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Amoeboid motion is a dynamic mode of cell motility essential for processes such as the immune response and wound healing. This review examines recent developments in the mathematical and computational modeling of amoeboid crawling, focusing…

Biological Physics · Physics 2026-03-17 Sergio Alonso , Carsten Beta

Cell migration is fundamental to development, tissue organization, immune response, and disease progression. Amoeboid motility is distinguished by rapid motion and strongly fluctuating cell shapes, reflecting the intrinsically nonlinear…

Soft Condensed Matter · Physics 2026-05-19 Winfried Schmidt , Chaouqi Misbah , Alexander Farutin

Cell migration is a fundamental process involved in physiological phenomena such as the immune response and morphogenesis, but also in pathological processes, such as the development of tumor metastasis. These functions are effectively…

Cell Behavior · Quantitative Biology 2018-12-26 Christèle Etchegaray , Nicolas Meunier

Cells perform directed motion in response to external stimuli that they detect by sensing the environment with their membrane protrusions. In particular, several biochemical and biophysical cues give rise to tactic migration in the…

Cell Behavior · Quantitative Biology 2020-07-15 N. Loy , M. Conte

Collective cell migration in response to a chemical cue occurs in many biological processes such as morphogenesis and cancer metastasis. Clusters of migratory cells in these systems are capable of responding to gradients of less than 1%…

Biological Physics · Physics 2016-08-24 Julien Varennes , Bumsoo Han , Andrew Mugler

Motile eukaryotic cells display distinct modes of migration that often occur within the same cell type. It remains unclear, however, whether transitions between the migratory modes require changes in external conditions, or whether the…

Pattern Formation and Solitons · Physics 2025-05-29 Jack M. Hughes , Cristina Martinez-Torres , Carsten Beta , Leah Edelstein-Keshet , Arik Yochelis

Chemotaxis combines three processes: directional sensing, polarity reorientation and migration. Directed migration plays an important role in immune response, metastasis, wound healing and development. To describe chemotaxis, we extend a…

Biological Physics · Physics 2023-12-04 Pedro C. Dal-Castel , Gilberto L. Thomas , Gabriel C. Perrone , Rita M. C. de Almeida

We present a COMSOL Multiphysics implementation of a continuum model for directed cell migration, a key mechanism underlying tissue self-organization and morphogenesis. The model is formulated as a partial integro-differential equation…

Biological Physics · Physics 2025-12-05 Malte Mederacke , Chengyou Yu , Roman Vetter , Dagmar Iber

Cell polarity and movement are fundamental to many biological functions. Experimental and theoretically studies have indicated that interactions of certain proteins lead to the cell polarization which plays a key role in controlling the…

Dynamical Systems · Mathematics 2022-08-12 Shuang Liu , Li-Tien Cheng , Bo Li

Mathematical and computational models can assist in gaining an understanding of cell behavior at many levels of organization. Here, we review models in the literature that focus on eukaryotic cell motility at 3 size scales: intracellular…

Cell Behavior · Quantitative Biology 2021-01-27 Andreas Buttenschön , Leah Edelstein-Keshet

This paper concerns a model for tumor cell migration through the surrounding extracellular matrix by considering mass balance phenomena involving the chemical interactions produced on the cell surface. The well-posedness of this model is…

Analysis of PDEs · Mathematics 2015-09-03 J. Nieto , L. Urrutia

Eukaryotic cell motility involves a complex network of interactions between biochemical components and mechanical processes. The cell employs this network to polarize and induce shape changes that give rise to membrane protrusions and…

Cell Behavior · Quantitative Biology 2022-01-03 E. Moreno , S. Flemming , F. Font , M. Holschneider , C. Beta , S. Alonso

Collective cell migration is a key driver of embryonic development, wound healing, and some types of cancer invasion. Here we provide a physical perspective of the mechanisms underlying collective cell migration. We begin with a catalogue…

Biological Physics · Physics 2019-10-08 Ricard Alert , Xavier Trepat

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…

Biological Physics · Physics 2023-07-25 Katsuhiko Sato

Multicellular collective migration is a ubiquitous strategy of cells to translocate spatially in diverse tissue environments to accomplish a wide variety of biological phenomena, viz. embryonic development, wound healing, and tumor…

Cell Behavior · Quantitative Biology 2022-01-20 Ushasi Roy , Tyler Collins , Mohit K. Jolly , Parag Katira

Morphologies of moving amoebae are categorized into two types. One is the ``neutrophil'' type in which the long axis of cell roughly coincides with its moving direction. This type of cell extends a leading edge at the front and retracts a…

Cell Behavior · Quantitative Biology 2007-05-23 Shin I. Nishimura , Masaki Sasai

Left-right axis specification establishes embryonic laterality through asymmetric signaling cascades originating at the cellular scale. We previously reported the presence of a directionality bias in confined pairs of endothelial (and…

Cell Behavior · Quantitative Biology 2026-03-31 Egun Im , Ghina Badih , Laetitia Kurzawa , Andreas Buttenschön , Calina Copos

Cell movement, for example during embryogenesis or tumor metastasis, is a complex dynamical process resulting from an intricate interplay of multiple components of the cellular migration machinery. At first sight, the paths of migrating…

Cell Behavior · Quantitative Biology 2009-04-17 Peter Dieterich , Rainer Klages , Roland Preuss , Albrecht Schwab

The migration behavior of colliding cells is critically determined by transient contact-interactions. During these interactions, the motility machinery, including the front-rear polarization of the cell, dynamically responds to surface…

Cells crawling through tissues migrate inside a complex fibrous environment called the extracellular matrix (ECM), which provides signals regulating motility. Here we investigate one such well-known pathway, involving mutually antagonistic…

Cell Behavior · Quantitative Biology 2017-07-05 William R. Holmes , JinSeok Park , Andre Levchenko , Leah Edelstein-Keshet
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