Evolutionary rescue and drug resistance on multicopy plasmids

Abstract

1Bacteria often carry "extra DNA" in form of plasmids in addition to their chro-2 mosome. Many plasmids have a copy number greater than one such that the genes 3 encoded on these plasmids are present in multiple copies per cell. This has evo-4 lutionary consequences by increasing the mutational target size, by prompting the 5 (transitory) co-occurrence of mutant and wild-type alleles within the same cell, and 6 by allowing for gene dosage effects. We develop and analyze a mathematical model for 7 bacterial adaptation to harsh environmental change if adaptation is driven by benefi-8 cial alleles on multicopy plasmids. Successful adaptation depends on the availability 9 of advantageous alleles and on their establishment probability. The establishment 10 process involves the segregation of mutant and wild-type plasmids to the two daugh-11 ter cells, allowing for the emergence of mutant-homozygous cells over the course of 12 several generations. To model this process, we use the theory of multi-type branch-13 ing processes, where a type is defined by the genetic composition of the cell. Both 14 factors -the number of adaptive alleles and their establishment probability -depend 15 on the plasmid copy number, and they often do so antagonistically. We find that 16 in the interplay of various effects, a lower or higher copy number may maximize the 17 probability of evolutionary rescue. The decisive factor is the dominance relationship 18 between mutant and wild-type plasmids and potential gene dosage effects. Results 19 from a simple model of antibiotic degradation indicate that the optimal plasmid copy 20 number may depend on the specific environment encountered by the population. 21 157 vidual establishes a permanent lineage of offspring. We provide an expression for p hom est in 158 Eq. (A.6). 159 Mathematical approach 160Whether the bacterial population successfully adapts or goes extinct depends on two factors: 161 the mutational supply and the establishment probability of the resistance mutation once 162