Collateral effects of drug resistance evolution: explaining repeatability and directionality patterns

Drug resistance evolution is hindering the treatment of various diseases. One possible solution could be exploiting trade-offs in resistance to different, existing drugs. Collateral sensitivity means that resistance to one drug increases susceptibility to another. Contrarily, cross-resistance means that resistance to one drug implies resistance to another. These two collateral effects are, however, not always repeatable, nor are they always independent of drug order, i.e. bidirectional. Understanding what drives repeatability and directionality would help define the clinical applicability of collateral sensitivity and avoid cross-resistance. Nevertheless, the genetic and evolutionary mechanisms causing non-repeatability and unidirectionality patterns are not yet fully understood. In this study, we aim to define which drug concentrations, population dynamics, and genetic architectures cause these patterns of collateral effects. We describe the fewest loci and conditions needed for repeatable and non-repeatable, uni- or bidirectional cross-resistance and collateral sensitivity to occur. We show that increasing drug concentration narrows the set of possible adaptive genotypes and thereby increases repeatability. As for selection regimes, clonal interference can explain unidirectional cross-resistance and can increase repeatability, whereas a strong selection, weak mutation regime increases non-repeatability. Overall, we show how non-repeatability and unidirectionality of collateral effects are not properties solely of a drug pair but also of the selection regime: drug dose and population dynamics. Further studies, combining extensive mathematical modelling with measurements of full dose-response curves for drug pairs with known patterns of collateral effects, are needed to shed more light on this problem.