Modeling proximal tubule cell homeostasis: Tracking changes in luminal flow. Weinstein, A. & Sontag, E. Bulletin of Mathematical Biology, 71:1285-1322, 2009. abstract bibtex 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 optimal linear feedback that stabilizes Na+ flux, cell volume, and cell pH. This optimal feedback control is largely consigned to three physiologic variables, cell volume, cell electrical potential, and lateral intercellular hydrostatic pressure. Transport modulation by cell volume stabilizes cell volume; transport 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 Na+-3HCO_3- 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.
@ARTICLE{weinstein07,
AUTHOR = {A.M. Weinstein and E.D. Sontag},
JOURNAL = {Bulletin of Mathematical Biology},
TITLE = {Modeling proximal tubule cell homeostasis: Tracking
changes in luminal flow},
YEAR = {2009},
OPTMONTH = {},
OPTNOTE = {},
OPTNUMBER = {},
PAGES = {1285-1322},
VOLUME = {71},
PDF = {../../FTPDIR/weinstein_sontag_bulletin_math_biology_proximal_tubule_2009.pdf},
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 optimal linear feedback that
stabilizes Na+ flux, cell volume, and cell pH. This optimal feedback
control is largely consigned to three physiologic variables, cell
volume, cell electrical potential, and lateral intercellular
hydrostatic pressure. Transport modulation by cell volume stabilizes
cell volume; transport 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 Na+-3HCO_3- 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. }
}
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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 optimal linear feedback that stabilizes Na+ flux, cell volume, and cell pH. This optimal feedback control is largely consigned to three physiologic variables, cell volume, cell electrical potential, and lateral intercellular hydrostatic pressure. Transport modulation by cell volume stabilizes cell volume; transport 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 Na+-3HCO_3- 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. ","bibtex":"@ARTICLE{weinstein07,\n AUTHOR = {A.M. Weinstein and E.D. Sontag},\n JOURNAL = {Bulletin of Mathematical Biology},\n TITLE = {Modeling proximal tubule cell homeostasis: Tracking \n changes in luminal flow},\n YEAR = {2009},\n OPTMONTH = {},\n OPTNOTE = {},\n OPTNUMBER = {},\n PAGES = {1285-1322},\n VOLUME = {71},\n PDF = {../../FTPDIR/weinstein_sontag_bulletin_math_biology_proximal_tubule_2009.pdf},\n ABSTRACT = {During normal kidney function, there are are routinely \n wide swings in proximal tubule fluid flow and proportional changes in \n Na+ reabsorption across tubule epithelial cells. This \n \"glomerulotubular balance\" occurs in the absence of any substantial \n change in cell volume, and is thus a challenge to coordinate luminal \n membrane solute entry with peritubular membrane solute exit. In this \n work, linear optimal control theory is applied to generate a \n configuration of regulated transporters that could achieve this \n result. A previously developed model of rat proximal tubule \n epithelium is linearized about a physiologic reference condition; the \n approximate linear system is recast as a dynamical system; and a \n Riccati equation is solved to yield optimal linear feedback that \n stabilizes Na+ flux, cell volume, and cell pH. This optimal feedback \n control is largely consigned to three physiologic variables, cell \n volume, cell electrical potential, and lateral intercellular \n hydrostatic pressure. Transport modulation by cell volume stabilizes \n cell volume; transport modulation by electrical potential or \n interspace pressure act to stabilize Na+ flux and cell pH. This \n feedback control is utilized in a tracking problem, in which \n reabsorptive Na+ flux varies over a factor of two. The resulting \n control parameters consist of two terms, an autonomous term and a \n feedback term, and both terms include transporters on both luminal \n and peritubular cell membranes. 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