The Influence of Nucleus Mechanics in Modelling Adhesion-independent Cell Migration in Structured and Confined Environments.

Recent biological experiments (Lämmermann et al. in Nature 453(7191):51-55, 2008; Reversat et al. in Nature 7813:582-585, 2020; Balzer et al.

A mathematical model of p62-ubiquitin aggregates in autophagy.

Aggregation of ubiquitinated cargo by oligomers of the protein p62 is an important preparatory step in cellular autophagy. In this work a mathematical model for the dynamics of these heterogeneous aggregates in the form of a system of ordinary differential equations is derived and analyzed. Three different parameter regimes are identified, where either aggregates are unstable, or their size saturates at a finite value, or their size grows indefinitely as long as free particles are abundant.

Hypocoercivity and Fast Reaction Limit for Linear Reaction Networks with Kinetic Transport.

The long time behavior of a model for a first order, weakly reversible chemical reaction network is considered, where the movement of the reacting species is described by kinetic transport. The reactions are triggered by collisions with a nonmoving background with constant temperature, determining the post-reactional equilibrium velocity distributions. Species with different particle masses are considered, with a strong separation between two groups of light and heavy particles.

Load Adaptation of Lamellipodial Actin Networks.

Actin filaments polymerizing against membranes power endocytosis, vesicular traffic, and cell motility. In vitro reconstitution studies suggest that the structure and the dynamics of actin networks respond to mechanical forces. We demonstrate that lamellipodial actin of migrating cells responds to mechanical load when membrane tension is modulated.

Existence of and decay to equilibrium of the filament end density along the leading edge of the lamellipodium.

A model for the dynamics of actin filament ends along the leading edge of the lamellipodium is analyzed. It contains accounts of nucleation by branching, of deactivation by capping, and of lateral flow along the leading edge by polymerization. A nonlinearity arises from a Michaelis-Menten type modeling of the branching process.

An extended Filament Based Lamellipodium Model produces various moving cell shapes in the presence of chemotactic signals.

The Filament Based Lamellipodium Model (FBLM) is a two-phase two-dimensional continuum model, describing the dynamics of two interacting families of locally parallel actin filaments (Oelz and Schmeiser, 2010b). It contains accounts of the filaments' bending stiffness, of adhesion to the substrate, and of cross-links connecting the two families. An extension of the model is presented with contributions from nucleation of filaments by branching, from capping, from contraction by actin-myosin interaction, and from a pressure-like repulsion between parallel filaments due to Coulomb interaction.

The flatness of Lamellipodia explained by the interaction between actin dynamics and membrane deformation.

The crawling motility of many cell types relies on lamellipodia, flat protrusions spreading on flat substrates but (on cells in suspension) also growing into three-dimensional space. Lamellipodia consist of a plasma membrane wrapped around an oriented actin filament meshwork. It is well known that the actin density is controlled by coordinated polymerization, branching, and capping processes, but the mechanisms producing the small aspect ratios of lamellipodia (hundreds of nm thickness vs.

Electron tomography and simulation of baculovirus actin comet tails support a tethered filament model of pathogen propulsion.

Several pathogens induce propulsive actin comet tails in cells they invade to disseminate their infection. They achieve this by recruiting factors for actin nucleation, the Arp2/3 complex, and polymerization regulators from the host cytoplasm. Owing to limited information on the structural organization of actin comets and in particular the spatial arrangement of filaments engaged in propulsion, the underlying mechanism of pathogen movement is currently speculative and controversial.

Arp2/3 complex is essential for actin network treadmilling as well as for targeting of capping protein and cofilin.

Lamellipodia are sheet-like protrusions formed during migration or phagocytosis and comprise a network of actin filaments. Filament formation in this network is initiated by nucleation/branching through the actin-related protein 2/3 (Arp2/3) complex downstream of its activator, suppressor of cAMP receptor/WASP-family verprolin homologous (Scar/WAVE), but the relative relevance of Arp2/3-mediated branching versus actin filament elongation is unknown. Here we use instantaneous interference with Arp2/3 complex function in live fibroblasts with established lamellipodia.

Actin branching in the initiation and maintenance of lamellipodia.

Using correlated live-cell imaging and electron tomography we found that actin branch junctions in protruding and treadmilling lamellipodia are not concentrated at the front as previously supposed, but link actin filament subsets in which there is a continuum of distances from a junction to the filament plus ends, for up to at least 1 μm. When branch sites were observed closely spaced on the same filament their separation was commonly a multiple of the actin helical repeat of 36 nm. Image averaging of branch junctions in the tomograms yielded a model for the in vivo branch at 2.

Actin filament tracking in electron tomograms of negatively stained lamellipodia using the localized radon transform.

The aim of this work was to develop a protocol for automated tracking of actin filaments in electron tomograms of lamellipodia embedded in negative stain. We show that a localized version of the Radon transform for the detection of filament directions enables three-dimensional visualizations of filament network architecture, facilitating extraction of statistical information including orientation profiles. We discuss the requirements for parameter selection set by the raw image data in the context of other, similar tracking protocols.

Simulation of lamellipodial fragments.

A steepest descent approximation scheme is derived for a recently developed model for the dynamics of the actin cytoskeleton in the lamellipodia of living cells. The scheme is used as a numerical method for the simulation of thought experiments, where a lamellipodial fragment is pushed by a pipette, and subsequently changes its shape and position.

Modeling of the actin-cytoskeleton in symmetric lamellipodial fragments.

The pushing structures of cells include laminar sheets, termed lamellipodia, made up of a meshwork of actin filaments that grow at the front and depolymerise at the rear, in a treadmilling mode.We here develop a mathematical model to describe the turnover and the mechanical properties of this network.Our basic modeling assumptions are that the lamellipodium is idealised as a two-dimensional structure, and that the actin network consists of two families of possibly bent, but locally parallel filaments.

Multistep navigation of leukocytes: a stochastic model with memory effects.

We present a model for the chemotactically directed migration of neutrophil leukocytes. It reproduces the multistep navigation by memory effects investigated experimentally by E. F.