Analysis of non-linearities in mutation frequency curves

Mutation frequency curves for ultraviolet light and other mutagens often exhibit non-linear, as well as linear components. A common pattern observed for UV-induced reversion of auxotrophy in yeast is a biphasic, linear-quadratic (or higher order) response. The non-linear component in such a biphasic frequency curve can arise in two distinct, but non-mutually exclusive, ways: (i) as a result of the existence of two-hit processes in the molecular mechanism(s) of mutagenesis; and (ii) as a result of the possible stochastic dependence of mutation and killing, such that the probability of clone formation by the mutant cells differs from that of the non-mutant cells in the population. We describe here a simple mathematical method for distinguishing between these two sources of non-linearity. It is based on the calculation of a quantity that we call 'apparent survival.' This is given, for any mutagen dose chi, by the ratio of the mutant yield to the corresponding linear component of mutation frequency. If the apparent survival rises to values greater than unity before declining at high doses, then there must exist positive two-hit (or higher order) components in the mutational mechanism. If the final slope of the apparent survival curve differs from that of the measured survival curve, then there also exists some degree of stochastic dependence between mutation and killing.