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| Ever since the experimental work of Hodgkin and Huxley, where the transmembrane voltage was clamped to a constant value, the dynamics of the cell membrane potential has been largely neglected. We now consider the origin of its fluctuations and investigate their time-dependent deterministic characteristics. In particular, we describe its time-varying dynamics with a time-dependent point attractor (driven steady state). In this way the system is able to resist external perturbations. In this talk we will present a mathematical model of the cell membrane potential and of how this could change with cancer. In particular, the interplay between the production of ATP in mitochondria and due to glycolysis is considered and the role of the oxygen supply is investigated. Cancer is associated with a state for which the oxygen supply is at a low level. The proposed model results in regions when the system can or cannot maintain a stable frequency of ATP production, in accordance with the recently-proposed theory of chronotaxic systems (from {\em chronos} -- time and {\em taxis} -- order). A comparison between theoretical and experimental results will be discussed. We conclude that the dynamics of the cell membrane potential, which is often considered to be fully stochastic, can contain a strong deterministic component due to its stability properties. In this way, the dynamics of cell membrane potential may be used to distinguish a cancer cell from normally functioning cell. |
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