Use of mathematical models for understanding the dynamics of gene amplification.

Recently it has been suggested that high levels of cancer drug resistance and poor prognosis are strongly associated with gene or oncogene amplification (GA). It has been further suggested that the molecular mechanisms underlying GA may be different for different genes, and that different amplification mechanisms may function concurrently or sequentially in the same gene. The aim of this review is to demonstrate the use of mathematical models in studying these intricate dynamics. We have provided mathematical models for the generation of extrachromosomal elements, their autonomous replication and equal or unequal mitotic segregation, the integration of the extrachromosomal elements within the chromosomes, and chromosomal GA in one or many unlinked genes. Using this formal description one can examine the potential role of each GA mechanism in the generation of specific distributions of gene-copy number in a cell population, under various levels of selection stringency. Thus one can specify the conditions for the emergence of drug-resistant mutants prior to selection, as well as the relationships between the stringency of the selecting environment and the characteristics of the resultant cellular phenotype.