Price equation captures the role of drug interactions and collateral effects in the evolution of multidrug resistance

Dynamic collateral sensitivity profiles highlight opportunities and challenges for optimizing antibiotic treatments

As failure rates for traditional antimicrobial therapies escalate, recent focus has shifted to evolution-based therapies to slow resistance. Collateral sensitivity-the increased susceptibility to one drug associated with evolved resistance to a different drug-offers a potentially exploitable evolutionary constraint, but the manner in which collateral effects emerge over time is not well understood. Here, we use laboratory evolution in the opportunistic pathogen Enterococcus faecalis to phenotypically characterize collateral profiles through evolutionary time. Specifically, we measure collateral profiles for 400 strain-antibiotic combinations over the course of 4 evolutionary time points as strains are selected in increasing concentrations of antibiotic. We find that at a global level-when results from all drugs are combined-collateral resistance dominates during early phases of adaptation, when resistance to the selecting drug is lower, while collateral sensitivity becomes increasingly likely with further selection. At the level of individual populations; however, the trends are idiosyncratic; for example, the frequency of collateral sensitivity to ceftriaxone increases over time in isolates selected by linezolid but decreases in isolates selected by ciprofloxacin. We then show experimentally how dynamic collateral sensitivity relationships can lead to time-dependent dosing windows that depend on finely timed switching between drugs. Finally, we develop a stochastic mathematical model based on a Markov decision process consistent with observed dynamic collateral profiles to show measurements across time are required to optimally constrain antibiotic resistance.

Environment by environment interactions (ExE) differ across genetic backgrounds (ExExG)

While the terms "gene-by-gene interaction" (GxG) and "gene-by-environment interaction" (GxE) are widely recognized in the fields of quantitative and evolutionary genetics, "environment-byenvironment interaction" (ExE) is a term used less often. In this study, we find that environmentby-environment interactions are a meaningful driver of phenotypes, and moreover, that they differ across different genotypes (suggestive of ExExG). To support this conclusion, we analyzed a large dataset of roughly 1,000 mutant yeast strains with varying degrees of resistance to different antifungal drugs. Our findings reveal that the effectiveness of a drug combination, relative to single drugs, often differs across drug resistant mutants. Remarkably, even mutants that differ by only a single nucleotide change can have dramatically different drug × drug (ExE) interactions. We also introduce a new framework that more accurately predicts the direction and magnitude of ExE interactions for some mutants. Understanding how ExE interactions change across genotypes (ExExG) is crucial not only for modeling the evolution of pathogenic microbes, but also for enhancing our knowledge of the underlying cell biology and the sources of phenotypic variance within populations. While the significance of ExExG interactions has been overlooked in evolutionary and population genetics, these fields and others stand to benefit from understanding how these interactions shape the complex behavior of living systems.

Distinguishing mutants that resist drugs via different mechanisms by examining fitness tradeoffs

There is growing interest in designing multidrug therapies that leverage tradeoffs to combat resistance. Tradeoffs are common in evolution and occur when, for example, resistance to one drug results in sensitivity to another. Major questions remain about the extent to which tradeoffs are reliable, specifically, whether the mutants that provide resistance to a given drug all suffer similar tradeoffs. This question is difficult because the drug-resistant mutants observed in the clinic, and even those evolved in controlled laboratory settings, are often biased towards those that provide large fitness benefits. Thus, the mutations (and mechanisms) that provide drug resistance may be more diverse than current data suggests. Here, we perform evolution experiments utilizing lineage-tracking to capture a fuller spectrum of mutations that give yeast cells a fitness advantage in fluconazole, a common antifungal drug. We then quantify fitness tradeoffs for each of 774 evolved mutants across 12 environments, finding these mutants group into classes with characteristically different tradeoffs. Their unique tradeoffs may imply that each group of mutants affects fitness through different underlying mechanisms. Some of the groupings we find are surprising. For example, we find some mutants that resist single drugs do not resist their combination, while others do. And some mutants to the same gene have different tradeoffs than others. These findings, on one hand, demonstrate the difficulty in relying on consistent or intuitive tradeoffs when designing multidrug treatments. On the other hand, by demonstrating that hundreds of adaptive mutations can be reduced to a few groups with characteristic tradeoffs, our findings may yet empower multidrug strategies that leverage tradeoffs to combat resistance. More generally speaking, by grouping mutants that likely affect fitness through similar underlying mechanisms, our work guides efforts to map the phenotypic effects of mutation.

