In the absence of signalling, single cells on a substrate perform a gentle persistent random walk. In the presence of chemical or physical cues they move ballistically at typical speeds of μm/min. Cells move by protruding the cell front and then retracting the rear, exploiting the ability of actin to reversibly self-assemble [1]. The cell is driven forward by actin polymerisation which results in the creation of lamellopodia and filopodia, protruding sheets or rods at the front of the cell. The back of the cell is contracted by focal conics, actin filaments that attach the surface, which are driven by myosin molecular motors to provide contractile stresses. Moreover there is increasing evidence that the activity of the cortex (a layer of actin under the cell membrane) also contributes to cell motility.

Single cells have been modelled as drops of active nematic or polar gel [2]. The active ‘cell’ is unstable to a shape change driven by a hydrodynamic instability and the resulting fore-aft asymmetry leads to motion [3],[4]. Similar cell shapes and propulsion result from a phase field model where the cell membrane is coupled to a chemical signalling network [5],[6] and from finite element approaches [7]. These models have been extended to multiple cells, giving visually realistic dynamics [8],[9], but as yet little is understood about the way in which moving cells interact.

There is growing experimental evidence documenting the motion of confluent cellular layers [10]. Such packed, motile cells move collectively and can initiate processes such as morphogenesis and wound healing. Increasingly physical arguments are being proposed as alternative ways to understand this motion. For example, protuburences that drive the motion of a cell front over a substrate have been attributed to the existence of `leader cells’, but can also be interpreted in terms of hydrodynamic instabilities [10], and the motion of confluent layers has variously been described in terms of glassy dynamics[11], and shown to resemble active turbulence [12]. Moreover there is now compelling evidence that the substrate has a considerable effect on cell motility: cells migrate from harder to softer surfaces [13]. Although experiments are usually performed on ideal surfaces, in vivo cells crawl through the extra-cellular matrix which is a tangled network of fibres.

Palmieri et al. use a phase field description where each cell is modelled as a highly deformable self-propelled droplet to study how the deformability of a given cell controls its ability to migrate [14]. The motivation is that cancer cells are more elastic than healthy cells. Thuan et al demonstrate that a confluent cellular layer can be mapped onto a continuum active nematic and identify topological defects with stress and strain fields that reproduce those measured experimentally [15]. Work from the Dresden group has mapped the cortex to a viscoelastic active gel, with impressive agreement between simulation and experiment [16]. Bi et al. model cells as self-propelled Voronoi polygons and predict a jamming transition [11]. The shape of individual cells and resolution of subcellular components has been represented by agent-based models [17].

The physical modelling of cell motility is in its infancy. This is a new direction that can be addressed by the mesoscale approaches that are familiar in soft matter physics. The science is particularly timely because of the advances in imaging techniques such as particle image velocimetry and traction force microscopy that are increasingly available to provide quantitative data on the dynamics of biological systems.

In the workshop we aim to:

(i) identify and work towards answering biological questions about the movement of cells where physical models can be useful to gain new understanding and help interpret experiments.
(ii) discuss the level of detail needed in the models so that they are sufficiently realistic to have predictive power but not so complicated that they obscure the important science.
(iii) discuss the best modelling approaches.

Questions that we currently find interesting and expect to address include:

1. How should the activity that drives the cells be modelled? Do we need details of the actin network? Is cortical activity related the cell motion? To what extent must chemical or mechanical signalling be included.

2. To what extent are cells viscoelastic, and to what extent are they elastic? How should the cell membrane be modelled? Is this critical to the success of the models?

3. How do cells sense each other and the substrate? What controls cell-cell scattering. To what extent does the adhesion between cells in confluent layers control their behaviour, and how is this best modelled?

4. How does the nature of the surface affect cell movement? How do cells move on hard and soft surfaces, and on fibres?

5. To what extent do active nematic models, vertex models or phase field models reproduce the correct mechanics of cellular layers. Can confluent layers be modelled by joining single cell models in some manner, or will a different approach be preferable?

6. What is the relation between activity, cell division and cell motility? How can cell division and cell death be incorporated in the models?

7. How do cellular layers expand to fill gaps (wound healing)? How do cells move in confinement or in the extra cellular matrix?

8. Continuum active nematic models appear to reproduce the behaviour of cells surprisingly effectively. Why? Does hydrodynamics matter?

9. How do individual cells detach from a colony, a question relevant to metastasis?

These questions will be most effectively answered by a dialogue between modellers and experimentalists and we have invited several experimentalists to the workshop. We have also tried to include representatives working with the different modelling approaches currently available.