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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…
We study the asymptotic behaviour of positive solutions of the Cauchy problem for the fast diffusion equation near the extinction time. We find a continuum of rates of convergence to a self-similar profile. These rates depend explicitly on…
An individual-based model of stochastic branching is proposed and studied, in which point particles drift in $\bar{\mathds{R}}_{+}:=[0,+\infty)$ towards the origin (edge) with unit speed, where each of them splits into two particles that…
Microbial growth and division are fundamental processes relevant to many areas of life science. Of particular interest are homeostasis mechanisms, which buffer growth and division from accumulating fluctuations over multiple cycles. These…
A recent burst of dynamic single-cell growth-division data makes it possible to characterize the stochastic dynamics of cell division control in bacteria. Different modeling frameworks were used to infer specific mechanisms from such data,…
We present a geometric framework to study the growth-division dynamics of cells and protocells, and demonstrate that self-reproduction emerges only when a system's growth dynamics and division strategy are mutually compatible. Using several…
Thermodynamically consistent fractional Burgers constitutive models for viscoelastic media, divided into two classes according to model behavior in stress relaxation and creep tests near the initial time instant, are coupled with the…
Continuum models for the spatial dynamics of growing cell populations have been widely used to investigate the mechanisms underpinning tissue development and tumour invasion. These models consist of nonlinear partial differential equations…
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…
Solving population balance equations, we derive analytical steady-state cell size distributions for single-lineage experiments, such as the mother machine. These experiments are fundamentally different from batch cultures where populations…
In this paper, a two-dimensional model for the growth of multi-layer tumors is presented. The model consists of a free boundary problem for the tumor cell membrane and the tumor is supposed to grow or shrink due to cell proliferation or…
We introduce a general theoretical framework to study the shape dynamics of actively growing and remodeling surfaces. Using this framework we develop a physical model for growing bacterial cell walls and study the interplay of cell shape…
Under hard-agar and nutrient-rich conditions, a cell of $Bacillus$ $subtilis$ grows as a single filament owing to the failure of cell separation after each growth and division cycle. The self-elongating filament of cells shows sequential…
Cells of the human body have nearly identical genome but exhibit very different phenotypes that allow them to carry out specific functions and react to changes in their surrounding environment. This division of labour is achieved by…
It is well known that the different cell-division models, such as Timer, Sizer, and Adder, can be distinguished based on the correlations between different single-cell-level quantities such as birth-size, division-time, division-size, and…
We model the growth of a cell population by a piecewise deterministic Markov branching tree. Each cell splits into two offsprings at a division rate $B(x)$ that depends on its size $x$. The size of each cell grows exponentially in time, at…
Cell size control and homeostasis is a major topic in cell biology yet to be fully understood. Several growth laws like the timer, adder, and sizer were proposed, and mathematical approaches that model cell growth and division were…
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,…
We consider the problems of the numerical solution of the Cauchy problem for an evolutionary equation with memory when the kernel of the integral term is a difference one. The computational implementation is associated with the need to work…
We study the existence and uniqueness of the solution of a non-linear coupled system constituted of a degenerate diffusion-growth-fragmentation equation and a differential equation, resulting from the modeling of bacterial growth in a…