A mathematic model for relating the drug sensitivity of tumors to their spontaneous mutation rate

Abstract

A mathematic model has been developed relating the drug sensitivity of a tumor to its own spontaneous mutation rate towards phenotypic drug resistance. The proportion as well as the absolute numbers of resistant cells will increase with time and the fraction of resistant cells within tumor colonies of the same size with vary depending on whether mutation occurs as an early or late event. Analysis of the model indicates that the probability of the appearance of a resistant phenotype increases with the mutation rate. Furthermore, for any population of tumors with a non-zero mutation rate the likelihood of there being at least one resistant cell will go from a condition of low to high probability over a very short interval in the tumor's biologic history.