A preliminary model of double-minute-mediated gene amplification

A mathematical model of double minute (dm) population dynamics has been developed based upon current concepts of the saltatory replication, random partitioning, nuclear exclusion and loss, and cellular growth inhibition of these extrachromosomal elements. A highly accurate approximate analytical solution has been obtained for the dm frequency distribution at steady state and preliminary analysis of transient states has been performed. The steady state solution has been fit to experimental frequency data of the SW527N carcinoma line, the excellent goodness of fit (X2 = 2.6, d.f. = 29) providing preliminary evidence for the consistency of this set of mechanisms. Two special cases are examined in which extrareplicative dms are produced on both the chromosome and existing dms at equal rates or on the chromosome alone. The model predicts that the population--average rate of extrareplicative dm production is 0.039 +/- S.E. 0.009 dms/hr/cell in the first case and is tenfold higher than when such replication occurs on the chromosome alone (0.0043 +/- S.E. 0.0004 dms/hr/cell). Allowable ranges of the extent of dm-related growth inhibition and dm loss are determined for the SW527N cell line. It is found that dm-related growth inhibition can be nearly as high as that observed for the S180 sarcoma lines (on the order of 0.5% per dm lengthening of the doubling time) or as low as zero.