Phase-field modeling and isogeometric analysis of cell crawling
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- Teses de doutoramento [2150]
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Phase-field modeling and isogeometric analysis of cell crawlingAutor(es)
Director(es)
Gómez, HéctorData
2017Resumo
[Abstract]
A fascinating feature of eukaryotic cells is their ability to move. Cellular motility
controls crucial biological processes such as, e.g., cellular nourishment, wound
healing, tissue growth, pathogen removal, or metastatic disease. Cell migration
through biological tissues is an exceedingly complex process, which is usually
understood as a continuous cycle of five interdependent steps, namely: protrusion
and elongation of the leading edge driven by actin polymerization; cell-matrix
interaction and formation of focal contacts via transmembrane adhesion proteins;
extracellular matrix degradation by cell surface proteases; actomyosin contraction
generated by active myosin II bound to actin filaments; and detachment of the
trailing edge and slow glide forward. Cell migration may be directed by different
external stimuli perceived through the cell’s membrane via membrane proteins.
Those stimuli, which may take the form of chemical cues or changes in the physical
properties of the environment, produce a cellular response that modifies the motile
behavior of the cell. Moreover, motile cells may exhibit a number of morphological
variants, called modes of migration, as a function of endogenous and exogenous
factors such as, e.g., cell-cell and cell-extracellular matrix adhesion, extracellular
matrix degradation, orientation of the extracellular matrix fibers, or the predominant
cytoskeleton structure. The prominent modes of individual cell migration
are mesenchymal, amoeboid, and blebbing motion. Cells can compensate the loss
of a particular motile ability by developing migratory strategies, which include
the transition between different modes of cell migration.
In this thesis we develop three mathematical models of individual cell migration.
The models account for the interactions between the cytosolic, membrane, and
extracellular compounds involved in cell motility. The motion of the cell is driven
by the actin filament network, which is assumed to be a Newtonian fluid subject to
forces caused by the cell motion machinery. Those forces are the surface tension
of the membrane, cell-substrate adhesion, actin-driven protrusion, and myosin contraction. Also, a repulsive force acting on the cell’s membrane accounts for the
interaction with obstacles, which may represent fibers or walls. The models are
grounded on the phase-field method, which permits to solve the partial-differential
equations posed on the different domains (i.e., the cytosol, the membrane, and
the extracellular medium) by using a fixed mesh only. The solution of the higherorder
equations derived from the phase-field theory entails a number of challenges.
To overcome those challenges, we develop a numerical methodology based on
isogeometric analysis, a generalization of the finite element method. For the spatial
discretization we employ B-splines as basis functions, which possess higher-order
continuity. We propose a time integration algorithm based on the generalized-
method.
The first model focuses on mesenchymal motion. The model proposes a novel
description of the actin phase transformations based on a free-energy functional.
The results show that the model effectively reproduces the behavior of actin in
keratocytes. The simpler case of cell migration in flat surfaces produces stationary
states of motion that are in good agreement with experiments. Also, by considering
obstacles, we are able to reproduce complex modes of motion observed in
microchannels, such as, e.g., oscillatory and bipedal motion.
The second model is used to analyze the spontaneous migration of amoeboid cells.
The model accounts for a membrane-bound species that interacts with the cytosolic
compounds. The model results show quantitative agreement with experiments of
free and confined migration. These results suggest that coupling membrane and
intracellular dynamics is crucial to understand amoeboid motion. We also show
simulations of a cell moving in a three-dimensional fibrous environment, which
we interpret as an initial step toward the computational study of cell migration
in the extracellular matrix.
The third model focuses on chemotaxis of amoeboid cells. The model captures
the interactions between the extracellular chemoattractant, the membrane-bound
proteins, and the cytosolic components involved in the signaling pathway that
originates cell motility. The two-dimensional results reproduce the main features
of chemotactic motion. The simulations unveil a complicated interplay between the
geometry of the cell’s environment and the chemoattractant dynamics that tightly
regulates cell motility. We also show three-dimensional simulations of chemotactic
cells moving on planar substrates and fibrous networks. These examples may
constitute a first approach to simulate cell migration through biological tissues.
Palabras chave
Eucariotas
Células madre mesenquimatosas-Migración
Análisis isogeométrico-Informática
Células madre mesenquimatosas-Migración
Análisis isogeométrico-Informática
Descrición
Programa Oficial de Doutoramento en Enxeñaría Civil . 5011V01
Dereitos
Atribución-NoComercial-SinDerivadas 3.0 España