Mean-square displacement (MSD) of a bead (averaged over all the beads of the chain) confined chromosome chains.
In (a),(b), and (c), MSD are calculated from simulations for phantom chains (ϵ = 0), repulsive chains (ϵ = 0.25), and attractive chains (ϵ = 0.5) for a confinement volume equivalent to a bead volume fraction of ϕ = 0.4. Within this confinement, the MSD of the bead increases with time, and when its value reaches the square of the confinement radius, the MSD saturates at a constant value. (a) When beads are disconnected, for ϵ = 0, the MSD increases linearly with time (MSD ∼ τ) and for ϵ = 0.25 and 0.5, MSD ∼ τ0.8. These results demonstrate that for ϵ = 0, beads behave as independent diffusive particles, and sub-diffusion occurs when we introduce interactions (repulsion or attraction) between them. MSD of chain with persistence lengths of (b) 1 bead and (c) 5 beads, for different interaction strengths, ϵ, are shown. For ϵ = 0, MSD ∼ τ0.5 is the result expected from Rouse chains . For repulsive (ϵ = 0.25) and attractive (ϵ = 0.5) interactions, MSD ∼ τ0.4 . We note that reptation from the spherical wall speeds up the collapse of the chain compared to the unconfined case in S5f Fig. (d) MSD is calculated from our block copolymer model in the presence of lamina, for a confinement volume equivalent to a bead volume fraction of ϕ = 0.3. This result reveals very slow mixing dynamics, as evidenced by the MSD ∼ τ0.26 scaling law. Remarkably, the exponent of time in the MSD matches that predicted by reptation dynamics .