Modeling Proximal Tubule Cell Homeostasis: Tracking Changes in Luminal Flow

Abstract

During normal kidney function, there are are routinely 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 any substantial change in cell volume, and is thus a challenge to coordinate luminal membrane solute entry with peritubular membrane solute exit. 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 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 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. Overall, the increase in Na + flux is achieved with upregulation of luminal Na + /H + exchange and Na + -glucose cotransport, with increased peritubular 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 the cytoskeletal effects of luminal flow. Keywordscell volume regulation; cell pH regulation; proximal tubule; glomerulotubular balance Modeling proximal tubule cell homeostasis: tracking changes in luminal flowAll transporting epithelial cells routinely face the challenge of varying solute throughput, while avoiding lethal changes in cell volume or composition (Schultz, 1981;Schultz, 1992). In the proximal tubule of the kidney, this challenge presents itself with the tubular response to minuteby-minute variations in glomerular filtration (the delivered load to the tubule), for which solute NIH-PA Author ManuscriptNIH-PA Author Manuscript NIH-PA Author Manuscript and water reabsorption varies proportionally (Schnermann et al., 1968). This "glomerulotubular balance" derives from both peritubular capillary and luminal factors (Gertz and Boylan, 1973;Haberle and von Baeyer, 1983;Weinstein, 1990). The most important luminal factor is a direct effect of axial flow velocity on transport (Wilcox and Baylis, 1985;Romano et al., 1998), and along with its impact on sodium reabsorption, luminal flow has been found to i...

Regulation of glomerulotubular balance. II. Impact of angiotensin II on flow-dependent transport

“…In all of the steady-state models of the proximal tubule, achieving volume homeostasis in response to increased luminal entry has required activation of peritubular K ϩ -Cl Ϫ and/or Na ϩ -3HCO 3 Ϫ cotransporters, either by volume (51) or by other signals (54); increasing peritubular K ϩ conductance alone was not sufficient. To maintain cell volume homeostasis throughout transient changes in luminal flow, Weinstein and Sontag (52) suggested that a feed-forward signal from the luminal to the peritubular membrane would be required. It was envisioned that this signal would be transmitted by the actin cytoskeleton.…”

Cell Volume Regulation in the Proximal Tubule of Rat Kidney

“…In a series of studies based on control theory [29–32], Weinstein identified plausible mechanisms that would allow the proximal tubule cell to adapt to minute-by-minute variations in glomerular filtration without substantial changes in cell volume and composition. Simulations in which transport parameters were varied as a function of cell volume predicted that apical anion exchangers, basolateral Na + -dependent anion exchangers, and basolateral K + channels have very little homeostatic efficiency, whereas modulation of peritubular K + -Cl − and ${\text{Na}}^{+}-{\text{HCO}}_3^{-}$ cotransport dampens increases in cell volume without diminishing transcellular Na + transport [30].…”

Flow stimulated endocytosis in the proximal tubule

“…Apical microvilli on PT cells have been suggested to function as mechanosensors that transduce changes in FSS to regulate ion transporter trafficking and activity (1–4). For example, changes in GFR and the accompanying FSS and stretch lead to increases in Na + reabsorption mediated primarily by the insertion of active transporters into the luminal membrane (3, 5–7). Changes in actin dynamics are thought to play a role in this process; however the exact mechanism for how this leads to altered transporter distribution has not been determined.…”