The population genetics of collateral resistance and sensitivity

  1. Sarah M Ardell
  2. Sergey Kryazhimskiy

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Abstract

Resistance mutations against one drug can elicit collateral sensitivity against other drugs. Multi-drug treatments exploiting such trade-offs can help slow down the evolution of resistance. However, if mutations with diverse collateral effects are available, a treated population may evolve either collateral sensitivity or collateral resistance. How to design treatments robust to such uncertainty is unclear. We show that many resistance mutations in Escherichia coli against various antibiotics indeed have diverse collateral effects. We propose to characterize such diversity with a joint distribution of fitness effects (JDFE) and develop a theory for describing and predicting collateral evolution based on simple statistics of the JDFE. We show how to robustly rank drug pairs to minimize the risk of collateral resistance and how to estimate JDFEs. In addition to practical applications, these results have implications for our understanding of evolution in variable environments.

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  1. Version published to 10.7554/elife.73250 on eLife
  2. Version published to 10.1101/2020.08.25.267484v2 on bioRxiv
  3. eLife

    ###Reviewer #3:

    The goal of this manuscript “to develop predictive tools for inferring fitness trajectories in new environments” is an important goal and I appreciate the synthesis of theoretical modeling with parameter estimation from empirical mutation studies.

    Reading through the manuscript, however, I found myself repeatedly wondering whether the stated application of the methods developed here doesn't constitute something of a tautology. This could be a misreading on my end, but I'll explain: the authors state that they have the central goal of predicting whether a population adapting to one environment will lose fitness in another "non-home" environment. Yet the parameter estimation they develop and propose for estimating fitness trajectories requires fitness measurements in both the home and non-home environments. If one already has fitness measurements for both home and non-home, how much more information is added by estimating the JDFE? I understand that the authors are estimating the fitness trajectories over time, with the incorporation of population genetic parameters, but again, I was unsure of how much information was added with the JDFE particularly given large discrepancies in the Wright-Fisher models and the decreasing predictive capacity with time. The bottom row of Figure 1 provided perhaps the most convincing evidence of the usefulness of the JDFE, but the unintuitive result was not adequately explored nor explained (see comment below). Also, perhaps an exploration of how the predictions could be extended to unmeasured environments is possible (as in Kinsler et al 2020)?

    Further specific conceptual comments and suggestions:

    1. The authors demonstrate in Figure 1 that JDFEs even with similar shapes produce markedly different fitness trajectories. They argue that the correlation coefficient of the JDFE is not a reliable predictor of fitness trajectories in the home environment. I was struck by this counterintuitive result, and found myself searching for further explanation. Are the authors arguing that the practice of simply looking at the correlation coefficient in tradeoff studies in general is insufficient for predicting the fates of pleiotropic mutations? Either way, it would be helpful to the reader to elaborate on why and under which conditions the discrepancy with the correlation coefficient and fitness trajectories arises.

    2. The modeling results throughout the manuscript reveal poor predictive capabilities in Wright-Fisher simulations. For example, the results in figure 2 show substantial discrepancy between the theoretical predictions and the results of the Wright-Fisher simulations. The authors address this only briefly stating that outside of the strong selection, weak mutation model (SSWM) the pleiotropy statistics are only "statistical predictors". But the discrepancy was systematic and wide, suggesting rather little insight from the pleiotropy statistics in sequential adaptation scenarios. I could not find discussion of this discrepancy between the SSWM and Wright-Fisher modeling predictions.

  4. eLife

    ###Reviewer #2:

    The authors present a theoretical framework for analysing pleiotropic effects in populations evolving in different environments based on the concept of a joint distribution of fitness effects (JDFE). Simple correlation measures are derived from the JDFE that allow one to predict the evolutionary outcome in the non-home environment. Analytic theory is derived in the SSWM regime and complemented by simulations covering the regime of large mutation supply. A proof-of-concept application to collateral antibiotic resistance and sensitivity in bacteria based on a published data set for knockout strains is presented. Overall, this is an important, systematic contribution to a very timely subject.

    Major Concerns:

    1. I do not quite share the authors' surprise at the outcomes shown in Figure 1. In fact there is a simple heuristic that allows one to predict the direction of the fitness change in the non-home environment in all cases: Simply look at the y-coordinate of the tail of the JDFE corresponding to the largest beneficial effects along the x-axis.

    2. Along the three rows of panels in Figure 2, there appears to be a systematic but in two cases non-monotonic variation of the slope with the mutation supply NU_b. Do the authors have a (tentative) explanation for this behavior?

  5. eLife

    ###Reviewer #1:

    Ardell and Kryazhimskiy use bacterial TnSeq data in multiple conditions to study the structure of pleiotropy, that is the degree to which a genetic perturbation affects multiple phenotypes, and present a theoretical framework to predict and assess fitness trajectories observed in environments other than the one selection is operating in. The work is thoroughly done and has potentially interesting implications for sequential drug therapy.

    The central object of their framework is the joint distribution of fitness effects of mutations in multiple environments where the distribution is over all mutations in the genome. The dynamics in the space of fitness in multiple environments is then modeled as a random walk (described by a diffusion equation) assuming that mutations sweep separated in time (SSWM). The model and the calculations necessary to arrive at the predictions are simple and transparent. The results quantitatively predict simulation results with the range of validity of SSWM. Outside this range, the model predicts the qualitative behavior, but is quantitatively wrong.

    1. My main disappointment with the paper is the inability to quantitatively describe the dynamics outside the SSWM regime. I would expect that the effects of competing mutations or weak selection could be accounted for at least perturbatively. Alternatively, one could determine the distribution of the effects of fixed mutations in the "home" environment in simulations and use this distribution to predict the dynamics in other environments.

    1. My other substantial concern is the question whether anything can be learned about drug resistance evolution or collateral sensitivity/resistance from TnSeq experiments. While some drug resistance evolution involves loss-of-function mutations (e.g. porin losses), it often proceeds via point mutations, up-regulation, or horizontal acquisition. Furthermore, the statistical treatment here requires many mutations to sample the joint effect distribution to give reliable answers. In clinical resistance evolution, the number of mutations observed is often quite small and their effect distributions are wide. The practical relevance of this is therefore far from clear.

    2. While the similarity of this work to similar questions in quantitative genetics is discussed in the introduction, I would like to see an extended discussion to determine whether some limits of the model at hand can be described by the quantitative genetics approach.

  6. eLife

    ##Preprint Review

    This preprint was reviewed using eLife’s Preprint Review service, which provides public peer reviews of manuscripts posted on bioRxiv for the benefit of the authors, readers, potential readers, and others interested in our assessment of the work. This review applies only to version 1 of the manuscript.

    ###Summary:

    The reviewers agreed that pleiotropy of mutations and the resulting adaptive trajectories across different environments are important topics that are both of theoretical and applied interest. Your theoretical framework predicts fitness trajectories observed in environments other than the one selection is operating in (home environment). These trajectories in non-Home environments are calculated via integrals over the joint fitness effect distribution weighted by the fixation probability in the home environment. However, your framework assumes strong selection and weak mutation (SSWM) and deviations from this assumption seem to have strong effects. We think that these effects need to be at least partially understood. Furthermore, application to the KO library is a useful proof-of-concept, but the practical relevance of these patterns for understanding collateral sensitivity/resistance is far from obvious. In summary, we felt that the manuscript needs to make more substantive theoretical advances and/or provide more robust actionable insights into drug resistance evolution.

  7. Version published to 10.1101/2020.08.25.267484v1 on bioRxiv