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Register a new userPolymer translocation across a corrugated channel: Fick-Jacobs approximation extended beyond the mean first passage time
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Added by
Paolo Malgaretti Mr
Publication date
2019
fields
Physics
and research's language is
English
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Polymer translocation across a corrugated channel is a paradigmatic stochastic process encountered in diverse systems. The instance of time when a polymer first arrives to some prescribed location defines an important characteristic time scale for various phenomena, which are triggered or controlled by such an event. Here we discuss the translocation dynamics of a Gaussian polymer in a periodically-corrugated channel using an appropriately generalized Fick-Jacobs approach. Our main aim is to probe an effective broadness of the first passage time distribution (FPTD), by determining the so-called coefficient of variation $gamma$ of the FPTD, defined as the ratio of the standard deviation versus the mean first passage time (MFPT). We present a systematic analysis of $gamma$ as a function of a variety of systems parameters. We show that $gamma$ never significantly drops below 1 and, in fact, can attain very large values, implying that the MFPT alone cannot characterize the first-passage statistics of the translocation process exhaustively well.
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We examine the dispersion of Brownian particles in a symmetric two dimensional channel, this classical problem has been widely studied in the literature using the so called Fick-Jacobs approximation and its various improvements. Most studies rely on the reduction to an effective one dimensional diffusion equation, here we drive an explicit formula for the diffusion constant which avoids this reduction. Using this formula the effective diffusion constant can be evaluated numerically without resorting to Brownian simulations. In addition a perturbation theory can be developed in $varepsilon = h_0/L$ where $h_0$ is the characteristic channel height and $L$ the period. This perturbation theory confirms the results of Kalinay and Percus (Phys. Rev. E 74, 041203 (2006)), based on the reduction, to one dimensional diffusion are exact at least to ${cal O}(varepsilon^6)$. Furthermore, we show how the Kalinay and Percus pseudo-linear approximation can be straightforwardly recovered. The approach proposed here can also be exploited to yield exact results an appropriate limit $varepsilon to infty$, we show that here the diffusion constant remains finite and show how the result can be obtained with a simple physical argument. Moreover we show that the correction to the effective diffusion constant is of order $1/varepsilon$ and remarkably has a some universal characteristics. Numerically we compare the analytical results obtained with exact numerical calculations for a number of interesting channel geometries.
Using two dimensional Langevin dynamics simulations, we investigate the dynamics of polymer translocation into a fluidic channel with diameter $R$ through a nanopore under a driving force $F$. Due to the crowding effect induced by the partially translocated monomers, the translocation dynamics is significantly altered in comparison to an unconfined environment, namely, we observe a nonuniversal dependence of the translocation time $tau$ on the chain length $N$. $tau$ initially decreases rapidly and then saturates with increasing $R$, and a dependence of the scaling exponent $alpha$ of $tau$ with $N$ on the channel width $R$ is observed. The otherwise inverse linear scaling of $tau$ with $F$ breaks down and we observe a minimum of $alpha$ as a function of $F$. These behaviors are interpreted in terms of the waiting time of an individual segment passing through the pore during translocation.
We analyse the dynamics of polymer translocation in the strong force regime by recasting the problem into solving a differential equation with a moving absorbing boundary. For the total translocation time, $tau_{rm tr}$, our simple mean-field model predicts that $tau_{rm tr}sim$ (number of monomers)$^{1.5}$, which is in agreement with the exponent found in previous simulation results. Our model also predicts intricate dependencies of $tau_{rm tr}$ on the variations of the pulling force and of the temperature.
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.
We investigate the mean first passage time of an active Brownian particle in one dimension using numerical simulations. The activity in one dimension is modeled as a two state model; the particle moves with a constant propulsion strength but its orientation switches from one state to other as in a random telegraphic process. We study the influence of a finite resetting rate $r$ on the mean first passage time to a fixed target of a single free Active Brownian Particle and map this result using an effective diffusion process. As in the case of a passive Brownian particle, we can find an optimal resetting rate $r^*$ for an active Brownian particle for which the target is found with the minimum average time. In the case of the presence of an external potential, we find good agreement between the theory and numerical simulations using an effective potential approach.
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