Biomathematics Seminar
Tuesday 1/30/07

Speaker: Anita Layton
Assistant Professor
Department of Mathematics, Duke University

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

Abstract:

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 investigation was motivated by a modeling study which predicts that 
NaCl backleak from a nephron's thick ascending limb permits multiple 
stable oscillatory states that are mediated by TGF (Am. J. Physiol. Renal 
Physiol. 291: F79-F97, 2006). In that study, a characteristic equation 
obtained via linearization from a single-nephron model having NaCl 
backleak, in conjunction with numerical solutions of the full, nonlinear 
model equations for two and three coupled neph rons, was used in the 
formulation of a comprehensive, multifaceted hypothesis for the emergence 
of complex dynamics in SHR. In the present study we have derived a 
characteristic equation for a model of an arbitrary 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 number of differing behaviors in these regions. Some behaviors 
are markedly irregular and exhibit a degree of spectral complexity that is 
consistent with physiologic experiments in SHR. Effects of coupling and 
irregular oscillations on fluid and NaCl delivery are also discussed.