Ultrasensitive Response Explains the Benefit of Combination Chemotherapy Despite Drug Antagonism

Most aggressive lymphomas are treated with combination chemotherapy, commonly as multiple cycles of concurrent drug administration. Concurrent administration is in theory optimal when combination therapies have synergistic (more than additive) drug interactions. We investigated pharmacodynamic interactions in the standard 4-drug "CHOP" regimen in peripheral T-cell lymphoma (PTCL) cell lines and found that CHOP consistently exhibits antagonism and not synergy. We tested whether staggered treatment schedules could improve tumor cell kill by avoiding antagonism, using in vitro models of concurrent or staggered treatments. Surprisingly, we observed that tumor cell kill is maximized by concurrent drug administration despite antagonistic drug-drug interactions. We propose that an ultrasensitive dose response, as described in radiology by the linear-quadratic (LQ) model, can reconcile these seemingly contradictory experimental observations. The LQ model describes the relationship between cell survival and dose, and in radiology has identified scenarios favoring hypofractionated radiotherapy-the administration of fewer large doses rather than multiple smaller doses. Specifically, hypofractionated treatment can be favored when cells require an accumulation of DNA damage, rather than a "single hit," to die. By adapting the LQ model to combination chemotherapy and accounting for tumor heterogeneity, we find that tumor cell kill is maximized by concurrent administration of multiple drugs, even when chemotherapies have antagonistic interactions. Thus, our study identifies a new mechanism by which combination chemotherapy can be clinically beneficial that is not contingent on positive drug-drug interactions.

Distinguishing mutants that resist drugs via different mechanisms by examining fitness tradeoffs

There is growing interest in designing multidrug therapies that leverage tradeoffs to combat resistance. Tradeoffs are common in evolution and occur when, for example, resistance to one drug results in sensitivity to another. Major questions remain about the extent to which tradeoffs are reliable, specifically, whether the mutants that provide resistance to a given drug all suffer similar tradeoffs. This question is difficult because the drug-resistant mutants observed in the clinic, and even those evolved in controlled laboratory settings, are often biased towards those that provide large fitness benefits. Thus, the mutations (and mechanisms) that provide drug resistance may be more diverse than current data suggests. Here, we perform evolution experiments utilizing lineage-tracking to capture a fuller spectrum of mutations that give yeast cells a fitness advantage in fluconazole, a common antifungal drug. We then quantify fitness tradeoffs for each of 774 evolved mutants across 12 environments, finding these mutants group into 6 classes with characteristically different tradeoffs. Their unique tradeoffs may imply that each group of mutants affects fitness through different underlying mechanisms. Some of the groupings we find are surprising. For example, we find some mutants that resist single drugs do not resist their combination, while others do. And some mutants to the same gene have different tradeoffs than others. These findings, on one hand, demonstrate the difficulty in relying on consistent or intuitive tradeoffs when designing multidrug treatments. On the other hand, by demonstrating that hundreds of adaptive mutations can be reduced to a few groups with characteristic tradeoffs, our findings may yet empower multidrug strategies that leverage tradeoffs to combat resistance. More generally speaking, by grouping mutants that likely affect fitness through similar underlying mechanisms, our work guides efforts to map the phenotypic effects of mutation.

