Modeling adhesion-independent cell migration

Jankowiak, Gaspard; Peurichard, Diane; Reversat, Anne; Schmeiser, Christian; Sixt, Michael

doi:10.1142/s021820252050013x

Cited by 3 publications

(13 citation statements)

References 24 publications

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“…We can examine the relationship between shape and speed of cells by the cell-level model. In addition, by regarding the segments in our model as the cortex in cells, we are able to investigate cortical flow within moving cells, as in previously published studies (Jankowiak et al, 2020). A key point of the present model is that due to the discreteness of this model, we can easily set the parameter values that specify key characteristics of the cells we are modeling.…”

Section: Discussionmentioning

confidence: 98%

“…Friction force on the cell boundary should not depend on discretization of the cell boundary, but instead, should satisfy a continuous limit (i.e., the frictional force is expressed by a quantity per unit length of the cell boundary). Recently a 2D continuous mathematical model has been proposed that successfully reproduces the adhesion-independent movement of a single cell confined in a 3D space under axisymmetric conditions (Jankowiak et al, 2020). However, this model can assess only one cell.…”

Section: Introductionmentioning

confidence: 99%

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A cell membrane model that reproduces cortical flow-driven cell migration and collective movement

Sato

2023

Front. Cell Dev. Biol.

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Many fundamental biological processes are dependent on cellular migration. Although the mechanical mechanisms of single-cell migration are relatively well understood, those underlying migration of multiple cells adhered to each other in a cluster, referred to as cluster migration, are poorly understood. A key reason for this knowledge gap is that many forces—including contraction forces from actomyosin networks, hydrostatic pressure from the cytosol, frictional forces from the substrate, and forces from adjacent cells—contribute to cell cluster movement, making it challenging to model, and ultimately elucidate, the final result of these forces. This paper describes a two-dimensional cell membrane model that represents cells on a substrate with polygons and expresses various mechanical forces on the cell surface, keeping these forces balanced at all times by neglecting cell inertia. The model is discrete but equivalent to a continuous model if appropriate replacement rules for cell surface segments are chosen. When cells are given a polarity, expressed by a direction-dependent surface tension reflecting the location dependence of contraction and adhesion on a cell boundary, the cell surface begins to flow from front to rear as a result of force balance. This flow produces unidirectional cell movement, not only for a single cell but also for multiple cells in a cluster, with migration speeds that coincide with analytical results from a continuous model. Further, if the direction of cell polarity is tilted with respect to the cluster center, surface flow induces cell cluster rotation. The reason why this model moves while keeping force balance on cell surface (i.e., under no net forces from outside) is because of the implicit inflow and outflow of cell surface components through the inside of the cell. An analytical formula connecting cell migration speed and turnover rate of cell surface components is presented.

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Section: Discussionmentioning

confidence: 98%

Section: Introductionmentioning

confidence: 99%

A cell membrane model that reproduces cortical flow-driven cell migration and collective movement

Sato

2023

Front. Cell Dev. Biol.

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“…Concerning the evolution of the cell membrane, we refer to the model proposed in Jankowiak et al. ( 2020 ), properly modified in order to take into account the presence of the nucleus and the MT structure. The evolution of the actin density, describing the active component of the model due to the heterogeneity of the polymerization rate across the cortex, is given by Jankowiak et al.…”

Section: The Mathematical Modelmentioning

confidence: 99%

“…The evolution of the actin density, describing the active component of the model due to the heterogeneity of the polymerization rate across the cortex, is given by Jankowiak et al. ( 2020 ): where is the rate of actin density increase ( ) or decrease ( ).…”

Section: The Mathematical Modelmentioning

confidence: 99%

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

Giverso,

Jankowiak,

Preziosi

et al. 2023

Bull Math Biol

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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. in ASEB J Off Publ Fed Am Soc Exp Biol 26(10):4045–4056, 2012) have shown that certain types of cells are able to move in structured and confined environments even without the activation of focal adhesion. Focusing on this particular phenomenon and based on previous works (Jankowiak et al. in Math Models Methods Appl Sci 30(03):513–537, 2020), we derive a novel two-dimensional mechanical model, which relies on the following physical ingredients: the asymmetrical renewal of the actin cortex supporting the membrane, resulting in a backward flow of material; the mechanical description of the nuclear membrane and the inner nuclear material; the microtubule network guiding nucleus location; the contact interactions between the cell and the external environment. The resulting fourth order system of partial differential equations is then solved numerically to conduct a study of the qualitative effects of the model parameters, mainly those governing the mechanical properties of the nucleus and the geometry of the confining structure. Coherently with biological observations, we find that cells characterized by a stiff nucleus are unable to migrate in channels that can be crossed by cells with a softer nucleus. Regarding the geometry, cell velocity and ability to migrate are influenced by the width of the channel and the wavelength of the external structure. Even though still preliminary, these results may be potentially useful in determining the physical limit of cell migration in confined environments and in designing scaffolds for tissue engineering.

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Cellular locomotion using environmental topography

Reversat

Gaertner

Merrin

et al. 2020

Nature

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184

166

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Eukaryotic cells migrate by coupling the intracellular force of the actin cytoskeleton to the environment. While force-coupling is usually mediated by transmembrane adhesion receptors, especially these of the integrin family, amoeboid cells like leukocytes can migrate extremely fast despite very low adhesive forces 1 . We show that leukocytes cannot only migrate under low adhesion but indeed can transduce forces in the complete absence of transmembrane force coupling. When confined within three-dimensional environments, they use the topographic features of the substrate to propel themselves. Here, the retrograde flow of the actin cytoskeleton follows the texture of the substrate, creating shear forces sufficient to drive deformations towards the back of the cell. Notably, adhesion dependent and adhesion independent migration are not exclusive but rather variants of the same principle of coupling retrograde actin flow to the environment and thus can potentially operate simultaneously. As adhesion free migration is independent of the chemical composition of the environment it renders cells completely autonomous in their locomotive behavior..

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Modeling adhesion-independent cell migration

Cited by 3 publications

References 24 publications

A cell membrane model that reproduces cortical flow-driven cell migration and collective movement

A cell membrane model that reproduces cortical flow-driven cell migration and collective movement

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

Cellular locomotion using environmental topography

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