Abstract
Understanding cell fate selection remains a central challenge in
developmental biology. We present a class of simple yet biologically-motivated
mathematical models for cell differentiation that generically generate
oscillations and hence suggest alternatives to the standard framework based on
Waddington's epigenetic landscape. The models allow us to suggest two generic
dynamical scenarios that describe the differentiation process. In the first
scenario gradual variation of a single control parameter is responsible for
both entering and exiting the oscillatory regime. In the second scenario two
control parameters vary: one responsible for entering, and the other for
exiting the oscillatory regime. We analyse the standard repressilator and four
variants of it and show the dynamical behaviours associated with each scenario.
We present a thorough analysis of the associated bifurcations and argue that
gene regulatory networks with these repressilator-like characteristics are
promising candidates to describe cell fate selection through an oscillatory
process.