Numerical Treatment of the Filament-Based Lamellipodium Model (FBLM)

Manhart, Angelika; Oelz, Dietmar; Schmeiser, Christian; Sfakianakis, Nikolaos

doi:10.1007/978-3-319-45833-5_7

Cited by 12 publications

(29 citation statements)

References 29 publications

(60 reference statements)

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“…We predict flexocytes of puller type to be reflected by walls with a preferred reflection angle. This finding is very different from steady-state accumulation of active Brownian particles at walls [46,47], and it can also not be expected for filament-based cell-motility models that require a manually added chemoattractant gradient or intracellular processes to drive motility [19,22]. It reflects the internal reorganization of the filaments and reproduces the behavior of keratocytes at interfaces between adhesive and passivated, microgrooved interfaces [48,49].…”

Section: Discussionmentioning

confidence: 73%

“…Motility is controlled mainly by actin polymerization and actomyosin contractility [12,13]; it is challenging to study cell motility theoretically because of the large length-scale gap between single filaments and entire cells. Therefore, generic continuum models have been developed to predict cell shape and motility on homogenous substrates [12,[14][15][16][17], on striped substrates substrates and at interfaces [18][19][20], as well as for cell-cell collisions [21]. Alternative continuum models with governing equations derived from the filamentous microstructure have been employed to include details of the cytoskeletal organization [19,22].…”

Section: Introductionmentioning

confidence: 99%

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Vesicles with internal active filaments: self-organized propulsion controls shape, motility, and dynamical response

2019

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Self-propulsion and navigation due to the sensing of environmental conditions-such as durotaxis and chemotaxis-are remarkable properties of biological cells that cannot be modeled by singlecomponent self-propelled particles. Therefore, we introduce and study 'flexocytes', deformable vesicles with enclosed attached self-propelled pushing and pulling filaments that align due to steric and membrane-mediated interactions. Using computer simulations in two dimensions, we show that the membrane deforms under the propulsion forces and forms shapes mimicking motile biological cells, such as keratocytes and neutrophils. When interacting with walls or with interfaces between different substrates, the internal structure of a flexocyte reorganizes, resulting in a preferred angle of reflection or deflection, respectively. We predict a correlation between motility patterns, shapes, characteristics of the internal forces, and the response to micropatterned substrates and external stimuli. We propose that engineered flexocytes with desired mechanosensitive capabilities enable the construction of soft-matter microbots.Models with explicit filaments have been used to study specific biological processes, such as filopodia formation [23] and lamellipodial waves [24,25].Many self-organized machineries constructed from various active and passive components inherently include regulation and sensing capability. The internal components react differently to stimuli and the machinery can therefore process external information. The interplay between active and spatial selforganization can be found in biological cells and engineered colloidal systems, as well as in biological or artificial systems on significantly larger length scales. For example, diffusiophoretic Janus colloids form spinning superstructures that can autonomously regulate themselves [26], groups of ants collectively carry a large cargo to their nest [27], and microbots in deformable mobile confinement [28] demonstrate complex responses to environmental cues.Here, we introduce self-propelled 'flexocytes', a minimal model system to study the motility of mechanosensitive active vesicles based on self-organization of explicit protrusion and retraction forces. The model consists of active filaments in vesicles pulling or pushing on the membrane, and is suitable for singleagent and multi-agent simulations. We perform Brownian dynamics simulations for this system in the overdamped regime to model substrate friction and internal noise. We find that the filaments in the flexocytes self-organize to reproduce cellular shapes and motility patterns, giving rise to dynamical phase transitions. Furthermore, we show that explicit pulling forces are sufficient to recover behavior of keratocytes: such flexocytes are reflected at walls and deflected at friction interfaces. Motility in our simulations is subject to noise. Interestingly, additional explicit pushing forces lead to less persistent motion, induce trapping at walls, and reduce deflection at interfaces. Therefore, we propose 'scatte...

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Section: Discussionmentioning

confidence: 73%

Section: Introductionmentioning

confidence: 99%

Vesicles with internal active filaments: self-organized propulsion controls shape, motility, and dynamical response

2019

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“…We present here only the main components of the FBLM and refer to [18,16,15,10,11,3,23] for more details.…”

Section: The Fblmmentioning

confidence: 99%

“…The effect of cell-cell adhesion is evident primarily in the cells that are found in the ridges of Table 1: Basic set of parameter values used in the numerical simulations of the FBLM in all the experiment of this work. These parameters have been adopted from [11,23].…”

Section: Experiments 3 (Cluster Formation)mentioning

confidence: 99%

Modelling cell-cell collision and adhesion with the filament based lamellipodium model

Sfakianakis

Peurichard²,

Brunk³

et al. 2018

BIOMATH

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We extend the live-cell motility Filament Based Lamellipodium Model to incorporate the forces exerted on the lamellipodium of the cells due to cell-cell collision and cadherin induced cell-cell adhesion. We take into account the nature of these forces via physical and biological constraints and modelling assumptions. We investigate the effect these new components have in the migration and morphology of the cells through particular experiments. We exhibit moreover the similarities between our simulated cells and HeLa cancer cells.

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“…Among models describing spontaneous motion of cells, two types appear : those who heuristically mimic macroscopic features and models based on a microscopic description that are in some sense homogenized. The Filament Based Lamelipodium Model (FBLM) 18 belongs to the second category and has reached a certain level of maturity 10,11 .…”

Section: Introductionmentioning

confidence: 99%

From delayed and constrained minimizing movements to the harmonic map heat equation

Milisic

2020

Journal of Functional Analysis

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In the context of cell motility modelling and more particularly related to the Filament Based Lamelipodium Model 18,10,11 , this work deals with a rigorous mathematical proof of convergence between solutions of two problems : we start from a microscopic description of adhesions using a delayed and constrained vector valued equation with spacial diffusion and show the convergence towards the corresponding friction limit. The convergence is performed with respect to the bond characteristic lifetime ε whose inverse is also proportional to the stifness of the bonds. The originality of this work is the extension of gradient flow techniques to our setting. Namely, the discrete finite difference term in the gradient flow energy is here replaced by a delay term which complicates greatly the mathematical analysis. Contrarily to the standard approach 2,19 , compactness in time is not provided by the energy minimization process : a series of past times are taken into account in our discrete energy. A supplementary equation on the time derivative is obtained requiring uniform estimate with respect to ε of the Lagrange multiplier and provides compactness. Due to the non-linearity induced by the constraint, a specific stability estimate useful in our previous works, is not at hand here. Numerical simulations even showed that this estimate does not hold. Nevertheless, transposing our delay operator, we succeed in proving convergence under slightly weaker hypotheses. The result relies on a careful initial layer analysis, extending 15 to the space dependent setting.

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Numerical Treatment of the Filament-Based Lamellipodium Model (FBLM)

Cited by 12 publications

References 29 publications

Vesicles with internal active filaments: self-organized propulsion controls shape, motility, and dynamical response

Vesicles with internal active filaments: self-organized propulsion controls shape, motility, and dynamical response

Modelling cell-cell collision and adhesion with the filament based lamellipodium model

From delayed and constrained minimizing movements to the harmonic map heat equation

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