Stretching dynamics of semiflexible polymers

We analyze the nonequilibrium dynamics of single inextensible semiflexible biopolymers as stretching forces are applied at the ends. Based on different (contradicting) heuristic arguments, various scaling laws have been proposed for the propagation speed of the backbone tension which is induced in response to stretching. Here, we employ a newly developed unified theory to systematically substantiate, restrict, and extend these approaches. Introducing the practically relevant scenario of a chain equilibrated under some prestretching force f _pre that is suddenly exposed to a different external force f _ext at the ends, we give a concise physical explanation of the underlying relaxation processes by means of an intuitive blob picture. We discuss the corresponding intermediate asymptotics, derive results for experimentally relevant observables, and support our conclusions by numerical solutions of the coarse-grained equations of motion for the tension.     

Activated dynamics of semiflexible polymers on structured substrates

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.     

Statistical mechanics of semiflexible polymers

We present the statistical-mechanical theory of semiflexible polymers based on the connection between the Kratky-Porod model and the quantum rigid rotator in an external homogeneous field, and treatment of the latter using the quantum mechanical propagator method. The expressions and relations existing for flexible polymers can be generalized to semiflexible ones, if one replaces the Fourier-Laplace transform of the end-to-end polymer distance, 1/(k ²/3 + p), through the matrix , where D and M are related to the spectrum of the quantum rigid rotator, and considers an appropriate matrix element of the expression under consideration. The present work provides also the framework to study polymers in external fields, and problems including the tangents of semiflexible polymers. We study the structure factor of the polymer, the transversal fluctuations of a free end of the polymer with fixed tangent of another end, and the localization of a semiflexible polymer onto an interface. We obtain the partition function of a semiflexible polymer in half space with Dirichlet boundary condition in terms of the end-to-end distribution function of the free semiflexible polymer, study the behaviour of a semiflexible polymer in the vicinity of a surface, and adsorption onto a surface.Received: 23 March 2004, Published online: 23 July 2004PACS: 36.20.-r Macromolecules and polymer molecules - 61.41. + e Polymers, elastomers, and plastics - 82.35.Gh Polymers on surfaces; adhesion     

On the origin of the heterogeneous orientation dynamics of semiflexible polymers in solutions

Collective rotational motion in nondilute isotropic solutions of semirigid chains is sensitively probed by depolarized light scattering over a broad time range. The bimodal shape and the peculiar dependence of the orientational relaxation function on the scattering angle might arise from the coupling between orientational and shear modes of molecular motion (P.G. de Gennes, Mol. Cryst. Liq. Cryst. 12, 193 (1971)). The dynamic heterogeneity, i.e. the separation of the time scales and the shape of the relaxation functions appears to be system specific.     

Anisotropic random networks of semiflexible polymers

Motivated by the organization of cross-linked cytoskeletal biopolymers, we present a semimicroscopic replica field theory for the formation of anisotropic random networks of semiflexible polymers. The networks are formed by introducing random permanent cross-links which fix the orientations of the corresponding polymer segments to align with one another. Upon increasing the cross-link density, we obtain a continuous gelation transition from a fluid phase to a gel where a finite fraction of the system gets localized at random positions. For sufficiently stiff polymers, this positional localization is accompanied by a continuous isotropic-to-nematic (IN) transition occurring at the same cross-link density. As the polymer stiffness decreases, the IN transition becomes first order, shifts to a higher cross-link density, and is preceded by an amorphous solid where the average polymer orientations freeze in random directions.     

Stretching of semiflexible polymers with elastic bonds

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.PACS: 87.15.-v Biomolecules: structure and physical properties - 87.15.Aa Theory and modeling; computer simulation - 87.15.La Mechanical properties     

Force-induced desorption and unzipping of semiflexible polymers

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.     

Triple points in solutions of polydisperse semiflexible polymers

When a mother solution of semiflexible polymers with differing molecular weights is forced to undergo phase transition, cloud and shadow curves emerge instead of a coexistence curve. For the first time, we calculate the cloud and shadow curves for an isotropic-nematic transition coupled to polydispersity and predict novel triple points. Because of the emergence of new triple points, polydispersity allows the occurrence of anisotropic phases at much lower polymer concentrations than for the monodisperse solutions.     

Collapse transition of two-dimensional flexible and semiflexible polymers

The nature of the globule-coil transition of surface-confined polymers has been an issue of debate. Here this 2D collapse transition is studied through a partially directed lattice model. In the general case of polymers with positive bending stiffness (Delta>0), the collapse transition is first order; it becomes second order only in the limiting case of zero bending stiffness (Delta triple bond 0). These analytical results are confirmed by Monte Carlo simulations. We also suggest some possible future experiments.     

Triple minima in the free energy of semiflexible polymers

We study the free energy of the worm-like-chain model, in the constant-extension ensemble, as a function of the stiffness lambda for finite chains of length L. We find that the polymer properties obtained in this ensemble are qualitatively different from those obtained using constant-force ensembles. In particular, we find that as we change the stiffness parameter, t=L/lambda, the polymer makes a transition from the flexible to the rigid phase and there is an intermediate regime of parameter values where the free energy has three minima and both phases are stable. This leads to interesting features in the force-extension curves.     

