Maintenance of alternative chromatin states through cell divisions pose some fundamental constraints on the dynamics of histone modifications. In this paper, we study the systems biology of epigenetic inheritance by defining and analyzing general classes of mathematical models. We discuss how the number of modification states involved plays an essential role in the stability of epigenetic states. In addition, DNA duplication and the consequent dilution of marked histones act as a large perturbation for a stable state of histone modifications. The requirement that this large perturbation falls into the basin of attraction of the original state sometimes leads to additional constraints on effective models. Two such models, inspired by two different biological systems, are compared in their fulfilling the requirements of multistability and of recovery after DNA duplication. We conclude that in the presence of multiple histone modifications that characterize alternative epigenetic stable states, these requirements are more easily fulfilled.
