Bifurcation analysis of TGF-mediated oscillations in SNGFR

Abstract

Recent micropuncture studies in rats have demonstrated the existence of oscillatory states in nephron filtration mediated by tubuloglomerular feedback (TGF). We develop a minimal mathematical model of the TGF system, consisting of a first-order hyperbolic partial differential equation describing thick ascending limb (TAL) NaCl reabsorption and an empirical feedback relation. An analytic bifurcation analysis of this model provides fundamental insight into how oscillatory states depend on the physiological parameters of the model. In the special case of no solute backleak in the TAL, the emergence of oscillations explicitly depends on two nondimensional parameters. The first corresponds to the delay time of the TGF response across the juxtaglomerular apparatus, and the second corresponds to the product of the slope of the TGF response curve at the steady-state operating point and the space derivative of the steady-state NaCl concentration profile in the TAL at the macula densa. Numerical calculations for the case without TAL backleak are consistent with this result. Numerical simulation of the more general case with TAL backleak shows that the bifurcation analysis still provides useful predictions concerning nephron dynamics. With typical parameter values, the analysis predicts that the TGF system will be in oscillatory state. However, the system is near enough to the boundary of the nonoscillatory region so that small changes in parameter values could result in nonoscillatory behavior.