Quantification of tension to explain bias dependence of driven polymer translocation dynamics

Motivated by identifying the origin of the bias dependence of tension propagation we investigate methods for measuring tension propagation quantitatively in computer simulations of driven polymer translocation. Here the motion of flexible polymer chains through a narrow pore is simulated using Langevin dynamics. We measure tension forces, bead velocities, bead distances, and bond angles along the polymer at all stages of translocation with unprecedented precision. Measurements are done at a standard temperature used in simulations and at zero temperature to pin down the effect of fluctuations. The measured quantities were found to give qualitatively similar characteristics, but the bias dependence could be determined only using tension force. We find that in the scaling relation $\tau \sim N^\beta f_d^\alpha$ for translocation time $\tau$, the polymer length $N$, and the bias force $f_d$ the increase of the exponent $\beta$ with bias is caused by center-of-mass diffusion of the polymer toward the pore on the \textit{cis} side. We find that this diffusion also causes the exponent $\alpha$ to deviate from the ideal value $-1$. The bias dependence of $\beta$ was found to result from combination of diffusion and pore friction and so be relevant for polymers that are too short to be considered asymptotically long. The effect is relevant in experiments all of which are made using polymers whose lengths are far below the asymptotic limit. Thereby our results also corroborate the theoretical prediction by Sakaue's theory [Polymers 8(12), 424 (2016)] that there should not be bias dependence of $\beta$ for asymptotically long polymers. By excluding fluctuations we also show that monomer crowding at the pore exit cannot have a measurable effect on translocation dynamics under realistic conditions.