Recently several experiments have shown that REST is bound to the chromatin of miR-21, and miR-21 inhibits the self-renewal of mouse embryonic stem (ES) cells by decreasing the expression of SOX2, NANOG and OCT4. Thus, REST is believed to be a core transcription factor together with miR-21 to regulate differentiation and self-renewal of ES cells. In this paper, a mathematical model is established for investigating the roles of the REST-miR-21 regulatory pathway in the core regulatory network of ES cells. Results show that REST plays a significant role of differentiation and self-renewal by blocking the expression of miR-21, and the changes of expression of REST affects the expression of miR-21, correspondingly leads to the bistable switching curve shift and the length of the bistable region changes, which accordingly makes more opportunities of ES cells in the state of differentiation or self-renewal. Furthermore, results show that the over-expression of REST or miR-21 will lead to an irreversible bistable switch. With appropriate combination of two input external signals of embryonic stem cells, a more robust bistable switch can be obtained. In addition, a model of proliferation cell population is given to explain the relationship between abnormal expression levels of REST (or miR-21) and abnormal proliferation cell population, which will lead to a series of diseases, such as tumors.
Keywords: Differentiation, self- renewal, embryonic stem cell, bistable switch.