On the theory of cell migration: durotaxis and chemotaxis

Cell migration is a fundamental element in a variety of physiological and pathological processes. Alteration of its regulatory mechanisms leads to loss of adhesion and increased motility, critical steps in the initial stages of metastasis. Consequently, cell migration has become the focus of intensive experimental and theoretical studies; however the understanding many of its mechanisms remains elusive. Cell migration is the result of a periodic sequence of protrusion, adhesion remodeling and contraction stages that leads to directed movement towards external stimuli. The spatio-temporal coordination of these processes depends on the activation of the signaling networks that regulate them at specific subcellular locations. Particularly, the family of small RhoGTPases plays a central role in regulating cell polarization, 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 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 traction and protrusion forces. The forces are determined by the activation level of the RhoGTPases, whose distribution in the cell is described by a set of reaction-diffusion equations. Adhesion sites are modeled as punctual clusters of transmembrane receptors that dynamically bind and unbind the extracellular matrix depending on the force transimtted to them and the distance with ligands coating the substrate. On the theoretical level, the major findings relate the topology of a Crosstalk Scheme and the properties inherited by the associated reaction network as a gradient sensing and regulatory system: reversible polarization, adaptation to uniform stimulus, multi-stimuli response and amplification. Models formulated according to these principles remain functional against the biological diversity associated to different cell types and match the observed behavior in Chemotaxis essays: the capacity of cells to detect shallow gradients, polarize without featuring Turing patterns of activation, and switch the direction of migration after the stimulus source is changed. The biological implications challenge a long held view on the mechanisms of RhoGTPase crosstalk and suggests that the role of GDIs, GEFs and GAPs has to be revised, as supported by recent experimental evidence. In addition, the model recapitulates a continuous transition from the tear-like shape adopted by neutrophiles to the fan-like shape of keratocytes during migration by varying the magnitudes of protrusion and contraction forces or, alternatively, the strength of RhoGTPase Crosstalk. The second mechanism represents a novel explanation of the different morphologies observed in migrating cells. On cell mechanosensing, a new hypothesis is proposed to explain how cells sense the mechanical properties of the ECM. The hypothesis provides a unifying explanation to apparently conflicting observations on force development and growth in real time at cell Focal adhesions, previously attributed to differences in experimental set-ups or cell types studied. An interpretation for the observed relationships between polarization time, migration speed, mechano-sensing limits and substrate rigidity follows from this hypothesis. Further, the theory directly suggests the currently unknown mechanisms that could explain the universal preference of cells (bar neurons) to migrate along stiffness gradients, and for the first time, a plausible biological function for the existence of this phenomenon. It is known as Durotaxis, and its abnormal regulation has been associated to the malignant behaviour of cancer cells