Institute of Mathematics and Informatics Bulgarian Academy of Sciences
Abstract
2000 Mathematics Subject Classification: 60J80.This paper is concerned with an age-dependent branching process with particles (cells) bearing a label, the latter being treated as a continuous parameter. The proposed stochastic model is motivated by applications in cell biology. It is assumed that the mitotic division results in a random distribution of the label among daughter cells in accordance with some bivariate probability distribution. In the event of cell death the label borne by that cell disappears. The main focus is on the label distribution as a function of the time elapsed from the moment of label administration. Explicit expressions for this distribution are derived in some particular cases which are of practical interest in the analysis of cell cycle. The Markov branching process with the same evolution of a continuously distributed label is considered as well.This research is supported in part by NIH/NINDS grant NS39511 (Yakovlev), ECO-NET-06 action 12634TJ funded by French Foreign Office (Yanev) and grant VU-MI-105/2005 by NSF
