Given the input-output data of the mammalian cell cycle network under a parallel updating scheme, an attempt to construct a threshold Boolean network with the same dynamics is presented. To accomplish this, mutual information is used to find the network structure, then a swarm intelligence optimization technique called the bees algorithm is used to find the weights and thresholds for the network. It is shown that out of the ten regulatory elements (nodes) of the network, only nine can be modeled as a single threshold function, thus, the resulting network is almost a threshold Boolean network with the exception of the CycA protein which remains with its logical rules instead. The robustness of the network is explored with respect to update perturbations, in particular, what happens to the limit cycle attractors when changing from parallel to a sequential updating scheme. Results shows that the network is not robust since different limit cycles of different lengths appear.