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The aim of this study is to compare the growth speed of different cell populations measured by their Malthus parameter. We focus on both the age-structured and size-structured equations. A first population (of reference) is composed of…
We analyse a model consisting of a population of individuals which is subdivided into a finite set of demes, each of which has a fixed but differing number of individuals. The individuals can reproduce, die and migrate between the demes…
We formulate a general, high-dimensional kinetic theory describing the internal state (such as gene expression or protein levels) of cells in a stochastically evolving population. The resolution of our kinetic theory also allows one to…
Various rod-shaped bacteria such as the canonical gram negative Escherichia coli or the well-studied gram positive Bacillus subtilis divide symmetrically after they approximately double their volume. Their size at division is not constant,…
Cycling tissues such as the intestinal epithelium, germ line, and hair follicles, require a constant flux of differentiated cells. These tissues are maintained by a population of stem cells, which generate differentiated progenies and…
In this paper, we investigate a stochastic model describing the time evolution of a polymerization process. A polymer is a macro-molecule resulting from the aggregation of several elementary sub-units called monomers. Polymers can grow by…
Cell layers eliminate unwanted cells through the extrusion process, which underlines healthy versus flawed tissue behaviors. Although several biochemical pathways have been identified, the underlying mechanical basis including the forces…
Mathematical and computational models can assist in gaining an understanding of cell behavior at many levels of organization. Here, we review models in the literature that focus on eukaryotic cell motility at 3 size scales: intracellular…
Quantitative single cell measurements have shown that cell cycle duration (the time between cell divisions) for diverse cell types is a noisy variable. The underlying distribution is mean scalable with a universal shape for many cell types…
The first chapter concerns monotype population models. We first study general birth and death processes and we give non-explosion and extinction criteria, moment computations and a pathwise representation. We then show how different scales…
Diffusion processes are central to human interactions. One common prediction of the current modeling frameworks is that initial spreading dynamics follow exponential growth. Here, we find that, ranging from mobile handsets to automobiles,…
We develop a minimal model to describe growing dense active matter such as biological tissues, bacterial colonies and biofilms, that are driven by a competition between particle division and steric repulsion. We provide a detailed numerical…
In this work, we study a protein synthesis degradation process by defining a general mathematical model. Using generating function technique we present a method that allows exact calculation of joint probability distribution of protein…
The growth of several biological tissues is known to be controlled in part by local geometrical features, such as the curvature of the tissue interface. This control leads to changes in tissue shape that in turn can affect the tissue's…
Cellular self-assembly and organization are fundamental steps for the development of biological tissues. In this paper, within the framework of a cellular automata model, we address how an ordered tissue pattern spontaneously emerges from a…
Alzheimer's disease (AD) is a serious neurodegenerative disease consisting of four stages where the illness gets progressively worse. It is of great significance to detect the gene regulatory mechanism as AD progresses and, thus, to help us…
The homeostasis of epithelial tissue relies on a balance between the self-renewal of stem cell populations, cellular differentiation, and loss. Although this balance needs to be tightly regulated to avoid pathologies, such as tumor growth,…
Isologous diversification theory for cell differentiation is proposed, based on simulations of interacting cells with biochemical networks and cell division process following consumption of some chemicals. According to the simulations of…
Center-based models are used to simulate the mechanical behavior of biological cells during embryonic development or cancer growth. To allow for the simulation of biological populations potentially growing from a few individual cells to…
Partial differential equations are a convenient way to describe reaction- advection-diffusion processes of signalling models. If only one cell type is present, and tissue dynamics can be neglected, the equations can be solved directly.…