Related papers: Mitotic waves in an import-diffusion model with mu…
A protocell model consisting of mutually catalyzing molecules is studied in order to investigate how chemical compositions are transferred recursively through cell divisions under replication errors. Depending on the path rate, the numbers…
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…
Navigation of microorganisms is controlled by internal processes ultimately sensitive to mechanical or chemical signaling encountered along the path. In many natural environments, such as porous soils or physiological ducts, motile species…
Electrical waves in the heart form rotating spiral or scroll waves during life-threatening arrhythmias such as atrial or ventricular fibrillation. The wave dynamics are typically modeled using coupled partial differential equations, which…
We present models and computational results which indicate that the spatial and temporal regularity seen in Proteus mirabilis swarm-colony development is largely an expression of a sharp age of dedifferentiation in the cell cycle from…
A hallmark of a plethora of intracellular signaling pathways is the spatial separation of activation and deactivation processes that potentially results in precipitous gradients of activated proteins. The classical Metabolic Control…
Cells coexist together in colonies or as tissues. Their behaviour is controlled by an interplay between intercellular forces and biochemical regulation. We develop a simple model of the cell cycle, the fundamental regulatory network…
Cell crawling requires the generation of intracellular forces by the cytoskeleton and their transmission to an extracellular substrate through specific adhesion molecules. Crawling cells show many features of excitable systems, such as…
Intracellular protein patterns regulate a variety of vital cellular processes such as cell division and motility, which often involve dynamic changes of cell shape. These changes in cell shape may in turn affect the dynamics of…
Dynamics maintaining diversity of cell types in a multi-cellular system are studied in relationship with the plasticity of cellular states. By adopting a simple theoretical framework for intra-cellular chemical reaction dynamics with…
The reaction-diffusion models have been extensively applied to explain the mechanism of pattern formations in early embryogenesis based on geometrically confined microtissues consisting of human pluripotent stem cells. Recently, mechanical…
In many adult tissues, stem cells and differentiated cells are not homogeneously distributed : stem cells are arranged in periodic "niches", and differentiated cells are constantly produced and migrate out of these niches. In this article,…
Diffusion models are a class of generative models that learn to synthesize samples by inverting a diffusion process that gradually maps data into noise. While these models have enjoyed great success recently, a full theoretical…
Understanding how patterns and travelling waves form in chemical and biological reaction-diffusion models is an area which has been widely researched, yet is still experiencing fast development. Surprisingly enough, we still do not have a…
Cytoskeletal motor proteins are involved in major intracellular transport processes which are vital for maintaining appropriate cellular function. The motor exhibits distinct states of motility: active motion along filaments, and…
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…
During overflow metabolism, cells excrete glycolytic byproducts when growing under aerobic conditions in a seemingly wasteful fashion. While potentially advantageous for microbes with finite oxidative capacity, its role in higher organisms…
Cellular membranes are elastic lipid bilayers that contain a variety of proteins, including ion channels, receptors, and scaffolding proteins. These proteins are known to diffuse in the plane of the membrane and to influence the bending of…
Signaling molecules play an important role for many cellular functions. We investigate here a general system of two membrane reaction-diffusion equations coupled to a diffusion equation inside the cell by a Robin-type boundary condition and…
The motility of eukaryotic cells is strongly influenced by their environment, with confined cells often developing qualitatively different motility patterns from those migrating on simple two-dimensional substrates. Recent experiments,…