We suggest a governing equation that describes the process of polymer-chain translocation through a narrow pore and reconciles the seemingly contradictory features of such dynamics: (i) a Gaussian probability distribution of the translocated number of polymer segments at time $t$ after the process has begun, and (ii) a subdiffusive increase of the distribution variance $\Delta (t)$ with elapsed time $\Delta (t)\propto t^{\alpha }$. The latter quantity measures the mean-squared number $s$ of polymer segments that have passed through the pore $\Delta (t)=\langle [s(t)-s(t=0)]{}^2\rangle$, and is known to grow with an anomalous diffusion exponent $\alpha <1$. Our main assumption [i.e., a Gaussian distribution of the translocation velocity $v(t)$] and some important theoretical results, derived recently, are shown to be supported by extensive Brownian dynamics simulation, which we performed in $3\text{D}$. We also numerically confirm the predictions made recently that the exponent $\alpha$ changes from $0.91$ to $0.55$ to $0.91$ for short-, intermediate-, and long-time regimes, respectively.

• Received 22 July 2010

DOI:https://doi.org/10.1103/PhysRevE.83.011802