Graphical Abstract Highlights d Quantitative analysis of K27 and K36 methylation over several histone generations d Computational model invokes the existence of distinct methylation state domains d K27me3 on pre-existing histones stimulates the rate of de novo K27me3 establishment d K27/K36 methylation antagonism enhances stability of epigenetic states

Highlights d Rare coordinated high expression states in cancer cells can drive therapy resistance d Gene networks with transcriptional bursting recapitulate these transcriptional states d Networks with low connectivity favorably give rise to these states d Parameters affecting transcriptional bursting are critical to produce these states

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Chromatin states must be maintained during cell proliferation to uphold cellular identity and genome integrity. Inheritance of histone modifications is central in this process. However, the histone modification landscape is challenged by incorporation of new unmodified histones during each cell cycle and the principles governing heritability remain unclear. Here, we take a quantitative computational modeling approach to describes propagation of K27 and K36 methylation states. We measure combinatorial K27 and K36 methylation patterns by quantitative mass spectrometry on subsequent generations of histones. Using model comparison, we reject active global demethylation and invoke the existence of domains defined by distinct methylation endpoints. We find that K27me3 on pre-existing histones stimulates the rate of de novo K27me3 establishment, supporting a read-write mechanism in timely chromatin restoration. Finally, we provide a detailed, quantitative picture of the mutual antagonism between K27 and K37 methylation, and propose that it stabilizes epigenetic states across cell division.

SUMMARYHistone modifications regulate chromatin architecture and thereby control gene expression. Rapid cell divisions and DNA replication however lead to a dilution of histone modifications and can thus affect chromatin mediated gene regulation So how does the cell-cycle shape the histone modification landscape, in particular during embryogenesis when a fast and precise control of cell-specific gene expression is required?We addressed this question in vivo by manipulating the cell-cycle during early Xenopus laevis embryogenesis. The global distribution of un-, mono- di- and tri-methylated histone H4K20 was measured by mass spectrometry in normal and cell-cycle arrested embryos over time. Using multi-start maximum likelihood optimization and quantitative model selection, we found that three specific methylation rate constants were required to explain the measured H4K20 methylation state kinetics. Interestingly, demethylation was found to be redundant in the cycling embryos but essential in the cell-cycle arrested embryos.Together, we present the first quantitative analysis of in vivo histone H4K20 methylation kinetics. Our computational model shows that demethylation is only essential for regulating H4K20 methylation kinetics in non-cycling cells. In rapidly dividing cells of early embryos, we predict that demethylation is dispensable, suggesting that cell-cycle mediated dilution of chromatin marks is an essential regulatory component for shaping the epigenetic landscape during early embryonic development.

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Non-genetic transcriptional variability at the single-cell level is a potential mechanism for therapy resistance in melanoma. Specifically, rare subpopulations of melanoma cells occupy a transient pre-resistant state characterized by coordinated high expression of several genes. Importantly, these rare cells are able to survive drug treatment and develop resistance. How might these extremely rare states arise and disappear within the population? It is unclear whether the canonical stochastic models of probabilistic transcriptional pulsing can explain this behavior, or if it requires special, hitherto unidentified molecular mechanisms. Here we use mathematical modeling to show that a minimal network comprising of transcriptional bursting and interactions between genes can give rise to rare coordinated high states. We next show that although these states occur across networks of different sizes, they depend strongly on three (out of seven) model parameters and require network connectivity to be ≤ 6. Interestingly, we find that while entry into the rare coordinated high state is initiated by a long transcriptional burst that also triggers entry of other genes, the exit from it occurs through the independent inactivation of individual genes. Finally, our model predicts that increased network connectivity can lead to transcriptionally stable states, which we verify using network inference analysis of experimental data. In sum, we demonstrate that established principles of gene regulation are sufficient to describe this new class of rare cell variability and argue for its general existence in other biological contexts.

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