Semiflexible Polymers
1 Follower
Recent papers in Semiflexible Polymers
Semiflexible polymers and filaments play an important role in biological and chemical physics. Single filaments are characterized by a certain bending rigidity which governs their persistence length and buckling instabilities. Attractive... more
Semiflexible polymers and filaments play an important role in biological and chemical physics. Single filaments are characterized by a certain bending rigidity which governs their persistence length and buckling instabilities. Attractive mutual interactions of filaments in bundles or the attractive interaction with an adhesive substrate lead to equilibrium phase transitions, such as bundling and adsorption. Finally, on the level of active systems consisting of many interacting filaments, we discuss cooperative ordering effects in non-equilibrium systems such as motility assays. In motility assays filaments are adsorbed and driven by motor proteins, which are anchored to a planar two-dimensional substrate. The interaction with motor proteins leads to enhanced ordering of filaments. Motility assays containing patterns of adsorbed motors, i.e., stripes of low motor density with increasing widths can be used to sort filaments according to their lengths.
A semiflexible harmonic chain model with extensible bonds is introduced and applied to the stretching of semiflexible polymers or filaments. The semiflexible harmonic chain model allows to study effects from bending rigidity, bond... more
A semiflexible harmonic chain model with extensible bonds is introduced and applied to the
stretching of semiflexible polymers or filaments. The semiflexible harmonic chain model allows to study
effects from bending rigidity, bond extension, discrete chain structure, and finite length of a semiflexible
polymer in a unified manner. The interplay between bond extension and external force can be described by
an effective inextensible chain with increased stretching force, which leads to apparently reduced persistence
lengths in force-extension relations. We obtain force-extension relations for strong- and weak-stretching
regimes which include the effects of extensible bonds, discrete chain structure, and finite polymer length.We
discuss the associated characteristic force scales and calculate the crossover behaviour of the force-extension
curves. Strong stretching is governed by the discrete chain structure and the bond extensibility. The linear
response for weak stretching depends on the relative size of the contour length and the persistence length
which affects the behaviour of very rigid filaments such as F-actin. The results for the force-extension
relations are corroborated by transfer matrix and variational calculations.
stretching of semiflexible polymers or filaments. The semiflexible harmonic chain model allows to study
effects from bending rigidity, bond extension, discrete chain structure, and finite length of a semiflexible
polymer in a unified manner. The interplay between bond extension and external force can be described by
an effective inextensible chain with increased stretching force, which leads to apparently reduced persistence
lengths in force-extension relations. We obtain force-extension relations for strong- and weak-stretching
regimes which include the effects of extensible bonds, discrete chain structure, and finite polymer length.We
discuss the associated characteristic force scales and calculate the crossover behaviour of the force-extension
curves. Strong stretching is governed by the discrete chain structure and the bond extensibility. The linear
response for weak stretching depends on the relative size of the contour length and the persistence length
which affects the behaviour of very rigid filaments such as F-actin. The results for the force-extension
relations are corroborated by transfer matrix and variational calculations.
We study the activated motion of adsorbed polymers which are driven over a structured substrate by a localized point force. Our theory applies to experiments with single polymers using, for example, tips of scanning force microscopes to... more
We study the activated motion of adsorbed polymers which are driven over a structured substrate by a localized point force. Our theory applies to experiments with single polymers using, for example, tips of scanning force microscopes to drag the polymer. We consider both flexible and semiflexible polymers, and the lateral surface structure is represented by double-well or periodic potentials. The dynamics is governed by kink-like excitations for which we calculate shapes, energies, and critical point forces. Thermally activated motion proceeds by the nucleation of a kink-antikink pair at the point where the force is applied and subsequent diffusive separation of kink and antikink. In the stationary state of the driven polymer, the collective kink dynamics can be described by a one-dimensional symmetric simple exclusion process.
