https://doi.org/10.1140/epjst/e2020-900089-7
Regular Article
Process equation as a model for the development of cells
1
Biomedical Engineering Department, Amirkabir University of Technology, Tehran 15875-4413, Iran
2
Department of Psychology, Florida International University, Miami FL, USA
3
Ministry of Higher Education and Scientific Research, Baghdad, Iraq
4
Department of Physics, University of Wisconsin, Madison, WI 53706, USA
a e-mail: fahimenazarimehr@yahoo.com
Received:
20
May
2019
Received in final form:
9
September
2019
Published online:
26
March
2020
This paper proposes a behavioral model for cells that shows their different dynamics from a high pluripotent stem cell to any distinct cell fate. The proposed model considers a cell as a black-box for a living system and tries to depict the presumed behaviors of the system. The model is a multistable iterated map with sensitive dependence on initial conditions. It indicates various stages of cell evolution in strict order from stem cells in embryos to differentiated cells functioning in an organ. The results show that the dynamical system inters to a situation with an infinite number of coexisting attractors by decreasing the parameter g. In the first stages of division, the system has a more complex dynamic, and so the model has chaotic attractor. Passing the time in the division process results in stronger cell-cell interactions and so the dynamic of the system becomes more ordered and simpler. Finally, at the end of the division process, the system has the simplest dynamic, which is an equilibrium in the model.
© EDP Sciences, Springer-Verlag GmbH Germany, part of Springer Nature, 2020