Evolutionary druggability for low-dimensional fitness landscapes toward new metrics for antimicrobial applications

The term 'druggability' describes the molecular properties of drugs or targets in pharmacological interventions and is commonly used in work involving drug development for clinical applications. There are no current analogues for this notion that quantify the drug-target interaction with respect to a given target variant's sensitivity across a breadth of drugs in a panel, or a given drug's range of effectiveness across alleles of a target protein. Using data from low-dimensional empirical fitness landscapes composed of 16 β-lactamase alleles and 7 β-lactam drugs, we introduce two metrics that capture (i) the average susceptibility of an allelic variant of a drug target to any available drug in a given panel ('variant vulnerability'), and (ii) the average applicability of a drug (or mixture) across allelic variants of a drug target ('drug applicability'). Finally, we (iii) disentangle the quality and magnitude of interactions between loci in the drug target and the seven drug environments in terms of their mutation by mutation by environment (G x G x E) interactions, offering mechanistic insight into the variant variability and drug applicability metrics. Summarizing, we propose that our framework can be applied to other datasets and pathogen-drug systems to understand which pathogen variants in a clinical setting are the most concerning (low variant vulnerability), and which drugs in a panel are most likely to be effective in an infection defined by standing genetic variation in the pathogen drug target (high drug applicability).

Modeling spatial evolution of multi-drug resistance under drug environmental gradients

Multi-drug combinations to treat bacterial populations are at the forefront of approaches for infection control and prevention of antibiotic resistance. Although the evolution of antibiotic resistance has been theoretically studied with mathematical population dynamics models, extensions to spatial dynamics remain rare in the literature, including in particular spatial evolution of multi-drug resistance. In this study, we propose a reaction-diffusion system that describes the multi-drug evolution of bacteria based on a drug-concentration rescaling approach. We show how the resistance to drugs in space, and the consequent adaptation of growth rate, is governed by a Price equation with diffusion, integrating features of drug interactions and collateral resistances or sensitivities to the drugs. We study spatial versions of the model where the distribution of drugs is homogeneous across space, and where the drugs vary environmentally in a piecewise-constant, linear and nonlinear manner. Although in many evolution models, per capita growth rate is a natural surrogate for fitness, in spatially-extended, potentially heterogeneous habitats, fitness is an emergent property that potentially reflects additional complexities, from boundary conditions to the specific spatial variation of growth rates. Applying concepts from perturbation theory and reaction-diffusion equations, we propose an analytical metric for characterization of average mutant fitness in the spatial system based on the principal eigenvalue of our linear problem, λ1. This enables an accurate translation from drug spatial gradients and mutant antibiotic susceptibility traits to the relative advantage of each mutant across the environment. Our approach allows one to predict the precise outcomes of selection among mutants over space, ultimately from comparing their λ1 values, which encode a critical interplay between growth functions, movement traits, habitat size and boundary conditions. Such mathematical understanding opens new avenues for multi-drug therapeutic optimization.

Synergistic Drug Combinations Promote the Development of Resistance in Acute Myeloid Leukemia

Combination therapy is an important part of cancer treatment and is often employed to overcome or prevent drug resistance. Preclinical screening strategies often prioritize synergistic drug combinations; however, studies of antibiotic combinations show that synergistic drug interactions can accelerate the emergence of resistance because resistance to one drug depletes the effect of both. In this study, we aimed to determine whether synergy drives the development of resistance in cancer cell lines using live-cell imaging. Consistent with prior models of tumor evolution, we found that when controlling for activity, drug synergy is associated with increased probability of developing drug resistance. We demonstrate that these observations are an expected consequence of synergy: the fitness benefit of resisting a drug in a combination is greater in synergistic combinations than in nonsynergistic combinations. These data have important implications for preclinical strategies aiming to develop novel combinations of cancer therapies with robust and durable efficacy.

SIGNIFICANCE

Preclinical strategies to identify combinations for cancer treatment often focus on identifying synergistic combinations. This study shows that in AML cells combinations that rely on synergy can increase the likelihood of developing resistance, suggesting that combination screening strategies may benefit from a more holistic approach rather than focusing on drug synergy. See related commentary by Bhola and Letai, p. 81. This article is featured in Selected Articles from This Issue, p. 80.

