Genotypic context modulates fitness landscapes: Effects on the speed and direction of evolution for antimicrobial resistance

Understanding the forces that drive the dynamics of adaptive evolution is a goal of many subfields within evolutionary biology. The fitness landscape analogy has served as a useful abstraction for addressing these topics across many systems, and recent treatments have revealed how different environments can frame the particulars of adaptive evolution by changing the topography of fitness landscapes. In this study, we examine how the larger, ambient genotypic context in which the fitness landscape being modeled is embedded affects fitness landscape topography and subsequent evolution. Using simulations on empirical fitness landscapes, we discover that genotypic context, defined by genetic variability in regions outside of the locus under study (in this case, an essential bacterial enzyme target of antibiotics), influences the speed and direction of evolution in several surprising ways. These findings have implications for how we study the evolution of drug resistance in nature, and for presumptions about how biological evolution might be expected to occur in genetically-modified organisms. More generally, the findings speak to theory surrounding how “difference can beget difference” in adaptive evolution: that small genetic differences between organisms can greatly alter the specifics of how evolution occurs, which can rapidly drive even slightly diverged populations further apart. Author summary Technological advances enable scientists to engineer individual mutations at specific sites within an organism’s genome with increasing ease. These breakthroughs have provided scientists with tools to study how different engineered mutations affect the function of a given gene or protein, yielding useful insight into genotype-phenotype mapping and evolution. In this study, we use engineered strains of bacteria to show how the dynamics (speed and direction) of evolution of drug resistance in an enzyme depends on the species-type of that bacterial enzyme, and on the presence/absence of mutations in other genes in the bacterial genome. These findings have broad implications for public health, genetic engineering, and theories of speciation. In the context of public health and biomedicine, our results suggest that future efforts in managing antimicrobial resistance must consider genetic makeup of different pathogen populations before predicting how resistance will occur, rather than assuming that the same resistance pathways will appear in different pathogen populations. With regard to broader theory in evolutionary biology, our results show how even small genetic differences between organisms can alter how future evolution occurs, potentially causing closely-related populations to quickly diverge.


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The fitness landscape analogy has undergone a subtle makeover in recent years, with 18 larger data sets and improved methods (laboratory and computational) greatly 19 increasing the scope of systems and questions that the analogy can be used to 20 responsibly address. For example, recent studies have examined how environments 21 change adaptive landscape topography [1,2], employed methods to construct adaptive 22 landscapes in natural populations [3,4], and conducted large scale examinations of 23 epistasis acting across fitness landscapes [5][6][7][8][9][10]. Other examinations have extracted new 24 September 21, 2018 2/16 information out of empirical fitness landscapes, including how landscapes changes in 25 shape during adaptive evolution [11], how indirect pathways are traversed during 26 evolution [12], and how features of a landscape determine the speed of some adaptive 27 trajectories relative to others [13]. The theme across many of these recent 28 breakthroughs is a growth in our understanding of how various contexts can frame our 29 expectations for how evolution will occur, and render it challenging to predict [14][15][16][17]. 30 This is of particular importance in studies utilizing empirically determined fitness 31 landscapes to understand the evolution of drug resistance, where the hope is to one day 32 understand how the evolution of resistance occurs such that disease can be treated more 33 effectively [18][19][20] 34 Importantly, specific portions of the genome that are the object of study in model  competition (C w ), a metric that has been shown to govern the speed of evolution across 64 a trajectory [13] under standard assumptions of replicator dynamics [22]. Our findings 65 are striking beyond the basic observation that genotypic context frames adaptive 66 evolution. We show that the speed of adaptation differs drastically between contexts, 67 and in a pattern that defies our intuition. For example, in modeling the evolution of 68 resistance to Trimethoprim, we find that off-target mutations influence the landscape as 69 much or more than those within the actual drug target. We discuss these findings with 70 regard to how they speak to our efforts at modeling drug resistance, and more generally, 71 how they affect our understanding of which forces craft how populations diverge.

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Empirical Fitness Landscapes 74 We utilized data that were previously generated to determine the biophysical 75 components of a fitness landscape for resistance [21]. given species in a given PQC genetic profile) comprise a fitness landscape, as illustrated 91 in Fig. 1. Note that four of these nine small fitness landscapes contain suboptimal 92 peaks, reflecting the highly epistatic interactions between the three mutations [21].  Table 2. L. grayi data. Measured IC 50 values (in µg/ml) and inferred growth rates (r) for L. grayi exposed to 10 5 µM of Trimethoprim. NA means the data were not available.

