Evolutionary concepts have long been applied to the problem of antimicrobial resistance. For example, our understanding of how resistance evolves has improved through studies of protein evolution (Weinreich et al., 2006; Lozovsky et al., 2009; Toprak et al., 2011), reversion (Tan et al., 2011; Baym et al., 2016; Ogbunugafor and Hartl, 2016a), and higher order interactions between drugs (Michel et al., 2008; Yeh et al., 2009) or mutations (Weinreich et al., 2013; Lozovsky et al., 2021). While stepwise, de novo evolution (via mutations and subsequent selection) is a critical force in the evolution of antimicrobial resistance, evolution in natural settings often involves other processes, including horizontal gene transfer (Bergstrom et al., 2000; Turner et al., 2014; Loftie-Eaton et al., 2017) and selection on standing genetic variation (Pennings, 2012; Pelleau et al., 2015). Consequently, perspectives that consider variation in pathogens (and their drug targets) are important for understanding treatment at the bedside. Recent studies have made important strides in this arena. Some have utilized large data sets and population genetics theory to measure cross-resistance and collateral sensitivity (Gjini and Wood, 2021; Ardell and Kryazhimskiy, 2021; Herencias et al., 2021; Nichol et al., 2019). Fewer studies have used evolutionary concepts to establish metrics that apply to the general problem of antimicrobial treatment on standing genetic variation in pathogen populations, or for evaluating the utility of certain drugs’ ability to treat the underlying genetic diversity of pathogens (Yeh et al., 2006; Yeh et al., 2009; Mira et al., 2021).

Despite these gaps in the world of antimicrobial resistance, a robust literature in immunobiology—specifically concerning the problem of evaluating broadly neutralizing antibodies to counteract the widespread genetic diversity of viral infections—has addressed analogous concepts. Studies have profiled mutations in influenza that allow them to escape antibodies (Doud et al., 2017; Doud et al., 2018), and reconstructed ‘binding affinity landscapes’ that define the constraints around viral escape (Phillips et al., 2021; Phillips et al., 2023). These studies, which focus on both the antiviral antibody and their targets (viruses), demonstrate that metrics capturing the susceptibility of a target, or efficacy of an antimicrobial actor, are highly relevant in our quest to prevent, diagnose, and treat infectious diseases.

This study examines data from protein fitness landscapes across a panel of antimicrobial drugs to develop new metrics for antimicrobial applications. Specifically, we propose novel druggability framings, a concept that relates to the interaction between drugs and their targets. We propose an extension of this concept in the form of two metrics: (i) The average susceptibility of alleles of a drug target across drugs in a panel (‘variant vulnerability’) and (ii) the efficacy of drugs across alleles of a given drug target (‘drug applicability’). Lastly, we statistically deconstruct the peculiar interactions that underlie these metrics: interactions between drugs and the genetic variants at their target (${\displaystyle \beta }$-lactamases in this case). We label this last analysis as measuring the ‘environmental epistasis’ in the drug-target interaction, a concept developed recently to describe molecular evolution in the presence of environmental change (Lindsey et al., 2013).

Summarizing, we propose that these new metrics can be applied to pathogen-drug datasets to identify challenges associated with specific variants of pathogens, and evaluate the efficacy of certain drug types. Further, our results show how modern concepts in evolutionary genetics, like gene by gene by environment interactions (environmental epistasis) have practical utility in biomedicine.

Here, we describe several analyses, emphasizing two novel metrics we have developed: variant vulnerability and drug applicability. We first plotted the growth rates for the 16 alleles in the TEM-1/TEM-50 fitness landscapes across the seven drug environments (Figure 1). We then computed the variant vulnerability and drug applicability metrics and deconstructed the metrics by measuring the interactions between mutations and drug environments (including G x G x E interactions).

Figure 1

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Variant vulnerability

Low variant vulnerability implies low susceptibility of a genotype to the library of drugs in the panel (Figure 2). Of the alleles in our set, 0110 (MKSN) displayed the lowest susceptibility with resistance to 3/7 drugs—ceftazidime, cefotetan, and cefotaxime. Alternatively, the allele with the highest variant vulnerability was a triple mutant, 0111, corresponding to the MKSD allele.

Figure 2

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We can rank alleles from highest to lowest for a different interpretation of the variant vulnerability values (Table 1). Notably, the allele that had the highest variant vulnerability (0111, MKSD), and the one with the lowest variant vulnerability (0110, MKSN) differ by a single mutation (N276D). That a single mutation can significantly impact variant vulnerability highlights how single mutations dramatically affect the topography of the variant vulnerability fitness landscape, with the N276D mutation negatively affecting the susceptibility through interactions with the genetic background. Also, note that the alleles associated with TEM-1 (MEGN) and TEM-50 (LKSD) have variant vulnerability values that are close (ranked 12th and 11th respectively; among the lowest values).

