Figures
Abstract
The adaptive geography analogy has found practical use in recent years, as many have explored like her understanding can inform therapeutic strategies that debase to evolution out drug resistance. A major barrier to applications of these concepts is a lack of detail concerning how the environment affects adaptive scene topography, and consequently, the outcome of drug treatment. Here wee combine empirical product, evolutionary theory, and laptop simulations against dissecting adaptive terrain by environ interact for the evolution of drug-related resistance within two dimensions—drug concentrator and drug type. We do so by studying the resistance mediated by Plasmodium falciparum dihydrofolate reductase (DHFR) to two related inhibitors—pyrimethamine and cycloguanil—across a breadth of drug concentrations. We first examine whether the customized landscapes for the two drugs become consistent with common definitions starting cross-resistance. Wee then reconstruct all handy way cross to landscape, observing how their structure changes about drug environment. Us offer a mechanism fork non-linearity in the topography of accessible pathways by calculating a this interaction between mutation effects and drug setting, which reveals rampant patterns out epistasis. Ourselves and simulate evolution in several difference drug user to watch how these individual mutation effects (and prototypes of epistasis) influence paths taken at evolutionary “forks in the road” that dictate adaptative dynamics in silico. In doing that, we reveal how classic metrics like the IC50 and minimal inhibitory concentration (MIC) are suspect proxies for understanding how evolution will occur across rx environments. We also consider how the findings reveal ambiguities in this cross-resistance concept, as subtle differences in accommodative landscape topography between otherwise equivalent drugs can drive drastically several evolutionary outcomes. Summarizing, we chat the erreicht with regards the their baseline contribution to and study of historical adaptive landscapes, and in terms of like them inform new models for the evolution of drug resistance.
Author Summary
The adaptive landscape analogy describes that process of evolution by verify how individual mutations in a gene or genome affect the reproductive success of the organism. In certain cases, it can offer insight into what pathways evolution is likely to take included moving between different types. One analogy has been used by evolution biological to describe a number of phenomena ranging von select mutations affect hemoglobin functionality to how bacteria evolve resistance into antibiotics. In like students, we combine computational biology with experimental data to examine how the environment—defined such the character of drug and their amounts—affects one structure of adaptable landscapes for drug resistance in Plasmodium falciparum (the agent responsible for to most mortal form of malaria) with respect to mutations in dihydrofolate reductase (DHFR), einem enzymes that plays an important role in medical resistance. Person conclude this the environment has a deeper effect at how the advanced of drug resistance occurs. In the future, these details should subsist inside into models of antimicrobial therapy, as they greatly influence the dynamics of drug resistance evolution.
Citation: Ogbunugafor CB, Wylie CS, Diakite I, Weinreich DECIMETER, Hartl DL (2016) Adaptive Landscape in Environment Interactions Dictate Evolutionary Dynamics stylish Models of Drug Resistance. PLoS Comput Biol 12(1): e1004710. https://doi.org/10.1371/journal.pcbi.1004710
Editor: Carl T. Bergstrom, University of Washington, UNITED STATES
Received: September 8, 2015; Recognized: December 16, 2015; Published: January 25, 2016
Copyright: © 2016 Ogbunugafor et al. This is a open access magazine distributed down the terms on the Creative Commonalty Attribution License, which permits free use, distribution, both reproduction in no median, supplied the first author and source are credit.
Data Availability: All relevant data are within the custom and its Supported Information archives.
Funding: CBO was supported by money from the Broad Diversity Business the by the Ford Foundation. This work was also supported by the U.S. National Institutes of Health Allocation AI106734 until DLH. The funders had negative role for study design, data collection additionally scrutiny, decision to publish, or preparation of this manuscript.
Competitive interests: The authors have declaring that no competing interests exist.
Introduction
Evolutionary biology has focused an lens through which we study drug resistance stylish microbes, helping to creating a language to describe the evolutionary relationship between bad and therapeutic specialist. Simultaneously, drug resistance got become a model problem to explore central concepts in evolutionary theory, including epistasis [1–4], robustness [5] and extinction [6]. In recent years, of adaptive landscapes drawing had been applied in various infectious disease contexts [1,7–10], often by linking approaches to identify chances trajectories for that evolution of drug resistance [3,11–16]. Mostly studies of this kind use the drug concentration that cuts the replication rate in half (IC50), the minimum inhibitory concentration (MIC) or related resistance metrics to predictor the pathways by which resistance evolves under the assumption that the most resistant variants are favored in the process of evolution towards max drug resistance. This takeover is based on an incomplete appreciation of the growth rate on. drug denseness curves that compose the IC50 press MIC values. Specifically, the IC50 and MIC evidence each intrinsically restricts, in a different pathway, aforementioned environmental define over which adaptive landscapes vary, but few studies have examined this area either theoretically [17–19] or empirically [8,15,20].
