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posted on 2023-05-25, 17:45 authored by Gaurav Bajpai, Samuel Safran

(a) A schematic diagram representing the contact map of a genome consisting of 4 chromosomes. Intra- and inter-chromosomal contacts are shown by dark and light orange colors, respectively. (b) The evolution of the chromosome mixing index, α, over time, indicates that phantom chains quickly achieve equilibrium. The right panel of (b) is the time-average of the chromosome mixing index () as a function of the chain volume fraction (ϕ) in the nucleus. For relatively large volume fractions α is approximately equal to three (the maximal value of α is 3 for this case of 4 chains) which indicates that phantom chains achieve maximal mixing in small confinement volumes. The chromosome mixing index is smaller than 3 for smaller volume fractions because the larger confinement volume (smaller volume fraction of chains), means that any two beads (even within the same chain) are less likely to be “in contact”. (c) The average contact probability Pc(s) within a single chain, averaged 4 phantom chains as a function of the bead separation distance s with the scaling exponent γ defined by Pc(s) ∝ sγ. (d) Long time snapshot (t = 106τ time steps) of simulations of 4 phantom chains for a low volume fraction of chains ϕ = 0.001, shows that the different chains are not mixed, since they can diffuse away from each other. The snapshot was zoomed out because its actual size was too large to be shown without taking up an excessive amount of space. (e) Late time snapshot (t = 106τ time steps) of simulations of 4 phantom chains for a relatively large volume fraction ϕ = 0.1, shows that the chains are mixed. Note that in (d) and (e), each color represents a different chain corresponding to a different chromosome. The confinement volume in (d) and (e) is shown in light grey. (f) and (g) Contact maps calculated from phantom chain simulations for volume fraction ϕ = 0.001 and ϕ = 0.1 respectively. Note that contact maps were generated by applying the log2 transformation to the raw counts of the contact matrix and displaying the color bar in log2 ratios. In contact maps (f) and (g), vertical and horizontal colored lines have been added to distinguish the chains, which correspond to the colors of the chromosomes.