Effects of microtubule mechanics on hydrolysis and catastrophes.

We introduce a model for microtubule (MT) mechanics containing lateral bonds between dimers in neighboring protofilaments, bending rigidity of dimers, and repulsive interactions between protofilaments modeling steric constraints to investigate the influence of mechanical forces on hydrolysis and catastrophes. We use the allosteric dimer model, where tubulin dimers are characterized by an equilibrium bending angle, which changes from 0° to 22° by hydrolysis of a dimer. This also affects the lateral interaction and bending energies and, thus, the mechanical equilibrium state of the MT. As hydrolysis gives rise to conformational changes in dimers, mechanical forces also influence the hydrolysis rates by mechanical energy changes modulating the hydrolysis rate. The interaction via the MT mechanics then gives rise to correlation effects in the hydrolysis dynamics, which have not been taken into account before. Assuming a dominant influence of mechanical energies on hydrolysis rates, we investigate the most probable hydrolysis pathways both for vectorial and random hydrolysis. Investigating the stability with respect to lateral bond rupture, we identify initiation configurations for catastrophes along the hydrolysis pathways and values for a lateral bond rupture force. If we allow for rupturing of lateral bonds between dimers in neighboring protofilaments above this threshold force, our model exhibits avalanche-like catastrophe events.

Characterization of single semiflexible filaments under geometric constraints.

Confinement effects on single semiflexible macromolecules are of central importance for a fundamental understanding of cellular processes involving biomacromolecules. To analyze the influence of confinement on the fluctuations of semiflexible macromolecules we study individual actin filaments in straight and curved microchannels. We experimentally characterize the segment distributions for fluctuating semiflexible filaments in microchannels as a function of the channel width. Moreover, the effect of channel curvature on the filament fluctuations is investigated. We find quantitative agreement between experimental results, Monte Carlo simulations, and the analytical description. This allows for determination of the persistence length of actin filaments, the deflection length, which characterizes the confinement effects, and the scaling exponents for the segment distribution of semiflexible macromolecules.

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.

Slow crack propagation in heterogeneous materials.

Statistics and thermally activated dynamics of crack nucleation and propagation in a two-dimensional heterogeneous material containing quenched randomly distributed defects are studied theoretically. Using the generalized Griffith criterion we derive the equation of motion for the crack tip position accounting for dissipation, thermal noise, and the random forces arising from the defects. We find that aggregations of defects generating long-range interaction forces (e.g., clouds of dislocations) lead to anomalously slow creep of the crack tip or even to its complete arrest. We demonstrate that heterogeneous materials with frozen defects contain a large number of arrested microcracks and that their fracture toughness is enhanced to the experimentally accessible time scales.

Competitive localization of vortex lines and interacting bosons.

We present a theory for the localization of three-dimensional vortex lines or two-dimensional bosons with a short-ranged repulsive interaction which are competing for a single columnar defect or potential well. For two vortices we use a necklace model approach to find a new kind of delocalization transition between two different states with a single bound particle. This exchange-delocalization transition is characterized by the onset of vortex exchange on the defect for sufficiently weak vortex-vortex repulsion or sufficiently weak binding energy corresponding to high temperature. We calculate the transition point and order of the exchange-delocalization transition. A generalization of this transition to an arbitrary vortex number is proposed.

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.

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.

Theory of plastic vortex creep

We develop a theory for plastic vortex creep in a topologically disordered (dislocated) vortex solid phase in type-II superconductors in terms of driven thermally activated dislocation dynamics. Plastic barriers for dislocations show a power-law divergence at small driving currents j, U(pl)( j) approximately j(-&mgr;), with &mgr; = 1 for a single dislocation and &mgr; = 2/5 for creep of dislocation bundles. This implies a suppression of the creep rate at the transition from the ordered vortex phase ( &mgr; = 2/11) to the dislocated glass and can manifest itself as an observed increase of the apparent critical current (second peak). Our approach applies to general dynamics of disordered elastic media on a random substrate.