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| In cell biology, certain time-dependent processes or characteristics can have time-dependent and stochastic-like dynamics. However, simultaneously this dynamics is stable and it resists external perturbations. We now ask, what is a mechanism of stability that can account for such time-dependent dynamics? We present an answer to this question and discuss it in detail using the non-excitable cell membrane potential dynamics as an example. The membrane potential in such cells is typically considered to be fluctuating stochastically around a constant value. However, under metabolic or oxidative stress a membrane potential can have strong and stable deterministic oscillations which resist external perturbations. Considering a detailed model, we show that the considered example belongs to a special class of nonautonomous deterministic oscillatory systems which have a time-dependent point attractor (driven steady state). Such systems were recently introduced and named chronotaxic (from chronos - time and taxis - order) because they possess a time-dependent point attractor which makes the dynamics ordered in time. Thus, chronotaxic systems are able to model complex, time-dependent dynamics which may look stochastic. |
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