  Maintaining tissue homeostasis requires appropriate regulation of stem cell
differentiation. The Waddington landscape posits that gene circuits in a cell
form a potential landscape of different cell types, wherein cells follow
attractors of the probability landscape to develop into distinct cell types.
However, how adult stem cells achieve a delicate balance between self-renewal
and differentiation remains unclear. We propose that random inheritance of
epigenetic states plays a pivotal role in stem cell differentiation and present
a hybrid model of stem cell differentiation induced by epigenetic
modifications. Our comprehensive model integrates gene regulation networks,
epigenetic state inheritance, and cell regeneration, encompassing multi-scale
dynamics ranging from transcription regulation to cell population. Through
model simulations, we demonstrate that random inheritance of epigenetic states
during cell divisions can spontaneously induce cell differentiation,
dedifferentiation, and transdifferentiation. Furthermore, we investigate the
influences of interfering with epigenetic modifications and introducing
additional transcription factors on the probabilities of dedifferentiation and
transdifferentiation, revealing the underlying mechanism of cell reprogramming.
This \textit{in silico} model provides valuable insights into the intricate
mechanism governing stem cell differentiation and cell reprogramming and offers
a promising path to enhance the field of regenerative medicine.
