Discipline: Mathematics and Statistics
Subcategory: Mathematics and Statistics
DeMarcus Boone - North Carolina Agricultural and Technical State University
The mammalian cell cycle consists of four primary phases: Growth (G1), Synthesis (S), Pre-mitosis, and Mitosis. There is a restriction point (R-point) within the G1 phase and the S phase that determines the likelihood of a cell transitioning from the G1 phase to the S phase. It has been discovered that retinoblastoma proteins (Rb) interact with E2F proteins to affect cell progression, i.e. the Rb-E2F switch. The results in Yao et. al’s (2008) study reveal that the network of Rb and E2F proteins functions as a bi-stable switch that allows the cell to either synthesize or revert to a resting state.
This study focuses on exploring and examining the Rb-E2F bistable switch by using the mathematical models. We start with the eight differential equations given in Yao’s study. With the aid of computer programming, we gain the ability to further comprehend the relationship among the Rb-E2F switch and the mammalian cell cycle.
First, the system is coded into a Matlab program. Numerous simulations are conducted to observe the bistable switch for various situations. Then, the major parameters and major nodes are identified, and the system is reduced to lower dimensions accordingly. Finally, a prototypical system is obtained to preserve the bistable behavior while the dimension is low. In the process, all the parameters values are estimated from the previous lab experiments at Duke University. From this study, the dynamics of the bistable switch is analyzed in certain depth. The switch is essential regarding the ability for cells to either synthesize or revert to a resting state. Therefore, the findings in this study provide useful insight for the basic design for the robust control of the bistable cell cycle entry at the R-point.
Funder Acknowledgement(s): This study was supported, in part, by the Talent-21 Program, Dr. Liping Liu, mentor, Dr. Guoqing Tang, PI, North Carolina A&T State University, NC, 27411.
Faculty Advisor: Liping Liu,