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has been cited by the following article:

• TITLE: A Mathematical Model of the Cell Differentiation in Multicellular Eukaryotes

  AUTHORS: Jinya Otsuka

  KEYWORDS: Stochastic Process, Long-Range Interaction, Short-Range Interaction, Signal Transduction, Transcriptional Regulation

  JOURNAL NAME: Applied Mathematics, Vol.11 No.3, March 11, 2020

  ABSTRACT: The cell differentiation in multicellular eukaryotes is one of the most curious phenomena. The recent gene and genome sequencing reveals that most of differentiated cells in a multicellular eukaryote carry a common genome and that such a genome contains the expanded repertoire of genes of proteins associated with the cell-cell adhesion, intercellular and intracellular signal transduction and transcriptional regulation. The cell differentiation occurs in the assembly consisting of a large number of cells after the cell proliferation,　and this process is regarded as a stochastic process. Its formulation starts with the master equation in the present paper. The cell differentiation is reproduced in the equation of the most probable path derived from the master equation, when the short-range and long-range interactions between the cells as well as the transition probability between the proliferation and differentiation modes are considered. Moreover, the equation of the most probable path explains the experimental results such as the “memory”, tissue culture and the preparation of induced pluripotent stem (iPS) cells in embryology, if the long-range interaction is considered to be the regulation of gene transcription under the influence of intracellular signal transduction from the receptor accepting the ligand secreted by other types of cells and the short-range interaction is considered to stabilize the intracellular signal transduction by the contact between the same type of cells. The “organizer” found in the initial development of embryo is also explained as the cells that preferentially express the specific gene of a ligand to rouse the long-range interaction. In conclusion, the present study proposes that the complicated intercellular and intracellular signal transduction causing the cell differentiation is ascribed to the long-range interaction between distinctive types of cells and the short-range interaction between the same type of cells.