Related papers: Analytical cell size distribution: lineage-populat…
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…
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…
The mechanism of bacterial cell size control has been a mystery for decades, which involves the well-coordinated growth and division in the cell cycle. The revolutionary modern techniques of microfluidics and the advanced live imaging…
We show how one may analytically compute the stationary density of the distribution of molecular constituents in populations of cells in the presence of noise arising from either bursting transcription or translation, or noise in…
The mean size of exponentially dividing E. coli cells cultured in different nutrient conditions is known to depend on the mean growth rate only. However, the joint fluctuations relating cell size, doubling time and individual growth rate…
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…
It has been recently shown that the exponential growth rate of a population of bacterial cells starting from a single cell shows transient oscillations due to early synchronized bursts of division. These oscillations are enhanced by cell…
Many of the existing stochastic models of gene expression contain the first-order decay reaction term that may describe active protein degradation or dilution. If the model variable is interpreted as the molecule number, and not…
The aim of this work is twofold. First, we survey the techniques developed in (Perthame, Zubelli, 2007) and (Doumic, Perthame, Zubelli, 2008) to reconstruct the division (birth) rate from the cell volume distribution data in certain…
Regulation of cell growth and division is essential to achieve cell-size homeostasis. Recent advances in imaging technologies, such as ``mother machines" for bacteria or yeast, have allowed long-term tracking of cell-size dynamics across…
Protein distributions measured under a broad set of conditions in bacteria and yeast were shown to exhibit a common skewed shape, with variances depending quadratically on means. For bacteria these properties were reproduced by temporal…
Isogenic Escherichia coli growing exponentially in a constant environment display large variation in growth-rates, division-sizes and generation-times. It is unclear how these seemingly random cell cycles can be reconciled with the precise…
Cell lineage statistics is a powerful tool for inferring cellular parameters, such as division rate, death rate or the population growth rate. Yet, in practice such an analysis suffers from a basic problem: how should we treat incomplete…
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…
In this paper, experimental data is presented and a simple model is developed for the time evolution of a F-amp \textit{E. Coli} culture population. In general, the bacteria life cycle as revealed by monitoring a culture's population…
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…
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,…
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…
Single-cell experiments have revealed cell-to-cell variability in generation times and growth rates for genetically identical cells. Theoretical models relating the fluctuating generation times of single cells to the population growth rate…
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…