Time scale of entropic segregation of flexible polymers in confinement: Implications for chromosome segregation in filamentous bacteria

We report molecular dynamics simulations of the segregation of two overlapping chains in cylindrical confinement. We find that the entropic repulsion between chains can be sufficiently strong to cause segregation on a time scale that is short compared to the one for diffusion. This result implies that entropic driving forces are sufficiently strong to cause rapid bacterial chromosome segregation.

Figure 1

Two partly overlapping chains in a spherical cylinder of width $D$. The chains consist of $N$ beads of size $\sigma$ each. $L$ denotes the chain extension and $R_{\mathrm{c}2\mathrm{c}}$ the distance of the centers of mass.

Figure 2

Example simulation run for $D=7$, $N=200$, starting from the removal of the interconnecting bonds. The two gray bands give the total extent along the tube axis of the two chains for a single run, the black lines the positions of their centers of masses. The positions are relative to the total center of mass, $R$, of the system and rescaled by the equilibrium length $L_{\mathrm{eq}}$ of a single confined chain.

Figure 3

Schematic view of the segregation process. A line is fitted to the center-of-mass distance $R_{\mathrm{c}2\mathrm{c}}$ in the range from $D$ to $L_{\mathrm{eq}}-D$. From this fit, the induction time $t_i$ is determined as intersection with $R_{\mathrm{c}2\mathrm{c}}=0$ and the segregation speed $V_{\mathrm{c}2\mathrm{c}}$ as its slope. The segregation time is then $t_s=L_{\mathrm{eq}}∕V_{\mathrm{c}2\mathrm{c}}$.

Figure 4

Measured segregation speed $V_{\mathrm{c}2\mathrm{c}}$ rescaled by $1∕N$. For better visualization, we actually plot its inverse $1∕\left(N{V}_{\mathrm{c}2\mathrm{c}}\right)$. The dashed line demonstrates the linear scaling of the segregation time with $D$. The inset shows the segregation time $t_s$, rescaled by $N^2$, as a function of $D$.

Figure 5

Measured induction times $t_i$ rescaled by $N^3$. The lines are just guides to the eye.

Figure 6

(Color online) Monomer density $\rho \left(r\right)$ along the cylinder axis for $N=200$, $D=8$, averaged over all configurations with a center-of-mass distance $R_{\mathrm{c}2\mathrm{c}}=0$ (a), $R_{\mathrm{c}2\mathrm{c}}=20$ (b), $R_{\mathrm{c}2\mathrm{c}}=48$ (c), and $R_{\mathrm{c}2\mathrm{c}}=80$ (d). The graphs are centered around the systems center of mass, $R$.