A Markovian growth dynamics on rooted binary trees evolving according to the Gompertz curve

Telomere are nucleo-proteins located at the end terminal of eukaryotic chromosomes which shorten at each cell division. Recent evidences points to telomere as a cell clock mechanism which limits the total number of cell divisions (Hayflick limit) and decelerates cellular proliferation. In a recent work, simulations of a discrete time stochastic telomere regulated model for cell division produced growth curves similar to those observed in mesenchymal human stem cells and quantitatively very similar to Gompertzian Growth. In this work we considered the continuous time version of the stochastic telomere regulated model for cultured cell division. Instead of simulations, we obtained the analytic expression for the expected mean cell population. The growth curve obtained is still very close to a Gompertzian growth, within the limit of 2% of the final size. Moreover, Gompertzian growth is retrieved as a limit case. We also evaluate the mean telomere length, which can be checked against cell culture data. Gompertzian growth is observed in tumors, animals and tissue regeneration but its biological foundations are still unclear. This work adds a possible intrinsic control mechanism for this growth model. keywords: telomere, growth, stem cells, model, stochastic, Gompertz. IMPA, Estrada Dona Castorina 110, 22460-320 Rio de Janeiro, Brazil (@impa.br) Partially supported by Brazilian CNPq scholarship . Faculty of Medicine, Federal University of Rio de Janeiro IMPA, Estrada Dona Castorina 110, 22460-320 Rio de Janeiro, Brazil ([email protected]) Partially supported by CNPq grants 300755/2005-8, 475647/2006-8 and by PRONEXOptimization 1