Da Veiga, Jorgelindo; Lafitte, Olivier; Schwartz, Laurent A simple mathematical model for the growth and division of cells. (English) Zbl 1406.92146 MathS In Action 8, 1-8 (2017). Summary: 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. MSC: 92C37 Cell biology 92C15 Developmental biology, pattern formation Keywords:cell growth; cell division; electrostatic-electrodynamic model; Hodgkin-Huxley model generalization × Cite Format Result Cite Review PDF Full Text: DOI References: [1] J. Boonstra et al, “Cation transport and growth in neuroblastoma cells, modulation of \(K^+\) transport and electrical membrane properties during the cell cycle”, Journal of cellular physiology (1981) [2] L. Groigno & M. Whitaker, “An anaphase calcium signal controls chromosome disjunction in early sea urchin embryos”, Cell92 (1998), p. 193-204 · doi:10.1016/S0092-8674(00)80914-9 [3] A.L. Hodgkin & A.F. Huxley, “A quantitative description of membrane current and its application to conduction and excitation in nerves”, Journal of Physiology117 (1952), p. 500-544 · doi:10.1113/jphysiol.1952.sp004764 [4] Cronin J., Mathematical aspects of Hodgkin-Huxley neural theory, Cambridge University Press, 1987 · Zbl 0627.92005 [5] Rafelski S.M. Jayashankar V., “Shaping the multiscale architecture of mitochondria”, Current opinion in cell biology38 (2016), p. 45-51 · doi:10.1016/j.ceb.2016.02.006 [6] Levy Noriega M. Lafitte O. Steyaerts J.M. Bakardjan H. Dubois B. Hampel H. Schwartz L., “Mechanical stress related to brain atrophy in Alzheimer’s disease”, Alzheimer’s and Demential12 (2016) no. 1, p. 11-20 · doi:10.1016/j.jalz.2015.03.005 [7] C. Poignard et al O. Kavian, “Classical electropermeabilization modelling at the cell scale”, Journal of theoretical biology68(1-2) (2014) no. 1-2, p. 235-265 · Zbl 1300.92023 [8] L. Schwartz, Cancer, un traitement simple et non toxique, Thierry Souccar Collection ’Medecine’, 2016 [9] Fleury V. Schwartz L., “Diffusion Limited Aggregation from Shear Stress As a Simple Model of Vasculogenesis 1999”, Fractals7 (1999) no. 1, p. 33-39 · doi:10.1142/S0218348X99000050 [10] E. Desmond-Le Quéméner T. Bouchez, “A thermodynamic theoriy of microbial growth”, The ISME Journal8 (2014), p. 1747-1751 · doi:10.1038/ismej.2014.7 [11] Mummery C. Van Zoelen E., “Membrane regulation of the \(N a^+, K^+\)-ATPase During the Neuroblastoma Cell Cycle: correlation with protein mobility”, J. Cellular Biochemistry21 (1983), p. 77-91 Published by · doi:10.1002/jcb.240210109 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.