  A toggle switch consists of two genes that mutually repress each other. This
regulatory motif is active during cell differentiation and is thought to act as
a memory device, being able to choose and maintain cell fate decisions. In this
contribution, we study the stability and dynamics of a two-stage gene
expression switch within a probabilistic framework inspired by the properties
of the Pu/Gata toggle switch in myeloid progenitor cells. We focus on low mRNA
numbers, high protein abundance and monomeric transcription factor binding.
Contrary to the expectation from a deterministic description, this switch shows
complex multi-attractor dy- namics without autoactivation and cooperativity.
Most importantly, the four attractors of the system, which only emerge in a
probabilistic two-stage description, can be identified with committed and
primed states in cell differentiation. We first study the dynamics of the
system and infer the mechanisms that move the system between attractors using
both the quasi-potential and the probability flux of the system. Second, we
show that the residence times of the system in one of the committed attractors
are geometrically distributed and provide an analytical expression of the
distribution. Most importantly we find that the mean residence time increases
linearly with the mean protein level. Finally, we study the implications of
this distribution for the stability of a switch and discuss the influence of
the stability on a specific cell differentiation mechanism. Our model explains
lineage priming and proposes the need of either high protein numbers or long
term modifications such as chromatin remodeling to achieve stable cell fate
decisions. Notably we present a system with high protein abundance that
nevertheless requires a probabilistic description to exhibit multistability,
complex switching dynamics and lineage priming.
