Multistable Dynamics Mediated by Tubuloglomerular Feedback in a Model of Coupled Nephrons |
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Authors: | Anita T Layton Leon C Moore Harold E Layton |
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Institution: | (1) Department of Mathematics, Duke University, Durham, NC 27708-0320, USA;(2) Department of Physiology and Biophysics, State University of New York, Stony Brook, NY 11794-8661, USA |
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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 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. |
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Keywords: | Renal hemodynamic control Spontaneously hypertensive rat Negative feedback loop Delay differential equation Nonlinear dynamics |
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