Experiments have shown that in embryonic stem cells, the promoters of many lineagecontrol genes contain "bivalent domains", within which the nucleosomes possess both active (H3K4me3) and repressive (H3K27me3) marks. Such bivalent modifications play important roles in maintaining pluripotency in embryonic stem cells. Here, to investigate gene expression dynamics when there are regulations in bivalent histone modifications and random partition in cell divisions, we study how positive feedback to histone methylation/demethylation controls the transition dynamics of the histone modification patterns along with cell cycles. We constructed a computational model that includes dynamics of histone marks, three-stage chromatin state transitions, transcription and translation, feedbacks from protein product to enzymes to regulate the addition and removal of histone marks, and the inheritance of nucleosome state between cell cycles. The model reveals how dynamics of both nucleosome state transition and gene expression are dependent on the enzyme activities and feedback regulations. Results show that the combination of stochastic histone modification at each cell division and the deterministic feedback regulation work together to adjust the dynamics of chromatin state transition in stem cell regenerations.

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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...

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Cancer stem‐like cells (CSCs) have a unique translation mode, but little is understood about the process of elongation, especially the contribution of tRNA modifications to the maintenance of CSCs properties. Here, it is reported that, contrary to the initial aim, a tRNA‐modifying methylthiotransferase CDKAL1 promotes CSC‐factor SALL2 synthesis by assembling the eIF4F translation initiation complex. CDKAL1 expression is upregulated in patients with worse prognoses and is essential for maintaining CSCs in rhabdomyosarcoma (RMS) and common cancers. Translatome analysis reveals that a group of mRNAs whose translation is CDKAL1‐dependent contains cytosine‐rich sequences in the 5’ untranslated region (5’UTR). Mechanistically, CDKAL1 promotes the translation of such mRNAs by organizing the eIF4F translation initiation complex. This complex formation does not require the enzyme activity of CDKAL1 but requires only the NH2‐terminus domain of CDKAL1. Furthermore, sites in CDKAL1 essential for forming the eIF4F complex are identified and discovered candidate inhibitors of CDKAL1‐dependent translation.