Computational Modeling of Protrusion-Based 3D Cell Migration through a Degradable Viscoelastic Extracellular Matrix

The ability of cells to migrate through a tissue in the human body is vital for many processes such as tissue development, growth and regeneration. At the same time, abnormal cell migration is observed in many diseases such as cancer. In order to discover the origin of these abnormalities and develop new treatment strategies, an improved understanding of the cell migration process and its regulation is required. Mechanics of the cell and the surrounding extracellular matrix plays an important role as a cell needs to adhere and apply forces to its environment in order to move. Since it is challenging to investigate cell migration through a biological tissue in experiments, computational modeling can make a valuable contribution. In this thesis a computational model of 3D cell migration is developed and used to investigate the role of extracellular matrix mechanics and actin protrusion dynamics in cell migration. First, a computational model of a degradable viscoelastic extracellular matrix is developed by means of the Lagrangian particle-based smoothed particle hydrodynamics method. An existing boundary method is extended to allow modeling of a moving cell model in contact with the solid extracellular matrix. Simulations are performed to validate the model and a first simplified model of cell migration through the extracellular matrix is developed to demonstrate that this model is able to capture the fundamental aspects of 3D cell migration. Next, the extracellular matrix model is extended to model isotropic and anisotropic fibrillar matrices such as a collagen gel. The model captures strain stiffening and buckling under compression, which are representative for fibrillar materials. The model is validated by comparison with experimental uniaxial stretching data from literature. This model is then used to estimate the force distribution in the collagen gel surrounding an angiogenic sprout based on an experimentally measured displacement field. It is demonstrated that fiber buckling, rather than strain stiffening, explains the further propagation of displacements into a collagen gel, compared to a linear elastic material, that is observed in experiments. The cell is modeled as an active deformable object that describes the viscoelastic actin cortex mechanics and subcellular processes underlying 3D cell migration. The cell migrates by forming long, thin protrusions that grow, adhere to the extracellular matrix and contract in order to displace the cell body. Local degradation of the extracellular matrix is captured by fluidization and permits the cell to migrate through the extracellular matrix. By adaptation of the contractile strength to the local matrix stiffness in a mechanosensing process and by force-dependent adhesion disassembly, competition between protrusions arises that results in 3D cell migration regulated by the extracellular matrix mechanics. A parameter study shows that changes in extracellular matrix stiffness and cell strength result in changes in cell migration velocity and protrusion dynamics (number, length and lifetime), while directly changing these protrusion dynamics does not affect cell migration velocity. A stochastic variability in protrusion lifetimes appears to be enough to explain differences in cell migration velocity. Force-dependent adhesion disassembly does not affect cell migration velocity, but instead makes migration more efficient by decreasing the required total number of protrusions. It is also demonstrated that an optimal number of simultaneous protrusions exists for 3D cell migration and that this number is either 1 or 2, depending on the ECM anisotropy. Altogether, the model is able to not only simulate the process of 3D cell migration, but can also provide additional insights beyond experimental observations and therefore increases the understanding of 3D cell migration.

Jaar van publicatie:2019

Toegankelijkheid:Open