An autonomous mathematical model for the mammalian cell cycle

Abstract

A mathematical model for the mammalian cell cycle is developed as a system of 13 coupled nonlinear ordinary differential equations. The variables and interactions included in the model are based on detailed consideration of available experimental data. Key features are that the model is autonomous, except for dependence on external growth factors; variables are continuous in time, without instantaneous resets at phase boundaries; cell cycle controllers and completion of tasks associated with cell cycle progression are represented; mechanisms to prevent rereplication are included; and cycle progression is independent of cell size. Eight variables represent cell cycle controllers: Cyclin D1 in complex with Cdk4/6, APCCdh1, SCF{beta}Trcp, Cdc25A, MPF, NUMA, securin-separase complex, and separase. Five variables represent task completion, with four for the status of origins and one for kinetochore attachment. The model predicts distinct behaviors consistent with each main phase of the cell cycle. The response to growth factors shows restriction-point behavior. These results imply that the main features of the mammalian cell cycle can be accounted for in a quantitative mechanistic way based on known interactions among cycle control factors and their coupling to tasks involved in replication of DNA. The model is robust to parameter changes, in that cycling is maintained over at least a five-fold range of each parameter when varied individually. The most sensitive parameters are those associated with the initiation and completion of mitosis. The model is suitable for exploring how extracellular factors affect cell cycle progression, including responses to metabolic conditions and to anti-cancer therapies. Author SummaryWe created a model, that is, a set of mathematical equations, to represent the entire cell cycle in mammals. All terms in our equations correspond to actual biological mechanisms. We solved the equations and verified that they show similar behavior to real-life cell cycles. We designed our model to cycle only when enough external growth factors stimulate it, as real cells do. Our model helps us better understand how the cell cycle is controlled. One very important aspect of control is how the cell ensures that its DNA is copied only once per cell cycle. If "rereplication" (copying a section of DNA twice in the same cycle) occurs, it can cause harmful DNA damage. We considered several mechanisms that some biologists believe play a role, and found that most could not explain how rare rereplication is. Two mechanisms did work well, and we used them to make two variants of the model, which show similar behavior. The model has many potential applications. The cell cycle is altered in most cancer cells, so understanding how these changes affect control is useful. Many widely-used drugs affect the cell cycle, and our model can be used to study these effects.