Adapted from Y. Iwasa, et al., Proc R soc Lond B Sci, 270: 2573–8, 2003.
In this example, genes can mutate at the rate u per gene, per cell division. Gross chromosomal changes occur at the rate p. For this tumor suppressor gene, TSP, Cancer cells have two functioning alleles prior to chemotherapy. Cell reproductive rates Ro-R4 are assumed equal, and a = R/(1-R). Therefore, the critical population size before escape from the therapeutic could happen, N*, can be represented by the equation N* = 1/[a(1 + 2a)u(u + 2p)]. Supposing a given u and a given R, cancers with chromosomal instability, defined by increased rate p, have a much lower critical population size for escape from chemotherapy.
Natural selection remains modern biology's leitmotif 145 years after Darwin published On the Origin of Species: Tumor resistance offers a devastating reminder of its potency. Clinicians often hope they have destroyed a ...
