Related papers: Criticality in Tissue Homeostasis: Models and Expe…
As the cover of embryos and adult organisms, epithelial tissues are subjected to substantial mechanical forces in tissue morphogenesis. However, the finite deformation behaviors of epithelial tissues remain largely unexplored. This study…
This thesis investigates critical phenomena and equilibrium states in various stochastic models through three interconnected studies. In the first chapter, we analyze the Activated Random Walk model on a one-dimensional ring in the…
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…
We study a probabilistic cellular automaton to describe two population biology problems: the threshold of species coexistence in a predator-prey system and the spreading of an epidemic in a population. By carrying out time-dependent…
To maintain homeostasis, living cells process information with networks of interacting molecules. Traditional models for cellular information processing have focused on networks of chemical reactions between molecules. Here, we describe how…
In view of ever-changing conditions both in the external world and in intrinsic brain states, maintaining the robustness of computations poses a challenge, adequate solutions to which we are only beginning to understand. At the level of…
Cancer stem cells have been shown to be critical to the development of a variety of solid cancers. The precise interplay mechanisms between cancer stem cells and the rest of a tissue are still not elucidated. To shed light on the…
Local stresses in a tissue, a collective property, regulate cell division and apoptosis. In turn, cell growth and division induce active stresses in the tissue. As a consequence, there is a feedback between cell growth and local stresses.…
We investigate the long-time evolution of branching diffusion processes (starting with a finite number of particles) in inhomogeneous media. The qualitative behavior of the processes depends on the intensity of the branching. In the…
A celebrated and controversial hypothesis conjectures that some biological systems --parts, aspects, or groups of them-- may extract important functional benefits from operating at the edge of instability, halfway between order and…
Cell populations are often characterised by phenotypic heterogeneity in the form of two distinct subpopulations. We consider a model of tumour cells consisting of two subpopulations: non-cancer promoting (NCP) and cancer-promoting (CP).…
The contact process is a non-equilibrium Hamiltonian model that, even in one dimension, lacks an exact solution and has been extensively studied via Monte Carlo simulations, both in steady-state and time-dependent scenarios. Although the…
Soft biological tissues exhibit a tendency to maintain a preferred state of tensile stress, known as tensional homeostasis, which is restored even after external mechanical stimuli. This macroscopic behavior can be described using the…
During embryonic morphogenesis, tissues undergo dramatic deformations in order to form functional organs. Similarly, in adult animals, living cells and tissues are continually subjected to forces and deformations. Therefore, the success of…
A branching process in varying environment with generation-dependent immigration is a modification of the standard branching process in which immigration is allowed and the reproduction and immigration laws may vary over the generations.…
We study branching processes in an i.i.d. random environment, where the associated random walk is of the oscillating type. This class of processes generalizes the classical notion of criticality. The main properties of such branching…
Using a population dynamics inspired by an ensemble of growing cells, a set of fluctuation theorems linking observables measured at the lineage and population levels are derived. One of these relations implies specific inequalities…
Two powerful and complementary experimental approaches are commonly used to study the cell cycle and cell biology: One class of experiments characterizes the statistics (or demographics) of an unsynchronized exponentially-growing…
The importance of individual cells in a developing multicellular organism is well known but precisely how the individual cellular characteristics of those cells collectively drive the emergence of robust, homeostatic structures is less well…
A simple, but ``classical``, stochastic model for epidemic spread in a finite, but large, population is studied. The progress of the epidemic can be divided into three different phases that requires different tools to analyse. Initially the…