A stochastic model for neural progenitor dynamics in the mouse cerebral cortex

We have designed a stochastic model of embryonic neurogenesis in the mouse cerebral cortex, using the formalism of compound Poisson processes. The model accounts for the dynamics of different progenitor cell types and neurons. The expectation and variance of the cell number of each type are derived analytically and illustrated through numerical simulations. The effects of stochastic transition rates between cell types, and stochastic duration of the cell division cycle have been investigated sequentially. The model does not only predict the number of neurons, but also their spatial distribution into deeper and upper cortical layers. The model outputs are consistent with experimental data providing the number of neurons and intermediate progenitors according to embryonic age in control and mutant situations

A stochastic model for neural progenitor dynamics in the mouse cerebral cortex

We have designed a stochastic model of embryonic neurogenesis in the mouse cerebral cortex, using the formalism of compound Poisson processes. The model accounts for the dynamics of different progenitor cell types and neurons. The expectation and variance of the cell number of each type are derived analytically and illustrated through numerical simulations. The effects of stochastic transition rates between cell types, and stochastic duration of the cell division cycle have been investigated sequentially. The model does not only predict the number of neurons, but also their spatial distribution into deeper and upper cortical layers. The model outputs are consistent with experimental data providing the number of neurons and intermediate progenitors according to embryonic age in control and mutant situations

A stochastic model for neural progenitor dynamics in the mouse cerebral cortex

We have designed a stochastic model of embryonic neurogenesis in the mouse cerebral cortex, using the formalism of compound Poisson processes. The model accounts for the dynamics of different progenitor cell types and neurons. The expectation and variance of the cell number of each type are derived analytically and illustrated through numerical simulations. The effects of stochastic transition rates between cell types, and stochastic duration of the cell division cycle have been investigated sequentially. The model does not only predict the number of neurons, but also their spatial distribution into deeper and upper cortical layers. The model outputs are consistent with experimental data providing the number of neurons and intermediate progenitors according to embryonic age in control and mutant situations

Redirection de flux pour le contrôle d'une réaction-diffusion épidémique

We show we can control an epidemic reaction-diffusion on a directed, and heterogeneous, network by redirecting the flows, thanks to the optimisation of well-designed loss functions, in particular the basic reproduction number of the model. We provide a final size relation linking the basic reproduction number to the epidemic final sizes, for diffusions around a reference diffusion with basic reproduction number less than 1. Experimentally, we show control is possible for different topologies, network heterogeneity levels, and speeds of diffusion. Our experimental results highlight the relevance of the basic reproduction number loss, compared to more straightforward losses.Nous contrôlons une réaction-diffusion épidémique sur un graphe orienté et hétérogène, en redirigeant les flux, grâce à l'optimisation de fonctions de perte bien choisies, en particulier le nombre de reproduction de base du modèle. Nous démontrons une relation de taille finale liant le nombre de reproduction de base aux tailles finales des épidémies, pour des diffusions proches d'une diffusion de référence dont le nombre de reproduction de base est inférieur à 1. Numériquement, nous montrons que le contrôle est possible pour différentes topologies, différents niveaux d'hétérogénéité du réseau, et différentes vitesses de diffusion. Nos résultats expérimentaux mettent en évidence la pertinence du nombre de reproduction de base en tant que perte, comparé à d'autres pertes d'obtention plus directe

Redirection de flux pour le contrôle d'une réaction-diffusion épidémique

We show we can control an epidemic reaction-diffusion on a directed, and heterogeneous, network by redirecting the flows, thanks to the optimisation of well-designed loss functions, in particular the basic reproduction number of the model. We provide a final size relation linking the basic reproduction number to the epidemic final sizes, for diffusions around a reference diffusion with basic reproduction number less than 1. Experimentally, we show control is possible for different topologies, network heterogeneity levels, and speeds of diffusion. Our experimental results highlight the relevance of the basic reproduction number loss, compared to more straightforward losses.Nous contrôlons une réaction-diffusion épidémique sur un graphe orienté et hétérogène, en redirigeant les flux, grâce à l'optimisation de fonctions de perte bien choisies, en particulier le nombre de reproduction de base du modèle. Nous démontrons une relation de taille finale liant le nombre de reproduction de base aux tailles finales des épidémies, pour des diffusions proches d'une diffusion de référence dont le nombre de reproduction de base est inférieur à 1. Numériquement, nous montrons que le contrôle est possible pour différentes topologies, différents niveaux d'hétérogénéité du réseau, et différentes vitesses de diffusion. Nos résultats expérimentaux mettent en évidence la pertinence du nombre de reproduction de base en tant que perte, comparé à d'autres pertes d'obtention plus directe

Estimation of the lifetime distribution from fluctuations in Bellman-Harris processes

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 lifetime of individuals is assumed to be independent and identically distributed. Here, we are interested in the estimation of the parameters of the Bellman-Harris model, motivated by the estimation of cell division time. Lifetimes are distributed according a Gamma distribution and we follow a population that starts from a small number of individuals by performing time-resolved measurements of the population size. The exponential growth of the population size at the beginning offers an easy estimation of the mean of the lifetime. Going farther and describing lifetime variability is a challenging task however, due to the complexity of the fluctuations of non-Markovian branching processes. Using fine and recent results on these fluctuations, we describe two time-asymptotic regimes and explain how to estimate the parameters. Then, we both consider simulations and biological data to validate and discuss our method. The results described here provide a method to determine single-cell parameters from time-resolved measurements of populations without the need to track each individual or to know the details of the initial condition

Estimation of the lifetime distribution from fluctuations in Bellman-Harris processes

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 lifetime of individuals is assumed to be independent and identically distributed. Here, we are interested in the estimation of the parameters of the Bellman-Harris model, motivated by the estimation of cell division time. Lifetimes are distributed according a Gamma distribution and we follow a population that starts from a small number of individuals by performing time-resolved measurements of the population size. The exponential growth of the population size at the beginning offers an easy estimation of the mean of the lifetime. Going farther and describing lifetime variability is a challenging task however, due to the complexity of the fluctuations of non-Markovian branching processes. Using fine and recent results on these fluctuations, we describe two time-asymptotic regimes and explain how to estimate the parameters. Then, we both consider simulations and biological data to validate and discuss our method. The results described here provide a method to determine single-cell parameters from time-resolved measurements of populations without the need to track each individual or to know the details of the initial condition