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Fig 2 -

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

(a) Simulation snapshots at long times (t = 106τ) are shown for different attraction strengths (ϵ) and for a volume fraction of ϕ = 0.001. Each color represents a different chain corresponding to a different chromosome. For ϵ = 0.3, the chains are open and not mixed. For ϵ = 0.5, the chains are collapsed and mixed slowly. For ϵ = 1, each chain is collapsed but rarely mixes with the others. Note that spherical confinement has not been shown in snapshots because it was too large relative to the chain size to be represented. (b) For small attraction strength (ϵ ≤ 0.3), chromosomes do not mix as they diffuse in the large confinement volume, with a mixing exponent of β ≈ 0. When the attraction strength is moderate (0.4 ≤ ϵ ≤ 0.75), the chromosome mixing index increases as a power-law with time, with the exponent β characterizing the time exponent of the mixing. For strong attraction strength (ϵ = 1), two mixing exponents are observed. Initially, chromosomes mix with an exponent of β1 = 0.14, but later mixing slows down similar to “jamming”, as indicated by the small value of the second exponent (β2 = 0.04). From the right panel of (b), we find that the value of the exponent first increases and then decreases as the attraction increases. (c) Contact maps from the simulations calculated by averaging the last 500 frames are shown for different attraction strengths (ϵ); in all these simulations, the volume fraction of chains is ϕ = 0.001. (d) The average contact probability (Pc(s)) calculated within each chain is the normalized frequency of contact between beads at a separation distance of s within a single chain. The contact probability shows a power-law relation Pc(s) ∝ sγ, where γ is the exponent. The right panel of (d) shows the scaling exponent (γ) for the contact probability within a single chain as a function of self-attraction strength, ϵ for persistence lengths lp = 1 (gray color) and lp = 5 (black color).