Calcium dynamics and homeostasis in a mathematical model of the principal cell of the cortical collecting tubule.

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Abstract
Calcium (Ca) dynamics are incorporated into a mathematical model of the principal cell in the cortical collecting tubule developed earlier in Strieter et al. (1992a. Am. J Physiol. 263:F1063-1075). The Ca components are modeled after the Othmer-Tang model for IP(3)-sensitive calcium channels (1993, in Experimental and Theoretical Advances in Biological Pattern Formation, 295-319). There are IP(3)-sensitive Ca channels and ATP-driven pumps on the membrane of the endoplasmic reticulum. Calcium enters the cell passively down its electrochemical gradient. A Ca pump and Na/Ca exchange in the basolateral membrane are responsible for the extrusion of cytoplasmic calcium. Na/Ca exchange can also operate in reverse mode to transport Ca into the cell. Regulatory effects of cytoplasmic Ca on the apical Na channels are modeled after experimental data that indicate apical Na permeability varies inversely with cytoplasmic Ca concentration. Numerical results on changes in intracellular Ca caused by decreasing NaCl in the bath and the lumen are similar to those from 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 oscillatory when extracellular Na is severely decreased, as observed in experiments of cultured principal cells (Koster, H., C. van Os and R. Bindels. 1993. Kidney Int.43:828-836). This essentially pathological situation arises because the hyperpolarization of membrane potential caused 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 longer move Ca out of the cell effectively. The raising of the total amount of intracellular Ca induces oscillatory Ca movement between the cytoplasm and the endoplasmic reticulum. Ca homeostasis is investigated under the condition of severe extracellular Ca variations. As extracellular 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 regulated apical sodium or potassium permeability are essential for regulation of cytoplasmic Ca in the principal cell of the cortical collecting tubule.

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