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

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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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Authors and Affiliations

  1. Department of Mathematics, Duke University, Durham, NC, 27708-0320, USA

    Anita T. Layton & Harold E. Layton

  2. Department of Physiology and Biophysics, State University of New York, Stony Brook, NY, 11794-8661, USA

    Leon C. Moore

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  1. Anita T. Layton
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Layton, A.T., Moore, L.C. & Layton, H.E. Multistable Dynamics Mediated by Tubuloglomerular Feedback in a Model of Coupled Nephrons. Bull. Math. Biol. 71, 515–555 (2009). https://doi.org/10.1007/s11538-008-9370-x

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