Acid/base Transport in the Inner Medullary Collecting Duct of the Rat
Catherine
Lloyd
Bioengineering Institute, University of Auckland
Model Status
This CellML model variant describes the renal H+/K+ ATPase.
Model Structure
ABSTRACT: A mathematical model of the inner medullary collecting duct (IMCD) of the rat has been developed that is suitable for simulating luminal buffer titration and ammonia secretion by this nephron segment. Luminal proton secretion has been assigned to an H-K-ATPase, which has been represented by adapting the kinetic model of the gastric enzyme by Brzezinski et al. (P. Brzezinski, B. G. Malmstrom, P. Lorentzon, and B. Wallmark. Biochim. Biophys. Acta 942: 215-219, 1988). In shifting to a 2 H+:1 ATP stoichiometry, the model enzyme can acidify the tubule lumen approximately 3 pH units below that of the cytosol, when luminal K+ is in abundance. Peritubular base exit is a combination of ammonia recycling and HCO3- flux (either via Cl-/HCO3- exchange or via a Cl- channel). Ammonia recycling involves NH4(+) uptake on the Na-K-ATPase followed by diffusive NH3 exit [S. M. Wall. Am. J. Physiol. 270 (Renal Physiol. 39): F432-F439, 1996]; model calculations suggest that this is the principal mode of base exit. By virtue of this mechanism, the model also suggests that realistic elevations in peritubular K+ concentration will compromise IMCD acid secretion. Although ammonia recycling is insensitive to carbonic anhydrase (CA) inhibition, the base exit linked to HCO3- flux provides a CA-sensitive component to acid secretion. In model simulations, it is observed that increased luminal NaCl entry increases ammonia cycling but decreases peritubular Cl-/HCO3- exchange (due to increased cell Cl-). This parallel system of peritubular base exit stabilizes acid secretion in the face of variable Na+ reabsorption.
The complete original paper reference is cited below:
A mathematical model of the inner medullary collecting duct of the rat: acid/base transport, Alan M. Weinstein, 1998,
American Journal of Physiology
, 274(5 Pt 2), F856-67.
PubMed ID: 6496750
pathway_rendering
Conventional rendering of the renal H-K-ATPase adapted from the gastric H-K-ATPase model. This model has a stoichiometry of two H
+
and two K
+
per ATP. E
1
and E
2
are the cytosolic- and luminal-facing enzymes, respectively.
$\frac{d \mathrm{K2\_E1}}{d \mathrm{time}}=\mathrm{k9}\mathrm{K2\_E2}+\mathrm{k1\_}\mathrm{K2\_E1\_ATP}-\mathrm{k9\_}\mathrm{K2\_E1}+\mathrm{k1}\mathrm{ATP}\mathrm{K2\_E1}$
$\frac{d \mathrm{K2\_E1\_ATP}}{d \mathrm{time}}=\mathrm{k1}\mathrm{ATP}\mathrm{K2\_E1}+\mathrm{k11}\mathrm{K2\_E2\_ATP}+\mathrm{k2a\_}K\mathrm{K\_E1\_ATP}-\mathrm{k11\_}\mathrm{K2\_E1\_ATP}+\mathrm{k1\_}\mathrm{K2\_E1\_ATP}+\mathrm{k2a}\mathrm{K2\_E1\_ATP}$
$\frac{d \mathrm{K\_E1\_ATP}}{d \mathrm{time}}=\mathrm{k2a}\mathrm{K2\_E1\_ATP}+\mathrm{k2b\_}K\mathrm{E1\_ATP}-\mathrm{k2a\_}\mathrm{K\_E1\_ATP}+\mathrm{k2b}\mathrm{K\_E1\_ATP}$
$\frac{d \mathrm{E1\_ATP}}{d \mathrm{time}}=\mathrm{k2b}\mathrm{K\_E1\_ATP}+\mathrm{k3a\_}\mathrm{H\_E1\_ATP}-\mathrm{k2b\_}K\mathrm{E1\_ATP}+\mathrm{k3a}H\mathrm{E1\_ATP}$
$\frac{d \mathrm{H\_E1\_ATP}}{d \mathrm{time}}=\mathrm{k3a}H\mathrm{E1\_ATP}+\mathrm{k3b\_}\mathrm{H2\_E1\_ATP}-\mathrm{k3a\_}\mathrm{H\_E1\_ATP}+\mathrm{k3b}H\mathrm{H\_E1\_ATP}$
$\frac{d \mathrm{H2\_E1\_ATP}}{d \mathrm{time}}=\mathrm{k3b}H\mathrm{H\_E1\_ATP}+\mathrm{k4\_}\mathrm{ADP}\mathrm{H2\_E1\_P}-\mathrm{k3b\_}\mathrm{H2\_E1\_ATP}+\mathrm{k4}\mathrm{H2\_E1\_ATP}$
$\frac{d \mathrm{H2\_E1\_P}}{d \mathrm{time}}=\mathrm{k4}\mathrm{H2\_E1\_ATP}+\mathrm{k5\_}\mathrm{H2\_E2\_P}-\mathrm{k4\_}\mathrm{ADP}\mathrm{H2\_E1\_P}+\mathrm{k5}\mathrm{H2\_E1\_P}$
