Cell migration in confined environments is a burning topic, since it is one of the main biological processes ruling embryo-genesis, cancer metastasis or an organism immune system. Based on a previously developed cell confined migration model and the observation of micro-channels experiments, we decided to focus on two main aspects during this thesis. First, the evidence that the nucleus was capable of breaking its lamina to pass through narrow sub-nuclear constrictions led us to reconsider the way it was defined: we decided to use two different rheological models for the lamina and the nucleoplasm. While the latter is modeled as a viscoelastic medium, the first is defined as a viscoelastoplastic medium. Indeed the introduction of plasticity in the lamina could account for its ability to break down. We tested this new model in a compression test and then implemented it in the previous confined migration model. During confined migration, we highlighted the rate-limiting role of the nucleus and the effect of plasticity on the model. Our confined migration model relied on an adhesion-based migration mode, while all the recent interest in cell migration through confined environments featured a compression-based migration mode in which the cell would not need to form any focal adhesions with the substrate. We thus decided to focus on improving our migration mode to describe this adhesion-free mode that mostly occurs during three-dimensional confined migration and is referred to as 'chimneying', since it mimics the behaviour of a rock climber in a chimney. During chimneying, the cell rear contraction triggers an increase in internal hydrostatic pressure, which then leads to the nucleation of a bleb - a herniation of the cell membrane - at the leading edge. When the bleb expands and touches the surface in which the cell is confined, it 'pushes' against it, creating a perpendicular force that acts as an anchor for the cell to move forward. The cycle repeats and the cell migrates. We developed a first simple and deterministic model in which the cell has frontal and rear blebs that cyclically expand and retract and that push on the walls of the micro-channel to migrate through it. In this model, we ensure the synchronization between adhesion forces and active strains. A second model kept the same motion cycle but introduced the notion of self-regulation. Indeed, the cell is given conditions, and depending on whether they are met or not, the cell governs the migration steps. Eventually, we began developing a model with a motion that more closely resembles how chimneying looks like in live cells, with the rear contraction governing the bleb expansion. The model presented here is still preliminary and will be improved in the future.
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