Related papers: Three-dimensional phase field model for actin-base…
Cell migration in fibreous extracellular matrix (ECM) is crucial to many physiological and pathological processes such as tissue regeneration, immune response and cancer progression. During migration, individual cells can generate active…
The finite solid-liquid interface width in phase field models results in non-equilibrium effects, including solute trapping. Prior phase field modeling has shown that this extra degree of freedom, when compared to sharp-interface models,…
Two-dimensional (2D) mechanical models of confluent tissues have related the mechanical state of a monolayer of cells to the average perimeter length of the cell cross sections, predicting floppiness or rigidity of the material. For the…
Phase separation has emerged as an essential concept for the spatial organization inside biological cells. However, despite the clear relevance to virtually all physiological functions, we understand surprisingly little about what phases…
In this paper, we use the cell dynamics method to study the dynamics of phase transformation when three phases exist. The system we study is a two-dimensional system. The system is able to achieve three phases coexistence, which for…
In multicellular systems, adhesion complexes, such as those composed of E-cadherin and associated catenins, mechanically couple neighboring cells by directly linking their actin-based cytoskeletal assemblies. However, the mechanics of how…
We introduce a generic, purely mechanical model for environment sensitive motion of mammalian cells that is applicable to chemotaxis, haptotaxis, and durotaxis as modes of motility. It is able to theoretically explain all relevant…
We present a minimal continuum model of strongly adhering cells as active contractile isotropic media and use the model to study the effect of the geometry of the adhesion patch in controlling the spatial distribution of traction and…
Cell migration is a fundamental process underlying the survival and function of both unicellular and multicellular organisms. Crawling motility in eukaryotic cells arises from cyclic protrusion and retraction driven by the cytoskeleton,…
This paper presents a phase-field model for simulating the three-dimensional deformation of vesicle membranes, incorporating area-difference elasticity, with constraints on bulk volume and surface area. We develop efficient numerical…
The mechanics of crawling cells on a substrate is investigated by using a minimal model that satisfies the force-free condition. A cell is described by two subcellular elements connected by a linear actuator that changes the length of the…
Cortical actin networks are highly dynamic and play critical roles in shaping the mechanical properties of cells. The actin cytoskeleton undergoes significant reorganization over the course of the cell cycle, when cortical actin transitions…
We consider a three-dimensional lattice model consisting of layers of vertex models coupled with interlayer interactions. For a particular non-trivial interlayer interaction between charge-conserving vertex models and using a transfer…
A thermodynamic approach to rapid phase transformations within a diffuse interface in a binary system is developed. Assuming an extended set of independent thermodynamic variables formed by the union of the classic set of slow variables and…
Experiments show that the movement of eukaryotic cells is regulated by a process of phase separation of two competing enzymes on the cell membrane, that effectively amplifies shallow external gradients of chemical attractant. Notably, the…
The dynamics of an interface between the normal and superconducting phases under nonstationary external conditions is studied within the framework of the time-dependent Ginzburg-Landau equations of superconductivity, modified to include…
This contribution presents a diffuse framework for modeling cracks in heterogeneous media. Interfaces are depicted by static phase-fields. This concept allows the use of non-conforming meshes. Another phase-field is used to describe the…
The actin cortex is a thin layer of actin filaments and myosin motors beneath the outer membrane of animal cells. It determines the cells' mechanical properties and forms important morphological structures. Physical descriptions of the…
The interactions between diffusing molecules and membrane-bound receptors drive numerous cellular processes. In this work, we develop a spatial model of molecular interactions with membrane receptors by homogenizing the cell membrane and…
Mathematical and computational models can assist in gaining an understanding of cell behavior at many levels of organization. Here, we review models in the literature that focus on eukaryotic cell motility at 3 size scales: intracellular…