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L We simulated evolution on the 9 empirical fitness landscapes described above using  with three genetic backgrounds (columns) exposed to 10 5 µM of Trimethoprim. Nodes represent the genotypes indicated in the upper left diagram, where edges connect single-mutational neighbors. Node diameters and shading are proportional to the logarithm of the growth rates shown in Tables 1-3 (no growth rates were available for the square node labeled NA). Simulations (e.g., as shown in Fig. 2) starting from the wild type (WT, circled in green) follow the 1-3 step trajectories shown by the thick blue edges; each edge is labeled with the within-path competition (C w ) for that step and the C w for the entire trajectory is shown above each landscape. Each trajectory terminates at either the optimal genotype (i.e., that with the maximum growth rate, circled in red) or a suboptimal peak (circled in cyan).
timestep, the number of individuals of each genotype grows exponentially according to 99 its growth rate with stochastic single locus mutation, and then the entire population is 100 reduced to the carrying capacity by frequency proportionate selection. We note that the 101 classic Wright-Fisher model [25,26] is a constant population size abstraction of the 102 process implemented directly in DARPS. DARPS is described in more detail in [13] and 103 open source code is available at [27].

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For the simulation results reported here, mutation rates were assumed to be 105 approximately 1 × 10 −10 per locus per replication. In our DARPS model, the 106 probability of mutation P m refers to one mutation in any of the 3 loci being studied per 107 replication, so we used P m = 3 × 10 −10 . Bacterial population carrying capacity was set 108 to K = 10 10 . Each simulation was initialized with a wild type population at carrying when the terminal genotype dominated over 50% of the population (T d ), and (iv) when 115 the terminal genotype became "fixed" (T f ), which we defined to be when it exceeded 116 99% of the population (due to ongoing mutational events, the terminal genotype will 117 never comprise 100% of the population). We ran 1000 stochastic replicates of each 118 simulation on the nine fitness landscapes.

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Within-path competition 120 We quantified the amount of within-path competition (C w ) along the evolutionary 121 trajectory followed in each of the simulations using the equation derived in [13], as 122 follows: where r i represents the growth rate of genotype i along a trajectory comprising m steps 124 from the genotype 1 (the wild type) to genotype m + 1 (the terminal genotype).

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The topographies of all nine unique fitness landscapes are illustrated in terms of relative 127 growth rates in Fig. 1 DHFR landscapes for the malaria parasite revealed that the "greediest" paths are not 132 always those preferred by evolution [13], in these simulations we found that the 133 greediest paths (shown by the thick blue trajectories in Fig. 1) were followed in all of 134 the 1000 stochastic evolutionary simulations on each of these nine small landscapes.

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One representative simulation for each landscape is shown in Fig. 2. Below, we point 136 out several notable findings in these results. peaks. For the C. muridarum/WT-PQC landscapes, evolution proceeds along the 167 single-step path to the optimal peak at L28R genotype. In the C. muridarum/∆lon 168 landscape the population also becomes fixed on the L28R genotype, but in this case this 169 is a suboptimal peak that prevents evolution from reaching the optimal peak at 170 P21L:A26T:L28R. In contrast, in C. muridarum/GroEL+ the population follows a 171 two-step path to the optimal peak of A26T:L28R.

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Effect of species-background on the direction of evolution. It is also important to note how the overall growth rates of the genotypes in a  although the E. coli growth rates are much higher than those of L. grayi and C.

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muridarum across all PQC backgrounds ( Fig. 1 and Table 1), evolution does not always 192 proceed fastest along these landscapes (Fig. 3). This is an important reminder that the 193 speed of evolution is not a function of the fitness of individual genotypes, but is largely 194 governed by the differences in fitnesses of adjacent genotypes in an evolutionary 195 trajectory [13], as quantified by the within-path competition (C w ) shown in Eq. (1).

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For example, in these simulations T d is shown be a slightly sublinear function of Cw shown above each landscape in Fig. 1. Genotypic context alters fitness landscape topography.

