We develop a theory for polymer translocation driven by a time-dependent force through an oscillating nanopore. To this end, we extend the iso-flux tension propagation theory (IFTP) [Sarabadani textit{et al., J. Chem. Phys.}, 2014, textbf{141}, 21490
7] for such a setup. We assume that the external driving force in the pore has a component oscillating in time, and the flickering pore is similarly described by an oscillating term in the pore friction. In addition to numerically solving the model, we derive analytical approximations that are in good agreement with the numerical simulations. Our results show that by controlling either the force or pore oscillations, the translocation process can be either sped up or slowed down depending on the frequency of the oscillations and the characteristic time scale of the process. We also show that while in the low and high frequency limits the translocation time $tau$ follows the established scaling relation with respect to chain length $N_0$, in the intermediate frequency regime small periodic fluctuations can have drastic effects on the dynamical scaling. The results can be easily generalized for non-periodic oscillations and elucidate the role of time dependent forces and pore oscillations in driven polymer translocation.
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 $tau propto N_0^{1+ u}$, where $N_0$ is the chain length and $ u$ is the Flory exponent. In addition, we derive the leading correction-to-scaling term to $tau$ and show that all terms of order $N_0^{2 u}$ 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.
