Simulations of Two-Dimensional Unbiased Polymer Translocation Using the Bond Fluctuation Model

We use the Bond Fluctuation Model (BFM) to study the pore-blockade times of a translocating polymer of length $N$ in two dimensions, in the absence of external forces on the polymer (i.e., unbiased translocation) and hydrodynamic interactions (i.e., the polymer is a Rouse polymer), through a narrow pore. Earlier studies using the BFM concluded that the pore-blockade time scales with polymer length as $\tau_d \sim N^\beta$, with $\beta=1+2\nu$, whereas some recent studies with different polymer models produce results consistent with $\beta=2+\nu$, originally predicted by us. Here $\nu$ is the Flory exponent of the polymer; $\nu=0.75$ in 2D. In this paper we show that for the BFM if the simulations are extended to longer polymers, the purported scaling $\tau_d \sim N^{1+2\nu}$ ceases to hold. We characterize the finite-size effects, and study the mobility of individual monomers in the BFM. In particular, we find that in the BFM, in the vicinity of the pore the individual monomeric mobilities are heavily suppressed in the direction perpendicular to the membrane. After a modification of the BFM which counters this suppression (but possibly introduces other artifacts in the dynamics), the apparent exponent $\beta$ increases significantly. Our conclusion is that BFM simulations do not rule out our theoretical prediction for unbiased translocation, namely $\beta=2+\nu$.