Two-way feedback between chromatin compaction and histone modification state explains Saccharomyces 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. However, a broader hypothesis suggests that chroma-tin compaction can be both a cause and a consequence of the locus histone modification state, with a tight bidirectional interaction underpinning bistable transcriptional states. To rigorously test this hypothesis, we developed a mathematical model for the dynamics of the HMR locus in Saccharomyces cerevisiae, that incorporates activating histone mod-ifications, 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/histone  modification  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. Such bidirectional feedback between chroma-tin compaction and the histone modification state may be a widespread and important regulatory mechanism given the hallmarks of many heterochromatic regions: physical chromatin compaction and dimerizing (or multivalent) silencing proteins.