Math @ Duke

Publications [#287297] of Harold Layton
Papers Published
 Layton, HE; Pitman, EB; Moore, LC, Instantaneous and steadystate gains in the tubuloglomerular feedback system,
American Journal of Physiology Renal Physiology, vol. 268 no. 1 371
(January, 1995),
pp. F163F174
(last updated on 2019/06/19)
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 TGFmediated oscillations. Mathematical modeling studies have shown that the openfeedbackloop 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 steadystate gain, a readily measurable quantity corresponding to the steadystate reduction in singlenephron glomerular filtration rate (SNGFR) subsequent to a sustained increase 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 steadystate and instantaneous openfeedbackloop 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 steadystate gain. With typical physiological parameters for the rat, calculations with a model previously devised by us show that the gains differ by 510%. Hence, experimental measurements of the steadystate 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.


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