Searcharxiv⌕ Search

arXiv subjects

Jan Kierfeld

Publications and source records attributed to Jan Kierfeld.

45 records · Page 3Linked to original sources
arXiv2012

Dynamics and length distribution of microtubules under force and confinement

We investigate the microtubule polymerization dynamics with catastrophe and rescue events for three different confinement scenarios, which mimic typical cellular environments: (i) The microtubule is confined by rigid and fixed walls, (ii) it grows under constant force, and (iii) it grows against an elastic obstacle with a linearly increasing force. We use realistic catastrophe models and analyze the microtubule dynamics, the resulting microtubule length distributions, and force generation by stochastic and mean field calculations; in addition, we perform stochastic simulations. We also investigate the force dynamics if growth parameters are perturbed in dilution experiments. Finally, we show the robustness of our results against changes of catastrophe models and load distribution factors.

q-bio.SC↗
arXiv2012

Localization transition of stiff directed lines in random media

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. On the basis of the two-replica problem, we propose a relation between the localization of stiff directed lines in 1+d dimensions and of directed lines under tension in 1+3d dimensions, which is strongly supported by identical free energy distributions. This shows that pair interactions in the replicated Hamiltonian determine the nature of directed line localization transitions with consequences for the critical behavior of the Kardar-Parisi-Zhang (KPZ) equation. Furthermore, we quantify how the persistence length of the stiff directed line is reduced by disorder.

cond-mat.stat-mech↗
arXiv2011

Buckling of Spherical Capsules

We investigate buckling of soft elastic capsules under negative pressure or for reduced capsule volume. Based on nonlinear shell theory and the assumption of a hyperelastic capsule membrane, shape equations for axisymmetric and initially spherical capsules are derived and solved numerically. A rich bifurcation behavior is found, which is presented in terms of bifurcation diagrams. The energetically preferred stable configuration is deduced from a least-energy principle both for prescribed volume and prescribed pressure. We find that buckled shapes are energetically favorable already at smaller negative pressures and larger critical volumes than predicted by the classical buckling instability. By preventing self-intersection for strongly reduced volume, we obtain a complete picture of the buckling process and can follow the shape from the initial undeformed state through the buckling instability into the fully collapsed state. Interestingly, the sequences of bifurcations and stable capsule shapes differ for prescribed volume and prescribed pressure. In the buckled state, we find a relation between curvatures at the indentation rim and the bending modulus, which can be used to determine elastic moduli from experimental shape analysis.

cond-mat.soft↗
arXiv2011

Persistence length of semiflexible polymers and bending rigidity renormalization

The persistence length of semiflexible polymers and one-dimensional fluid membranes is obtained from the renormalization of their bending rigidity. The renormalized bending rigidity is calculated using an exact real-space functional renormalization group transformation based on a mapping to the one-dimensional Heisenberg model. The renormalized bending rigidity vanishes exponentially at large length scales and its asymptotic behaviour is used to define the persistence length. For semiflexible polymers, our result agrees with the persistence length obtained using the asymptotic behaviour of tangent correlation functions. Our definition differs from the one commonly used for fluid membranes, which is based on a perturbative renormalization of the bending rigidity.

cond-mat.stat-mech↗
arXiv2011

Coupling of actin hydrolysis and polymerization: Reduced description with two nucleotide states

The polymerization of actin filaments is coupled to the hydrolysis of adenosine triphosphate (ATP), which involves both the cleavage of ATP and the release of inorganic phosphate. We describe hydrolysis by a reduced two-state model with a cooperative cleavage mechanism, where the cleavage rate depends on the state of the neighboring actin protomer in a filament. We obtain theoretical predictions of experimentally accessible steady state quantities such as the size of the ATP-actin cap, the size distribution of ATP-actin islands, and the cleavage flux for cooperative cleavage mechanisms.

cond-mat.stat-mech↗
arXiv2011

Stall force of polymerizing microtubules and filament bundles

We investigate stall force and polymerization kinetics of rigid protofilaments in a microtubule or interacting filaments in bundles under an external load force in the framework of a discrete growth model. We introduce the concecpt of polymerization cycles to describe the stochastic growth kinetics, which allows us to derive an exact expression for the stall force. We find that the stall force is independent of ensemble geometry and load distribution. Furthermore, the stall force is proportional to the number of filaments and increases linearly with the strength of lateral filament interactions. These results are corroborated by simulations, which also show a strong influence of ensemble geometry on growth kinetics below the stall force.

cond-mat.stat-mech↗
arXiv2010

Duality mapping and unbinding transitions of semiflexible and directed polymers

Directed polymers (strings) and semiflexible polymers (filaments) are one-dimensional objects governed by tension and bending energy, respectively. They undergo unbinding transitions in the presence of a short-range attractive potential. Using transfer matrix methods we establish a duality mapping for filaments and strings between the restricted partition sums in the absence and the presence of a short-range attraction. This allows us to obtain exact results for the critical exponents related to the unbinding transition, the transition point and transition order.

cond-mat.stat-mech↗
arXiv1995

Replica Symmetry Breaking in Renormalization: Application to the Randomly Pinned Planar Flux Array

The randomly pinned planar flux line array is supposed to show a phase transition to a vortex glass phase at low temperatures. This transition has been examined by using a mapping onto a 2D XY-model with random an\-iso\-tropy but without vortices and applying a renormalization group treatment to the replicated Hamiltonian based on the mapping to a Coulomb gas of vector charges. This renormalization group approach is extended by deriving renormalization group flow equations which take into account the possibility of a one-step replica symmetry breaking. It is shown that the renormalization group flow is unstable with respect to replica asymmetric perturbations and new fixed points with a broken replica symmetry are obtained. Approaching these fixed points the system can optimize its free energy contributions from fluctuations on large length scales; an optimal block size parameter $m$ can be found. Correlation functions for the case of a broken replica symmetry can be calculated. We obtain both correlations diverging as $\ln{r}$ and $\ln^2{r}$ depending on the choice of $m$.

cond-mat↗