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Mathematical Analysis of Mutation-Induction Kinetics

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Chemical Mutagens

Abstract

Mathematical analysis of dose-response relationships is necessary in the formulation of quantitative hypotheses regarding the macromolecular processes involved in the induction of genetic changes in cells. Such analysis is also important for the assessment of risks to human health that may be associated with exposure to mutagens or other genetically active agents.p(48) It is useful to distinguish formal descriptions of dose-response relationships from mathematical models of the underlying molecular mechanisms. In this chapter, we are concerned primarily with the formal description of mutation yields and frequencies in unicellular systems, but we also indicate how this formalism can be linked to current ideas on repair-mediated mutagenesis.p(54) Formal expressions for induced mutagenesis can be derived on the basis of either stochastic or deterministic assumptions. Stochastic models used in similar problems generally involve the application of the probit-log dose distribution 14,111 or the Poisson distribution.p(21,24,26,46) Deterministic models, so far applied only to cell-survival kinetics, are based on differential equations analogous to the law of mass action (e.g., Calkinsp(5)); other expressions, such as the allometric equation for differential growth, p(37) might be useful empirically in the analysis of frequency curves that appear to increase at nonintegral powers of dose. Here we adopt a stochastic approach and use the Poisson distribution in the analysis of UV-induced forward and reverse mutations in haploid strains of the yeast Saccharomyces cerevisiae. However, the formalism is sufficiently general to be applied to other mutagens, to other unicellular systems, and to other genetic end points such as mitotic recombination or malignant transformation.

A condensed version of this chapter is to be found in R. H. Haynes and F. Eckardt, Analysis of dose-response patterns in mutation research, Can. J. Genet. Cytol. 21, 277-302 (1979).

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Author information

Author notes

  1. Friederike Eckardt

    Present address: Gesellschaft für Strahlenforschung, 8042, Neuherberg, Bundesrepublik Deutschland

Authors and Affiliations

  1. Department of Biology, York University, Toronto, Ontario, Canada, M3J 1P3

    R. H. Haynes & Friederike Eckardt

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  1. R. H. Haynes
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  2. Friederike Eckardt
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Editors and Affiliations

  1. National Institute of Environmental Health Sciences, Research Triangle Park, North Carolina, USA

    Frederick J. de Serres

  2. Associated Universities, Inc., Washington, D. C., USA

    Alexander Hollaender

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© 1980 Plenum Press, New York

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Haynes, R.H., Eckardt, F. (1980). Mathematical Analysis of Mutation-Induction Kinetics. In: de Serres, F.J., Hollaender, A. (eds) Chemical Mutagens. Springer, Boston, MA. https://doi.org/10.1007/978-1-4613-3072-1_10

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  • DOI: https://doi.org/10.1007/978-1-4613-3072-1_10

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-1-4613-3074-5

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