Application of Lie Symmetry to a Mathematical Model that Describes a Cancer Sub-Network

In this paper, a mathematical model of a cancer sub-network is analysed from the view point of Lie symmetry methods. This model discusses a human cancer cell which is developed due to the dysfunction of some genes at the R-checkpoint during the cell cycle. The primary purpose of this paper is to apply the techniques of Lie symmetry to the model and present some approximated solutions for the three-dimensional system of first-order ordinary differential equations describing a cancer sub-network. The result shows that the phosphatase gene (Cdc25A) regulates the cyclin-dependent kinases inhibitor ($P{27}^{Kip1}$). Furthermore, this research discovered that the activity that reverses the inhibitory effects on cell cycle progression at the R-checkpoint initiates a pathway.