Two-way feedback between chromatin compaction and histone modification state explains S. cerevisiae heterochromatin bistability

Compact chromatin is closely linked with gene silencing in part by sterically masking access to promoters, inhibiting transcription factor binding and preventing polymerase from efficiently transcribing a gene. Here, we propose a broader view: chromatin compaction can be both a cause and a consequence of the histone modification state, and this tight bidirectional interaction can underpin bistable transcriptional states. To test this theory, we developed a mathematical model for the dynamics of the HMR locus in S. cerevisiae, that incorporates activating histone modifications, silencing proteins and a dynamic, acetylation-dependent, three-dimensional locus size. Chromatin compaction enhances silencer protein binding, which in turn feeds back to remove activating histone modifications, leading to further compaction. The bistable output of the model was in good agreement with prior quantitative data, including switching rates from expressed to silent states, and vice versa, and protein binding levels within the locus. We then tested the model by predicting changes in switching rates as the genetic length of the locus was increased, which were then experimentally verified. This bidirectional feedback between chromatin compaction and the histone modification state may be an important regulatory mechanism at many loci.