Polymer Translocation in Crowded Environments

We study the effect of the crowded environments on the translocation of a polymer through a pore in a membrane. By systematically treating the entropic penalty due to crowding, we show that the translocation dynamics are significantly altered, leading to novel scaling behaviors of the translocation time. We also observe new and qualitatively different translocation regimes depending upon the extent of crowding, transmembrane chemical potential asymmetry, and polymer length.

Figure 1

Schematic illustration of the translocation process of a polymer in the presence of crowding.

Figure 2

Translocation time $\tau$ (in units of $b^2/D_P$) of a polymer of length $N$ releasing out of the crowded cis side with static obstacles (solid lines: ${\varphi }_c=0.1$, $0.3$, $0.5$ in descending order), dynamic obstacles (dotted lines: for the same values of ${\varphi }_c$), and no crowding (dashed-dotted line: ${\varphi }_c=0$). Inset: $\tau$ vs obstacle volume concentration ${\varphi }_c$ for static (solid lines: $N={10}^5$, ${10}^4$, ${10}^3$ in descending order) and dynamic obstacles (dotted lines: for the same values of $N$). Note ${\varphi }_t=\Delta \mu =0$ here and the value of $b/a=0.3$ is used throughout the Letter.

Figure 3

Translocation time $\tau$ (in units of $b^2/D_P$) vs $N$ for (a) static and (c) dynamic obstacles on the trans side (${\varphi }_t=0.3$, ${\varphi }_c=0$) for different values of chemical potential gradient, showing the asymptotic power law scalings as well as the plateau regime at intermediate length scales. Note ${\mu }^{*}$ denotes the value of the prefactor of the $n$-linear term of $F_{\mathrm{cr}}$ in Eqs. (2, 3), respectively. Different scaling behaviors (exponential, plateau, power law) of $\tau$ in the (${\varphi }_t$, $\mu$) phase space for (b) static and (d) dynamic obstacles at a fixed $N={10}^5$.

Figure 4

$\tau$ (in units of $b^2/D_P$) vs $N$ for (a) static (${\varphi }_t=0.05$) and (c) dynamic obstacles (${\varphi }_t=0.2$) for different values of ${\varphi }_c$. Different scaling behaviors (exponential, plateau, power law) of $\tau$ in the (${\varphi }_t$, ${\varphi }_c$) phase space for (b) static and (d) dynamic obstacles at a fixed $N=3\times {10}^4$. Note that $\Delta \mu =0$ here.