High fidelity epigenetic inheritance: Information theoretic model predicts k-threshold filling of histone modifications post replication

Beyond the genetic code, there is another layer of information encoded as chemical modifications on histone proteins positioned along the DNA. Maintaining these modifications is crucial for survival and identity of cells. How the information encoded in the histone marks gets inherited, given that only half the parental nucleosomes are transferred to each daughter chromatin, is a puzzle. Mapping DNA replication and reconstruction of modifications to equivalent problems in communication of information, we ask how well enzymes can recover the parental modifications, if they were ideal computing machines. Studying a parameter regime where realistic enzymes can function, our analysis predicts that, pragmatically, enzymes may implement a threshold - k filling algorithm which fills unmodified regions of length at most k. This algorithm, motivated from communication theory, is derived from the maximum a posteriori probability (MAP) decoding which identifies the most probable modification sequence based on available observations. Simulations using our method produce modification patterns similar to what has been observed in recent experiments. We also show that our results can be naturally extended to explain inheritance of spatially distinct antagonistic modifications.