USE OF MATHEMATICAL-MODELS FOR UNDERSTANDING THE DYNAMICS OF GENE AMPLIFICATION

Recently it has been suggested that high levels of cancer drug resista nce and poor prognosis are strongly associated with gene or oncogene a mplification (GA). It has been further suggested that the molecular me chanisms underlying GA may be different for different genes, and that different amplification mechanisms may function concurrently or sequen tially in the same gene. The aim of this review is to demonstrate the use of mathematical models in studying these intricate dynamics. We ha ve provided mathematical models for the generation of extrachromosomal elements, their autonomous replication and equal or unequal mitotic s egregation, the integration of the extrachromosomal elements within th e 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 nu mber in a cell population, under various levels of selection stringenc y. Thus one can specify the conditions for the emergence of drug-resis tant mutants prior to selection, as well as the relationships between the stringency of the selecting environment and the characteristics of the resultant cellular phenotype.