A Preliminary Model of Double-Minute-Mediated Gene Amplification
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Develops a mathematical model of double minute (dm) population dynamics based on 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 (chi squared = 2.6, d.f. = 29) providing preliminary evidence of the consistency of this set of mechanisms. Two special cases are examined. The model predicts that the population-average rate of extrareplicative dm production is .039 +/- S.E.009 dms/hr/cell in the first case and is tenfold higher than when such replication occurs on the chromosome alone. It is found that dm-related growth inhibition can be nearly as high as that observed for the S180 sarcoma lines (about 0.5 percent per dm lengthening of the doubling time) or as low as zero.
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