Frequency-Dependent Ecological Interactions Increase the Prevalence, and Shape the Distribution, of Preexisting Drug Resistance

Abstract

The evolution of resistance remains one of the primary challenges for modern medicine, from infectious diseases to cancers. Many of these resistance-conferring mutations often carry a substantial fitness cost in the absence of treatment. As a result, we would expect these mutants to undergo purifying selection and be rapidly driven to extinction. Nevertheless, preexisting resistance is frequently observed from drug-resistant malaria to targeted cancer therapies in non-small-cell lung cancer (NSCLC) and melanoma. Solutions to this apparent paradox have taken several forms, from spatial rescue to simple mutation supply arguments. Recently, in an evolved resistant NSCLC cell line, we found that frequency-dependent ecological interactions between ancestor and resistant mutant ameliorate the cost of resistance in the absence of treatment. Here, we hypothesize that frequency-dependent ecological interactions in general play a major role in the prevalence of preexisting resistance. We combine numerical simulations with robust analytical approximations to provide a rigorous mathematical framework for studying the effects of frequency-dependent ecological interactions on the evolutionary dynamics of preexisting resistance. First, we find that ecological interactions significantly expand the parameter regime under which we expect to observe preexisting resistance. Next, even when positive ecological interactions between mutants and ancestors are rare, these resistant clones provide the primary mode of evolved resistance because even weak positive interaction leads to significantly longer extinction times. We then find that even in the case where mutation supply alone is sufficient to predict preexisting resistance, frequency-dependent ecological forces still contribute a strong evolutionary pressure that selects for increasingly positive ecological effects (negative frequency-dependent selection). Finally, we genetically engineer several of the most common clinically observed resistance mechanisms to targeted therapies in NSCLC, a treatment notorious for preexisting resistance. We find that each engineered mutant displays a positive ecological interaction with their ancestor. As a whole, these results suggest that frequency-dependent ecological effects can play a crucial role in shaping the evolutionary dynamics of preexisting resistance.

FIG. 1.

Illustrated abstraction demonstrating how frequency-dependent ecological interactions might increase the likelihood of preexisting resistance. (a) Visualization of a typical frequency-dependent growth experiment. The ancestor (black line) is assumed to grow at a constant rate. Two hypothetical resistant mutants are depicted. Both mutants share the same intrinsic fitness and fitness cost, however the positive ecological mutant (red, growth increases as the fraction of ancestor cells increases) has a significantly higher ecological fitness $\left(f_e\approx 1\right)$ than the negative ecological mutant (blue, growth decreases as the fraction of ancestor cells increases). (b) Top: Visualization of an evolving population with no ecological interactions. All mutants are assumed to have a noninsignificant fitness cost $f_c$, and as a result go extinct. Bottom: The same evolving population, assuming ecological interactions are present. Note that an identical number of mutants emerge, however semirare mutants with positive ecological interactions demonstrate an increased time to extinction. As a result, when a drug intervention is administered, preexistence is much more likely to be present.

FIG. 2.

Analytical approximations and simulations predict that extinction times depend on ecological interactions. (a) Closed form extinction time distributions are calculated and visualized for a generalized Moran process ($N=100,f_c=0.25$). The red distribution results from a mutant with a positive ecological interaction with the ancestor ($f_e=1.0$), while the blue population has no ecological interaction with the ancestor ($f_e=1-f_c=0.75$). (b) Wright-Fisher simulations are used to numerically calculate the mean extinction time as a function of $f_e(N=10000,\mu ={10}^{-6},500$ generations, $f_i$ is drawn uniformly in $\left[0,1-f_c\right],f_i$ is drawn uniformly in [0,1]). (c) Wright-Fisher simulations are repeated for varying values of $f_c,\mu$, and $N$ to confirm theoretical prediction that the extinction time distribution depends only on $f_e$. (d) Phase diagram depicting the three regimes of preexisting resistance.

FIG. 3.

Positive ecological interactions make preexistence more likely and dominate the stationary distribution of mutants. (a) Representative Wright-Fisher trajectory in the “rare mutant regime.” Black corresponds to the ancestral population. Mutants exist in higher fractions and for longer periods with ecological interactions. Each mutant is colored by its ecological fitness, where red represents an $f_e$ value near 1 and blue represents an $f_e$ value near 0. (b) Representative trajectory in the “many mutant regime.” Strong positive ecological interactions dominate the stationary distribution of mutants (visually the mutants appear red, not blue). (c) Left: Stationary distribution of mutant ecological fitnesses when the mutant-generating function is uniform across ecological fitness. Right: joint distribution density plot between intrinsic and ecological fitness. (d) Same as c, however the mutant-generating function is now Gaussian centered about $f_e=0.5$.

FIG. 4.

Positive ecological fitnesses above 1 result in a stable fixed point between mutant and ancestor. (a) Stationary distribution of mutant ecological fitnesses when the mutant generating function has uniform probability in [0,1.10]. (b) Stationary distribution of mutant intrinsic fitnesses. (c) Joint distribution density plot between intrinsic and ecological fitness reveals the size of the fitness cost now has a significant impact on mutant survival. (d) Illustration of why two mutants with identical values of $f_e$ can result in different extinction times. Colored arrows point to stabled fixed points between mutant and ancestor.

FIG. 5.

Common clinically observed resistance mutations in NSCLC harbor strong positive ecological interactions with their ancestor in a model system of preexisting resistance. Stacked bar chart: Visual representation of the known resistance mechanisms to osimertinib, a third-generation TKI and the current standard of care for EGFR-positive NSCLC. Mutation frequencies and categorical definitions from Leonetti et al. [57]. Top: Evolved gefitinib-resistant NSCLC PC9 mutant (previously reported [40]) exhibits a positive ecological interaction with its ancestor. Fresh sequencing analysis identifies clinically observed resistant mutations including KRASG12D, MET amplification, and CCND1 amplification (cell cycle gene). Bottom: Measured positive ecological interactions between engineered resistant mutants (KRAS-G12V top left, PIK3CA-E545K top right, BRAF-V600F bottom) and their ancestor.