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Center for Nonlinear Studies |
Lymphocyte populations, stimulated in vitro or in vivo, grow as cells divide. If individual cells behave independently,then each cell’s fate can be imagined as an independent random sample from a probability distributionof times to division and death. The exponential distribution is the most mathematically and computationallyconvenient choice, but it overestimates the probability of short division times. With the aim of preserving theadvantages of a Markovian framework while improving the representation of experimentally-observed divisiontimes, a multi-stage model of cellular division and death is developed. Erlang-distributed times to division, andexponentially distributed times to death are used. Cells are classified into generations, using the rule that thedaughters of cells in generation g are in generation g+1. The theoretical predictions of the model are linked witha published experimental data set, where cell counts were reported after T cells were transferred to lymphopenicmice.Time-lapse microscopy experiments identified cellular fate correlations within family trees of immune cells. Asthe multi-stage model cannot account for such correlations, a two-type branching process is considered to modelcellular population dynamics with fate decision at birth. A population of cells is divided into two pools: cells thatare going to divide and individuals whose fate is apoptosis. When a division occurs, daughter cells join the divisionpool with probability p1, enter the apoptosis pool with probability p2, or have different fates with probabilityp3 = 1 − p1 − p2. After the decision at birth, cellular fate takes some random time to happen. Exponential andErlang probability distributions are used to model cellular time to division and death. Cellular fate correlationis introduced in the model through the definition of correlation factors. The theoretical predictions of the modelare compared to a data set of stimulated naive B cells, followed for 120 hours using time-lapse microscopy.
Host: Carmen Molina-Paris