animals. [12][13][14][15][16][17] We do not have evidence that the increases in DT [Ca 2ϩ ] i contributed to or were associated with the activation of afferent arteriole smooth muscle cell [Ca 2ϩ ] I ; however, these new findings are at least suggestive and should stimulate future research efforts in understanding communication processes between tubule and glomerular structures.…”