Appearance of phase-locked Wenckebach-like rhythms, devil's staircase and universality in intracellular calcium spikes in non-excitable cell models.

In this paper we show that Wenckebach-like patterns of intracellular calcium concentration, [Ca2+]i, arise in non-excitable cell models when driven repetitively by the application of agonists that activate the phospholinositide-signalling pathway. These patterns are similar to action potential responses observed in excitable cells when driven periodically by external current stimuli. A model exclusively studied in this paper is based on the receptor-operated model of Cuthbertson & Chay (1991, Cell Calcium 12, 97-108), which is formulated under the assumptions that phospholipase C is a GTPase activating protein and a build-up of the GTP-bound alpha-subunit is a slow dynamic variable responsible for the refractory period. Similarities between [Ca2+]i response and action potential response make it possible to reduce the full dynamic system to a one-dimensional discrete equation designed for cardiac rhythms. The Devil's staircase constructed from both the dynamic traces and one-dimensional maps shows that the rules governing this staircase are indeed universal even in the agonist phase-locking system. This work thus provides a theoretical explanation for the appearance of blocked and delayed responses of [Ca2+]i spikes observed in the hepatocytes in response to pulsed phenylephrine agonist and, moreover, demonstrates the existence of universality in the agonist pulsed phase-locking system.