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

(a) Heat map of mixing time for different pairs (88 pairs) of volume fractions (confinement) and self-attraction (ϕ, ϵ) where 0.001 ≤ ϕ ≤ 0.6 and 0.1 ≤ ϵ ≤ 1. The different colors indicate the order of the time when the four chains in our model are approximately maximally mixed (α ≈ 3). Various colors represent different times when chromosomes completely mix. The time difference between the mixing order that is shortest (represented by the green color) and longest (represented by the red color) is about 1000. The extremes of the green color region, for which the pair ϕ = 0.4 and ϵ = 0.75 completely mix in time t = 2.68 × 1012τ, corresponds to 5 years and is denoted as the critical time. Note that the red color signifies extremely slow mixing, three orders of magnitude in time longer than tc, while the other colors show mixing times shorter than (due to overlap with no reptation) or on the order of (due to reptation) tc. (b) State diagram showing the transition from slow mixing (ttc) to almost no mixing within tc (t > tc) of the chains. The bars represent the simulation results, while the line serves as a guide for the eye. In the heat map (a), we observe violet, indigo, blue and green regions for which the chains are completely mixed by confinement and/or self-attractions for times shorter than the critical time (tc), and the red region for which the mixing time (due to confinement and/or self-attractions) is 3 orders of magnitude longer than the critical time.