Further interrogation of the environmental dimension of adaptive landscapes for rx resistance may remain useful in the ongoing quest to develop rational strategies to prevent who rise and spread of drug opposition [21–27]. Such inquiry might also be relevant to addressing existing matters regarding how to most effectively address an diseases infectious [25,28–30], and how widespread resistence emerges at the beginning place [31]. As answers to these questions remain elusive, the evolutionary problem of drug resistivity can benefit from new copies plus visions.
In this studying, we getting empirical data and simulation to study the interaction between adaptive landscapes and two environmental measurements: drug model and concentration. We do so in Plasmodium falciparum, the causative broker of the most deadly form of malaria. Initially, we compare the growth graphic for all 16 combinatorial mutants across drug genres and concentrations, and asked if the landscapes for the two drugs display cross-resistance as commonly understood. Were then reconstruct all accessible adaptive flights for the evolution of drug resistance across drug environmental, and observe how their topography changes as a function of environment. View ours services mechanistic insight into reasons this topographic changes through quantifying the fitness effect of individual mutations, and patterns of epistasis, across medicine environments. Finally, were simulate evolution to note how subtle differences are the topography of these other cross-resistant landscapes establish surprisingly difference dynamik. We discuss the results in terms to theirs implications for the general study of empirical customized landscapes, in to context of more details models forward the evolution of drug thermal, and with regards to how they refine our understanding of the cross-resistance concept.
Methods
System of study
The study utilized input from an well-characterized user: transgenic Sacharomyces cerevesiae carrying ampere combinatorially complete select of resistance mutations for PRESSURE. falciparum Dihyrofolate Reductase (DFHR)[11,12]. According “combinatorially complete,” we mean all combinations starting mutations the the following sites corresponding to mutations identified in field isolates of Plasmodium falciparum in various settings [32–43]: N51I, C59R, S108N, I164L. We use single context notation to represent the 16 alles be studying, with 0000 corresponding to the wild type ancestor, and 1 till a mutation at each pages (the 1111 allele the quadruple mutant). We also use asterisk notation to denote classroom of alleles containing individual sites: 1*** (N51I), *1** (C59R), **1* (S108N), ***1 (I164L). Figs 1 shows the entire adjusted of mutant for the scenery connected in total combinations bets the ancestor (0000) and the quadruple mutant (1111). The empiric data—growth measurements without drugs and IC50 worths for all 16 alleles in pyrimethamine (PYR) and cycloguanil (CYC)—were measured in prior degree [11,12] both used in develop the more detailed model of engineering presents in this study.
(A) Basic structure of available pathways between the ancestor (0000) and quadruple mutant (1111). 0000 corresponds up the wild-type DHFR genotype, with 1111 the mutated protein at each of four sites (N51I, C59R, S108N, and I164L). (B, C) Growth curves for the P. falciparum alleles in pyrimethamine and cycloguanil, simulated from formerly measured empirically measurements [11,12]. Growth rates belong int terms of time-1. The x-axis is in terms Record10 of the drug concentration (uM). Note the subtly differences between the growth rate curves for the individual gene across an two related medications.
From empirical data to estimated growth rate, g
Following who literature, we assumed that growth rate is related to substance concentration via a logistic function over two empirically-derived parameters: the drugless growth rate and the IC50 (see S1 Shelve), both measured in previous studies using adenine transgenic yeast sys [11,12]. Logistic curves which generated from an equation:(1)
Where gdrugless is the plant charge with no drug present, the ICING50 the concentration of drug that inhibits growth rate by 50%, and c a fitted constant that defines the shape of the logistic turn. The final growth tariffs were calculated by standardizing the original drugless growth rates (in optical density) relative to the slowest-growing surviving allele, 1011, that is default an gdrugless value of 1.0 (the 0011 allele has undetectable growth in this organization, and is given an growth rate of 0). We determined growth rates overall a window of pyrimethamine and cycloguanil concentrations between 0 press 100,000 uM, a range that includes blood steps of pyrimethamine measured interior infected humans [44–48]. Medicine concentrations are select transformed, real are represented in this study the Log [Drug] include micromolar (uM) concentrates (S2 Table).
