Instantaneous and steady-state gains in the tubuloglomerular feedback system

Abstract

The load of water and solute entering each nephron of the mammalian kidney is regulated by the tubuloglomerular feedback (TGF) mechanism, a negative feedback loop. Experiments in rats have shown that key variables of this feedback system may exhibit TGF-mediated oscillations. Mathematical modeling studies have shown that the open-feedback-loop gain is a crucial parameter for determining whether oscillations will emerge. However, two different formulations of this gain have been used. The first is the steady-state gain, a readily measurable quantity corresponding to the steady-state reduction in single-nephron glomerular filtration rate (SNGFR) subsequent to a sustained increased in ascending limb flow rate. The second is an instantaneous gain, a variable arising from theoretical considerations corresponding to the maximum reduction in SNGFR resulting from an instantaneous shift of the ascending limb flow column, with the assumption that the SNGFR response is also instantaneous. 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, the two formulations of gain are equivalent; however, in the presence of solute backleak, the instantaneous gain is larger in magnitude than the steady-state gain. With typical physiological parameters for the rat, calculations with a model previously devised by us show that the gains differ by 5-10%. Hence, experimental measurements of the steady-state 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 limb transport is compromised by abnormally high NaCl permeability.