In this paper, we derive an electrostatic-electrodynamic model of the exchanges of ions between a cell and its exterior during its growth, as well as a model of exchange of ions within the cell. Observations show that, in the phase G1, the growth of the volume explains the variation of density of ions (by dilution), hence explains the change of electrostatic potential inside the cell. The potential encounters a threshold at the beginning of phase S, and the ion channels open (the conductance of the membrane increases). This afflux of ions leads to a change of potential, which will trigger the disappearance of the nucleus double membrane (through the calcium channels).

From these remarks on the electric phenomena in the cell, one deduces a simple mathematical model, which is a generalization of the Hodgkin-Huxley model for the axons, for the cell cycle.

@article{MSIA_2017__8_1_1_0, author = {Jorgelindo da Veiga and Olivier Lafitte and Laurent Schwartz}, title = {A simple mathematical model for the growth and division of cells}, journal = {MathematicS In Action}, publisher = {Soci\'et\'e de Math\'ematiques Appliqu\'ees et Industrielles}, volume = {8}, number = {1}, year = {2017}, pages = {1-8}, doi = {10.5802/msia.10}, zbl = {1406.92146}, mrnumber = {3745382}, language = {en}, url = {msia.centre-mersenne.org/item/MSIA_2017__8_1_1_0/} }

Jorgelindo da Veiga; Olivier Lafitte; Laurent Schwartz. A simple mathematical model for the growth and division of cells. MathematicS In Action, Volume 8 (2017) no. 1, pp. 1-8. doi : 10.5802/msia.10. https://msia.centre-mersenne.org/item/MSIA_2017__8_1_1_0/

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