Mutagenesis and mathematics: the allure of numbers

This paper sets out the "formal," "empirical," and "mechanistic" equations that my colleagues and I have developed for the description and analysis of dose-response data on the lethal and genetic effects of mutagens in microorganisms. These three types of equations are interrelated inasmuch as they are all based ultimately on the use of the Poisson distribution in the formal definition of lethal and mutational hit functions. Explicit mathematical expressions for these functions can be written down in either empirical or mechanistic terms. The empirical equations are obtained simply by writing the hit functions as finite polynomials with adjustable coefficients. The mechanistic equations are based on the assumptions of the "DNA damage-repair hypothesis." The mathematical formulation of this hypothesis entails an important change in the definition of the word "hit" from that used in the classical hit/target theory of radiation biology. The theoretical and practical applications of these various equations in mutation research are summarized briefly and their merits are assessed in light of recent advances in our understanding of the biochemical basis of mutagenesis.