Figure 5.

The Transition between the Growing (AC) and Senescent (DC) Phase Is Abrupt and History Dependent

(A) The distance $\overline{z}$ between the center of mass of the chromosome and the NL, averaged over five simulation runs in which we fix ${\mathrm{ϵ}}_{\text{HH}}=1.0$ and gradually decrease ${\mathrm{ϵ}}_{\text{HL}}$ from 1.2 to 0.2 over ${10}^6$ Brownian time steps, before increasing it back to 1.2 over the same time (its path in the phase diagram is shown in the inset). The shaded area around the curve reports the SD of the mean. The dashed line marks the predicted transition point between the adsorbed and desorbed regime at ${\mathrm{ϵ}}_{\text{HH}}=1.0$ (see Figures 2A and 2C). Hysteresis occurs in the region ${\mathrm{ϵ}}_{\text{HL}}\sim 0.3$–0.6.

(B) Snapshots of the system at ${\mathrm{ϵ}}_{\text{HL}}=0.5$ showing that it can either be in the AC (growing) or the DC (senescent) phase, depending on its history.

(C) The probability density function of $\overline{z}$ at ${\mathrm{ϵ}}_{\text{HL}}=0.3$, 0.4, and 0.5 (${\mathrm{ϵ}}_{\text{HH}}=1.0$; 50 simulations were sampled for each parameter set). A bimodal behavior is found when ${\mathrm{ϵ}}_{\text{HL}}\sim 0.4$, suggesting the coexistence of both the AC and DC phases.

(D) Snapshots of our simulation modeling the process of LADs detachment from the NL, during which we change ${\mathrm{ϵ}}_{\text{HL}}$ instantaneously from 1.2 to 0.2.

(E) The probability density function of the distance z of each bead from the NL at time t after ${\mathrm{ϵ}}_{\text{HL}}$ has been reduced (sampled from ten simulations).

(F) The corresponding cumulative distribution of z. The inset shows the distribution for small z in log-linear form.

(G) A log-linear plot of the fraction of beads ψ in contact with the NL (those whose distance from the NL is less than δ) at time t after the weakening in ${\mathrm{ϵ}}_{\text{HL}}$, for three different thresholds of δ. The black curves are stretch exponential fits $f\left(t\right)=\kappa \exp \left(-\alpha t^{\beta }\right)$. The fitted stretch exponents β are 0.56, 0.58, and 0.61 for $\delta =2$, 3, and $4\sigma$, respectively.