  We construct a model of cell reprogramming (the conversion of fully
differentiated cells to a state of pluripotency, known as induced pluripotent
stem cells, or iPSCs) which builds on key elements of cell biology viz. cell
cycles and cell lineages. Although reprogramming has been demonstrated
experimentally, much of the underlying processes governing cell fate decisions
remain unknown. This work aims to bridge this gap by modelling cell types as a
set of hierarchically related dynamical attractors representing cell cycles.
Stages of the cell cycle are characterised by the configuration of gene
expression levels, and reprogramming corresponds to triggering transitions
between such configurations. Two mechanisms were found for reprogramming in a
two level hierarchy: cycle specific perturbations and a noise-induced
switching. The former corresponds to a \emph{directed} perturbation that
induces a transition into a cycle state of a different cell type in the potency
hierarchy (mainly a stem cell) whilst the latter is a priori undirected and
could be induced, e.g., by a (stochastic) change in the cellular environment.
These reprogramming protocols were found to be effective in large regimes of
the parameter space and make specific predictions concerning reprogramming
dynamics which are broadly in line with experimental findings.
