We study translocation dynamics of a driven compressible semi-flexible chain consisting of alternate blocks of stiff ($S$) and flexible ($F$) segments of size $m$ and $n$ respectively for different chain length $N$ in two dimension (2D). The free par
ameters in the model are the bending rigidity $kappa_b$ which controls the three body interaction term, the elastic constant $k_F$ in the FENE (bond) potential between successive monomers, as well as the segmental lengths $m$ and $n$ and the repeat unit $p$ ($N=m_pn_p$) and the solvent viscosity $gamma$. We demonstrate that due to the change in entropic barrier and the inhomogeneous viscous drag on the chain backbone a variety of scenarios are possible amply manifested in the waiting time distribution of the translocating chain. These information can be deconvoluted to extract the mechanical properties of the chain at various length scales and thus can be used to nanopore based methods to probe bio-molecules, such as DNA, RNA and proteins.
We present a unified scaling description for the dynamics of monomers of a semiflexible chain under good solvent condition in the free draining limit. We consider both the cases where the contour length $L$ is comparable to the persistence length $el
l_p$ and the case $Lgg ell_p$. Our theory captures the early time monomer dynamics of a stiff chain characterized by $t^{3/4}$ dependence for the mean square displacement(MSD) of the monomers, but predicts a first crossover to the Rouse regime of $t^{2 u/{1+2 u}}$ for $tau_1 sim ell_p^3$, and a second crossover to the purely diffusive dynamics for the entire chain at $tau_2 sim L^{5/2}$. We confirm the predictions of this scaling description by studying monomer dynamics of dilute solution of semi-flexible chains under good solvent conditions obtained from our Brownian dynamics (BD) simulation studies for a large choice of chain lengths with number of monomers per chain N = 16 - 2048 and persistence length $ell_p = 1 - 500$ Lennard-Jones (LJ) units. These BD simulation results further confirm the absence of Gaussian regime for a 2d swollen chain from the slope of the plot of $langle R_N^2 rangle/2L ell_p sim L/ell_p$ which around $L/ell_p sim 1$ changes suddenly from $left(L/ell_p right) rightarrow left(L/ell_p right)^{0.5} $, also manifested in the power law decay for the bond autocorrelation function disproving the validity of the WLC in 2d. We further observe that the normalized transverse fluctuations of the semiflexible chains for different stiffness $sqrt{langle l_{bot}^2rangle}/L$ as a function of renormalized contour length $L/ell_p$ collapse on the same master plot and exhibits power law scaling $sqrt{langle l_{bot}^2rangle}/L sim (L/ell_p)^eta $ at extreme limits, where $eta = 0.5$ for extremely stiff chains ($L/ell_p gg 1$), and $eta = -0.25$ for fully flexible chains.
Semiflexible polymers characterized by the contour length $L$ and persistent length $ell_p$ confined in a spatial region $D$ have been described as a series of ``{em spherical blobs} and ``{em deflecting lines} by de Gennes and Odjik for $ell_p < D$
and $ell_p gg D$ respectively. Recently new intermediate regimes ({em extended de Gennes} and {em Gauss-de Gennes}) have been investigated by Tree {em et al.} [Phys. Rev. Lett. {bf 110}, 208103 (2013)]. In this letter we derive scaling relations to characterize these transitions in terms of universal scaled fluctuations in $d$-dimension as a function of $L,ell_p$, and $D$, and show that the Gauss-de Gennes regime is absent and extended de Gennes regime is vanishingly small for polymers confined in a 2D strip. We validate our claim by extensive Brownian dynamics (BD) simulation which also reveals that the prefactor $A$ used to describe the chain extension in the Odjik limit is independent of physical dimension $d$ and is the same as previously found by Yang {em et al.}[Y. Yang, T. W. Burkhardt, G. Gompper, Phys. Rev. E {bf 76}, 011804 (2007)]. Our studies are relevant for optical maps of DNA stretched inside a nano-strip.
We present a unified scaling theory for the dynamics of monomers for dilute solutions of semiflexible polymers under good solvent conditions in the free draining limit. Our theory encompasses the well-known regimes of mean square displacements (MSDs)
of stiff chains growing like t^{3/4} with time due to bending motions, and the Rouse-like regime t^{2 u / (1+ 2 u)} where u is the Flory exponent describing the radius R of a swollen flexible coil. We identify how the prefactors of these laws scale with the persistence length l_p, and show that a crossover from stiff to flexible behavior occurs at a MSD of order l^2_p (at a time proportional to l^3_p). A second crossover (to diffusive motion) occurs when the MSD is of order R^2. Large scale Molecular Dynamics simulations of a bead-spring model with a bond bending potential (allowing to vary l_p from 1 to 200 Lennard-Jones units) provide compelling evidence for the theory, in D=2 dimensions where u=3/4. Our results should be valuable for understanding the dynamics of DNA (and other semiflexible biopolymers) adsorbed on substrates.
We study the dynamics of driven polymer translocation using both molecular dynamics (MD) simulations and a theoretical model based on the non-equilibrium tension propagation on the {it cis} side subchain. We present theoretical and numerical evidence
that the non-universal behavior observed in experiments and simulations are due to finite chain length effects that persist well beyond the relevant experimental and simulation regimes. In particular, we consider the influence of the pore-polymer interactions and show that they give a major contribution to the non-universal effects. In addition, we present comparisons between the theory and MD simulations for several quantities, showing extremely good agreement in the relevant parameter regimes. Finally, we discuss the potential limitations of the present theories.
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 fric
tion, 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.
Polymer translocation through a nano-pore in a thin membrane is studied using a coarse-grained bead-spring model and Langevin dynamics simulation with a particular emphasis to explore out of equilibrium characteristics of the translocating chain. We
analyze the out of equilibrium chain conformations both at the $cis$ and the $trans$ side separately either as a function of the time during the translocation process or as as function of the monomer index $m$ inside the pore. A detailed picture of translocation emerges by monitoring the center of mass of the translocating chain, longitudinal and transverse components of the gyration radii and the end to end vector. We observe that polymer configurations at the $cis$ side are distinctly different from those at the $trans$ side. During the translocation, and immediately afterwards, the chain is clearly out of equilibrium, as different parts of the chain are characterized by a series of effective Flory exponents. We further notice that immediately after the translocation the last set of beads that have just translocated take a relatively compact structure compared to the first set of beads that translocated earlier, and the chain immediately after translocation is described by an effective Flory exponent $0.45 pm 0.01$. The analysis of these results is further strengthened by looking at the conformations of chain segments of equal length as they cross from the $cis$ to the $trans$ side, We discuss implications of these results to the theoretical estimates and numerical simulation studies of the translocation exponent reported by various groups.
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 r
ecent 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.
