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Mechanics of living cells migration:
modelling and numerical simulations

Version française : Mécanique de la migration de cellules vivantes : modélisation et simulations numériques
PhD at Laboratoire Interdisciplinaire de Physique
Keywords: Biophysics, Rheology, Complex fluids, Continuum mechanics, Cell biology, Interdisciplinary research.
Jocelyn Étienne,
Claude Verdier,
Funding: 1452 € per calendar month.

Many biological functions of living cells require that they exert mechanical stress on their environment. One of the most spectavular instance is cell crawling (migration), which is crucial to immune cells in order to reach an inflammation spot, but is also observed e.g. in tumor cells during metastasis formation. The understanding of these mechanics are thus primordial both for our fundamental understanding and for clinical research.

Figure: Actin network of a crawling cell.
Image fluo_actin

Adhesion molecules allow cells to transmit to their environment forces that are generated within an internal structure, the cytoskeleton. An essential component of the cytoskeleton is made a network of polymers, actin filaments, which undegoes continuous re-shaping and is crosslinked by molecular linkers whose binding times is a few seconds only. In addition to these links, molecular motors (myosins) act as links but are able to modify their anchorage point along the actin filament, and thus, to exert contractile forces within this network. A precise description of these molecular processes is available [Rossier et al, 2011], as well as the steps necessary to the migration of cells on a flat substrate [Mitchison & Cramer, 1996]. However, the first predictive simulations of cell crawling on a flat substrate [Wolgemuth et al, 2011] remain purely qualitative, and are based on ad hoc models of a specific type of cells, keratocytes, which have an atypical behaviour, simpler than the one of most other cells. The aim of this PhD project is to explain and predict quantitatively cell crawling (in particular of tumor cells). This will be based on a model that relies on the cytoskeleton molecular function and tested against cell migration experiments that are lead within the research team.

Figure: Prediction of traction forces exerted by a migrating cell on a substrate: left, model prediction for a given cell shape, right, measured forces. (Preliminary results).
Image migration_simul

Starting from the basis of a rheological model that has already been validated against quantitative force-deformation experiments [Etienne et al, 2015], the PhD candidate will elaborate a rheological model adapted to cell migration. In particular, this will include boundary conditions of force transmission at the interface between the cytoskeleton and the substrate. The current model describes as a modified Maxwell tensorial law the relaxation of the actin network as crosslinkers detach. It also describes its contraction under the effect of myosin motors. It allows to take into account the local anisotropy of actin filaments, which can be observed by fluorescence microscopy (see fig. [*]). Preliminary work allowed to demonstrate that a simplified version of this model is already sufficient to predict appropriately the traction forces that a cell of a given shape exerts on its substrate (see fig. [*]).

The objective of the PhD project is to improve these results, in particular by taking into account the local anisotropy of actin network, and by modelling the actin polymerisation dynamics. 3D migration will be the following focus, and will again be supported by a joint theoretical and experimental approach within the group (see fig. [*]).

Figure: Migrating cell in a collagen gel (red). Actin is labelled in green, yellow denotes colocalisation of actin and collagen. Grid: 7.11 µm spacing.
Image laure

The PhD candidate will use a finite element library software which specializes in rheology [Rheolef,, co-developed par J Etienne]. S/he will base investigations on existing traction force microscopy experimental results, to which s/he will be able to compare numerical results. S/he will take part in the planning of new experiments, and may take part in the experiments themselves.

Skills required:

The Laboratoire Interdisciplinaire de Physique is located in Grenoble.

Grenoble is the unique conjunction of a well-established university city with world-class research groups, within a breathtaking mountain landscape.

The Laboratoire was originally a Physics department, but is now highly interdisciplinary with many mechanicists, applied mathematicians and biologists working there as staff, post-docs or graduate students.

Funding is subject to acceptance by the University, and consists in a 1452 € salary par calendar month for 3 years. Health insurance is included. A paid complementary activity during the PhD, consisting of either teaching, research dissemination or valorisation, can be applied for. This complementary activity corresponds to 1/6 of the work time and increases the monthly salary to 1744 €.

Applications should include a letter detailing the motivation and relevance of the applicant's background for this particular project, a full CV and the names and email addresses of two referees. Please direct enquiries and applications to before 24th May 2016.

Start date between 1st September 2016 and 30th November 2016.


J. Étienne, J. Fouchard, D. Mitrossilis, N. Bufi, P. Durand, A. Asnacios, Cells as liquid motors: Mechanosensitivity emerges from collective dynamics of actomyosin cortex. PNAS - Proc. Natl.Acad. Sci. USA 112(9):2740-2745 (2015)

R. Michel, V. Peschetola, J. Étienne, A. Duperray, G. Vitale, D. Ambrosi, L. Preziosi, C. Verdier, Mathematical framework for Traction Force Microscopy, ESAIM Proceedings, 42:61-83 (2013)

T. J. Mitchison and L. P. Cramer, Actin-Based Cell Motility and Cell Locomotion, Cell, 84(3):371-379 (1996)

V. Peschetola, V. Laurent, A. Duperray, R. Michel, D. Ambrosi, L. Preziosi, C. Verdier, Time-dependent traction force microscopy for cancer cells as a measure of invasiveness, Cytoskeleton, 70:201-214 (2013)

O. M. Rossier, N. Gauthier, N. Biais, W. Vonnegut, M.-A. Fardin, P. Avigan, E. R. Heller, A. Mathur, S. Ghassemi, M. S. Koeckert, J. C. Hone, M. P. Sheetz, Force generated by actomyosin contraction builds bridges between adhesive contacts, EMBO J., 29(10):1033-1044 (2010)

C. Verdier, J. Etienne, A. Duperray, L. Preziosi, Review : Rheological properties of biological materials, C. R. Physique, 10:790-811 (2009)

G. Vitale, L. Preziosi, D. Ambrosi, A numerical method for the inverse problem of cell traction in 3D, Inverse Problems, 28 (9):095013

C. W. Wogelmuth, J. Stajic and A. Mogilner, Redundant Mechanisms for Stable Cell Locomotion Revealed by Minimal Models, Biophys. J., 101(3):545-553 (2011)

Jocelyn Etienne 2015-05-06