Mathematical analysis of a 3-variable cell cycle model

Abstract

Mathematical analysis is performed on a 3-variable nonlinear ordinary differential equation system which had been previously introduced to model the regulation of the G1 phase of the cell cycle. The nature and stability of the model's steady states and periodic solutions are described. These results are obtained via linear stability analysis, bifurcation theory and computational techniques using AUTO. The model exhibits different types of bifurcations. The bifurcation results are further confirmed by numerical simulations. This original model (three variables) and a model for a special biological case (the original reduced to two variables) are compared. Some mathematical properties of the 3-variable model are preserved, while others are lost, when the model is reduced to a 2-variable system. The possible biological relevance of the mathematical results is discussed.