Cell plasticity is important for tissue developments during which somatic cells may switch between distinct states. Genetic networks to yield multistable states are usually required to yield multiple states, and either external stimuli or noise in gene expressions are trigger signals to induce cell-type switches between the states. In many biological systems, cells show highly plasticity and can switch between different state spontaneously, but maintaining the dynamic equilibrium of the cell population. Here, we considered a mechanism of spontaneous cell-type switches through the combination between gene regulation network and stochastic epigenetic state transitions. We presented a mathematical model that consists of a standard positive feedback loop with changes of histone modifications during with cell cycling. Based on the model, nucleosome state of an associated gene is a random process during cell cycling, and hence introduces an inherent noise to gene expression, which can automatically induce cell-type switches in cell cycling. Our model reveals a simple mechanism of spontaneous cell-type switches through a stochastic histone modification inheritance during cell cycle. This mechanism is inherent to the normal cell cycle process, and is independent to the external signals.2010 Mathematics Subject Classification. Primary: 92B05, 91B70; Secondary : 92D25. 1 2 RONGSHENG HUANG AND JINZHI LEI changes in the activities of regulators in the gene regulation network is one of the driving force to induce cell type switch, e.g., stem cell differentiation [10,23,24,42]. During development, cells undergo a unidirectional course of differentiation, which can be viewed as a dynamical process on the Waddington epigenetic landscape with multistable states, the input signals can change the landscape to guide the transition between different states [15,19,72].Chromatin regulators play crucial roles in establishing and maintaining gene expression states [4,30]. Histone modifications and DNA methylations are important epigenetic states that can regulate the chromatin state of a DNA sequence, and modulate the gene expression dynamics. These epigenetic modifications are modulated by intercellular enzyme activities, and hence dynamically change over time and during cell cycle [50]. The stochastic epigenetic inheritance during cell cycle can result in spontaneous alteration of epigenetic state during development; epigenetic changes in regulatory loci often correlate with expression changes during stem cell differentiation [3,8,27,58,73].Here, to investigate how stochastic epigenetic inheritance affect the dynamical process of cell fate decision, we studied a computational model that combines positive feedback regulation with histone modification of the gene promoter. Moreover, cell cycle was included in the model through the stochastic inheritance during cell cycle. We show that the dynamic behavior of histone modification in the cell division can induce spontaneous cell-type switches during normal development process, from which t...