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

Manhart, Angelika; Schmeiser, Christian

doi:10.1007/s00285-016-1027-z

Cited by 3 publications

(2 citation statements)

References 27 publications

(49 reference statements)

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“…is stable. In separate work [21] we prove that this qualitative behavior carries over to the corresponding transport-reaction system with prescribed lateral flow velocities.…”

Section: Length Distribution and Filament Number Regulationmentioning

confidence: 67%

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

Manhart

Oelz

Schmeiser

et al. 2015

Journal of Theoretical Biology

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The Filament Based Lamellipodium Model (FBLM) is a two-phase two-dimensional continuum model, describing the dynamcis of two interacting families of locally parallel actin filaments [31]. 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 effect of a chemoattractant is described by a simple signal transduction model influencing the polymerization speed. Simulations with the extended model show its potential for describing various moving cell shapes, depending on the signal transduction procedure, and for predicting transients between nonmoving and moving states as well as changes of direction.

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“…is stable. In separate work [21] we prove that this qualitative behavior carries over to the corresponding transport-reaction system with prescribed lateral flow velocities.…”

Section: Length Distribution and Filament Number Regulationmentioning

confidence: 67%

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

Manhart

Oelz

Schmeiser

et al. 2015

Journal of Theoretical Biology

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“…Computational modelling is a valuable complement to experiments in the understanding of complex cell migration mechanics. Modeling of cell motility on flat 2D surfaces is very advanced due to a relative simplicity of 2D cell motile appendages that are amenable to description in terms of partial differential equations [19]. 3D cell migration and respective modeling are much more complex.…”

Section: Introductionmentioning

confidence: 99%

Computational estimates of mechanical constraints on cell migration through the extracellular matrix

2020

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Cell migration through a three-dimensional (3D) extracellular matrix (ECM) underlies important physiological phenomena and is based on a variety of mechanical strategies depending on the cell type and the properties of the ECM. By using computer simulations of the cell's mid-plane, we investigate two such migration mechanisms-'push-pull' (forming a fingerlike protrusion, adhering to an ECM node, and pulling the cell body forward) and 'rearsqueezing' (pushing the cell body through the ECM by contracting the cell cortex and ECM at the cell rear). We present a computational model that accounts for both elastic deformation and forces of the ECM, an active cell cortex and nucleus, and for hydrodynamic forces and flow of the extracellular fluid, cytoplasm, and nucleoplasm. We find that relations between three mechanical parameters-the cortex's contractile force, nuclear elasticity, and ECM rigidity-determine the effectiveness of cell migration through the dense ECM. The cell can migrate persistently even if its cortical contraction cannot deform a near-rigid ECM, but then the contraction of the cortex has to be able to sufficiently deform the nucleus. The cell can also migrate even if it fails to deform a stiff nucleus, but then it has to be able to sufficiently deform the ECM. Simulation results show that nuclear stiffness limits the cell migration more than the ECM rigidity. Simulations show the rear-squeezing mechanism of motility results in more robust migration with larger cell displacements than those with the push-pull mechanism over a range of parameter values. Additionally, results show that the rear-squeezing mechanism is aided by hydrodynamics through a pressure gradient.

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Stability, Convergence, and Sensitivity Analysis of the FBLM and the Corresponding FEM

Sfakianakis

Brunk

2018

Bull Math Biol

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We study in this paper the filament-based lamellipodium model (FBLM) and the corresponding finite element method (FEM) used to solve it. We investigate fundamental numerical properties of the FEM and justify its further use with the FBLM. We show that the FEM satisfies a time step stability condition that is consistent with the nature of the problem and propose a particular strategy to automatically adapt the time step of the method. We show that the FEM converges with respect to the (two-dimensional) space discretization in a series of characteristic and representative chemotaxis and haptotaxis experiments. We embed and couple the FBLM with a complex and adaptive extracellular environment comprised of chemical and adhesion components that are described by their macroscopic density and study their combined time evolution. With this combination, we study the sensitivity of the FBLM on several of its controlling parameters and discuss their influence in the dynamics of the model and its future evolution. We finally perform a number of numerical experiments that reproduce biological cases and compare the results with the ones reported in the literature.

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

Cited by 3 publications

References 27 publications

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

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

Computational estimates of mechanical constraints on cell migration through the extracellular matrix

Stability, Convergence, and Sensitivity Analysis of the FBLM and the Corresponding FEM

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