Table 1

TEM allelic variant	Binary	Rank (1=highest variant vulnerability)
MKSD	0111	1
LESD	1011	2
LEGN	1000	3
MEGD	0001	4
MKGN	0100	5
LESN	1010	6
LKGN	1100	7
LEGD	1001	8
MKGD	0101	9
LKGD	1101	10
LKSD	1111	11
MEGN	0000	12
MESD	0011	13
LKSN	1110	14
MESN	0010	15
MKSN	0110	16

1. Source: The authors.

How do we interpret the low variant vulnerabilities of TEM-1 and TEM-50—indicative of low susceptibility to the panel of drugs? Whatever the selective pressures that drove the evolution of TEM-1 and TEM-50 in natural settings, these findings suggest that the resulting resistance phenotypes associated with evolved ${\displaystyle \beta }$-lactamases seem to confer general survivability across drugs. This observation is consistent with prior notions of ‘cross resistance’ (Oz et al., 2014; Cândido et al., 2019; Colclough et al., 2019).

One-step neighbor variant vulnerability

Our findings regarding large variant vulnerability differences between mutational neighbors like MKSN (0110; the lowest variant vulnerability value of the 16 alleles) and MKSD (0111; the highest variant vulnerability value of the 16 alleles) inspired further analysis of the relationship between the variant vulnerability of an allelic variant and its mutant neighbors. As the mutants analyzed in this study compose a combinatorically complete set, they can be depicted in the formal structure of a canonical fitness graph that outlines changes between TEM-1 and TEM-50 (Figure 1). And while this study focuses on the individual properties of variants/alleles of TEM-1/TEM-50, one might ask how the variant vulnerability values are distributed across the fitness graph, which may speak to its evolvability. Is there a correlation between the variant vulnerability values and those of one-step mutant neighbors? Alternatively, are variant vulnerability values uncorrelated from that of their neighbors?

To answer these questions, we calculated each allele’s average variant vulnerability of one-step mutational neighbors. Figure 3 depicts the variant vulnerability values for the 16 allelic values (from Figure 2), and a scatterplot depicting the relationship between allelic variants and the average variant vulnerability of one-step neighbors (each variant has four neighbors). Correlation between variant vulnerability values and those of their nearest neighbors (linear regression ${\displaystyle R^2=0.01,P=0.69}$). The lack of correlation suggests that the fitness landscape for variant vulnerability is rugged, where individual mutations contribute nonlinearly to the susceptibility of a given allelic variant.

Figure 3

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Analysis of environmental epistasis

Finally, we conducted a statistical decomposition of the individual effect sizes associated with individual SNPs, SNP x SNP interactions (epistasis), SNP x environment (plasticity), and SNP x SNP x environment (environmental epistasis) interactions (Figure 4). Here, we observe that the four-way interaction between all four loci has a powerful positive effect on recovering growth rate defects in three drugs—amoxicillin, cefotaxime, and ceftazidime (5.8, 8.4, and 5.5 standard deviations respectively). Note how the four-way interaction only has a small effect on the drug mixtures that include ${\displaystyle \beta }$-lactamase inhibitors: amoxicillin/clavulanic acid and piperacillin/tazobactam. For amoxicillin/clavulanic acid—the drug regime with the highest drug applicability, only two mutation interactions have a meaningful impact on the effect of those drugs across variants: a pairwise interaction between sites M69L and N276D (labeled A x D in Figure 4), and a three-way interaction between M69L, E104K, and N276D (A x B x D). Most interactions either have no effects or negative effects. This observation is consistent with the amoxicillin/clavulanic drug having the highest drug applicability, with few mutation interactions meaningfully providing resistance.

Figure 4

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In this study, we examine a data set from an empirical fitness landscape of an antimicrobial drug target to develop metrics for identifying (i) which allelic variants are most likely to be resistant to whole panels of drugs, and (ii) which drugs are most likely to be effective against a suite of resistance allelic variants of a given drug target. We then measure the interactions between individual loci and drug environments that underlie these two metrics.

We focused on mutations associated with the TEM-1/TEM-50 class of ${\displaystyle \beta }$-lactamases, associated with resistance in bacteria, and seven ${\displaystyle \beta }$-lactam drugs. We study a combinatorial set of four different mutations, allowing us to compute the epistasis x environment (also known as ‘environmental epistasis’; see Lindsey et al., 2013) relationships between alleles.

With respect to variant vulnerability, which measures how susceptible a given allele is across drug types, we observe several intriguing phenomena. Firstly, the allelic variant with the highest variant vulnerability (most susceptible across drug types; MKSD or 0111) and lowest variant vulnerability (MKSN or 0110) are only a single mutation apart (N276D) (Figure 1). That a single mutation can have large consequences for treatment across drugs in a panel is not surprising from one perspective—individual mutations can certainly have strong effects. The analysis of environmental epistasis (Figure 4) highlights, however, that the dramatic difference in phenotype between MKSD and MKSN is as much about how that mutation effect depends on the other amino acids in the protein background. The context-dependence of mutations contributing to variant vulnerability highlights the continued need to resolve the population genetic particulars of a given infection. For example, in a clinical setting, inaccurate identification of the SNP or amino acid at a single locus (N276D in our study) could create an entirely different picture of the clinical course of infection.

