A branching process model of gene amplification following chromosome breakage

We have devised a mathematical model of gene amplification utilizing recent experimental observations concerning dihydrofolate reductase (DHFR) gene amplification in CHO cells. The mathematical model, based on a biological model which proposes that acentric elements are the initial intermediates in gene amplification, includes the following features: (1) initiation of amplification by chromosomal breakage to produce an acentric structure; (2) replication of acentric DNA, once per cell cycle; (3) dissociation of replicated acentric DNA; (4) unequal segregation of acentric DNA fragments to daughter cells at mitosis; (5) subsequent reintegration of acentric fragments into chromosomes. These processes are assumed to be independent for each element present in a cell at a given time. Thus, processes of unequal segregation and integration may occur in parallel, not necessarily in a unique sequence, and may be reiterated in one or multiple cell cycles. These events are described mathematically as a Galton-Watson branching process with denumerable infinity of object types. This mathematical model qualitatively and quantitatively reproduces the major elements of the dynamical behavior of DHFR genes observed experimentally. The agreement between the mathematical model and the experimental data lends credence to the biological model proposed by Windle et al. (1991), including the importance of chromosome breakage and subsequent gene deletion resulting from resection of the broken chromosome ends as initial events in gene amplification.