TGF-mediated bifurcation in two coupled nephrons

Experiments have found synchronized oscillations of 20-50 mHz in proximal tubule flow in nephrons identified as arising from the same cortical radial artery (CRA). We use explicit analysis and numerical studies to investigate the properties, of a simple mathematical model that includes a representation of two nephrons arising from the same CRA. The model includes a representation of ascending limb dynamics, tubuloglomerular feed-back (TGF). and vascular coupling between the nephrons. As in single-nephron models, analysis shows that increasing the gain of the TGF loop beyond a critical value, or increasing the signal delay time at the macula densa, destabilizes a time-independent model solution and leads to sustained TGF-mediated oscillations in tubular flow. Analysis and numerical studies indicate that sustained oscillations in one nephron may induce sustained oscillations in the second nephron. For a physiologically relevant parameter range, the amplitude of the oscillations varies, with a long period, exemplifying the dynamics of "beats"' that arises in weakly coupled oscillators.