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One of the most important cellular behaviors is cell migration. It is observed in many cellular systems both in culture and in vivo, and involved in many essential physiological or pathological processes (wound healing, embryonic development, cancer metastasis etc).
Project:
The lamellipodium is a cellular structure composed of a dense interconnected network of actin filaments and several accessory proteins. Many cell types use this structure to crawl on flat surfaces through adhesion with the substrate. More specifically we are interested in keratocyte migration.
The goal of the present study is to use the framework of the Filament-Based Lamellipodium Model developed in the team, to study (i) collisions in multi-cellular systems and (ii) the role of the attachment of the lamellipodium at an internal bundle on the geometry of moving cells.
The FBLM is a two phase continuum model which has been derived from a microscopic model describing the cytoskeleton as a set of interconnected actin filaments modelled as inextensible beams. An interactive overview over our group's efforts to understand cell movement mathematically has been done by Angelika Manhart, see Understanding the Lamellipoium - A Mathematical Approach
Collaborations:
C. Schmeiser (Faculty of mathematics, University of Vienna), A. Manhart (Courant institute of mathematical sciences, NYU), N. Sfakianakis (Mainz, Germany), D. Oelz (RICAM,Wien)
Related publications:
N. Sfakianakis, D. Peurichard, A. Brunk, C. Schmeiser, Modelling cell-cell collision and adhesion with the Filament Based Lamellipodium Model, (2018), Biomath, lien arxiv
D. Ölz, C. Schmeiser, How do cells move? mathematical modelling of cytoskeleton dynamics and cell migration, in Cell mechanics: from single scale-based models to multiscale modelling,eds. A. Chauviere, L. Preziosi, and C. Verdier, Chapman and Hall / CRC Press, 2010.
D. Ölz, C. Schmeiser, Derivation of a model for symmetric lamellipodia with instantaneous cross-link turnover, Archive Rat. Mech. Anal. 198 (2010), pp. 963-980.
D. Ölz, C. Schmeiser, Simulation of lamellipodial fragments, J. Math. Biol. 64 (2012), pp. 513-528.
A. Manhart, D. Oelz, C. Schmeiser , N. Sfakianakis, An extended Filament Based Lamellipodium Model produces various moving cell shapes in the presence of chemotactic signals. Journal of Theoretical Biology, 382 (2015), pp. 244-258 (Movie1, Movie2)
S. Hirsch, D. Oelz, C. Schmeiser, Existence and uniqueness of solutions for a model of non-sarcomeric actomyosin bundles, DCDS-A 36 (2016), pp. 4945-4962.
A. Manhart, C. Schmeiser, Decay to equilibrium of the filament end density along the leading edge of the lamellipodium. Journal of Mathematical Biology (2016), online first.
S. Hirsch, A. Manhart, C. Schmeiser, Mathematical Modeling of Myosin Induced Bistability of Lamellipodial Fragments (Movie).Journal of Mathematical Biology (2016), online first.
A. Manhart, D. Oelz, C. Schmeiser, N. Sfakianakis, Numerical Treatment of the Filament Based Lamellipodium Model (Movie1, Movie2) - to appear in: Modeling Cellular Systems, Springer (2016)
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