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Register a new userDriven translocation of a polymer: role of pore friction and crowding
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Force-driven translocation of a macromolecule through a nanopore is investigated by taking into account the monomer-pore friction as well as the crowding of monomers on the {it trans} - side of the membrane which counterbalance the driving force acting in the pore. The set of governing differential-algebraic equations for the translocation dynamics is derived and solved numerically. The analysis of this solution shows that the crowding of monomers on the trans side hardly affects the dynamics, but the monomer-pore friction can substantially slow down the translocation process. Moreover, the translocation exponent $alpha$ in the translocation time - vs. - chain length scaling law, $tau propto N^{alpha}$, becomes smaller when monomer-pore friction coefficient increases. This is most noticeable for relatively strong forces. Our findings may explain the variety of $alpha$ values which were found in experiments and computer simulations.
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We investigate the influence of polymer-pore interactions on the translocation dynamics using Langevin dynamics simulations. An attractive interaction can greatly improve translocation probability. At the same time, it also increases translocation time slowly for weak attraction while exponential dependence is observed for strong attraction. For fixed driving force and chain length the histogram of translocation time has a transition from Gaussian distribution to long-tailed distribution with increasing attraction. Under a weak driving force and a strong attractive force, both the translocation time and the residence time in the pore show a non-monotonic behavior as a function of the chain length. Our simulations results are in good agreement with recent experimental data.
We investigate several scaling properties of a translocating homopolymer through a thin pore driven by an external field present inside the pore only using Langevin Dynamics (LD) simulation in three dimension (3D). Specifically motivated by several recent theoretical and numerical studies that are apparently at odds with each other, we determine the chain length dependence of the scaling exponents of the average translocation time, the average velocity of the center of mass, $<v_{CM}>$, the effective radius of gyration during the translocation process, and the scaling exponent of the translocation coordinate ($s$-coordinate) as a function of the translocation time. We further discuss the possibility that in the case of driven translocation the finite pore size and its geometry could be responsible that the veclocity scaling exponent is less than unity and discuss the dependence of the scaling exponents on the pore geometry for the range of $N$ studied here.
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.
The impact of thermal fluctuations on the translocation dynamics of a polymer chain driven through a narrow pore has been investigated theoretically and by means of extensive Molecular-Dynamics (MD) simulation. The theoretical consideration is based on the so-called velocity Langevin (V-Langevin) equation which determines the progress of the translocation in terms of the number of polymer segments, $s(t)$, that have passed through the pore at time $t$ due to a driving force $f$. The formalism is based only on the assumption that, due to thermal fluctuations, the translocation velocity $v=dot{s}(t)$ is a Gaussian random process as suggested by our MD data. With this in mind we have derived the corresponding Fokker-Planck equation (FPE) which has a nonlinear drift term and diffusion term with a {em time-dependent} diffusion coefficient $D(t)$. Our MD simulation reveals that the driven translocation process follows a {em super}diffusive law with a running diffusion coefficient $D(t) propto t^{gamma}$ where $gamma < 1$. This finding is then used in the numerical solution of the FPE which yields an important result: for comparatively small driving forces fluctuations facilitate the translocation dynamics. As a consequence, the exponent $alpha$ which describes the scaling of the mean translocation time $<tau>$ with the length $N$ of the polymer, $<tau> propto N^{alpha}$ is found to diminish. Thus, taking thermal fluctuations into account, one can explain the systematic discrepancy between theoretically predicted duration of a driven translocation process, considered usually as a deterministic event, and measurements in computer simulations. In the non-driven case, $f=0$, the translocation is slightly subdiffusive and can be treated within the framework of fractional Brownian motion (fBm).
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