Cell migration is a fundamental element in a variety of physiological and pathological processes. Alteration of its regulatory mechanisms leads to loss of cellular adhesion and increased motility, which are critical steps in the initial stages of metastasis, before a malignant cell colonizes a distant tissue or organ. Consequently, cell migration has become the focus of intensive experimental and theoretical studies; however the understanding of many of its mechanism remains elusive. Cell migration is the result of a periodic sequence of protrusion, adhesion remodeling and contraction stages that leads to directed movement of cells towards external stimuli. The spatio-temporal coordination of these processes depends on the di erential activation of the signaling networks that regulate them at specific subcellular locations. Particularly, proteins from the family of small RhoGTPases play a central role in establishing cell polarization, setting the direction of migration, regulating the formation of adhesion sites and the generation of the forces that drive motion.
Theoretical models based on an independent description of these processes have a limited capacity to predict cellular behavior observed in vitro, since their functionality depends intrinsically on the cross-regulation between their signaling pathways. This thesis presents a model of cell migration that integrates a description of force generation and cell deformation, adhesion site dynamics and RhoGTPases activation. The cell is modeled as a viscoelastic body capable of developing active traction and protrusion forces. The magnitude of stresses is determined by the activation level of the RhoGTPases, whose distribution in the cell body is described by a set of reaction-di usion equations. Adhesion sites are modeled as punctual clusters of transmembrane receptors that dynamically bind and unbind the extracellular matrix depending on the force transmitted to them and the distance with ligands on the substrate.
Onthe theoretical level, the major findings concern the relationship between the topology of a crosstalk scheme and the properties, as defined in , inherited by the associated reaction network as a gradient sensing and regulatory system: persistent and transient polarization triggered by external gradients, adaptation to uniform stimulus, reversible polarization, multi-stimuli response and amplification. This leads to models that remain functional against the biological diversity associated to di erent cell types and matches the observed cell behaviour in Chemotaxis essays [2, 3, 4, 5]: the capacity of cells to amplify gradients, polarize without featuring Turing patterns of activation, and switch the polarization axis and the direction of migration after the source of the external stimulus is changed. The RhoGTPase model, derived on theoretical premises, challenges a long held view on the mechanisms of RhoGTPase crosstalk and suggests that the role of GDIs, GEFs and GAPs has to be revised. Recent experimental evidence supports this idea.
In addition, the model allows to recapitulate a continuous transition between the tear-like shape adopted by neutrophiles and the fan-like shape of keratocytes during migration  by varying the relative magnitudes of protrusion and contraction forces or, alternatively, the strength of RhoGTPase Crosstalk. The second mechanism represents a novel explanation of the di erent morphologies observed in migrating cells. Di erences in RhoGTPase crosstalk strength could be mediated by di erences between the activity or concentration of GEFs, GAPs and GDIs in di erent cell types; an idea that can be explored experimentally.
On cell mechanosensing, a new hypothesis based on a simple physical principle is proposed as the mechanism that might explain the universal preference of cells (bar neurons) to migrate along sti ness gradients. The theory provides a simple unifying explanation to a number of recent observations on force development and growth in real time at cell Focal adhesions [8, 9, 10, 11]. The apparently conflicting results have been attributed to the di erences in experimental set-ups and cell types used, and have fueled a longstanding controversy on how cells prove the mechanical properties of the extra-cellular matrix. The predictions of the theory recapitulate these experimental observations, and its founding hypothesis can be tested experimentally. This hypothesis directly suggests the mechanism that could explain the preference of cells to migrate along sti ness gradients, and for the first time, a plausible biological function for its existence. This phenomenon is known as Durotaxis, and its abnormal regulation has been associated to the malignant behaviour of cancer cells.
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