Estimating the life-span of oligodendrocytes from clonal data on their development in cell culture

Abstract

This paper presents a new method to analyze clonal data on oligodendrocyte development in cell culture. The process of oligodendrocyte generation from precursor cells is modelled as a multi-type Bellman–Harris branching process as suggested in an earlier paper [K. Boucher, A. Zorin, A.Y. Yakovlev, M. Mayer-Pröschel, M. Noble, An alternative stochastic model of generation of oligodendrocytes in cell culture, J. Math. Biol. 43 (2001) 22]. This model has been extended to allow for death of oligodendrocytes as well as a dissimilar distribution of the first mitotic cycle duration as compared to the subsequent cycles of precursor cells, which lengths are assumed to be independent and identically distributed random variables. Since the time-span of oligodendrocytes is not directly observable in clonal data, plausible parametric assumptions are invoked to make estimation problems tractable. In particular, the time to cell death follows a two-parameter gamma distribution, while the lapse of time between the event of cell death and the event of cell disintegration is assumed to be exponentially distributed. A simulated pseudo maximum likelihood method for estimation of model parameters has been developed using simulation-based approximations of the expected numbers and variance-covariance matrices for different types of cells. Finite sample properties of the estimation procedure are studied by computer simulations. The proposed method is illustrated with an analysis of the clonal development of O-2A progenitor cells isolated from the rat optic nerve and the corpus callosum.