CALCIUM DYNAMICS AND HOMEOSTASIS IN A MATHEMATICAL-MODEL OF THE PRINCIPAL CELL OF THE CORTICAL COLLECTING TUBULE

Calcium (Ca) dynamics are incorporated into a mathematical model of th e principal cell in the cortical collecting tubule developed earlier i n Strieter et al. (1992a. Am. J. Physiol. 263:F1063-1075). The Ca comp onents are modeled after the Othmer-Tang model for IP3-sensitive calci um channels (1993, in Experimental and Theoretical Advances in Biologi cal Pattern Formation, 295-319). There are IP3-sensitive Ca channels a nd ATP-driven pumps on the membrane of the endoplasmic reticulum. Calc ium enters the cell passively down its electrochemical gradient. A Ca pump and Na/Ca exchange in the basolateral membrane are responsible fo r the extrusion of cytoplasmic calcium. Na/Ca exchange can also operat e in reverse mode to transport Ca into the cell. Regulatory effects of cytoplasmic Ca on the apical Na channels are modeled after experiment al data that indicate apical Na permeability varies inversely with cyt oplasmic Ca concentration. Numerical results on changes in intracellul ar Ca caused by decreasing NaCl in the bath and the lumen are similar to those fi om experiments in Bourdeau and Lau (1990. Am. J. Physiol. 258:F1497-1503). This match of simulation and experiment requires the synergistic action of the Na/Ca exchanger and the Ca regulated apical Na permeability. In a homogeneous medium, cytoplasmic Ca becomes oscil latory when extracellular Na is severely decreased, as observed in exp eriments of cultured principal cells (Koster, H., C. van Os, and R. Bi ndels. 1993. Kidney Int. 43:828-836). This essentially pathological si tuation arises because the hyperpolarization of membrane potential cau sed by Na-free medium increases Ca influx into the cell, while the Na/ Ca exchanger is inactivated by the low extracellular Na and can no lon ger move Ca out of the cell effectively. The raising of the total amou nt of intracellular Ca induces oscillatory Ca movement between the cyt oplasm and the endoplasmic reticulum. Ca homeostasis is investigated u nder the condition of severe extracellular Ca variations. As extracell ular Ca is decreased, Ca regulation is greatly impaired if Ca does not regulate apical ionic transport. The simulations indicate that the Na /Ca exchanger alone has only limited regulatory capacity. The Ca regul ated apical sodium or potassium permeability are essential for regulat ion of cytoplasmic Ca in the principal cell of the cortical collecting tubule.