A model of calcium-mediated coupling between membrane activity and clock gene expression in neurons of the suprachiasmatic nucleus

Rhythms in electrical activity in the membrane of cells in the suprachiasmatic nucleus (SCN) are crucial for the function of the circadian timing system, which is characterized by the expression of the so-called clock genes. Intracellular Ca${}^{2+}$ ions seem to connect, at least in part, the electrical activity of SCN neurons with the expression of clock genes. In this paper, we introduce a simple mathematical model describing the linking of membrane activity to the transcription of one gene by means of a feedback mechanism based on the dynamics of intracellular calcium ions.