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Register a new userUniversal monomer dynamics of a two dimensional semi-flexible chain
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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.
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Self-assembling, semi-flexible polymers are ubiquitous in biology and technology. However, there remain conflicting accounts of the equilibrium kinetics for such an important system. Here, by focusing on a dynamical description of a minimal model in an overdamped environment, I identify the correct kinetic scheme that describes the system at equilibrium in the limits of high bonding energy and dilute concentration.
Using molecular dynamics simulation of a standard bead-spring model we investigate the density crossover scaling of strictly two-dimensional self-avoiding polymer chains focusing on properties related to the contact exponent set by the intrachain subchain size distribution. Irrespective of the density sufficiently long chains are found to consist of compact packings of blobs of fractal perimeter dimension dp = 5/4.
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 $ell_p$ 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.
The behavior of mobile linkers connecting two semi-flexible charged polymers, such as polyvalent counterions connecting DNA or F-actin chains, is studied theoretically. The chain bending rigidity induces an effective repulsion between linkers at large distances while the inter-chain electrostatic repulsion leads to an effective short range inter-linker attraction. We find a rounded phase transition from a dilute linker gas where the chains form large loops between linkers to a dense disordered linker fluid connecting parallel chains. The onset of chain pairing occurs within the rounded transition.
We study the driven translocation of a semi-flexible polymer through a nanopore by means of a modified version of the iso-flux tension propagation theory (IFTP), and extensive molecular dynamics (MD) simulations. We show that in contrast to fully flexible chains, for semi-flexible polymers with a finite persistence length $tilde{ell}_p$ the {it trans} side friction must be explicitly taken into account to properly describe the translocation process. In addition, the scaling of the end-to-end distance $R_N$ as a function of the chain length $N$ must be known. To this end, we first derive a semi-analytic scaling form for $R_N$, which reproduces the limits of a rod, an ideal chain, and an excluded volume chain in the appropriate limits. We then quantitatively characterize the nature of the {it trans} side friction based on MD simulations of semi-flexible chains. Augmented with these two factors, the modified IFTP theory shows that there are three main regimes for the scaling of the average translocation time $tau propto N^{alpha}$. In the stiff chain (rod) limit $N/tilde{ell}_p ll 1$, {$alpha = 2$}, which continuously crosses over in the regime $ 1 < N/tilde{ell}_p < 4$ towards the ideal chain behavior with {$alpha = 3/2$}, which is reached in the regime $N/tilde{ell}_p sim 10^2$. Finally, in the limit $N/tilde{ell}_p gg 10^6$ the translocation exponent approaches its symptotic value $1+ u$, where $ u$ is the Flory exponent. Our results are in good agreement with available simulations and experimental data.
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