Controlling segregation speed of entangled polymers by the shapes: A simple model for eukaryotic chromosome segregation

We report molecular dynamics simulations of the segregation of two overlapping polymers motivated by chromosome segregation in biological cells. We investigate the relationship between polymer shapes and segregation dynamics and show that elongation and compaction make entangled polymers segregate rapidly. This result suggests that eukaryotic chromosomes take such a characteristic rod-shaped structure, which is induced by condensins, to achieve rapid segregation.

Figure 1

Chromosome condensation in mitosis. The red and blue lines indicate two sister chromosomes. In mitosis, condensin-mediated chromosome condensation and nuclear envelope breakdown (NEBD) occur.

Figure 2

(a) Simple illustration of the effects of the loop structural interactions. The interaction makes a long chain compact. (b) Examples of a spherical shape (left) and a rod shape polymer (right). The spherical and rod-shaped polymers have the structural parameters $(N_l,C_l,N_p)=(40,21,1)$ and $(40,21,4)$, respectively. Here only springs are illustrated and beads are ignored for visiblity.

Figure 3

MD time evolution of the overlap fraction $o_v$, the distance of the center of masses $\mathrm{\Delta }{r}_{\mathrm{CM}}$ between two polymers, and the radius of gyration, $R_g$, of one polymer. $\mathrm{\Delta }{r}_{\mathrm{CM}}$ and $R_g$ are both divided by the equilibrium mean value of $R_g$ of one polymer. The small window shows the log-log plot of the overlap ($+$ symbol) and the fitting function (solid line). The polymers have the structural parameters $(N_l,C_l,N_p)=(40,21,1)$.

Figure 4

(a) The radius of gyration $R_g$ for several $N$ in the spherical shape polymer. (b) The induction time $t_i$ and (c) the segregation time $t_s$ for several $N$ in the spherical shape polymer. The small windows in each panels show the log-log plots.

Figure 5

(a) The induction time $t_i$ and (b) the segregation time $t_s$ for several $N$ in the rod-shaped polymer. The horizontal axis is multiplied by $\beta =\sqrt{3}/2$ to match the axis of the spherical cases, Figs. 4 and 4, where ${\overline{R}}_g=\beta \overline{D}$.