INSTANTANEOUS AND STEADY-STATE GAINS IN THE TUBULOGLOMERULAR FEEDBACK-SYSTEM

The load of water and solute entering each nephron of the mammalian ki dney is regulated by the tubuloglomerular feedback (TGF) mechanism, a negative feedback loop. Experiments in rats have shown that key Variab les of this feedback system may exhibit TGF-mediated oscillations. Mat hematical modeling studies have shown that the open-feedback-loop gain is a crucial parameter for determining whether oscillations will emer ge. However, two different formulations of this gain have been used. T he first is the steady-state gain, a readily measurable quantity corre sponding to the steady-state reduction in single-nephron glomerular fi ltration rate (SNGFR) subsequent to a sustained increase in ascending limb flow rate. The second is an instantaneous gain, a variable arisin g from theoretical considerations corresponding to the maximum reducti on in SNGFR resulting from an instantaneous shift of the ascending lim b flow column, with the assumption that the SNGFR response is also ins tantaneous. Here we show by an analytic argument how the steady-state and instantaneous open-feedback-loop gains for the ascending limb are related. In the case of no solute backleak into the ascending limb, th e two formulations of gain are equivalent; however, in the presence of solute backleak, the instantaneous gain is larger in magnitude than t he steady-state gain. With typical physiological parameters for the ra t, calculations with a model previously devised by us show that the ga ins differ by 5-10%. Hence, experimental measurements of the steady-st ate gain may provide useful lower-bound estimates of the instantaneous gain of the feedback system in the normal rat. However, the gains may diverge significantly in pathophysiological states where ascending li mb transport is compromised by abnormally high NaCl permeability.