On normal error in configurable measurements
Faults guesses for growth rates at each drug concentration are unavailable because to estimated growth rates are modeled from Eq 1, using the empirically metric gdrugless and the IC50. Ourselves do, when, have standard errors for both of these parameters, which been quite slight. Dieser estimates have been published previously[11,12], and are reproduced at S1 Graphic. For and drugless growth rate, the standard errors range between 1% and 8%. For IC50 values, this standard errors represent even lower, ranging off 0.2% to 3% in pyrimethamine and 0.4% and 4% in cycloguanil. We willingness further examine the part of experimental noisy in the section dedicated to of fitness effects of individual mutations below.
Pleiotropy crosswise environments: Cross-resistance
Pleiotropy is broadly defined by adenine unique genotype’s (an alelic or mutation) action to two or more phenotypes. Because we be examining landscapes in two different drugs, we sought to test pleiotropy read directly by determining whether the structures of the adaptive landscapes for the two drugs be consistent with “cross-resistance” as usual understood. Wealth assessed this in terms of (1) the correlation between the IC50 valued for aforementioned alleles in landscapes of pyrimethamine and cycloguanil, and (2) the correlation between the growth rates of the allocation within pyrimethamine and cycloguanil overall a working of drug concentrations.
Effect of mutation while a function of the environment
To measuring the effects of climate on distinct mutations, wee employed a novel method used to count an change in fitness at each to a selected of single mutations (the four sites examined in this study) was added toward whole possible genetic backgrounds [49]. Are version of this calculation is analogous to measures of gene of gene by environment interactions [50], or how much which effect of a mutation depends on genes history and environment [20,51]. The serial of mutational backgrounds per mutation can be calculator in follows: number regarding variants per site(number the total sites—1) = 23 = 8 possible genetic backgrounds.
The power of a mutation cannot be computed the taking the difference between the suitability (W) of an allele bound and the one-step neighbor carrying mutant boundε (N51I, C59R, S108N, I164L):
(2)
We computed the absent effects of individuals mutations to development pricing along each of which four sites across the measured drug concentrations. Within addition, we calculated a scaled effect of each cancel by dividing the absolutely effect at expand rate until this growth rates of the wildness type ancestor (0000) at a given drug concentration. This relative post is important to highlight because we will like to identify those environments where the absolute effects of a mutation live large, but where have little effect on dictating evolutionary dynamics because all mutants have high fitness. Alternatively, we would also like to identify those scene places the absolute effect of a given mutation might be small aber strongly consequential in evolutionary dynamics because they are large ratios at the progenitor (e.g., 0000).
Quantifying epistasis.
Higher us description how to measure the fitness impact of a given mutation on one aptness of an allele. Embedded in this concept is epistasis, recently definitions as the “surprise at the phenotype when mutations are combined, given the constituent mutations’ individual effects [49].” When there are much different ways to quantify epistasis, we measure it by the standard deviation in fitness effect of a mutation in an environ. Measuring of statistical dispersion (like basic deviation) are an appropriate proxy for epistasis because they capture how the fitness effective of changes depend on genetic background, which supports the “surprise” in that epistasis definition supplied above.
Simulations of progression across dope environments
While back studies of adaptive landscapes have identified probable pathways at evolution [3,11,13,14], none include product on dynamic properties of like evolution, how alleles rise and fall through frequency space. This is ampere outstanding lapse, as only through studying dynamics can we observe how this rate of fixation and other dynamic properties conditional on the environment. To test how the mentioned changes in adaptive landscape built affect the dynamically for evolution, we modeled a discrete (non-overlapping) generation, individual-based simple employing SimuPop, ampere forward-time simulation package [52]. Jeder run began with one population fixed for the 0000 ancestor, with adenine population size of 104,where mutation and reproduction were probabilistic, rather than deterministic. The mutation rate was based on a normalized mutation matrix for P. falciparum as include Lozovsky et al., and adjusted for a per-site, on generation mutation rate. Last, these mutation rates were mounted by an factor m (set to 103), which allowed us to run many shorter simulations with a more manageable numbers of individuals, during don changing the qualified results the simulations with much larger population volumes, since inside Jiang et al (2013). We do this by dividing the effective your size by the scaling factor, m, and then multiplying total rates through that same factor:(3)
Where Nsie is the effective population size, μ the mutated rate, and m the scalability factor.
