Modeling Epigenetic Dynamics Measured by Mass Spectrometry Using Continuous Time Markov Chains


Histone methylation plays an important role as an epigenetic regulator, capable of driving stable, persistent changes in gene expression without changing a cell's genetic code. Previous work has used stable isotope labeling (SILAC) in combination with mass spectrometry to observe the relationship between the methylation of two neighboring lysine sites on the H3 histone protein for two multiple myeloma patient-derived cell lines. The two sites of interest on the H3 histone are lysines 27 and 36, referred to as H3K27 and H3K36, respectively. While there are only 15 combinations of methylation possible for the H3K27/K36 system, SILAC labeling introduces heavy and light versions of methyl groups, increasing the total number of methylation combinations to 84. We build upon the previous observation and modeling of the H3K27/K36 methylation system, modeling it as a continuous time Markov chain, and fitting models to experimental data using weighted least squares regression. Our resultant models for the two cell lines shows far improved fits of experimental data compared to previously published models, allowing us to draw new inferences about the nature of the relationship between methylation of H3K27 and H3K36, as well as about the key differences in rates between the two cell lines being studied. We also develop a general method for constructing labeled continuous-time Markov chains such as the H3K27/K36 system from simpler unlabeled versions. Our general construction is relevant for any Markov chain where all states are characterized (at least in part) by a countable number of subcomponents, and with transitions between states consisting of the addition or removal of a single subcomponent. In the case of the H3K27/K36 system, the subcomponents are methyl groups that may be added or removed, and which are subject to SILAC labeling. The general construction is relevant not just for histone methylation, but can be used for expanding any type of histone modification, and can be used for systems with an arbitrary number of sites and label types. The improved modeling of the H3K27/K36 methylation system directly contributes to our understanding of epigenetic regulation in multiple myeloma, but in addition, the underlying methods of that work and our general construction for labeled systems provide tooling for modeling other epigenetic relationships in a variety of contexts.

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