Abstract

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 [1], 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[6]. 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 [7] 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.