Computational study of a budding yeast model of Tyson and Novák

A recent application field of bifurcation theory is in modelling the cell cycle. We refer in particular to the work of Tyson and Novák where the fundamental idea is that the cell cycle is an alternation between two stable steady states of a system of kinetic equations. The two states correspond to the G1 and S-G2-M phases of the cell cycle, respectively.We study the bifurcation structure of a budding yeast model of Tyson and Novák using the Matlab numerical bifurcation software MatCont.We find that not only the S-G2-M phase but also the G1 phase contains both stable steady states and stable periodic orbits. We find and discuss a relation between the growth rate of the cell and the mass increase after DNA-replication. We relate this to a constant phase fraction of a periodic orbit traversed during S-G2-M phase and derive a relation between the growth rate and time spent in S-G2-M space. This relation is consistent with experimental results but so far was not found in other models.We further find that the boundary value problem of the cell cycle can be computed efficiently as the fixed point of a map.As another result, we find that the constitutive expression of the Starter kinase not only leads to a premature transition from G1 to S phase and smaller cells (as is experimentally known and confirmed by other models) but in this model can also lead to nonviable cells.