Related papers: A cell-cell repulsion model on a hyperbolic Keller…
Cell populations invade through a combination of proliferation and motility. Proliferation depends on the internal timing of cell division: how long cells take to complete the cell cycle. This timing varies substantially within (and across)…
Chemotaxis plays a significant role in numerous physiological processes. The Keller-Segel equation serves as a mathematical model for simulating the phenomenon of cell population aggregation under chemotaxis, possessing physical properties…
In addressing the origins of Darwinian evolution, recent experimental work has been focussed on the discovery of simple physical effects which would provide a relevant selective advantage to protocells competing with each other for a…
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…
In this paper, we investigate the long-time dynamics of a repulsive Keller-Segel chemotaxis system. The model features negative chemotaxis, logistic growth and a cell death term, accounting for a lethal chemorepellent that is self-produced…
Recent studies at individual cell resolution have revealed phenotypic heterogeneity in nominally clonal tumor cell populations. The heterogeneity affects cell growth behaviors, which can result in departure from the idealized uniform…
The main topic of this thesis is the analysis of evolution equations reflecting issues in ecology and population dynamics. In mathematical modelling, the impact of environmental elements and the interaction between species is read into the…
This paper proposes a model for the growth two interacting populations of cells that do not mix. The dynamics is driven by pressure and cohesion forces on the one hand and proliferation on the other hand. Following earlier works on the…
The main purpose of this work is the mathematical modelling of large populations of cells under different deterministic interactions among themselves, in balance with naturally random diffusion. We focus on cell-cell adhesion mechanisms for…
A simple but useful method of reciprocal values is introduced, explained and illustrated. This method simplifies the analysis of hyperbolic distributions, which are causing serious problems in the demographic and economic research. It…
This paper investigates the formation of time--periodic and stable patterns of a two--competing--species Keller--Segel chemotaxis model with a focus on the effect of cellular growth. We carry out rigorous Hopf bifurcation analysis to obtain…
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…
Establishing a quantitative connection between the population growth rate and the generation times of single cells is a prerequisite for understanding evolutionary dynamics of microbes. However, existing theories fail to account for the…
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…
In this paper we present an individual-based mechanical model that describes the dynamics of two contiguous cell populations with different proliferative and mechanical characteristics. An off-lattice modelling approach is considered…
This paper aims to develop numerical approximations of the Keller--Segel equations that mimic at the discrete level the lower bounds and the energy law of the continuous problem. We solve these equations for two unknowns: the organism (or…
Cell-cell adhesion plays a vital role in the development and maintenance of multicellular organisms. One of its functions is regulation of cell migration, such as occurs, e.g. during embryogenesis or in cancer. In this work, we develop a…
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,…
Regulation of cell proliferation is a crucial aspect of tissue development and homeostasis and plays a major role in morphogenesis, wound healing, and tumor invasion. A phenomenon of such regulation is contact inhibition, which describes…
We introduce various models for cellulose bio-degradation by micro-organisms. Those models rely on complex chemical mechanisms, involve the structure of the cellulose chains and are allowed to depend on the phenotypical traits of the…