  Epigenetic mechanisms of silencing via heritable chromatin modifications play
a major role in gene regulation and cell fate specification. We consider a
model of epigenetic chromatin silencing in budding yeast and study the
bifurcation diagram and characterize the bistable and the monostable regimes.
The main focus of this paper is to examine how the perturbations altering the
activity of histone modifying enzymes affect the epigenetic states. We analyze
the implications of having the total number of silencing proteins given by the
sum of proteins bound to the nucleosomes and the ones available in the ambient
to be constant. This constraint couples different regions of chromatin through
the shared reservoir of ambient silencing proteins. We show that the response
of the system to perturbations depends dramatically on the titration effect
caused by the above constraint. In particular, for a certain range of overall
abundance of silencing proteins, the hysteresis loop changes qualitatively with
certain jump replaced by continuous merger of different states. In addition, we
find a nonmonotonic dependence of gene expression on the rate of histone
deacetylation activity of Sir2. We discuss how these qualitative predictions of
our model could be compared with experimental studies of the yeast system under
anti-silencing drugs.