We discuss the adsorption of semiflexible polymers to a planar attractive wall and focus on the questions of the adsorption threshold for polymers of finite length and their loop and tail distributions using both Monte Carlo simulations... more
We discuss the adsorption of semiflexible polymers to a planar attractive wall and focus on the questions of the adsorption threshold for polymers of finite length and their loop and tail distributions using both Monte Carlo simulations and analytical arguments. For the adsorption threshold, we find three regimes: (i) a flexible or Gaussian regime if the persistence length is smaller than the adsorption potential range, (ii) a semiflexible regime if the persistence length is larger than the potential range, and (iii) for finite polymers, a novel crossover to a rigid rod regime if the deflection length exceeds the contour length. In the flexible and semiflexible regimes, finite size corrections arise because the correlation length exceeds the contour length. In the rigid rod regime, however, it is essential how the global orientational or translational degrees of freedom are restricted by grafting or confinement. We discuss finite size corrections for polymers grafted to the adsorbing surface and for polymers confined by a second (parallel) hard wall. Based on these results, we obtain a method to analyze adsorption data for finite semiflexible polymers such as filamentous actin. For the loop and tail distributions, we find power laws with an exponential decay on length scales exceeding the correlation length. We derive and confirm the loop and tail power law exponents for flexible and semiflexible polymers. This allows us to explain that, close to the transition, semiflexible polymers have significantly smaller loops and both flexible and semiflexible polymers desorb by expanding their tail length. The tail distribution allows us to extract the free energy per length of adsorption for actin filaments from
We study the buckling instability of filaments or elastic rods in two spatial dimensions in the presence of thermal fluctuations. We present an analytical solution based on a renormalizationlike procedure where we integrate out short... more
We study the buckling instability of filaments or elastic rods in two spatial dimensions in the presence of thermal fluctuations. We present an analytical solution based on a renormalizationlike procedure where we integrate out short wavelength fluctuations in order to obtain an effective theory governing the buckling instability. We calculate the resulting shift of the critical force by fluctuation effects and the average projected filament length parallel to the force direction as a function of the applied force and of the contour length of the filament. We find that, in the buckled state, thermal fluctuations lead to an increase in the mean projected length of the filament in the force direction. As a function of the contour length, the mean projected length exhibits a cusp at the buckling instability, which becomes rounded by thermal fluctuations. Our analytic results are confirmed by Monte Carlo simulations.
We discuss shapes and shape fluctuations of semiflexible polymers or filaments, which are polymers with an appreciable bending rigidity. The physical properties of semiflexible polymers are governed by their persistence length. On length... more
We discuss shapes and shape fluctuations of semiflexible polymers or filaments, which are polymers with an appreciable bending rigidity. The physical properties of semiflexible polymers are governed by their persistence length. On length scales smaller than the persistence length thermal fluctuations can be neglected and polymer shapes are obtained by bending energy minimization. On length scales larger than the persistence length, however, thermal shape fluctuations play an important role and cannot be neglected in general. After a general definition of the persistence length based on the bending rigidity renormalization we will review some problems related to single semiflexible polymers where both variational problems of energy minimization and thermal fluctuations play an important role. We will discuss the buckling instability of semiflexible polymers, their force‐induced desorption, and the shapes of adsorbed semiflexible polymers on structured substrates.
The behavior of semiflexible polymers and filaments is governed by their bending energy. The corresponding bending rigidity gives rise to material properties that are distinct from those of flexible polymers governed by entropy. In... more
The behavior of semiflexible polymers and filaments is governed by their bending energy. The corresponding bending rigidity gives rise to material properties that are distinct from those of flexible polymers governed by entropy. In particular, bending rigidity plays an important role for the shapes of these polymers and their ability to withstand and transmit forces. Recent theoretical studies and modelling approaches are briefly reviewed and used for a systematic analysis of shapes of adsorbed semiflexible polymers and buckling instabilities. Semiflexible polymers and filaments exhibit a buckling instability which is modified by thermal fluctuations and provides upper bounds on the generation of polymerization forces. Growing bundles of polymers or filaments can generate force via adhesive interactions. The latter mechanism remains effective even after single filaments have attained a buckled state.
Driven elastic manifolds in random media exhibit a depinning transition to a state with nonvanishing velocity at a critical driving force. We study the depinning of stiff directed lines, which are governed by a bending rigidity rather... more
Driven elastic manifolds in random media exhibit a depinning transition to a state with nonvanishing velocity at a critical driving force. We study the depinning of stiff directed lines, which are governed by a bending rigidity rather than line tension. Their equation of motion is the (quenched) Herring-Mullins equation, which also describes surface growth governed by surface diffusion. Stiff directed lines are particularly interesting as there is a localization transition in the static problem at a finite temperature and the commonly exploited time ordering of states by means of Middleton’s theorems [Phys. Rev. Lett. 68, 670 (1992)] is not applicable. We employ analytical arguments and numerical simulations to determine the critical exponents and compare our findings with previous works and functional renormalization group results, which we extend to the different line elasticity. We see evidence for two distinct correlation length exponents.
