TIME-CONTINUOUS BRANCHING WALK MODELS OF UNSTABLE GENE AMPLIFICATION

We consider a stochastic mechanism of the loss of resistance of cancer cells to cytotoxic agents, in terms of unstable gene amplification. T wo models being different versions of a time-continuous branching rand om walk are presented. Both models assume strong dependence in replica tion and segregation of the extrachromosomal elements. The mathematica l part of the paper includes the expression for the expected number of cells with a given number of gene copies in terms of modified Bessel functions. This adds to the collection of rare explicit solutions to b ranching process models. Original asymptotic expansions are also demon strated. Fitting the model to experimental data yields estimates of th e probabilities of gene amplification and deamplification. The thesis of the paper is that purely stochastic mechanisms may explain the dyna mics of reversible drug resistance of cancer cells. Various stochastic approaches and their limitations are discussed.