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

Abstract

mathematical model previously formulated by us predicts that limit-cycle oscillations (LCO) in nephron flow are mediated by tubuloglomerular feedback (TGF) and that the LCO arise from a bifurcation that depends heavily on the feedback gain magnitude, ␥, and on its relationship to a theoretically determined critical value of gain, ␥ c. In this study, we used that model to show how sustained perturbations in proximal tubule flow, a common experimental maneuver, can initiate or terminate LCO by changing the values of ␥ and ␥c, thus changing the sign of ␥ Ϫ ␥ c. This result may help explain experiments in which intratubular pressure oscillations were initiated by the sustained introduction or removal of fluid from the proximal tubule (Leyssac PP and Baumbach L. Acta Physiol Scand 117: 415-419, 1983). In addition, our model predicts that, for a range of TGF sensitivities, sustained perturbations that initiate or terminate LCO can yield substantial and abrupt changes in both distal NaCl delivery and NaCl delivery compensation, changes that may play an important role in the response to physiological challenge. kidney; renal hemodynamics; autoregulation; mathematical model; nonlinear dynamics THE TUBULOGLOMERULAR FEEDBACK (TGF) SYSTEM is a key moment-to-moment regulator of the single-nephron glomerular filtration rate (SNGFR). A large body of experimental and theoretical evidence indicates that TGF can mediate sustained, regular oscillations of 20-47 mHz in tubular flow, pressure, and intratubular thick ascending limb (TAL) NaCl concentration (4,6,7,12,18). These regular oscillations are called limit-cycle oscillations (LCO) because, after initiation, they tend to more and more closely approximate a fixed cycle, provided that system parameters do not change. Spontaneous LCO appear to occur in large numbers of nephrons, as they have been detected in recordings of renal blood flow and pressure taken in conscious, chronically instrumented dogs (8).A common and useful method of investigating TGF is to impose sustained perturbations of proximal tubule (PT) fluid flow in a freely flowing nephron where the TGF feedback loop is closed and functional (3,5,6,20,21,26). 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 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). A finding of fundamental importance is that the emergence of LCO depends on key TGF syst...

Multistable Dynamics Mediated by Tubuloglomerular Feedback in a Model of Coupled Nephrons

“…(3), at the steady-state operating point, (F op , C op ); and (ii) the nondimensionalized slope of the steady-state TAL tubular fluid chloride concentration S(x) alongside the MD (i.e., S (L), but in dimensionless form; see Appendix A). The gain magnitudes γ A and γ B characterize the strength of the feedback response (Layton et al, 1995;Oldson et al, 2003). We write "gain magnitude" because gain would be appropriately considered a negative quantity in a negative feedback system; however, for simplicity of exposition, we will frequently use "gain" and "gain magnitude" interchangeably to mean the absolute value of the gain.…”

Signal transduction in a compliant thick ascending limb

“…The dependence of waveform shape on mean TAL flow may be the source of the variable degree of distortion, relative to a sine wave, seen in experimental recordings of TGF-mediated oscillations. kidney; mathematical model; renal hemodynamics; sodium chloride transport; nonlinear system IN A SERIES OF STUDIES WE have used a mathematical model of the tubuloglomerular feedback (TGF) loop to propose plausible explanations for phenomena that have been reported in experimental studies and to predict phenomena that might be found in new experimental studies (23,24,28,29,30,31,32,34,36). Our mathematical model consists of simple components that have been individually well characterized in our publications.…”

Tubuloglomerular Feedback-Mediated Dynamics in Three Coupled Nephrons

“…The physiological significance could be that oscillations enhance renal sodium excretion (Layton et al, 2000 andOldson et al, 2003). This hypothesis is based on predictions that oscillations may enhance sodium delivery to the distal tubule and that oscillations limit the ability of the TGF system to compensate for perturbations in flow, e.g.…”