Criteria for minimal model of driven polymer translocation

While the characteristics of the driven translocation for asymptotically long polymers are well understood, this is not the case for finite-sized polymers, which are relevant for real-world experiments and simulation studies. Most notably, the behavior of the exponent $\alpha$, which describes the scaling of the translocation time with polymer length, when the driving force $f_p$ in the pore is changed, is under debate. By Langevin dynamics simulations of regular and modified translocation models using the freely jointed-chain polymer model we find that a previously reported incomplete model, where the trans side and fluctuations were excluded, gives rise to characteristics that are in stark contradiction with those of the complete model, for which $\alpha$ increases with $f_p$. Our results suggest that contribution due to fluctuations is important. We construct a minimal model where dynamics is completely excluded to show that close alignment with a full translocation model can be achieved. Our findings set very stringent requirements for a minimal model that is supposed to describe the driven polymer translocation correctly.

Figure 1

The simulation geometry, where the polymer is at its initial conformation on the cis side. Two infinite planes divide the space into cis and trans sides. The pore connects these sides allowing the polymer to pass.

Figure 2

Radii of gyration $R_g$ for the translocated polymers of lengths $N=50$, 100, 200, and 400 for pore force $f_p=1$ and 10. (Plots for polymers of different lengths are seen to end at their respective lengths.) The measured $R_g$ on the trans side are seen to be clearly smaller than the equilibrium $R_g$ for segments of equal lengths.

Figure 3

Translocation times for polymer plotted against polymer length using different kinds of bead removal. From top down: unmodified, no trans, and no cis translocation models (see text for details). Transfer times for only pore beads are given for reference. Pore force $f_p=1$.

Figure 4

The distance between all polymer beads separated by two bonds, shown by the black dashed line, was measured as a function of translocation coordinate $s$.

Figure 5

The distribution of distances $l\left(n\right)$ of polymer beads $n-1$ and $n+1$ as a function of the translocation coordinate $s$. The shade of the pixels in the figure give the distance according to the color bar on the right.

Figure 6

Number of beads in drag $n_d$ as a function of the translocation coordinate $s$ for $N=50$, 100, 200, and 400.

Figure 7

The quasistatic model in an initial conformation.

Figure 8

The quasistatic model during translocation.

Figure 9

Waiting times $w\left(s\right)$ for $N=50$, 100, 200, and 400. The minimum $w\approx 10$ is related to how the first bead is initially placed in the pore. The final rise is due to the the total pore force decreasing with the number of beads in the pore at the end. (The curves for different $N$ can be identified by their ending points on the abscissa.)

Figure 10

Scaled waiting time $\widehat{w}\left(s\right)$ and number of beads in drag ${\widehat{n}}_d\left(s\right)$ from the simulations and for the quasistatic model. Scaling was made so that the peak values of the polymers of $N=400$ approximately match.