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Register a new userNoise driven translocation of short polymers in crowded solutions
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In this work we study the noise induced effects on the dynamics of short polymers crossing a potential barrier, in the presence of a metastable state. An improved version of the Rouse model for a flexible polymer has been adopted to mimic the molecular dynamics by taking into account both the interactions between adjacent monomers and introducing a Lennard-Jones potential between all beads. A bending recoil torque has also been included in our model. The polymer dynamics is simulated in a two-dimensional domain by numerically solving the Langevin equations of motion with a Gaussian uncorrelated noise. We find a nonmonotonic behaviour of the mean first passage time and the most probable translocation time, of the polymer centre of inertia, as a function of the polymer length at low noise intensity. We show how thermal fluctuations influence the motion of short polymers, by inducing two different regimes of translocation in the molecule transport dynamics. In this context, the role played by the length of the molecule in the translocation time is investigated.
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The Rouse-Zimm equation for the position vectors of beads mapping the polymer is generalized by taking into account the viscous aftereffect and the hydrodynamic noise. For the noise, the random fluctuations of the hydrodynamic tensor of stresses are responsible. The preaveraging of the Oseen tensor for the nonstationary Navier-Stokes equation allowed us to relate the time correlation functions of the Fourier components of the bead position to the correlation functions of the hydrodynamic field created by the noise. The velocity autocorrelation function of the center of inertia of the polymer coil is considered in detail for both the short and long times when it behaves according to the t^(-3/2) law and does not depend on any polymer parameters. The diffusion coefficient of the polymer is close to that from the Zimm theory, with corrections depending on the ratio between the size of the bead and the size of the whole coil.
We investigate the translocation of stiff polymers in the presence of binding particles through a nanopore by two-dimensional Langevin dynamics simulations. We find that the mean translocation time shows a minimum as a function of the binding energy $epsilon$ and the particle concentration $phi$, due to the interplay of the force from binding and the frictional force. Particularly, for the strong binding the translocation proceeds with a decreasing translocation velocity induced by a significant increase of the frictional force. In addition, both $epsilon$ and $phi$ have an notable impact on the distribution of the translocation time. With increasing $epsilon$ and $phi$, it undergoes a transition from an asymmetric and broad distribution under the weak binding to a nearly Gaussian one under the strong binding, and its width becomes gradually narrower.
We study the translocation dynamics of a polymer chain threaded through a nanopore by an external force. By means of diverse methods (scaling arguments, fractional calculus and Monte Carlo simulation) we show that the relevant dynamic variable, the translocated number of segments $s(t)$, displays an {em anomalous} diffusive behavior even in the {em presence} of an external force. The anomalous dynamics of the translocation process is governed by the same universal exponent $alpha = 2/(2 u +2 - gamma_1)$, where $ u$ is the Flory exponent and $gamma_1$ - the surface exponent, which was established recently for the case of non-driven polymer chain threading through a nanopore. A closed analytic expression for the probability distribution function $W(s, t)$, which follows from the relevant {em fractional} Fokker - Planck equation, is derived in terms of the polymer chain length $N$ and the applied drag force $f$. It is found that the average translocation time scales as $tau propto f^{-1}N^{frac{2}{alpha} -1}$. Also the corresponding time dependent statistical moments, $< s(t) > propto t^{alpha}$ and $< s(t)^2 > propto t^{2alpha}$ reveal unambiguously the anomalous nature of the translocation dynamics and permit direct measurement of $alpha$ in experiments. These findings are tested and found to be in perfect agreement with extensive Monte Carlo (MC) simulations.
The probability distribution for the free energy of directed polymers in random media (DPRM) with uncorrelated noise in $d=1+1$ dimensions satisfies the Tracy-Widom distribution. We inquire if and how this universal distribution is modified in the presence of spatially correlated noise. The width of the distribution scales as the DPRM length to an exponent $beta$, in good (but not full) agreement with previous renormalization group and numerical results. The scaled probability is well described by the Tracy-Widom form for uncorrelated noise, but becomes symmetric with increasing correlation exponent. We thus find a class of distributions that continuously interpolates between Tracy-Widom and Gaussian forms.
Dynamics of a system that performs a large fluctuation to a given state is essentially deterministic: the distribution of fluctuational paths peaks sharply at a certain optimal path along which the system is most likely to move. For the general case of a system driven by colored Gaussian noise, we provide a formulation of the variational problem for optimal paths. We also consider the prehistory problem, which makes it possible to analyze the shape of the distribution of fluctuational paths that arrive at a given state. We obtain, and solve in the limiting case, a set of linear equations for the characteristic width of this distribution.
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