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  1. The pairing of homologous chromosomes (homologs) in meiosis is essential for distributing the correct numbers of chromosomes into haploid gametes. In budding yeast, pairing depends on the formation of 150 to 200 Spo11-mediated double-strand breaks (DSBs) that are distributed among 16 homolog pairs, but it is not known if all, or only a subset, of these DSBs contribute to the close juxtaposition of homologs. Having established a system to measure the position of fluorescently tagged chromosomal loci in three-dimensional space over time, we analyzed locus trajectories to determine how frequently and how long loci spend colocalized or apart. Continuous imaging revealed highly heterogeneous cell-to-cell behavior of foci, with the majority of cells exhibiting a “mixed” phenotype where foci move into and out of proximity, even at late stages of prophase, suggesting that the axial structures of the synaptonemal complex may be more dynamic than anticipated. The observed plateaus of the mean-square change in distance (MSCD) between foci informed the development of a biophysical model of two diffusing polymers that captures the loss of centromere linkages as cells enter meiosis, nuclear confinement, and the formation of Spo11-dependent linkages. The predicted number of linkages per chromosome in our theoretical model closely approximates the small number (approximately two to four) of estimated synapsis-initiation sites, suggesting that excess DSBs have negligible effects on the overall juxtaposition of homologs. These insights into the dynamic interchromosomal behavior displayed during homolog pairing demonstrate the power of combining time-resolved in vivo analysis with modeling at the granular level. 
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  3. We use a chromosome-scale simulation to show that the preferential binding of heterochromatin protein 1 (HP1) to regions high in histone methylation (specifically H3K9me3) results in phase segregation and reproduces features of the observed Hi-C contact map. Specifically, we perform Monte Carlo simulations with one computational bead per nucleosome and an H3K9me3 pattern based on published ChIP-seq signals. We implement a binding model in which HP1 preferentially binds to trimethylated histone tails and then oligomerizes to bridge together nucleosomes. We observe a phase reminiscent of heterochromatin—dense and high in H3K9me3—and another reminiscent of euchromatin—less dense and lacking H3K9me3. This segregation results in a plaid contact probability map that matches the general shape and position of published Hi-C data. Analysis suggests that a roughly 20-kb segment of H3K9me3 enrichment is required to drive segregation into the heterochromatic phase. 
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