Relação entre o volume da célula e dinâmica do ciclo celular em mamíferos

Abstract

The main goal of this work is to add and analyse an equation that represents the volume in a dynamical model of the mammalian cell cycle proposed by Gérard and Gold beter (2011). The cell division occurs when the cyclinB/Cdk1 (cyclin-dependent kinase) complex is totally degraded and it reaches a minimum value. At this point, the cell is divided into two newborn daughter cells and each one will contain the half of the cyto plasmic content of the mother cell. The equations of our base model are valid only if the cell volume, where the reactions occur, is constant. Whether the cell volume is not constant, that is, the rate of change of its volume with respect to time is explicitly taken into account in the mathematical model, then the equations of the original model are no longer valid. Therefore, every equations were modified from the mass conservation prin ciple for considering a volume that changes with time. Through this approach, the cell volume affects all model variables. Two different dynamic simulation methods were ac complished: deterministic and stochastic. In the stochastic simulation, the volume affects every model’s parameters which have molar unit, whereas in the deterministic one, it is incorporated into the differential equations. In deterministic simulation, the biochemical species may be in concentration units, while in stochastic simulation such species must be converted to number of molecules which are directly proportional to the cell volume. In an effort to understand the influence of the new equation over the model an stability analysis was performed. This elucidates how the new parameter µ, cell volume growth factor, impacts the stability of the model’s limit cycle. In order to find the approximated solution of the deterministic model, the fourth order Runge Kutta method was implemen ted. As for the stochastic model, the Gillespie’s Direct Method was used. In conclusion, a more precise model, in comparison to the base model, was created for the cell cycle as it now takes into consideration the rate of change of the cell volume.