Our findings on drug applicability highlight the complexity underlying drug mechanisms and their consequences. Though all seven drugs/combinations are ${\displaystyle \beta }$-lactams, they have widely varying effects across the 16 alleles. Some of the results are intuitive: for example, the drug regime with the highest drug applicability of the set—amoxicillin/clavulanic acid—is a mixture of a widely used ${\displaystyle \beta }$-lactam (amoxicillin) and a ${\displaystyle \beta }$-lactamase inhibitor (clavulanic acid; see Table 2). We might expect such a mixture to have a broader effect across a diversity of variants. However, this high applicability is hardly a rule, as another mixture in the set, piperacillin/tazobactam, has much lower drug applicability (ranking 5th out of the seven drugs in the set; Table 2). Intuition can over-simplify, with undesirable consequences: not all drug combinations/mixutures are more effective over a larger breadth of alleles. Because this study focused on mutations in combination, rather than drugs, we did not examine the drug applicability of the individual drugs in all the drug combinations (e.g. piperacillin alone and tazobactam alone). However, there is a rich literature covering the specific problem of drug combinations (Michel et al., 2008; Beppler et al., 2016; Singh and Yeh, 2017; Tekin et al., 2017).

The surprising results in both the variant vulnerability (regarding the ability of allelic variants to grow across niche breadth) and drug applicability (regarding the impact of drugs across allelic variants) highlight the importance of specific interactions between individual loci (individual sites in TEM-50) and drug environment (${\displaystyle \beta }$-lactam drugs). For example, we observe the strongly positive interaction between mutations at the four sites associated with TEM-50 in several drugs: amoxicillin, cefotaxime, cefprozil, and ceftazidime. Other higher-order interactions are associated with different effects: note the strongly negative effects of the three-way interaction between mutations at loci M69L, E104K, and G238S on ceftazidime growth rate (Figure 4). Regarding the main effects, we note the positive effect of the M69L mutation on the growth rate in cefotaxime, cefotetam, and ceftazidime. Alternatively, the G238S, N276D mutations have individual negative effects on ceftazidime. Interestingly, in combination, these mutations strongly positively affect ceftazidine (Figure 3). While our study does not delve into the biophysical underpinnings of any of these findings, they do support other studies that speak to the importance of how even slight structural differences between drugs can have strong implications for how they interact with allelic variants of a single protein (Ogbunugafor et al., 2016b; Lozovsky et al., 2021; Mira et al., 2021).

Code and data can be found on GitHub: https://github.com/OgPlexus/evodruggability (copy archived at Ogbunu, 2024).

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Author details

1. Rafael F Guerrero

   Department of Biological Sciences, North Carolina State University, Raleigh, United States

   Contribution

   Conceptualization, Data curation, Software, Formal analysis, Validation, Investigation, Visualization, Methodology, Writing - original draft, Writing - review and editing

   Competing interests

   No competing interests declared

   "This ORCID iD identifies the author of this article:" 0000-0002-8451-3609

2. Tandin Dorji

   Department of Mathematics and Statistics, University of Vermont, Burlington, United States

   Contribution

   Data curation, Formal analysis, Writing - review and editing

   Competing interests

   No competing interests declared

3. Ra'Mal M Harris

   Department of Chemistry, Massachusetts Institute of Technology, Cambridge, United States

   Contribution

   Investigation, Writing - review and editing

   Competing interests

   No competing interests declared

   "This ORCID iD identifies the author of this article:" 0000-0002-9537-371X

4. Matthew D Shoulders

   Department of Chemistry, Massachusetts Institute of Technology, Cambridge, United States

   Contribution

   Supervision, Investigation, Writing - original draft, Project administration, Writing - review and editing

   Competing interests

   No competing interests declared

   "This ORCID iD identifies the author of this article:" 0000-0002-6511-3431

5. C Brandon Ogbunugafor

   1. Department of Chemistry, Massachusetts Institute of Technology, Cambridge, United States
   2. Department of Ecology and Evolutionary Biology, Yale University, New Haven, United States
   3. Santa Fe Institute, Santa Fe, United States
   4. Public Health Modeling Unit, Yale School of Public Health, New Haven, United States

   Contribution

   Conceptualization, Data curation, Formal analysis, Supervision, Funding acquisition, Validation, Investigation, Visualization, Methodology, Writing - original draft, Project administration, Writing - review and editing

   For correspondence

   brandon.ogbunu@yale.edu

   Competing interests

   Reviewing editor, eLife

   "This ORCID iD identifies the author of this article:" 0000-0002-1581-8345

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