Kinetic Model of Water and Urea Permeability Regulation by Vasopressin in Collecting Duct
| Title: | Kinetic Model of Water and Urea Permeability Regulation by Vasopressin in Collecting Duct |
|---|---|
| Authors: | Knepper, Mark; Nielsen, Soren |
| Publisher: | American Journal of Physiology |
| Date Published: | August 01, 1993 |
| Reference Number: | 384 |
We present a mathematical model describing the kinetics of water-channel and urea-carrier regulation by vasopressin in the apical membrane of collecting duct cells. The rate of change of the number of activated channels or carriers in the apical membrane is modeled as a balance between the rate of activation (or exocytic insertion) and the rate of inactivation (or endocytic retrieval) of transporters. In a three-state version of the model, transporters are assumed to be partitioned into three physical states, i.e., an "activated" state that imparts a permeation pathway to the apical membrane, an "inactivated" state, and a "reserve" state. Both activation and inactivation are represented by first-order kinetic equations describing transition from reserve to activated transporters and from activated to inactivated transporters, respectively. A simplified two-state model is derived from the three-state model, with the assumption that the transformation from inactivated to reserve transporter occurs rapidly relative to the other state transitions. Simulated time courses obtained by solving model equations are compared with experimentally determined time courses to test whether the response to vasopressin in isolated inner medullary collecting duct segments can be explained by direct effects on the rate constants for activation or inactivation. The results indicate that, for both transporters, it must be assumed that vasopressin directly regulates rate constants for both activation (exocytosis) and inactivation (endocytosis) to account for the experimentally determined dynamic responses to vasopressin and its withdrawal. These studies provide a theoretical basis on which to design further experimental studies.
This translation by the NDI Foundation is to assist the lay reader. To provide a clear, accessible interpretation of the original article, we eliminated or simplified some technical detail and complicated scientific language. We concentrated our translation on those aspects of the article dealing directly with NDI. The NDI Foundation thanks the researchers for their work toward understanding and more effectively treating this disorder.
© Copyright NDI Foundation 2007 (JC)
Normally, the apical membrane of the principal cells do not let much water through, i.e. they have a low level of water permeability. But when AVP binds with receptors on the basolateral membranes of the CDs, it induces proteins called water channels (WCs) to travel to and insert themselves into the apical membrane. The WCs increase the apical membrane's water permeability so that more water can flow through them. And this is what allows the kidneys to reabsorb the water flowing through the kidney CDs. When AVP absents itself from the principal cells, the WCs are removed from the apical membrane, and it resumes its normal low water permeability.
The physical mechanisms involved in the increase of apical membrane urea and water permeability in response to AVP are poorly understood. In this paper, Knepper and Nielsen introduce a mathematical model that describes the dynamics of WC and urea carrier regulation by AVP in the apical membrane. The authors' model contains several assumptions. It assumes the CD cells contain a fixed number of transporters (WCs) that are distributed among three states: an activated state WCs present in the apical membrane), an inactivated state (those present in vesicles retrieved from the apical membrane), and a reserve state (those present in vesicles capable of bringing them to the apical membrane). Urea carriers could also fit into this three-state model, but apical membrane urea permeability regulation appears to occur, not through the urea transporters being directed into and out of the apical membrane, but by chemical modification of the urea transporters already present in the apical membrane.
The model also assumes that apical membrane permeability is determined by the number of transporters in the activated state (i.e. in the apical membrane). The number of transporters in the activated state is determined by a balance between rates of inactivation and activation of the WCs. The model assumes inactivated transporters cannot become activated without undergoing transformation to the reserve state. In the model, both activation and inactivation are represented by equations that describe the transition from reserve to activated transporters and from activated to inactivated transporters.
The authors derived a two-state model from their three-state model, assuming that the transformation of the WCs from inactivated to reserve state occurs rapidly relative to the other in its transitions to its active and inactive states. To see if the model accurately represented the dynamics of CD cell apical membrane permeability changes, the authors exposed rat CDs to AVP and measured the apical membrane water and urea permeability changes over time and correlated that measure to the number of WC or urea carriers present during the experiment. The authors wanted to see if the CD response to AVP could be explained by direct effects on the rate constants for activation or inactivation so they compared the results of the experiments with the predictions of their model.
The authors found that their model correctly predicted the response of the CDs to AVP only when they manipulated their model to assume that AVP directly regulates the rate constants for both the activation and inactivation of the WCs. This model should provide a sound theoretical basis on which to design further experimental studies on this process.