A simple time delay model for eukaryotic cell cycle

Abstract

We propose a seven variable model with time delay in one of the variables for the cell cycle in higher eukaryotes. The model consists of four important phosphorylation-dephosphorylation (P[D) cycles that govern the cell cycle, namely Pre-MPF-MPF, Cdc25P-Cdc25, Wee1P-Wee1 and APCP[APC. Other variables are cyclin, free cyclin dependent kinase (Cdk) and mass. The mass acts as a G2/M checkpoint and the checkpoint is represented by a saddle node loop bifurcation. The key feature of the model is that a time lag has been introduced in the activation of anaphase promoting complex (APC) by maturation promoting factor (MPF). This is effected by treating MPF as a time-delayed variable in the activation step of APC. The time lag acts as a spindle checkpoint. Absence of time delay induces a bistability in our model. Time delay also brings about variability in G1 phase timings. The model also reproduces the mutant phenotype experiments on wee1 cells. Stochasticity has been introduced in the model to simulate the dependence of the cycle time on cell birth length. Mutant phenotypes in the stochastic model reproduce the experimental observations better than the deterministic model.