The evolution of resistance to synergistic multi-drug combinations is more complex than evolving resistance to each individual drug component

Multidrug antibiotic resistance is an urgent public health concern. Multiple strategies have been suggested to alleviate this problem, including the use of antibiotic combinations and cyclic therapies. We examine how adaptation to (1) combinations of drugs affects resistance to individual drugs, and to (2) individual drugs alters responses to drug combinations. To evaluate this, we evolved multiple strains of drug resistant Staphylococcus epidermidis in the lab. We show that evolving resistance to four highly synergistic combinations does not result in cross-resistance to all of their components. Likewise, prior resistance to one antibiotic in a combination does not guarantee survival when exposed to the combination. We also identify four 3-step and four 2-step treatments that inhibit bacterial growth and confer collateral sensitivity with each step, impeding the development of multidrug resistance. This study highlights the importance of considering higher-order drug combinations in sequential therapies and how antibiotic interactions can influence the evolutionary trajectory of bacterial populations.

Modeling spatial evolution of multi-drug resistance under drug environmental gradients

Multi-drug combinations to treat bacterial populations are at the forefront of approaches for infection control and prevention of antibiotic resistance. Although the evolution of antibiotic resistance has been theoretically studied with mathematical population dynamics models, extensions to spatial dynamics remain rare in the literature, including in particular spatial evolution of multi-drug resistance. In this study, we propose a reaction-diffusion system that describes the multi-drug evolution of bacteria, based on a rescaling approach (Gjini and Wood, 2021). We show how the resistance to drugs in space, and the consequent adaptation of growth rate is governed by a Price equation with diffusion. The covariance terms in this equation integrate features of drug interactions and collateral resistances or sensitivities to the drugs. We study spatial versions of the model where the distribution of drugs is homogeneous across space, and where the drugs vary environmentally in a piecewise-constant, linear and nonlinear manner. Applying concepts from perturbation theory and reaction-diffusion equations, we propose an analytical characterization of average mutant fitness in the spatial system based on the principal eigenvalue of our linear problem. This enables an accurate translation from drug spatial gradients and mutant antibiotic susceptibility traits, to the relative advantage of each mutant across the environment. Such a mathematical understanding allows to predict the precise outcomes of selection over space, ultimately from the fundamental balance between growth and movement traits, and their diversity in a population.

Evolutionary druggability: leveraging low-dimensional fitness landscapes towards new metrics for antimicrobial applications

The term "druggability" describes the molecular properties of drugs or targets in pharmacological interventions and is commonly used in work involving drug development for clinical applications. There are no current analogues for this notion that quantify the drug-target interaction with respect to a given target variant's sensitivity across a breadth of drugs in a panel, or a given drug's range of effectiveness across alleles of a target protein. Using data from low-dimensional empirical fitness landscapes composed of 16 β-lactamase alleles and seven β-lactam drugs, we introduce two metrics that capture (i) the average susceptibility of an allelic variant of a drug target to any available drug in a given panel ("variant vulnerability"), and (ii) the average applicability of a drug (or mixture) across allelic variants of a drug target ("drug applicability"). Finally, we (iii) disentangle the quality and magnitude of interactions between loci in the drug target and the seven drug environments in terms of their mutation by mutation by environment (G × G × E) interactions, offering mechanistic insight into the variant variability and drug applicability metrics. Summarizing, we propose that our framework can be applied to other datasets and pathogen-drug systems to understand which pathogen variants in a clinical setting are the most concerning (low variant vulnerability), and which drugs in a panel are most likely to be effective in an infection defined by standing genetic variation in the pathogen drug target (high drug applicability).

Pervasive genotype-by-environment interactions shape the fitness effects of antibiotic resistance mutations

The fitness effects of antibiotic resistance mutations are a major driver of resistance evolution. While the nutrient environment affects bacterial fitness, experimental studies of resistance typically measure fitness of mutants in a single environment only. We explored how the nutrient environment affected the fitness effects of rifampicin-resistant rpoB mutations in Escherichia coli under several conditions critical for the emergence and spread of resistance-the presence of primary or secondary antibiotic, or the absence of any antibiotic. Pervasive genotype-by-environment (GxE) interactions determined fitness in all experimental conditions, with rank order of fitness in the presence and absence of antibiotics being strongly dependent on the nutrient environment. GxE interactions also affected the magnitude and direction of collateral effects of secondary antibiotics, in some cases so drastically that a mutant that was highly sensitive in one nutrient environment exhibited cross-resistance to the same antibiotic in another. It is likely that the mutant-specific impact of rpoB mutations on the global transcriptome underpins the observed GxE interactions. The pervasive, mutant-specific GxE interactions highlight the importance of doing what is rarely done when studying the evolution and spread of resistance in experimental and clinical work: assessing fitness of antibiotic-resistant mutants across a range of relevant environments.

