Related papers: Exact solution of a two-type branching process: Cl…
We study a cross-diffusion model for tissue regeneration which involves the dynamics of human mesenchymal stem cells interacting with chondrocytes in a medium containing a differentiation factor. The latter acts as a chemoattractant for the…
Cells actively regulate their size during the cell cycle to maintain volume homeostasis across generations. While various mathematical models of cell size regulation have been proposed to explain how this is achieved, relating these models…
Cells of the human body have nearly identical genome but exhibit very different phenotypes that allow them to carry out specific functions and react to changes in their surrounding environment. This division of labour is achieved by…
Development combines three basic processes asymmetric --- cell division, signaling and gene regulation --- in a multitude of ways to create an overwhelming diversity of multicellular life-forms. Here, we attempt to chart this diversity…
We construct a simple model of a proto-cell that simulates a stochastic dynamics of abstract chemicals on a two-dimensional lattice. We assume that chemicals catalyze their reproduction through interaction with each other, and that between…
Branching processes are classical growth models in cell kinetics. In their construction, it is usually assumed that cell lifetimes are independent random variables, which has been proved false in experiments. Models of dependent lifetimes…
Many fundamental biological processes are dependent on cellular migration. Although the mechanical mechanisms of single-cell migration are relatively well understood, those underlying migration of multiple cells adhered to each other in a…
Models of tissue growth are now well established, in particular in relation to their applications to cancer. They describe the dynamics of cells subject to motion resulting from a pressure gradient generated by the death and birth of cells,…
We model a general, hierarchically organized tissue by a multi compartment approach, allowing any number of mutations within a cell. We derive closed solutions for the deterministic clonal dynamics and the reproductive capacity of single…
Complex contagion adoption dynamics are characterised by a node being more likely to adopt after multiple network neighbours have adopted. We show how to construct multi-type branching processes to approximate complex contagion adoption…
How are granular details of stochastic growth and division of individual cells reflected in smooth deterministic growth of population numbers? We provide an integrated, multiscale perspective of microbial growth dynamics by formulating a…
Under mild non-degeneracy assumptions on branching rates in each generation, we provide a criterion for almost-sure extinction of a multi-type branching process with time-dependent branching rates. We also provide a criterion for the total…
This paper deals with a new model for clonal network dynamics. We describe in detail this model and derive special equations governing immune system dynamics based on the general gradient type principles that can be inherent to a wide class…
Diffusion and flow matching approaches to generative modeling have shown promise in domains where the state space is continuous, such as image generation or protein folding & design, and discrete, exemplified by diffusion large language…
A model of multicellular systems with several types of cells is developed from the phase field model. The model is presented as a set of partial differential equations of the field variables, each of which expresses the shape of one cell.…
The rate at which individual bacterial cells grow depends on the concentrations of cellular components such as ribosomes and proteins. These concentrations continuously fluctuate over time and are inherited from mother to daughter cells,…
We derive a self-duality relation for a one-dimensional model of branching and annihilating random walkers with an even number of offsprings. With the duality relation and by deriving exact results in some limiting cases involving fast…
We describe the evolution of the quantity of parasites in a population of cells which divide in continuous-time. The quantity of parasites in a cell follows a Feller diffusion, which is splitted randomly between the two daughter cells when…
A novel mechanism for cell differentiation is proposed, based on the dynamic clustering in a globally coupled chaotic system. A simple model with metabolic reaction, active transport of chemicals from media, and cell division is found to…
We investigate morphologies of proliferating cellular tissue using a newly developed numerical simulation model for mechanical cell division. The model reproduces structures of simple multi-cellular organisms via simple rules for selective…