Reducing the variance in the translocation times by prestretching the polymer

Langevin dynamics simulations of polymer translocation are performed where the polymer is stretched via two opposing forces applied on the first and last monomer before and during translocation. In this setup, polymer translocation is achieved by imposing a bias between the two pulling forces such that there is net displacement towards the trans side. Under the influence of stretching forces, the elongated polymer ensemble contains less variations in conformations compared to an unstretched ensemble. Simulations demonstrate that this reduced spread in initial conformations yields a reduced variation in translocation times relative to the mean translocation time. This effect is explored for different ratios of the amplitude of thermal fluctuations to driving forces to control for the relative influence of the thermal path sampled by the polymer. Since the variance in translocation times is due to contributions coming from sampling both thermal noise and initial conformations, our simulations offer independent control over the two main sources of noise and allow us to shed light on how they both contribute to translocation dynamics. Simulation parameter space corresponding to experimentally relevant conditions is highlighted and shown to correspond to a significant decrease in the spread of translocation times, thus indicating that stretching DNA prior to translocation could assist nanopore-based sequencing and sizing applications.

Figure 1

In this force configuration, the polymer is stretched by applying two equal and opposite forces $\pm F_{\mathrm{s}}\widehat{x}$ on the polymer ends. An additional force $F_{\mathrm{d}}\widehat{x}$ is applied to the first monomer to drive the polymer to the trans side. The translocation coordinate $s\left(t\right)$ is defined as the monomer index inside the pore.

Figure 2

Histogram distributions of the translocation time with different stretching forces $\widehat{F_{\mathrm{s}}}$. Three driving regimes are shown: (a) $\widehat{F_{\mathrm{d}}}=1$, (b) $\widehat{F_{\mathrm{d}}}=10$, and (c) $\widehat{F_{\mathrm{d}}}=100$.

Figure 3

The average translocation $\langle \tau \rangle$ time scaled by the driving force $F_{\mathrm{d}}$ as a function of the scaled stretching force $\widehat{F_{\mathrm{s}}}$.

Figure 4

Standard deviation ${\sigma }_{\tau }$ plotted as a function of the stretching force $\widehat{F_{\mathrm{s}}}$ for several values of the driving force $\widehat{F_{\mathrm{d}}}$.

Figure 5

Fluctuations of $s\left(t\right)$ vs scaled time $t/\langle \tau \rangle$. (a) A single stretching force together with a deterministic simulation and a $t^1$ line to guide the eye. (b) Different stretching situations as different curves. The curves contain a pair of circular markers. The first indicates the time where the variance contribution from the initial conformations disappears (obtained from the plateau of the deterministic simulation; see top panel). The second marker near $t=\langle \tau \rangle$ indicates the time for the first translocation of the ensemble, i.e., the ensemble population decreases from this point onwards.

Figure 6

(a) Coefficient of variation $c_v={\sigma }_{\tau }/\langle \tau \rangle$ plotted as a function of the stretching force $\widehat{F_{\mathrm{s}}}$ for several values of the driving force $\widehat{F_{\mathrm{d}}}$. (b) Plot of the percentage decrease of the coefficient of variation $c_v$ as a function of the driving force $\widehat{F_{\mathrm{d}}}$.

Figure 7

Phase diagram of the coefficient of variation $c_v$ as a function of the two variables that control the two noise sources: the stretching force $\widehat{F_{\mathrm{s}}}$ and the driving force $\widehat{F_{\mathrm{d}}}$. Note the nonlinear layout of both force axes.