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Register a new userConformations, Transverse Fluctuations and Crossover Dynamics of a Semi-Flexible Chain in Two Dimensions
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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.
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The cytoskeleton is an inhomogeneous network of semi-flexible filaments, which are involved in a wide variety of active biological processes. Although the cytoskeletal filaments can be very stiff and embedded in a dense and cross-linked network, it has been shown that, in cells, they typically exhibit significant bending on all length scales. In this work we propose a model of a semi-flexible filament deformed by different types of cross-linkers for which one can compute and investigate the bending spectrum. Our model allows to couple the evolution of the deformation of the semi-flexible polymer with the stochastic dynamics of linkers which exert transversal forces onto the filament. We observe a $q^{-2}$ dependence of the bending spectrum for some biologically relevant parameters and in a certain range of wavenumbers $q$. However, generically, the spatially localized forcing and the non-thermal dynamics both introduce deviations from the thermal-like $q^{-2}$ spectrum.
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 investigate the effect of stress fluctuations on the stochastic dynamics of an inclusion embedded in a viscous gel. We show that, in non-equilibrium systems, stress fluctuations give rise to an effective attraction towards the boundaries of the confining domain, which is reminiscent of an active Casimir effect. We apply this generic result to the dynamics of deformations of the cell nucleus and we demonstrate the appearance of a fluctuation maximum at a critical level of activity, in agreement with recent experiments [E. Makhija, D. S. Jokhun, and G. V. Shivashankar, Proc. Natl. Acad. Sci. U.S.A. 113, E32 (2016)].
Over the past few decades, oscillating flexible foils have been used to study the physics of organismal propulsion in different fluid environments. Here we extend this work to a study of flexible foils in a frictional environment. When the foil is oscillated by heaving at one end but not allowed to locomote freely, the dynamics change from periodic to non-periodic and chaotic as the heaving amplitude is increased or the bending rigidity is decreased. For friction coefficients lying in a certain range, the transition passes through a sequence of $N$-periodic and asymmetric states before reaching chaotic dynamics. Resonant peaks are damped and shifted by friction and large heaving amplitudes, leading to bistable states. When the foil is allowed to locomote freely, the horizontal motion smoothes the resonant behaviors. For moderate frictional coefficients, steady but slow locomotion is obtained. For large transverse friction and small tangential friction corresponding to wheeled snake robots, faster locomotion is obtained. Traveling wave motions arise spontaneously, and and move with horizontal speed that scales as transverse friction to the 1/4 power and input power that scales as transverse friction to the 5/12 power. These scalings are consistent with a boundary layer form of the solutions near the foils leading edge.
We study the surface fluctuations of a tissue with a dynamics dictated by cell-rearrangement, cell-division, and cell-death processes. Surface fluctuations are calculated in the homeostatic state, where cell division and cell death equilibrate on average. The obtained fluctuation spectrum can be mapped onto several other spectra such as those characterizing incompressible fluids, compressible Maxwell elastomers, or permeable membranes in appropriate asymptotic regimes. Since cell division and cell death are out-of-equilibrium processes, detailed balance is broken, but a generalized fluctuation-response relation is satisfied in terms of appropriate observables. Our work is a first step toward the description of the out-of-equilibrium fluctuations of the surface of a thick epithelium and its dynamical response to external perturbations.
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