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Modeling proximal tubule cell homeostasis: tracking changes in luminal flow. (English) Zbl 1171.92018
Summary: During normal kidney function, there are routinely wide swings in proximal tubule fluid flow and proportional changes in \(\text{Na}^{+}\) reabsorption across tubule epithelial cells. This “glomerulotubular balance” occurs in the absence of any substantial change in cell volume, and is thus a challenge to coordinate luminal membrane solute entries with peritubular membrane solute exits. In this work, linear optimal control theory is applied to generate a configuration of regulated transporters that could achieve this result. A previously developed model of rat proximal tubule epithelium is linearized about a physiologic reference condition; the approximate linear system is recast as a dynamical system, and a Riccati equation is solved to yield the optimal linear feedback that stabilizes \(\text{Na}^{+}\) flux, cell volume, and cell pH.
The first observation is that optimal feedback control is largely consigned to three physiologic variables: cell volume, cell electrical potential, and lateral intercellular hydrostatic pressure. Parameter modulation by cell volume stabilizes cell volume; parameter modulation by electrical potential or interspace pressure act to stabilize \(\text{Na}^{+}\) flux and cell pH. This feedback control is utilized in a tracking problem, in which reabsorptive \(\text{Na}^{+}\) flux varies over a factor of two, in order to represent a substantial excursion of glomerulotubular balance. The resulting control parameters consist of two terms, an autonomous term and a feedback term, and both terms include transporters on both luminal and peritubular cell membranes.
Overall, the increase in \(\text{Na}^{+}\) flux is achieved with upregulation of luminal \(\text{Na}^{+}/\text{H}^{+}\) exchange and \(\text{Na}^{+}\)-glucose cotransport, with increased peritubular \(N\text{Na}^{+}-3\text{HCO}_{3}^{-}\) and \(\text{K}^{+}-\text{Cl}^{-}\) cotransport, and with increased \(\text{Na}^{+}, \text{K}^{+}\)-ATPase activity. The configuration of activated transporters emerges as a testable hypothesis of the molecular basis for glomerulotubular balance. It is suggested that the autonomous control component at each cell membrane could represent the cytoskeletal effects of luminal flow.

MSC:
92C30 Physiology (general)
92C35 Physiological flow
93B52 Feedback control
93C95 Application models in control theory
92-08 Computational methods for problems pertaining to biology
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