Simulation of a Free Boundary Cell Migration Model through Physics Informed Neural Networks.

Understanding the complexities of single-cell migration is facilitated by computational modeling, which provides important insights into the physiological processes that underlie migration mechanisms. This study developed a computational model for one-dimensional actomyosin flow in a migrating cell with moving boundaries. The model incorporates the complex interplay of actin polymerization, substrate adhesion, and actomyosin dynamics through a system of coupled nonlinear partial differential equations.

Stretch-induced recruitment of myosin into transversal actin rings stabilises axonal large cargo transport.

We study the axonal transport of large cargo vesicles and its feedback with contractile transversal actomyosin rings in axons through modelling and simulation. To this end, we simulate a mathematical model that integrates forces generated by the molecular motors and forces exerted by transversal actin rings. Our results predict that cargo vesicles exhibit bidirectional movement along with pauses in agreement with observations.

Compression-dependent microtubule reinforcement enables cells to navigate confined environments.

Cells migrating through complex three-dimensional environments experience considerable physical challenges, including tensile stress and compression. To move, cells need to resist these forces while also squeezing the large nucleus through confined spaces. This requires highly coordinated cortical contractility.

A mathematical model for axonal transport of large cargo vesicles.

In this study, we consider axonal transport of large cargo vesicles characterised by transient expansion of the axon shaft. Our goal is to formulate a mathematical model which captures the dynamic mechanical interaction of such cargo vesicles with the membrane associated periodic cytoskeletal structure (MPS). It consists of regularly spaced actin rings that are transversal to the longitudinal direction of the axon and involved in the radial contraction of the axon.

F-actin bending facilitates net actomyosin contraction By inhibiting expansion with plus-end-located myosin motors.

Contraction of actomyosin networks underpins important cellular processes including motility and division. The mechanical origin of actomyosin contraction is not fully-understood. We investigate whether contraction arises on the scale of individual filaments, without needing to invoke network-scale interactions.

Spatial redistribution of neurosecretory vesicles upon stimulation accelerates their directed transport to the plasma membrane.

Through the integration of results from an imaging analysis of intracellular trafficking of labelled neurosecretory vesicles in chromaffin cells, we develop a Markov state model to describe their transport and binding kinetics. Our simulation results indicate that a spatial redistribution of neurosecretory vesicles occurs upon secretagogue stimulation leading vesicles to the plasma membrane where they undergo fusion thereby releasing adrenaline and noradrenaline. Furthermore, we find that this redistribution alone can explain the observed up-regulation of vesicle transport upon stimulation and its directional bias towards the plasma membrane.

Protein friction and filament bending facilitate contraction of disordered actomyosin networks.

We use mathematical modeling and computation to investigate how protein friction facilitates contraction of disordered actomyosin networks. We simulate two-dimensional networks using an agent-based model, consisting of a system of force-balance equations for myosin motor proteins and semiflexible actin filaments. A major advantage of our approach is that it enables direct calculation of the network stress tensor, which provides a quantitative measure of contractility.

Quasi-steady-state reduction of a model for cytoplasmic transport of secretory vesicles in stimulated chromaffin cells.

Neurosecretory cells spatially redistribute their pool of secretory vesicles upon stimulation. Recent observations suggest that in chromaffin cells vesicles move either freely or in a directed fashion by what appears to be a conveyor belt mechanism. We suggest that this observation reflects the transient active transport through molecular motors along cytoskeleton fibres and quantify this effect using a 1D mathematical model that couples a diffusion equation to advection equations.

Polarization wave at the onset of collective cell migration.

Collective cell migration underlies morphogenesis, tissue regeneration, and cancer progression. How the biomechanical coupling between epithelial cells triggers and coordinates the collective migration is an open question. Here, we develop a one-dimensional model for an epithelial monolayer which predicts that after the onset of migration at an open boundary, cells in the bulk of the epithelium are gradually recruited into outward-directed motility, exhibiting traveling-wave-like behavior.

Bidirectional sliding of two parallel microtubules generated by multiple identical motors.

It is often assumed in biophysical studies that when multiple identical molecular motors interact with two parallel microtubules, the microtubules will be crosslinked and locked together. The aim of this study is to examine this assumption mathematically. We model the forces and movements generated by motors with a time-continuous Markov process and find that, counter-intuitively, a tug-of-war results from opposing actions of identical motors bound to different microtubules.

Microtubule Dynamics, Kinesin-1 Sliding, and Dynein Action Drive Growth of Cell Processes.

Recent experimental studies of the role of microtubule sliding in neurite outgrowth suggested a qualitative model, according to which kinesin-1 motors push the minus-end-out microtubules against the cell membrane and generate the early cell processes. At the later stage, dynein takes over the sliding, expels the minus-end-out microtubules from the neurites, and pulls in the plus-end-out microtubules that continue to elongate the nascent axon. This model leaves unanswered a number of questions: why is dynein unable to generate the processes alone, whereas kinesin-1 can? What is the role of microtubule dynamics in process initiation and growth? Can the model correctly predict the rates of process growth in control and dynein-inhibited cases? What triggers the transition from kinesin-driven to dynein-driven sliding? To answer these questions, we combine computational modeling of a network of elastic dynamic microtubules and kinesin-1 and dynein motors with measurements of the process growth kinetics and pharmacological perturbations in Drosophila S2 cells.

Actomyosin contraction, aggregation and traveling waves in a treadmilling actin array.

We use perturbation theory to derive a continuum model for the dynamic actomyosin bundle/ring in the regime of very strong crosslinking. Actin treadmilling is essential for contraction. Linear stability analysis and numerical solutions of the model equations reveal that when the actin treadmilling is very slow, actin and myosin aggregate into equidistantly spaced peaks.

A Combination of Actin Treadmilling and Cross-Linking Drives Contraction of Random Actomyosin Arrays.

We investigate computationally the self-organization and contraction of an initially random actomyosin ring. In the framework of a detailed physical model for a ring of cross-linked actin filaments and myosin-II clusters, we derive the force balance equations and solve them numerically. We find that to contract, actin filaments have to treadmill and to be sufficiently cross linked, and myosin has to be processive.

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.

A viscous two-phase model for contractile actomyosin bundles.

A mathematical model in one dimension for a non-sarcomeric actomyosin bundle featuring anti-parallel flows of anti-parallel F-actin is introduced. The model is able to relate these flows to the effect of cross-linking and bundling proteins, to the forces due to myosin-II filaments and to external forces at the extreme tips of the bundle. The modeling is based on a coarse graining approach starting with a microscopic model which includes the description of chemical bonds as elastic springs and the force contribution of myosin filaments.

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.

Size distribution dependence of prion aggregates infectivity.

We consider a model for the polymerization (fragmentation) process involved in infectious prion self-replication and study both its dynamics and non-zero steady state. We address several issues. Firstly, we extend a previous study of the nucleated polymerization model [M.

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.