Multistable dynamics mediated by tubuloglomerular feedback in a model of coupled nephrons.
To help elucidate the causes of irregular tubular flow oscillations found in the nephrons of spontaneously hypertensive rats (SHR), we have conducted a bifurcation analysis of a mathematical model of two nephrons that are coupled through their tubuloglomerular feedback (TGF) systems. This analysis was motivated by a previous modeling study which predicts that NaCl backleak from a nephron's thick ascending limb permits multiple stable oscillatory states that are mediated by TGF (Layton et al. in Am. J. Physiol. Renal Physiol. 291:F79-F97, 2006); that prediction served as the basis for a comprehensive, multifaceted hypothesis for the emergence of irregular flow oscillations in SHR. However, in that study, we used a characteristic equation obtained via linearization from a single-nephron model, in conjunction with numerical solutions of the full, nonlinear model equations for two and three coupled nephrons. In the present study, we have derived a characteristic equation for a model of any finite number of mutually coupled nephrons having NaCl backleak. Analysis of that characteristic equation for the case of two coupled nephrons has revealed a number of parameter regions having the potential for differing stable dynamic states. Numerical solutions of the full equations for two model nephrons exhibit a variety of behaviors in these regions. Some behaviors exhibit a degree of complexity that is consistent with our hypothesis for the emergence of irregular oscillations in SHR.
Layton
Anita T
AT
Department of Mathematics, Duke University, Durham, NC 27708-0320, USA. alayton@math.duke.edu
Moore
Leon C
LC
Layton
Harold E
HE
D000818:Animals; D001683:Biological Clocks / Q000502:physiology; D003198:Computer Simulation; D005246:Feedback / Q000502:physiology; D008954:Models, Biological; D009399:Nephrons / Q000502:physiology*; D051381:Rats; D011918:Rats, Inbred SHR