Time-dependent induction of clonal heterogeneity in the neoplastic micro-environment is analysed within the context of a competitive ecology. A model that describes a constant source for clonal emergence was analysed by Michelson et al. (1987) as an extension of a model proposed by Jansson and Revesz (1974). The extended model has been termed the JRE Model. This paper extends these analyses to time-dependent emergence rates which may represent induction in the presence of a cytotoxic agent. If the analysis is constrained to the tumor micro-environment, and if the emergent subpopulation is drug resistant, then the model may describe the induction and emergence of drug resistant subclones in a growing neoplasm. Asymptotic closed form solutions are derived for a class of emergence rate functions which decay asymptotically to a constant mutation rate. This underlying mutation rate may represent spontaneous mutation to the resistant phenotype, and has been analysed stochastically (Coldman et al., 1985). The asymptotic solutions to the time-dependent model approach the steady state solution for the JRE Model which represents the dynamics observed in the presence of a constant, spontaneous mutation rate. The clinical and biological implications of these results are discussed.
ASJC Scopus subject areas
- Biochemistry, Genetics and Molecular Biology(all)
- Environmental Science(all)
- Agricultural and Biological Sciences(all)
- Computational Theory and Mathematics