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In this study, we have identified that genotypic context alters fitness landscape 206 topography for antibiotic resistance, which in turn influences 3 aspects of evolutionary 207 dynamics: (i) the distribution of optimal and suboptimal peaks on a fitness landscape, 208 (ii) the "preferred" direction of adaptive evolution and (iii) the speed at which said 209 evolution occurs.
Species differences in protein backbone alters the speed and 211 direction of evolution.

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Evolutionary simulations on these landscapes illustrate how evolution occurs differently 213 across species. With regard to the evolution of drug resistance, these findings indicate 214 that even subtle differences in the amino acid sequence for otherwise conserved enzymes 215 can have a powerful effect on how evolution occurs (both speed and direction). This 216 implies that we cannot assume that even closely related microbial pathogens will evolve 217 resistance to drugs using the same evolutionary trajectory, as the fitness landscape 218 underlying resistance may be different. This might be complicating news for the 219 burgeoning field of resistance management: instead of being able to adopt a 220 one-size-fits-all approach to managing resistance, we may have to engineer our 221 managements to very specific genotypic contexts. the lifetime and performance of enzymes in a cell [21,28]. In this setting, mutations may 229 alter resistance patterns not because they affect the way a drug binds but because they 230 affect the interaction between a protein effector and the PQC machinery. This would 231 suggest a mechanism for how resistance in microbes can be so biochemically and 232 biophysically diverse, even in well-characterized systems like DHFR and antifolates: an 233 enzyme might avoid the effects of a drug through altering its interaction with other 234 genes maybe even in lieu of altering the binding of a antibiotic drug.

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General note on the speed of evolution.

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The speed of evolution from the wild type genotype to the terminal genotype in 237 evolutionary simulations is shown to vary greatly across different genotypic contexts, 238 and in a manner that is not related to the absolute fitnesses of the nodes in the respective landscapes. More broadly, this study affirms the relationship between 240 within-path competition (C w , defined by Eq. (1)) and the speed of evolution 241 (determined via simulation) [13]. As a general observation, studies that examine the 242 speed of evolution have been all but ignored in the study of empirical fitness landscapes, 243 although it has recently been demonstrated to be an important property of evolutionary 244 dynamics [13]. In particular, discussions that invoke empirical fitness landscapes in 245 discussing how one might better prevent or manage drug resistance in plant and animal 246 infectious disease should be especially mindful of the speed of evolution: True resistance 247 management should not only consider which pathways evolution will traverse towards 248 maximal resistance, but how fast certain pathways might occur relative to others.

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Our findings highlight that, like the "preferred" direction of evolution, the speed of 250 evolution should be considered in any study that examines how and why fitness 251 landscape topography determines evolutionary outcomes. This suggests that future efforts at "resistance management" need to consider very 262 specific genomic and genetic details about the population being managed before 263 rigorous and effective management strategies are engineered.

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In addition, our results highlight how particular "off target" mutations (in our study, 265 PQC modifications) can have powerful influences on evolutionary outcomes.

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Consequently, genomic screens for "resistance mutations" should focus on potential 267 signals across the genome, rather than a singular focus on genes that are the 268 presumptive target of therapy. Our results illustrate that there are multiple ways to subvert the effects of a drug, sometimes involving genes and gene networks that are not 270 intuitively (or biophysically) linked to the phenotype of interest (in this case, protein 271 quality control genes having no specific connection to DHFR activity). Similarly, our 272 results underscore the potential perils of engineering mutations associated with a given 273 phenotype into different genomic backgrounds, as in CRISPR-mediated genetic 274 engineering. In such scenarios, differences in genomic background of strains in which a 275 given SNP is being engineered can not only influence the effect of the mutation being 276 introduced, but also, the downstream evolution of different populations.

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Lastly, our results speak to the notion that small genetic differences between 278 populations may be sufficient to induce larger downstream divergence, eventually 279 leading to speciation. Specifically, our study is consistent with the expectation that 280 reproductive isolation arises rapidly in rugged fitness landscapes (e.g., in a

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Bateson-Dobzhansky-Muller framework [29], or holey landscape [30]). By examining 282 genetic differences at various scales (single nucleotide polymorphisms in target 283 resistance genes, species-specific differences in genetic background, and changes to 284 off-target genes), we demonstrate how "difference can beget difference" in Darwinian 285 evolution, affecting both the degree and rate of divergence.