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Register a new userReducing the variance in the translocation times by pre-stretching the polymer
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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 textit{trans}-side. Under the influence of pre-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 translocations 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. Experimentally relevant conditions are 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 in nanopore-based sequencing and sizing applications.
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We employ 3D Langevin Dynamics simulations to study the dynamics of polymer chains translocating through a nanopore in presence of asymmetric solvent conditions. Initially a large fraction ($>$ 50%) of the chain is placed at the textit{cis} side in a good solvent while the $trans$ segments are placed in a bad solvent that causes the chain to collapse and promotes translocation from the $cis$ to the $trans$ side. In particular, we study the ratcheting effect of a globule formed at the textit{trans} side created by the translocated segment, and how this ratchet drives the system towards faster translocation. Unlike in the case of unbiased or externally forced translocation where the mean first passage time $langle tau rangle $ is often characterized by algebraic scaling as a function of the chain length $N$ with a single scaling exponent $alpha$, and the histogram of the mean first passage time $P(tau/langletau rangle)$ exhibits scaling, we find that scaling is not well obeyed. For relatively long chains we find $langle tau rangle sim N^alpha$ where $alpha approx 1$ for $varepsilon/k_{B}T > 1$. In this limit, we also find that translocation proceeds with a nearly constant velocity of the individual beads(monomers), which is attributed to the coiling of the globule. We provide an approximate theory assuming rotat ional motion restricted on a 2D disc to demonstrate that there is a crossover from diffusive behavior of the center of mass for short chains to a single file translocation for long chains, where the average translocation time scales linearly with the chain length $N$.
One of the most fundamental quantities associated with polymer translocation through a nanopore is the translocation time $tau$ and its dependence on the chain length $N$. Our simulation results based on both the bond fluctuation Monte Carlo and Molecular Dynamics methods confirm the original prediction $tausim N^{2 u+1}$, which scales in the same manner as the Rouse relaxation time of the chain except for a larger prefactor, and invalidates other scaling claims.
Two phase picture is a simple and effective methodology to capture the nonequilibrium dynamics of polymer associated with tension propagation. When applying it to the driven translocation process, there is a point to be noted, as briefly discussed in our recent article [Phys. Rev. E 85, 061803 (2012)]. In this article, we address this issue in detail and modify our previous prediction [Euro. Phys. J. E 34, 135 (2011)] by adopting an alternative steady-state ansatz. The modified scaling prediction turns out to be the same as that of the iso-flux model recently proposed by Rowghanian and Grosberg [J. Phys. Chem. B 115, 14127-14135 (2011)].
We present a theoretical argument to derive a scaling law between the mean translocation time $tau$ and the chain length $N$ for driven polymer translocation. This scaling law explicitly takes into account the pore-polymer interactions, which appear as a correction term to asymptotic scaling and are responsible for the dominant finite size effects in the process. By eliminating the correction-to-scaling term we introduce a rescaled translocation time and show, by employing both the Brownian Dynamics Tension Propagation theory [Ikonen {it et al.}, Phys. Rev. E {bf 85}, 051803 (2012)] and molecular dynamics simulations that the rescaled exponent reaches the asymptotic limit in a range of chain lengths that is easily accessible to simulations and experiments. The rescaling procedure can also be used to quantitatively estimate the magnitude of the pore-polymer interaction from simulations or experimental data. Finally, we also consider the case of driven translocation with hydrodynamic interactions (HIs). We show that by augmenting the BDTP theory with HIs one reaches a good agreement between the theory and previous simulation results found in the literature. Our results suggest that the scaling relation between $tau$ and $N$ is retained even in this case.
We present a Brownian dynamics model of driven polymer translocation, in which non-equilibrium memory effects arising from tension propagation (TP) along the cis side subchain are incorporated as a time-dependent friction. To solve the effective friction, we develop a finite chain length TP formalism, expanding on the work of Sakaue [Sakaue, PRE 76, 021803 (2007)]. The model, solved numerically, yields results in excellent agreement with molecular dynamics simulations in a wide range of parameters. Our results show that non-equilibrium TP along the cis side subchain dominates the dynamics of driven translocation. In addition, the model explains the different scaling of translocation time w.r.t chain length observed both in experiments and simulations as a combined effect of finite chain length and pore-polymer interactions.
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