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Since its introduction in 1952, Turing's (pre-)pattern theory ("the chemical basis of morphogenesis") has been widely applied to a number of areas in developmental biology. The related pattern formation models normally comprise a system of…
Spatial self-organization emerges in distributed systems exhibiting local interactions when nonlinearities and the appropriate propagation of signals are at work. These kinds of phenomena can be modeled with different frameworks, typically…
Cell biomechanics involve a great number of complex phenomena that are fundamental to the evolution of life itself and other associated processes, ranging from the very early stages of embryo-genesis to the maintenance of damaged structures…
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…
This paper introduces a continuous model for Multi-cellular Developmental Design. The cells are fixed on a 2D grid and exchange "chemicals" with their neighbors during the growth process. The quantity of chemicals that a cell produces, as…
Populations exhibiting partial migration consist of two groups of individuals: Those that mi- grate between habitats, and those that remain fixed in a single habitat. We propose several discrete-time population models to investigate the…
The processes taking place inside the living cell are now understood to the point where predictive computational models can be used to gain detailed understanding of important biological phenomena. A key challenge is to extrapolate this…
We present a modelling framework for the dynamics of cells structured by the concentration of a micromolecule they contain. We derive general equations for the evolution of the cell population and of the extra-cellular concentration of the…
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 develop a general modelling framework for compartmental epidemiological systems structured by continuous variables which are linked to the levels of expression of compartment-specific traits. We start by formulating an individual-based…
In many adult tissues, stem cells and differentiated cells are not homogeneously distributed : stem cells are arranged in periodic "niches", and differentiated cells are constantly produced and migrate out of these niches. In this article,…
Replication through cell division is one of the most fundamental processes of life and a major driver of dynamics in systems ranging from bacterial colonies to embryogenesis, tissues and tumors. While regulation often plays a role in…
Mathematical theory of selection is developed within the frameworks of general models of inhomogeneous populations with continuous time. Methods that allow us to study the distribution dynamics under natural selection and to construct…
The dynamical behavior of two types of non-equilibrium systems is discussed: $(a)$ two-dimensional cellular structures, and $(b)$ living polymers. Simple models governing their evolution are introduced and steady state distributions (cell…
Adaptive control in biological systems, such as intestinal immunity, remains poorly understood despite detailed knowledge of underlying regulatory networks. We propose an alternative framework based on stochastic martingale turnover, in…
Discrete time, spatially extended models play an important role in ecology, modelling population dynamics of species ranging from micro-organisms to birds. An important question is how 'bottom up', individual-based models can be…
We consider a model for the dynamics of growing cell populations with heterogeneous mobility and proliferation rate. The cell phenotypic state is described by a continuous structuring variable and the evolution of the local cell population…
We present a development of a model of the relationship between cells in three compartments of the intestinal crypt: stem cells, semi-differentiated cells and fully differentiated cells. Stem and semi-differentiated cells may divide to…
Among the different computational approaches modelling the dynamics of isogenic cell populations, discrete stochastic models can describe with sufficient accuracy the evolution of small size populations. However, for a systematic and…
Growth-fragmentation processes model systems of cells that grow continuously over time and then fragment into smaller pieces. Typically, on average, the number of cells in the system exhibits asynchronous exponential growth and, upon…