PMC

Efficiency of insulation for interacting polymer model. Interaction reduces long-range crossing of contacts as quantified in the graph by comparing inter- and intradomain contacts.

Set-up for studying insulator action: the green bead is an enhancer, red beads are insulators, magenta beads are equidistant intradomain promoters and cyan beads are equidistant interdomain promoters. Thick gray dashed lines correspond to intradomain interactions while thin black dashed lines correspond to interdomain interaction.

Probability of contact as a function of separation, for low-contact configurations and for high-contact ones. In this particular case, configurations with more than 10 contacts were taken to be high-contact and those with less than five were classified as low-contact.

The left box is a sketch of a typical contact map for the same number of contacts for random distribution of contacts and the right box, for our simulation of interacting nucleosomes. The solid line is the insulator contact (permanent) and dashed lines represent transient contacts between nucleosomes.

Time line plot (MC steps) of number of transient bonds formed in a window of a typical run. The red beads are the active beads that has formed transient bonds (green shadow) and the blue beads are inert. Portion of the 200 bead configuration shown. The box on the right shows the histogram of contact sizes, with the x-axis showing counts for different contact sizes.

Frequency of crossing of chords (discussion of mapping of contacts to chords on a circle is in the text) with a chosen bond length, against contact sizes. Data shown for two bond lengths. The 100 bond length chord is a diameter in our 200 bead simulation, and therefore corresponds to the insulator set-up. For comparison we have randomized the chords and computed the frequency of crossing. No insulation is expected for random contacts between any two beads, therefore the randomized chords serves as a benchmark.

Log-log plot of rms distance of bead pairs against separation for configurations selected by their number of contacts. The zero contact configurations are nearly Gaussian; deviation from the random walk scaling at short separations is owing to persistence of the polymer and at long separations owing to the finite size effect of the ring configuration studied here. For high number of contacts we see significant deviation from the random walk behavior; the polymer is more compact. However, these configurations are sporadic and rarer.

Contact probability for fixed availability and different attraction, zoomed in on the tail of the distribution, against enhancer-promoter separation. The typical contact probability is peaked around a separation determined by the choice of persistence length, and is excluded from this plot. As expected, the tail of the distribution falls off as a power law for the noninteracting case, but has a much slower fall-off for our interaction model. We present data for three different values of effective interaction and show that higher interaction leads to better long-range communication.