Related papers: Formation of vascular-like structures using a chem…
Motivated by experimental observations in 3D/organoid cultures derived from glioblastoma, we develop a mathematical model where tumour aggregate formation is obtained as the result of nutrient-limited cell proliferation coupled with…
The aim of our work is to study the effect of geometry variation on nucleation times and to address its role in the context of eukaryotic chemotaxis (i.e. the process which allows cells to identify and follow a gradient of chemical…
Angiogenesis is the formation of new blood vessels from pre-existing ones in response to chemical signals secreted by, for example, a wound or a tumour. In this paper, we propose a mesoscopic lattice-based model of angiogenesis, in which…
Mechanochemical models of pattern formation in biological tissues have been used to study a variety of biomedical systems and describe the physical interactions between cells and their local surroundings. These models generally consist of a…
We explore a biomimetic model that simulates a cell, with the internal cytoplasm represented by a two-dimensional circular domain and the external cortex by a surrounding ring, both modeled using FitzHugh-Nagumo systems. The external ring…
Cells collectively migrate as a cluster in three-dimensional (3D) tissues, such as in embryogenesis and cancer invasion. Here, numerical simulations using a 3D vertex model show that polarized interfacial tension, expressing cell adhesion…
There is increasing interest in the analysis of biological tissue, its organization and its dynamics with the help of mathematical models. In the ideal case emergent properties on the tissue scale can be derived from the cellular scale.…
Morphogenesis involves complex shape changes of biological tissues. Yet, tissue shape changes depend on tissue rheology, which in turn arises from the interplay of large numbers of cells. Here, we link cell- and tissue-scale mechanics by…
Chemotaxis is typically modeled in the context of cellular motion towards a static, exogenous source of chemoattractant. Here, we propose a time-dependent mechanism of chemotaxis in which a self-propelled particle ({\it e.g.}, a cell)…
In this paper, a class of reaction-diffusion equations for Multiple Sclerosis is presented. These models are derived by means of a diffusive limit starting from a proper kinetic description, taking account of the underlying microscopic…
The main objective of this article is to study the dynamic transition and pattern formation for chemotactic systems modeled by the Keller-Segel equations. We study chemotactic systems with either rich or moderated stimulant supplies. For…
Intracellular protein patterns govern essential cellular functions by dynamically redistributing proteins between membrane-bound and cytosolic states, conserving their total numbers. This review presents a theoretical framework for…
Collective cell migration is a fundamental biological process that drives events such as embryonic development, wound healing, and cancer metastasis. In this study, we develop a biophysically informed phase-field model to investigate the…
We investigate the hydrodynamic stability and the formation of patterns in a continuum model of epithelial layers, able to account for the interplay between mechanical activity, lateral adhesion and the $6-$fold orientational order…
In biological tissues, it is now well-understood that mechanical cues are a powerful mechanism for pattern regulation. While much work has focused on interactions between cells and external substrates, recent experiments suggest that cell…
Through mechanical forces, biological cells remodel the surrounding collagen network, generating striking deformation patterns. Tethers-tracts of high densification and fiber alignment-form between cells, thinner bands emanate from cell…
Morphogenesis, tissue regeneration and cancer invasion involve transitions in tissue morphology. These transitions, caused by collective cell migration (CCM), have been interpreted as active wetting/de-wetting transitions. This phenomenon…
Many essential cellular processes, including cell division and the establishment of cell polarity during embryogenesis, are regulated by pattern-forming proteins. These proteins often need to bind to a substrate, such as the cell membrane,…
This work presents the development, analysis and numerical simulations of a biophysical model for 3D cell deformation and movement, which couples biochemical reactions and biomechanical forces. We propose a mechanobiochemical model which…
Since its introduction in 1952, Turing's (pre-)pattern theory ("the chemical basis of morphogenesis") has been widely applied to a number of areas in developmental biology. The related pattern formation models normally comprise a system of…