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In vivo, eukaryotic cells are embedded in a matrix environment, where they grow and develop. Generally, this extracellular matrix (ECM) is an anisotropic fibrous structure, through which macromolecules and biochemical signaling molecules at…
Epithelial monolayers are some of the best-studied models for collective cell migration due to their abundance in multicellular systems and their tractability. Experimentally, the collective migration of epithelial monolayers can be…
The interface dynamics of a 3D cell immersed in a 3D extracellular matrix is investigated. We suggest a 3D generalization of a known 2D minimal phase field model suggested in [1] for the description of keratocyte motility. Our model…
Collective cell migration is crucial in many biological processes such as wound healing, tissue morphogenesis, and tumor progression. The leading front of a collective migrating epithelial cell layer often destabilizes into multicellular…
We introduce a 2D free boundary problem with nonlinear diffusion that models a living cell moving on a substrate. We prove that this nonlinearity results in a qualitative of solution behavior compared to the linear diffusion case (Rybalko…
A number of biological processes, such as embryo development, cancer metastasis or wound healing, rely on cells moving in concert. The mechanisms leading to the emergence of coordinated motion remain however largely unexplored. Although…
Living tissue is able to withstand large stresses in everyday life, yet it also actively adapts to dynamic loads. This remarkable mechanical behaviour emerges from the interplay between living cells and their non-living extracellular…
Myosin II molecular motors slide actin filaments relatively to each other and are essential for force generation, motility and mechanosensing in animal cells. For non-muscle cells, evolution has resulted in three different isoforms, which…
The movement of organisms and cells can be governed by occasional long distance runs, according to an approximate L\'evy walk. For T cells migrating through chronically-infected brain tissue, runs are further interrupted by long pauses, and…
We propose a physical model for developmental process at cellular level to discuss the mechanism of epigenetic landscape. In our simplified model, a minimal model, the network of the interaction among cells generates the landscape…
The directed migration of cells toward stiffer substrate regions or durotaxis is relevant to tissue development and tumor progression. Here, we introduce a phenomenological model for single cell durotaxis that incorporates both elastic…
Migration of animal cells is based on the interplay between actin polymerization at the front, adhesion along the cell-substrate interface, and actomyosin contractility at the back. Active gel theory has been used before to demonstrate that…
Eukaryotic cell motility involves a complex network of interactions between biochemical components and mechanical processes. The cell employs this network to polarize and induce shape changes that give rise to membrane protrusions and…
Active gels are a class of biologically-relevant material containing embedded agents that spontaneously generate forces acting on a sparse filament network. In vitro experiments of protein filaments and molecular motors have revealed a…
Deriving evolution equations accounting for both anomalous diffusion and reactions is notoriously difficult, even in the simplest cases. In contrast to normal diffusion, reaction kinetics cannot be incorporated into evolution equations…
During migration cells exhibit a rich variety of seemingly random migration patterns, which makes unraveling the underlying mechanisms that control cell migration a daunting challenge. For efficient migration cells require a mechanism for…
Cell crawling on flat substrates is based on intracellular flows of the actin cytoskeleton that are driven by both actin polymerization at the front and myosin contractility at the back. The new experimental tool of optogenetics makes it…
Cells perform directed motion in response to external stimuli that they detect by sensing the environment with their membrane protrusions. In particular, several biochemical and biophysical cues give rise to tactic migration in the…
Diverse processes--e.g. bioremediation, biofertilization, and microbial drug delivery--rely on bacterial migration in disordered, three-dimensional (3D) porous media. However, how pore-scale confinement alters bacterial motility is unknown…
We introduce an interacting particle system in which two families of reflected diffusions interact in a singular manner near a deterministic interface $I$. This system can be used to model the transport of positive and negative charges in a…