Mutators can drive the evolution of multi-resistance to antibiotics

Antibiotic combination therapies are an approach used to counter the evolution of resistance; their purported benefit is they can stop the successive emergence of independent resistance mutations in the same genome. Here, we show that bacterial populations with 'mutators', organisms with defects in DNA repair, readily evolve resistance to combination antibiotic treatment when there is a delay in reaching inhibitory concentrations of antibiotic-under conditions where purely wild-type populations cannot. In populations of Escherichia coli subjected to combination treatment, we detected a diverse array of acquired mutations, including multiple alleles in the canonical targets of resistance for the two drugs, as well as mutations in multi-drug efflux pumps and genes involved in DNA replication and repair. Unexpectedly, mutators not only allowed multi-resistance to evolve under combination treatment where it was favoured, but also under single-drug treatments. Using simulations, we show that the increase in mutation rate of the two canonical resistance targets is sufficient to permit multi-resistance evolution in both single-drug and combination treatments. Under both conditions, the mutator allele swept to fixation through hitch-hiking with single-drug resistance, enabling subsequent resistance mutations to emerge. Ultimately, our results suggest that mutators may hinder the utility of combination therapy when mutators are present. Additionally, by raising the rates of genetic mutation, selection for multi-resistance may have the unwanted side-effect of increasing the potential to evolve resistance to future antibiotic treatments.

Sequential antibiotic therapy in the laboratory and in the patient

Laboratory experiments suggest that rapid cycling of antibiotics during the course of treatment could successfully counter resistance evolution. Drugs involving collateral sensitivity could be particularly suitable for such therapies. However, the environmental conditions in vivo differ from those in vitro. One key difference is that drugs can be switched abruptly in the laboratory, while in the patient, pharmacokinetic processes lead to changing antibiotic concentrations including periods of dose overlaps from consecutive administrations. During such overlap phases, drug-drug interactions may affect the evolutionary dynamics. To address the gap between the laboratory and potential clinical applications, we set up two models for comparison-a 'laboratory model' and a pharmacokinetic-pharmacodynamic 'patient model'. The analysis shows that in the laboratory, the most rapid cycling suppresses the bacterial population always at least as well as other regimens. For patient treatment, however, a little slower cycling can sometimes be preferable if the pharmacodynamic curve is steep or if drugs interact antagonistically. When resistance is absent prior to treatment, collateral sensitivity brings no substantial benefit unless the cell division rate is low and drug cycling slow. By contrast, drug-drug interactions strongly influence the treatment efficiency of rapid regimens, demonstrating their importance for the optimal choice of drug pairs.

Challenges and potential solutions for studying the genetic and phenotypic architecture of adaptation in microbes

All organisms are defined by the makeup of their DNA. Over billions of years, the structure and information contained in that DNA, often referred to as genetic architecture, have been honed by a multitude of evolutionary processes. Mutations that cause genetic elements to change in a way that results in beneficial phenotypic change are more likely to survive and propagate through the population in a process known as adaptation. Recent work reveals that the genetic targets of adaptation are varied and can change with genetic background. Further, seemingly similar adaptive mutations, even within the same gene, can have diverse and unpredictable effects on phenotype. These challenges represent major obstacles in predicting adaptation and evolution. In this review, we cover these concepts in detail and identify three emerging synergistic solutions: higher-throughput evolution experiments combined with updated genotype-phenotype mapping strategies and physiological models. Our review largely focuses on recent literature in yeast, and the field seems to be on the cusp of a new era with regard to studying the predictability of evolution.