Rotational Brownian dynamics of semiflexible broken rods

Using the Brownian dynamics simulation technique, we study the rotational dynamics of a semiflexible broken rod. We employ a suitable bead model with stiff springs between beads and strong forces opposing to bending, except at the joint where flexibility is variable. We consider mostly broken rods with equal arms. From the simulated Brownian trajectories we obtain the correlation function for the second order Legendre polynomial of the reorientational angle of the end-to-end vector and of the arm vector. These correlation functions are closely related to fluorescence anisotropy decay and electric birefringence decay, respectively. In the first case, the relaxation time for a completely flexible rod agrees with the Harvey-Wegener theory, and in the second, the longest relaxation time agrees well with that obtained from the rigid-body treatment over the whole range of flexibility. Furthermore, we discuss the relative importance of flexibility in both types of decay. Finally, we present results for a case with unequal arms, confirming the validity of the Harvey-Wegener theory and the rigid-body treatment.     

Free energy of semiflexible polymers and structure of interfaces

The free energy of semiflexible polymers is calculated as a functional of the compositional scalar order parameter and the orientational order parameter of second-rank tensor S_ij on the basis of a microscopic model of wormlike chains with variable segment lengths. We use a density functional theory and a gradient expansion to evaluate the entropic part of the free energy, which is given in a power series of .The interaction term of the free energy is derived with a random phase approximation. For the rigid rod limit, the nematic-isotropic transition point is given by , N and w being the degree of polymerization and the anisotropic interaction parameter, respectively, and the degree of ordering at the transition point is 0.33448. We also find that the contour length of polymer chains becomes larger in a nematic phase than in an isotropic phase. Interface profiles are obtained numerically for some typical cases. In the neighborhood of isotropic-isotropic interfaces, polymer chains tend to align parallel to the interface on the polymer-rich side and perpendicular on the poor side. When an isotropic region and a nematic region coexist, orientational order parallel to the interface is preferred in the nematic region. Received: 28 May 1998 / Revised: 12 August 1998 / Accepted: 8 September 1998     

Elongation and fluctuations of semiflexible polymers in a nematic solvent

We directly visualize single polymers with persistence lengths l(p), ranging from 0.05 to 16 microm, dissolved in the nematic phase of rodlike fd virus. Polymers with a sufficiently large persistence length undergo a coil-rod transition at the isotropic-nematic transition of the background solvent. We quantitatively analyze the transverse fluctuations of the semiflexible polymers and show that at long wavelengths they are driven by the fluctuating nematic background. We extract the Odijk deflection length and the elastic constant of the background nematic phase from the data.     

Potts model,Dirac propagator,and conformational statistics of semiflexible polymers

A new discretized version of the Dirac propagator ind space and one time dimensions is obtained with the help of the 2d-state, one-dimensional Potts model. The Euclidean version of this propagator describes all conformational properties of semiflexible polymers. It also describes all properties of fully directed self-avoiding walks. The case of semiflexible copolymers composed of a random sequence of fully flexible and semirigid monomer units is also considered. As a by-product, some new results for disordered one-dimensional Ising and Potts models are obtained. In the case of the Potts model the nontrivial extension of the results to higher dimensions is discussed briefly.     

Relaxation dynamics of charged gravitational collapse

We study analytically the relaxation dynamics of charged test fields left outside a newly born charged black hole. In particular, we obtain a simple analytic expression for the fundamental quasinormal resonances of near-extremal Reissner-Nordström black holes. The formula is expressed in terms of the black-hole physical parameters: , where TBH and Φ are the temperature and electric potential of the black hole, and q is the charge of the field.     

Relaxation dynamics of a crumpled globule

The relaxation dynamics of elastic networks of crumpled (fractal) globules obtained by computer simulation of the collapse of a polymer chain in different modes is studied. It is shown that, in their dynamic properties, folded globules are similar to proteins, molecular machines.     

Molecular dynamics simulation of semiflexible polyampholyte brushes--The effect of charged monomers sequence

Planar brushes formed by end-grafted semiflexible polyampholyte chains, each chain containing an equal number of positively and negatively charged monomers, are studied using molecular dynamics simulations. Keeping the length of the chains fixed, the dependences of the average brush thickness and equilibrium statistics of the brush conformations on the grafting density and the salt concentration are obtained with various sequences of charged monomers. When similarly charged monomers of the chains are arranged in longer blocks, the average brush thickness is smaller and the dependence of brush properties on the grafting density and the salt concentration is stronger. With such long blocks of similarly charged monomers, the anchored chains bond to each other in the vicinity of the grafting surface at low grafting densities and buckle toward the grafting surface at high grafting densities.     

Relaxation dynamics in quantum electron glasses

It is experimentally shown that, depending on the carrier concentration of the system n, the dynamics of electron glasses either slows down with increasing temperature or it is independent of it. This also correlates with the dependence of a typical relaxation time (or "viscosity") on n. These linked features are argued to be consistent with a model for dissipative tunneling. The slow relaxation of the electron glass may emerge then as a manifestation of friction in a many-body quantum system. Our considerations may also explain why strongly localized granular metals are likely to show electron-glass effects while semiconductors are not.