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Cellular phenotype is characterized by different components such as cell size, protein content and cell cycle time. These are global variables that are the outcome of multiple internal microscopic processes. Accordingly, they display some…
We study the mathematical properties of a general model of cell division structured with several internal variables. We begin with a simpler and specific model with two variables, we solve the eigenvalue problem with strong or weak…
We model the growth of a cell population using a piecewise deterministic Markov branching tree. In this model, each cell splits into two offspring at a division rate $B(x)$, which depends on its size $x$. The size of each cell increases…
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…
Stochastic models of sequential mutation acquisition are widely used to quantify cancer and bacterial evolution. Across manifold scenarios, recurrent research questions are: how many cells are there with $n$ alterations, and how long will…
We study the interplay of population growth and evolutionary dynamics using a stochastic model based on birth and death events. In contrast to the common assumption of an independent population size, evolution can be strongly affected by…
The spatiotemporal coordination and regulation of cell proliferation is fundamental in many aspects of development and tissue maintenance. Cells have the ability to adapt their division rates in response to mechanical constraints, yet we do…
We study the long time behavior of an asymmetric size-structured measure-valued growth-fragmentation branching process that models the dynamics of a population of cells taking into account physiological and morphological asymmetry at…
Cell size is a fundamental determinant of cellular physiology, influencing processes such as growth, division, and function. In this study, we develop a segmented mathematical framework to investigate how different control mechanisms…
We examine the dynamics of an age-structured population model in which the life expectancy of an offspring may be mutated with respect to that of the parent. While the total population of the system always reaches a steady state, the…
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)…
Ageing of lithium-ion batteries results in irreversible reduction in performance. Intrinsic variability between cells, caused by manufacturing differences, occurs throughout life and increases with age. Researchers need to know the minimum…
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 exponential population growth, variability in the timing of individual division events and environmental factors (including stochastic inoculation) compound to produce variable growth trajectories. In several stochastic models of…
Density dependence is important in the ecology and evolution of microbial and cancer cells. Typically, we can only measure net growth rates, but the underlying density-dependent mechanisms that give rise to the observed dynamics can…
Most microorganisms regulate their cell size. We review here some of the mathematical formulations of the problem of cell size regulation. We focus on coarse-grained stochastic models and the statistics they generate. We review the…
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…
Existing studies comparing individual-based models of growing cell populations and their continuum counterparts have mainly focused on homogeneous populations, in which all cells have the same phenotypic characteristics. However,…
Motivated by the wide range of known self-replicating systems, some far from genetics, we study a system composed by individuals having an internal dynamics with many possible states that are partially stable, with varying mutation rates.…
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,…