Related papers: On distinguishability among cell-division models b…

Lymphocyte populations, stimulated in vitro or in vivo, grow as cells divide. Stochastic models are appropriate because some cells undergo multiple rounds of division, some die, and others of the same type in the same conditions do not…

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…

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…

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 derive the full kinetic equations describing the evolution of the probability density distribution for a structured population such as cells distributed according to their ages and sizes. The kinetic equations for such a "sizer-timer"…

We study time continuous branching processes with exponentially distributed lifetimes, with two types of cells that proliferate according to binary fission. A range of possible system dynamics are considered, each of which is characterized…

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…

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…

Development combines three basic processes asymmetric --- cell division, signaling and gene regulation --- in a multitude of ways to create an overwhelming diversity of multicellular life-forms. Here, we attempt to chart this diversity…

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…

Uncovering the quantitative laws that govern the growth and division of single cells remains a major challenge. Using a unique combination of technologies that yields unprecedented statistical precision, we find that the sizes of individual…

Many population genetic models have been developed for the purpose of inferring population size and growth rates from random samples of genetic data. We examine two popular approaches to this problem, the coalescent and the…

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…

Using demographic data of high spatial resolution for a region in the south of Europe, we study the population over fixed-size spatial cells. We find that, counterintuitively, the distribution of the number of inhabitants per cell increases…

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…

We consider a size-structured population describing the cell divisions. The cell population is described by an empirical measure and we observe the divisions in the continuous time interval [0, T ]. We address here the problem of estimating…

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,…

Cancer cells co-cultured in vitro reveal unexpected differential growth rates that classical exponential growth models cannot account for. Two non-interacting cell lines were grown in the same culture, and counts of each species were…

The growth of a population is often modeled as branching process where each individual at the end of its life is replaced by a certain number of offspring. An example of these branching models is the Bellman-Harris process, where the…

Self-organisation of individuals within large collectives occurs throughout biology. Mathematical models can help elucidate the individual-level mechanisms behind these dynamics, but analytical tractability often comes at the cost of…