  Post-translational modifications of histone proteins are an important factor
in epigenetic control that serve to regulate transcription, depending on the
particular modification states of the histone proteins. We study the stochastic
dynamics of histone protein states, taking into account a feedback mechanism
where modified nucleosomes recruit enzymes that diffuse to adjacent
nucleosomes. We map the system onto a quantum spin system whose dynamics is
generated by a non-Hermitian Hamiltonian. Making an ansatz for the solution as
a tensor product state leads to nonlinear partial differential equations that
describe the dynamics of the system. Multiple stable histone states appear in a
parameter regime whose size increases with increasing number of modification
sites. We discuss the role of the spatial dependance, and we consider the
effects of spatially heterogeneous enzymatic activity. Finally, we consider
multistability in a model of several types of correlated post-translational
modifications.
