Mathematical Models of Ionic Transport in the Distal Tubule of the Rat
Catherine
Lloyd
Auckland Bioengineering Institute, The University of Auckland
Model Status
This CellML model is a description of Chang and Fujita's 2001 mathematical model of a Na-H exchanger in the distal tubule of the rat: it is one component of an overall model of acid/base transport in a distal tubule.
Model Structure
ABSTRACT: The purpose of this study is to develop a numerical model that simulates acid-base transport in rat distal tubule. We have previously reported a model that deals with transport of Na(+), K(+), Cl(-), and water in this nephron segment (Chang H and Fujita T. Am J Physiol Renal Physiol 276: F931-F951, 1999). In this study, we extend our previous model by incorporating buffer systems, new cell types, and new transport mechanisms. Specifically, the model incorporates bicarbonate, ammonium, and phosphate buffer systems; has cell types corresponding to intercalated cells; and includes the Na/H exchanger, H-ATPase, and anion exchanger. Incorporation of buffer systems has required the following modifications of model equations: new model equations are introduced to represent chemical equilibria of buffer partners [e.g., pH = pK(a) + log(10) (NH(3)/NH(4))], and the formulation of mass conservation is extended to take into account interconversion of buffer partners. Furthermore, finite rates of H(2)CO(3)-CO(2) interconversion are taken into account in modeling the bicarbonate buffer system. Owing to this treatment, the model can simulate the development of disequilibrium pH in the distal tubular fluid. For each new transporter, a state diagram has been constructed to simulate its transport kinetics. With appropriate assignment of maximal transport rates for individual transporters, the model predictions are in agreement with free-flow micropuncture experiments in terms of HCO reabsorption rate in the normal state as well as under the high bicarbonate load. Although the model cannot simulate all of the microperfusion experiments, especially those that showed a flow-dependent increase in HCO reabsorption, the model is consistent with those microperfusion experiments that showed HCO reabsorption rates similar to those in the free-flow micropuncture experiments. We conclude that it is possible to develop a numerical model of the rat distal tubule that simulates acid-base transport, as well as basic solute and water transport, on the basis of tubular geometry, physical principles, and transporter kinetics. Such a model would provide a useful means of integrating detailed kinetic properties of transporters and predicting macroscopic transport characteristics of this nephron segment under physiological and pathophysiological settings.
The original paper reference is cited below:
A numerical model of acid-base transport in rat distal tubule, Hangil Chang and Toshiro Fujita, 2001, American Journal of Physiology, 281, F222-F243. PubMed ID: 11457714.
reaction_diagram1
State diagram of the Na-H exchanger. In this model, the Na-H exchanger has a single binding site (E) to which Na+, H+, and NH4
+ bind competitively. Only the bound forms of the transporter are able to cross the membrane. (Symbols with the asterisk (*) represent conformations facing the cytosol, symbols without indicate conformations facing the extracellular environment.)
$\frac{d E}{d \mathrm{time}}=\mathrm{k2}\mathrm{ENa}+\mathrm{k4}\mathrm{EH}+\mathrm{k6}\mathrm{ENH4}-\mathrm{k1}\mathrm{Na}E+\mathrm{k3}HE+\mathrm{k5}\mathrm{NH4}E$
$\frac{d \mathrm{ENa}}{d \mathrm{time}}=\mathrm{k1}E\mathrm{Na}+\mathrm{k14}\mathrm{ENa\_}-\mathrm{k2}\mathrm{ENa}+\mathrm{k13}\mathrm{ENa}$
$\frac{d \mathrm{EH}}{d \mathrm{time}}=\mathrm{k3}HE+\mathrm{k16}\mathrm{EH\_}-\mathrm{k4}\mathrm{EH}+\mathrm{k15}\mathrm{EH}$
$\frac{d \mathrm{ENH4}}{d \mathrm{time}}=\mathrm{k5}\mathrm{NH4}E+\mathrm{k18}\mathrm{ENH4\_}-\mathrm{k6}\mathrm{ENH4}+\mathrm{k17}\mathrm{ENH4}$
$\frac{d \mathrm{E\_}}{d \mathrm{time}}=\mathrm{k8}\mathrm{ENa\_}+\mathrm{k10}\mathrm{EH\_}+\mathrm{k12}\mathrm{ENH4\_}-\mathrm{k7}\mathrm{Na\_}\mathrm{E\_}+\mathrm{k9}\mathrm{H\_}\mathrm{E\_}+\mathrm{k11}\mathrm{NH4\_}\mathrm{E\_}$
$\frac{d \mathrm{ENa\_}}{d \mathrm{time}}=\mathrm{k7}\mathrm{E\_}\mathrm{Na\_}+\mathrm{k13}\mathrm{ENa}-\mathrm{k8}\mathrm{ENa\_}+\mathrm{k14}\mathrm{ENa\_}$
$\frac{d \mathrm{EH\_}}{d \mathrm{time}}=\mathrm{k9}\mathrm{H\_}\mathrm{E\_}+\mathrm{k15}\mathrm{EH}-\mathrm{k10}\mathrm{EH\_}+\mathrm{k16}\mathrm{EH\_}$
$\frac{d \mathrm{ENH4\_}}{d \mathrm{time}}=\mathrm{k11}\mathrm{NH4\_}\mathrm{E\_}+\mathrm{k17}\mathrm{ENH4}-\mathrm{k12}\mathrm{ENH4\_}+\mathrm{k18}\mathrm{ENH4\_}$
$W=\frac{\mathrm{H\_}}{\mathrm{H\_}+\mathrm{KH}}\mathrm{k13}=2.41E0W\mathrm{k14}=2.41E0W\mathrm{k15}=4.8E-1W\mathrm{k16}=4.8E-1W\mathrm{k17}=2.41E0W\mathrm{k18}=2.41E0W$
kidney
electrophysiology
distal tubule
renal
acid-base transport
ion transport
Na-H exchanger
The University of Auckland, Auckland Bioengineering Institute
Na-H exchanger extracellular side
E
Na-H exchanger intracellular side
E_
H+-loaded Na-H exchanger extracellular side
EH
NH4+-loaded Na-H exchanger intracellular side
ENH4_
c.lloyd@auckland.ac.nz
keyword
Chang and Fujita's 2001 mathematical model of a Na-H exchanger in the
distal tubule of the rat: it is one component of an overall model of
acid/base transport in a distal tubule.
Renal Distal Tubule
Rat
The University of Auckland
Auckland Bioengineering Institute
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.
The model runs in the PCEnv simulator but gives a flat output.
Catherine Lloyd
2007-06-05T09:57:38+12:00
Catherine
Lloyd
May
sodium-loaded Na-H exchanger intracellular side
ENa_
A numerical model of acid-base transport in rat distal tubule
281
F222
F243
H+-loaded Na-H exchanger intracellular side
EH_
sodium-loaded Na-H exchanger extracellular side
ENa
American Journal of Physiology
2007-05-29T00:00:00+00:00
11457714
NH4+-loaded Na-H exchanger extracellular side
ENH4
Catherine
Lloyd
May
This is the CellML description of Chang and Fujita's 2001 mathematical model of a Na-H exchanger in the distal tubule of the rat: it is one component of an overall model of acid/base transport in a distal tubule.
Toshiro
Fujita
2001-08
Hangil
Chang