Related papers: Exact solution of a two-type branching process: Cl…
We study time continuous branching processes with exponentially distributed lifetimes, with two types of cells that proliferate according to binary fission. A range of possible system dynamics are considered, each of which is characterized…
Biological tools such as genetic lineage tracing, three dimensional confocal microscopy and next generation DNA sequencing are providing new ways to quantify the distribution of clones of normal and mutated cells. Population-wide clone size…
Stem cells, through their ability to produce daughter stem cells and differentiate into specialized cells, are essential in the growth, maintenance, and repair of biological tissues. Understanding the dynamics of cell populations in the…
An explicit solution for a general two-type birth-death branching process with one way mutation is presented. This continuous time process mimics the evolution of resistance to treatment, or the onset of an extra driver mutation during…
The self-organization of cells into complex tissues relies on a tight coordination of cell behavior. Identifying the cellular processes driving tissue growth is key to understanding the emergence of tissue forms and devising targeted…
Stem cells are characterized by their ability to self-renew, as well as to differentiate and give rise to new populations of cells. Stem cell divisions are crucial for generative processes that occur during early development, and later in…
We introduce and analyze several aspects of a new model for cell differentiation. It assumes that differentiation of progenitor cells is a continuous process. From the mathematical point of view, it is based on partial differential…
The rules governing cell division and differentiation are central to understanding the mechanisms of development, aging and cancer. By utilising inducible genetic labelling, recent studies have shown that the clonal population in transgenic…
We model the growth of a cell population using a piecewise deterministic Markov branching tree. In this model, each cell splits into two offspring at a division rate $B(x)$, which depends on its size $x$. The size of each cell increases…
We build networks of genetic similarity in which the nodes are organisms sampled from biological populations. The procedure is illustrated by constructing networks from genetic data of a marine clonal plant. An important feature in the…
We study the Stochastic Thermodynamics of cell growth and division using a theoretical framework based on branching processes with resetting. Cell division may be split into two sub-processes: branching, by which a given cell gives birth to…
The deluge of single-cell data obtained by sequencing, imaging and epigenetic markers has led to an increasingly detailed description of cell state. However, it remains challenging to identify how cells transition between different states,…
We consider the time evolution of the supercritical Galton-Watson model of branching particles with extra parameter (mass). In the moment of the division the mass of the particle (which is growing linearly after the birth) is divided in…
We consider a generational and continuous-time two-phase model of the cell cycle. The first model is given by a stochastic operator, and the second by a piecewise deterministic Markov process. In the second case we also introduce a…
This paper presents an interesting experimental example of voter-model statistics in biology. In recent work on mouse tail-skin, where proliferating cells are confined to a two-dimensional layer, we showed that cells proliferate and…
We present and analyse a model for cell signalling processes in biological tissues. The model includes diffusion and nonlinear reactions on the cell surfaces, and both inter- and intracellular signalling. Using techniques from the theory of…
Multitype branching processes are ideal for studying the population dynamics of stem cell populations undergoing mutation accumulation over the years following transplant. In such stochastic models, several quantities are of clinical…
Tissue growth can be modeled in two dimension by only using circular granular cells, which can grow and produce child. Linear spring-dashpot model is used to bind the cells with a cut-off interaction range of 1.1 times sum of radii of…
A novel theory for cell differentiation is proposed, based on simulations with interacting artificial cells which have metabolic networks within, and divide into two when the final product is accumulated. Results of simulations with coupled…
A two-type two-sex branching process is introduced with the aim of describing the interaction of predator and prey populations with sexual reproduction and promiscuous mating. In each generation and in each species the total number of…