Signal transduction in a compliant short loop of Henle

Abstract

To study the transformation of fluctuations in filtration rate into tubular fluid chloride concentration oscillations alongside the macula densa, we have developed a mathematical model for tubuloglomerular feedback (TGF) signal transduction along the pars recta, the descending limb, and the thick ascending limb of a short-looped nephron. The model tubules are assumed to have compliant walls and thus a tubular radius that depends on the transmural pressure difference. Previously it has been predicted that TGF transduction by the thick ascending limb (TAL) is a generator of nonlinearities: if a sinusoidal oscillation is added to a constant TAL flow rate, then the time required for a fluid element to traverse the TAL is oscillatory in time but nonsinusoidal. The results from the new model simulations presented here predict that TGF transduction by the loop of Henle is also, in the same sense, a generator of nonlinearities. Thus this model predicts that oscillations in tubular fluid alongside the macula densa will be nonsinusoidal and will exhibit harmonics of sinusoidal perturbations of pars recta flow. Model results also indicate that the loop acts as a low-pass filter in the transduction of the TGF signal.

Modeling the effects of positive and negative feedback in kidney blood flow control

“…3(e)). These results are consistent with previous modeling studies (Ford Versypt et al, 2015; Layton et al, 1991, 2006; Ryu and Layton, 2012; Layton et al, 2012). …”

Control and Modulation of Fluid Flow in the Rat Kidney

“…To model hemodynamics control in the rat kidney, we developed a model that combines: (i) an afferent arteriole model previously developed by us [29]; (ii) a glomerular filtration model developed by Deen et al [5]; (iii) a renal tubule model previously developed by us [17]. A schematic diagram for the combined model is given in Fig.…”

“…In the case of spontaneously hypertensive rats, TGF-mediated oscillations can be irregular and appear to have characteristics of chaos [9, 32]. We have previously studied the signal transduction process along the loop of Henle [16, 17]. That transduction process involves the transformation of variations in tubular fluid flow rate into chloride ion concentration variations in tubular fluid alongside the macula densa.…”

Mathematical modeling of renal hemodynamics in physiology and pathophysiology

“…Motivated by the observation that tubular fluid [Cl − ], the key signal for TGF, changes most substantially along the thick ascending limb of the loop of Henle, Layton and co-workers developed a family of TGF models that represent tubular transport in more detail [42, 43, 44, 45, 46, 47, 48, 49]. This class of models explicitly represent tubular fluid and solute reasborption along the thick ascending limb; more recently these models have been extended to include the representation of the descending limb and proximal tubule [50, 51, 52]. Conservation of Cl − along the thick ascending limb is given by $$\pi r_T^2\left(x\right)\frac{\partial }{\partial t}{C}_T=-Q_T\left(t\right)\frac{\partial }{\partial x}{C}_T-2\pi r_{\mathrm{ss}}\left(x\right)true(\frac{V_{\max }{C}_T}{K_{\mathrm{normalM}}+C_T}+\kappa true(C_T-C_{\mathrm{ext}}\left(x\right)true)true)$$ where C T is tubular fluid [Cl − ], C ext is interstitial fluid [Cl − ], Q T is volume flow, r T is tubular radius, and r ss is the steady-state tubular radius.…”