Kinetic model of water and urea permeability regulation by vasopressin in collecting duct

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.