Modeling Proximal Tubule Cell Homeostasis: Tracking Changes in Luminal Flow

Abstract

Normally, there are wide swings in proximal tubule fluid flow and proportional changes in Na reabsorption across tubule epithelial cells. This “glomerulotubular balance” occurs in the absence of substantial change in cell volume, and is a challenge to coordinate luminal solute entry with peritubular solute exit. In this work, linear optimal control theory is applied to generate a configuration of regulated transporters that could achieve this result. A model of rat proximal tubule epithelium is linearized about a 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 Na flux, cell volume, and cell pH. The first observation is that optimal feedback control is largely consigned to three 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 stabilizes Na flux and cell pH. This feedback control is utilized in a tracking problem, in which reabsorptive Na flux varies over a factor of two. 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. The increase in Na flux is achieved with upregulation of luminal Na/H exchange and Na‐glucose cotransport, with increased peritubular Na‐3HCO3 and K‐Cl cotransport, and with increased Na,K‐ATPase activity. The configuration of activated transporters emerges as testable hypothesis of the molecular basis for glomerulotubular balance. It is suggested that the autonomous control component at each cell membrane could represent cytoskeletal effects of luminal flow. Supported by NIH RO1‐DK‐29857.