Related papers: From individual-based mechanical models of multice…
Continuum models for the spatial dynamics of growing cell populations have been widely used to investigate the mechanisms underpinning tissue development and tumour invasion. These models consist of nonlinear partial differential equations…
Existing studies comparing individual-based models of growing cell populations and their continuum counterparts have mainly focused on homogeneous populations, in which all cells have the same phenotypic characteristics. However,…
We consider a partial differential equation model for the growth of heterogeneous cell populations subdivided into multiple distinct discrete phenotypes. In this model, cells preferentially move towards regions where they feel less…
We consider a coupled bulk-surface system of partial differential equations with nonlinear coupling modelling receptor-ligand dynamics. The model arises as a simplification of a mathematical model for the reaction between cell surface…
The effect of mechanical interactions between cells in the spreading of bacterial populations was investigated in one-dimensional space. A continuum-mechanics approach, comprising cell migration, proliferation, and exclusion processes, was…
Self-organisation of individuals within large collectives occurs throughout biology. Mathematical models can help elucidate the individual-level mechanisms behind these dynamics, but analytical tractability often comes at the cost of…
This study builds upon a model proposed by Joanny and collaborators that examines the dynamics of interfaces between two distinct cell populations, particularly during tumor growth in healthy tissues. This framework leads to the…
Advances in synthetic biology allow us to engineer bacterial collectives with pre-specified characteristics. However, the behavior of these collectives is difficult to understand, as cellular growth and division as well as extra-cellular…
We consider a continuum mechanical model for the migration of multiple cell populations through parts of tissue separated by thin membranes. In this model, cells belonging to different populations may be characterised by different…
We present initial results regarding the existence, stability and interaction of linear and nonlinear vibrational modes in a system of two coupled, one dimensional lattices with unequal numbers of masses. The effects on these nonlinear…
The organization of live cells into tissues and their subsequent biological function involves inter-cell mechanical interactions, which are mediated by their elastic environment. To model this interaction, we consider cells as spherical…
The cell motility problem has been investigated for a long time. Today, many biologists, physicists, and mathematicians are looking for new research instruments for this process. A simple 2D model of a free-boundary cell moving on a…
We propose a simple mathematical model to describe the mechanical relaxation of cells within a curved epithelial tissue layer represented by an arbitrary curve in two-dimensional space. This model generalises previous one-dimensional models…
We consider a free boundary model of epithelial cell migration with logistic growth and nonlinear diffusion induced by mechanical interactions. Using numerical simulations, phase plane and perturbation analysis, we find and analyse…
The conventional no-slip boundary condition leads to a non-integrable stress singularity at a moving contact line. This makes numerical simulations challenging, especially when capillary effects are essential for the dynamics of the flow.…
Cell cultures exhibit rich and complex behaviors driven by dynamic metabolic interactions among cells. In this work, we present a model that captures these interactions through a framework inspired by statistical mechanics. Using Monte…
In multicellular organisms, several cell states coexist. For determining each cell type, cell-cell interactions are often essential, in addition to intracellular gene expression dynamics. Based on dynamical systems theory, we propose a…
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. In previous papers, we have established well-posedness of this problem and…
Based on symmetry consideration of migration and shape deformations, we formulate phenomenologically the dynamics of cell crawling in two dimensions. Forces are introduced to change the cell shape. The shape deformations induce migration of…
This paper proposes a model for the growth two interacting populations of cells that do not mix. The dynamics is driven by pressure and cohesion forces on the one hand and proliferation on the other hand. Following earlier works on the…