  How do mammalian cells that share the same genome exist in notably distinct
phenotypes, exhibiting differences in morphology, gene expression patterns, and
epigenetic chromatin statuses? Furthermore how do cells of different phenotypes
differentiate reproducibly from a single fertilized egg? These are fundamental
problems in developmental biology. Epigenetic histone modifications play an
important role in the maintenance of different cell phenotypes. The exact
molecular mechanism for inheritance of the modification patterns over cell
generations remains elusive. The complexity comes partly from the number of
molecular species and the broad time scales involved. In recent years
mathematical modeling has made significant contributions on elucidating the
molecular mechanisms of DNA methylation and histone covalent modification
inheritance. We will pedagogically introduce the typical procedure and some
technical details of performing a mathematical modeling study, and discuss
future developments.