Bundles of semiflexible polymers such as actin filaments are studied theoretically. The bundle formation is governed by attractive filament interactions mediated by cross-linking sticker molecules. Using a combination of analytical... more
Bundles of semiflexible polymers such as actin filaments are studied theoretically. The bundle formation is governed by attractive filament interactions mediated by cross-linking sticker molecules. Using a combination of analytical arguments and Monte Carlo simulations, it is shown that the formation of bundles of parallel filaments requires a threshold concentration of linkers which becomes independent of the filament number for large bundles. The unbinding of bundles happens in a single, discontinuous transition. We discuss the behavior of the bundle thickness at and below the transition. In the bound phase, large bundles tend to segregate into sub-bundles due to slow kinetics. Our results are in qualitative agreement with experiments on F-actin in the presence of the cross-linking protein α-actinin.
We study the thermally activated motion of semiflexible polymers in double-well potentials using field-theoretic methods. Shape, energy, and effective diffusion constant of kink excitations are calculated, and their dependence on the... more
We study the thermally activated motion of semiflexible polymers in double-well potentials using field-theoretic methods. Shape, energy, and effective diffusion constant of kink excitations are calculated, and their dependence on the bending rigidity of the semiflexible polymer is determined. For symmetric potentials, the kink motion is purely diffusive whereas kink motion becomes directed in the presence of a driving force. We determine the average velocity of the semiflexible polymer based on the kink dynamics. The Kramers escape over the potential barriers proceeds by nucleation and diffusive motion of kink-antikink pairs, the relaxation to the straight configuration by annihilation of kink-antikink pairs. We consider both uniform and point-like driving forces. For the case of point-like forces the polymer crosses the potential barrier only if the force exceeds a critical value. Our results apply to the activated motion of biopolymers such as DNA and actin filaments or of synthetic polyelectrolytes on structured substrates.
The thermally assisted force-induced desorption of semiflexible polymers from an adhesive surface or the unzipping of two bound semiflexible polymers by a localized force are investigated. The phase diagram in the force-temperature plane... more
The thermally assisted force-induced desorption of semiflexible polymers from an adhesive surface or the unzipping of two bound semiflexible polymers by a localized force are investigated. The phase diagram in the force-temperature plane is calculated both analytically and by Monte Carlo simulations. Force-induced desorption and unzipping of semiflexible polymers are first order phase transitions. A characteristic energy barrier for desorption is predicted, which scales with the square root of the polymer bending rigidity and governs the initial separation process before a plateau of constant separation force is reached. This leads to activated desorption and unzipping kinetics accessible in single molecule experiments.
We investigate the localization of stiff directed lines with bending energy by a short-range random potential. Using perturbative arguments, Flory arguments, and a replica calculation, we show that a stiff directed line in 1+ d dimensions... more
We investigate the localization of stiff directed lines with bending energy by a short-range random potential. Using perturbative arguments, Flory arguments, and a replica calculation, we show that a stiff directed line in 1+ d dimensions undergoes a localization transition with increasing disorder for d> 2/3. We demonstrate that this transition is accessible by numerical transfer matrix calculations in 1+ 1 dimensions and analyze the properties of the disorder-dominated phase.
We consider the motion of semiflexible polymers in double-well potentials. We calculate shape, energy, and effective diffusion constant of kink excitations, and in particular their dependence on the bending rigidity of the semiflexible... more
We consider the motion of semiflexible polymers in double-well potentials. We calculate shape, energy, and effective diffusion constant of kink excitations, and in particular their dependence on the bending rigidity of the semiflexible polymer. For symmetric potentials, the kink motion is purely diffusive, whereas kink motion becomes directed in the presence of a driving force on the polymer. We determine the average velocity of the semiflexible polymer based on the kink dynamics.
Related Topics