Iso-Flux Tension Propagation Theory of Driven Polymer Translocation: The Role of Initial Configurations

Abstract

We investigate the dynamics of pore-driven polymer translocation by theoretical analysis and molecular dynamics (MD) simulations. Using the tension propagation theory within the constant flux approximation we derive an explicit equation of motion for the tension front. From this we derive a scaling relation for the average translocation time $\tau$, which captures the asymptotic result $\tau \propto N_0^{1+\nu}$, where $N_0$ is the chain length and $\nu$ is the Flory exponent. In addition, we derive the leading correction-to-scaling term to $\tau$ and show that all terms of order $N_0^{2\nu}$ exactly cancel out, leaving only a finite-chain length correction term due to the effective pore friction, which is linearly proportional to $N_0$. We use the model to numerically include fluctuations in the initial configuration of the polymer chain in addition to thermal noise. We show that when the {\it cis} side fluctuations are properly accounted for, the model not only reproduces previously known results but also considerably improves the estimates of the monomer waiting time distribution and the time evolution of the translocation coordinate $s(t)$, showing excellent agreement with MD simulations.