Related papers: From individual-based mechanical models of multice…
In this paper, we present a cell motility model that takes into account the cell membrane effect. The model introduced is an incompressible Darcy free boundary problem. This model involves a nonlinear term in the boundary condition to model…
Cells self-organize into functional, ordered structures during tissue morphogenesis, a process that is evocative of colloidal self-assembly into engineered soft materials. Understanding how inter-cellular mechanical interactions may drive…
In the growth of bacterial colonies, a great variety of complex patterns are observed in experiments, depending on external conditions and the bacterial species. Typically, existing models employ systems of reaction-diffusion equations or…
We study the dynamics of proliferating cell collectives whose microscopic constituents' growth is inhibited by macroscopic growth-induced stress. Discrete particle simulations of a growing collective show the emergence of concentric-ring…
We introduce a model for describing the dynamics of large numbers of interacting cells. The fundamental dynamical variables in the model are sub-cellular elements, which interact with each other through phenomenological intra- and…
To model the morphogenesis of rod-shaped bacterial micro-colony, several individual-based models have been proposed in the biophysical literature. When studying the shape of micro-colonies, most models present interaction forces such as…
Multicellular organisms exhibit a high degree of structural organization with specific cell types always occurring in characteristic locations. The conventional framework for describing the emergence of such consistent spatial patterns is…
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…
Single and collective cell migration are fundamental processes critical for physiological phenomena ranging from embryonic development and immune response to wound healing and cancer metastasis. To understand cell migration from a physical…
We study molecular dynamics within populations of diffusively coupled cells under the assumption of fast diffusive exchange. As a technical tool, we propose conditions on boundedness and ultimate boundedness for systems with a singular…
Understanding the rules underlying organismal development is a major unsolved problem in biology. Each cell in a developing organism responds to signals in its local environment by dividing, excreting, consuming, or reorganizing, yet how…
We investigate the dynamics of a colony of crawling, proliferating cells with a minimal, mechanical cell model. The cells consist of two disks, modelling the cell body and a pseudopod, connected by a finite extensible spring. The cells…
We study a two-dimensional free boundary problem that models motility of eukaryotic cells on substrates. This problem consists of an elliptic equation describing the flow of cytoskeleton gel coupled with a convection-diffusion PDE for the…
There are numerous scenarios in which populations of cells migrate in crowded environments. Typical examples include wound healing, cancer growth and embryo development. In these crowded environments cells are able to interact with each…
Interactions between crawling cells, which are essential for many biological processes, can be quantified by measuring cell-cell collisions. Conventionally, experiments of cell-cell collisions are conducted on two-dimensional flat…
Considering the dynamics of non-interacting particles randomly moving on a lattice, the occurrence of a discontinuous transition in the values of the lattice parameters (lattice spacing and hopping times) determines the uprisal of two…
We derive a hydrodynamic description of metric-free active matter: starting from self-propelled particles aligning with neighbors defined by "topological" rules, not metric zones, -a situation advocated recently to be relevant for bird…
In this volume a theory for models of transport in the presence of a free boundary is developed. Macroscopic laws of transport are described by PDEs. When the system is open, there are several mechanisms to couple the system with the…
We consider a parabolic non-local free boundary problem that has been derived as a limit of a bulk-surface reaction-diffusion system which models cell polarization. The authors have justified the well-posedness of this problem and have…
The dynamics of a free boundary problem for electrostatically actuated microelectromechanical systems (MEMS) is investigated. The model couples the electric potential to the deformation of the membrane, the deflection of the membrane being…