$\frac{d \mathrm{H2\_E2\_P}}{d \mathrm{time}}=\mathrm{k6a\_}H\mathrm{H\_E2\_P}+\mathrm{k5}\mathrm{H2\_E1\_P}-\mathrm{k6a}\mathrm{H2\_E2\_P}+\mathrm{k5\_}\mathrm{H2\_E2\_P}$
$\frac{d \mathrm{H\_E2\_P}}{d \mathrm{time}}=\mathrm{k6a}\mathrm{H2\_E2\_P}+\mathrm{k6b\_}H\mathrm{E2\_P}-\mathrm{k6a\_}H\mathrm{H\_E2\_P}+\mathrm{k6b}\mathrm{H\_E2\_P}$
$\frac{d \mathrm{E2\_P}}{d \mathrm{time}}=\mathrm{k7a\_}\mathrm{K\_E2\_P}+\mathrm{k6b}\mathrm{H\_E2\_P}-\mathrm{k6b\_}H\mathrm{E2\_P}+\mathrm{k7a}K\mathrm{E2\_P}$
$\frac{d \mathrm{K\_E2\_P}}{d \mathrm{time}}=\mathrm{k7a}K\mathrm{E2\_P}+\mathrm{k7b\_}\mathrm{K2\_E2\_P}-\mathrm{k7a\_}\mathrm{K\_E2\_P}+\mathrm{k7b}K\mathrm{K\_E2\_P}$
$\frac{d \mathrm{K2\_E2\_P}}{d \mathrm{time}}=\mathrm{k7b}K\mathrm{K\_E2\_P}+\mathrm{k8\_}P\mathrm{K2\_E2}-\mathrm{k8}\mathrm{K2\_E2\_P}+\mathrm{k7b\_}\mathrm{K2\_E2\_P}$
$\frac{d \mathrm{K2\_E2}}{d \mathrm{time}}=\mathrm{k8}\mathrm{K2\_E2\_P}+\mathrm{k10\_}\mathrm{K2\_E2\_ATP}+\mathrm{k9\_}\mathrm{K2\_E1}-\mathrm{k8\_}P\mathrm{K2\_E2}+\mathrm{k10}\mathrm{ATP}\mathrm{K2\_E2}+\mathrm{k9}\mathrm{K2\_E2}$
$\frac{d \mathrm{K2\_E2\_ATP}}{d \mathrm{time}}=\mathrm{k10}\mathrm{ATP}\mathrm{K2\_E2}+\mathrm{k11\_}\mathrm{K2\_E1\_ATP}-\mathrm{k10\_}\mathrm{K2\_E2\_ATP}+\mathrm{k11}\mathrm{K2\_E2\_ATP}$
A mathematical model of the inner medullary collecting duct of the rat: acid/base transport (Renal H+/K+ ATPase Variant)
The University of Auckland, Bioengineering Institute
James Lawson
This CellML model represents only a small part of the model described in Weinstein et al.'s paper - namely, the H+ K+ ATPase pump
The University of Auckland
The Bioengineering Institute
Fixed documentation to show proper diagram.
Fixed a minor connection error - units defined for connected variables made consistent.
The new version of this model has been re-coded to remove the reaction element and replace it with a simple MathML description of the model reaction kinetics. This is thought to be truer to the original publication, and information regarding the enzyme kinetics etc will later be added to the metadata through use of an ontology.
For some reason I can't open this file in PCEnv - I'm not sure why. It may be something to do with the name of the file? This particular Weinstein publication has two models in it - a gastric and a renal one.
concentration of hydrogen in the luminal compartment
concentration of hydrogen in the luminal compartment
concentration of ATP in the cytosol compartment
concentration of hydrogen in the luminal compartment
concentration of ATP in the cytosol compartment
concentration of ADP in the cytosol compartment
concentration of ADP in the cytosol compartment
concentration of hydrogen in the luminal compartment
concentration of potassium in the luminal compartment
concentration of hydrogen in the luminal compartment
concentration of hydrogen in the luminal compartment
concentration of ATP in the cytosol compartment
concentration of potassium in the luminal compartment
concentration of ATP in the cytosol compartment
concentration of potassium in the luminal compartment
concentration of hydrogen in the luminal compartment
concentration of ADP in the cytosol compartment
concentration of potassium in the luminal compartment
concentration of potassium in the luminal compartment
The 1998 Weinstein mathematical model of the renal H-K-ATPase.
Renal Medullary Cell
Catherine Lloyd
This is the CellML description of Weinstein's 1998 mathematical model of the renal H-K-ATPase in rats.
A mathematical model of the inner medullary collecting duct of the
rat: acid/base transport
Journal of Physiology
acid-base transport
renal
electrophysiology
collecting duct
rat
kidney
concentration of potassium in the luminal compartment
concentration of ATP in the cytosol compartment
concentration of potassium in the luminal compartment