Mutational Switch-Backs Can Accelerate Evolution of Francisella to a Combination of Ciprofloxacin and Doxycycline

Combination antimicrobial therapy has been considered a promising strategy to combat the evolution of antimicrobial resistance. Francisella tularensis is the causative agent of tularemia and in addition to being found in the nature, is recognized as a threat agent that requires vigilance. We investigated the evolutionary outcome of adapting the Live Vaccine Strain (LVS) of F. tularensis subsp. holarctica to two non-interacting drugs, ciprofloxacin and doxycycline, individually, sequentially, and in combination. Despite their individual efficacies and independence of mechanisms, evolution to the combination arose on a shorter time scale than evolution to the two drugs sequentially. We conducted a longitudinal mutational analysis of the populations evolving to the drug combination, genetically reconstructed the identified evolutionary pathway, and carried out biochemical validation. We discovered that, after the appearance of an initial weak generalist mutation (FupA/B), each successive mutation alternated between adaptation to one drug or the other. In combination, these mutations allowed the population to more efficiently ascend the fitness peak through a series of evolutionary switch-backs. Clonal interference, weak pleiotropy, and positive epistasis also contributed to combinatorial evolution. This finding suggests that the use of this non-interacting drug pair against F. tularensis may render both drugs ineffective because of mutational switch-backs that accelerate evolution of dual resistance.

The mutation effect reaction norm (mu-rn) highlights environmentally dependent mutation effects and epistatic interactions

Since the modern synthesis, the fitness effects of mutations and epistasis have been central yet provocative concepts in evolutionary and population genetics. Studies of how the interactions between parcels of genetic information can change as a function of environmental context have added a layer of complexity to these discussions. Here I introduce the "mutation effect reaction norm" (Mu-RN), a new instrument through which one can analyze the phenotypic consequences of mutations and interactions across environmental contexts. It embodies the fusion of measurements of genetic interactions with the reaction norm, a classic depiction of the performance of genotypes across environments. I demonstrate the utility of the Mu-RN through the signature of a "compensatory ratchet" mutation that undermines reverse evolution of antimicrobial resistance. More broadly, I argue that the mutation effect reaction norm may help us resolve the dynamism and unpredictability of evolution, with implications for theoretical biology, genetic modification technology, and public health. This article is protected by copyright. All rights reserved.

The population genetics of collateral resistance and sensitivity

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.

Drugs known as antibiotics are the main treatment for most serious infections caused by bacteria. However, many bacteria are acquiring genetic mutations that make them resistant to the effects of one or more types of antibiotics, making them harder to eliminate.

One way to tackle drug-resistant bacteria is to develop new types of antibiotics; however, in recent years, the rate at which new antibiotics have become available has been dwindling. Using two or more existing drugs, one after another, can also be an effective way to eliminate resistant bacteria. The success of any such ‘multi-drug’ treatment lies in being able to predict whether mutations that make the bacteria resistant to one drug simultaneously make it sensitive to another, a phenomenon known as collateral sensitivity.

Different resistance mutations may have different collateral effects: some may increase the bacteria’s sensitivity to the second drug, while others might make the bacteria more resistant. However, it is currently unclear how to design robust multi-drug treatments that take this diversity of collateral effects into account.

Here, Ardell and Kryazhimskiy used a concept called JDFE (short for the joint distribution of fitness effects) to describe the diversity of collateral effects in a population of bacteria exposed to a single drug. This information was then used to mathematically model how collateral effects evolved in the population over time.

Ardell and Kryazhimskiy showed that this approach can predict how likely a population is to become collaterally sensitive or collaterally resistant to a second antibiotic. Drug pairs can then be ranked according to the risk of collateral resistance emerging, so long as information on the variety of resistance mutations available to the bacteria are included in the model.

Each year, more than 700,000 people die from infections caused by bacteria that are resistant to one or more antibiotics. The findings of Ardell and Kryazhimskiy may eventually help clinicians design multi-drug treatments that effectively eliminate bacterial infections and help to prevent more bacteria from evolving resistance to antibiotics. However, to achieve this goal, more research is needed to fully understand the range collateral effects caused by resistance mutations.