Multistable dynamics mediated by tubuloglomerular feedback in a model of coupled nephrons.

Journal Article

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.

Full Text

Duke Authors

Cited Authors

  • Layton, AT; Moore, LC; Layton, HE

Published Date

  • April 2009

Published In

Volume / Issue

  • 71 / 3

Start / End Page

  • 515 - 555

PubMed ID

  • 19205808

Pubmed Central ID

  • 19205808

Electronic International Standard Serial Number (EISSN)

  • 1522-9602

International Standard Serial Number (ISSN)

  • 0092-8240

Digital Object Identifier (DOI)

  • 10.1007/s11538-008-9370-x


  • eng