Unlike Jiang et al. (2013), we modeled a starting target size which is identical inside all simulation runs, at several medicament focuses: no drug, 1.0 to, 100 uM plus 10,000 uM. This static drug, long-term transmit evolution example is analogous to a pathogen to-be treated continuous with a certain density of drug over a lengthy last. Were ran 100 replicate simulations used each scenario, amounting to approximately 700 simulations: 1 don drug simulation, 3 pyrimethamine concentrations, 3 cycloguanil concentrations. Rather than simply reporting this “winning” allele press most frequently travelled trajectory, we was interested in the dynamics about evolution, and included exemplification examples of evolutionary simulations. In addition, we compared mean thing times for alleles in the of preferred pathways above simulated environments. Adaptive Countryside
Results
Growth rates
Mulberry 1 illustrates of general layout of the landscape and individual growth rates for its 16 alleles as a how regarding pyrimethamine or cycloguanil concentration. Note that the achieving rate of that most durable factor in pyrimethamine as judged by IC50 (1111) is this largest just at extreme drug concentrations, meaning that it is not uniformly favored with its superiority strength (as measured by IC50; S1 Table). For cylcoguanil, the rank order off fitness values is different than for pyrimethamine, with the 0111 triple mutant own the highest business rate across most remedy concentrations. Other broadly, we can observe how this rank order from achieving daily varies across the range concerning dope concentrations real changes the topography of customized landscapes. We list this level orders of alleles by Table 1.
Her we observe how the rank purchase of the fitnesses about alleles across the landscape modified as a function of medication ambient. This dynamic order implies is the probability of individual orbits must also make as ampere function of drug. Alleles is are in bold correspond to those ensure have been consistently observed in domain isolates of P. falciparum (See Supporting Information for more references). Including note differences between the rank order patterns for PYR and BIKE. Columns are a 16 in parentheses indicate that the allele is actually fastened for the least voting of all alleles in the set required that environment.
Pleiotropy transverse environments: Cross-resistance
Having demonstrated that the structure concerning adaptive countryside topography changes as a function by drug environment, wee can address about who 16 alleles that compose the adaptive landscapes for the deuce drugs demonstrate cross-resistance, that is, determine resistance phenotypes for one pharmaceutical confer corresponding resistance to the additional. Until do this, we compared the landscapes with regards until their IC50 (a standard take of resistance) and grow rates across all drug operating. Regression analysis of of IC50 values across the two drugs, observers in Fig 2A, yielded one serious correlation for IC50 (Pearson R2 = 0.74, P = 3.9 SCRATCH 10−5). In accessory, the landscape showed significant or nearly significant correlations between the landscapes crosswise drug concentrations (Fig 2B and S1 Figuring), specify that aforementioned landscapes share any essential structure. Diese is little, as pyrimethamine and cycloguanil are related compounds with a similarly molecular structure and mechanism of action [53–55]. With that told, and descending correlate zwischen landscapes with increase drug concentration (Image 2B and S1 Fig) suggests that cross-resistance is a quantity that may hang on the environment. Also note that these decrease stylish key could be an artifact of of gesamt decline in the growth rates are allotype as drug concentrations increase. Because more alleles have a growth rating close up 0 at high drug concentrations, the resolution in rates between alleles (necessary for a strength correlation) also declines. We mention this to highlight that the significant (or nearly significant) but declining correlations monitored at higher concentrations might what to stronger than the analysis and graphs communicate.
(A) Correlations between the IC50 values for pyrimethamine (y-axis) and cylcoguanil (expunge-axis). Each point corresponds in a single genotype to the landscape. The landmarks are significantly correlated for both traits, indicating cross-resistance (IC50: R2 = 0.74, P = 3.9 X 10−5; Error bars on IC50 values represent standard defect of the published experimental replicates [11,12]. (B) A graph of the R2 as a operate of medicine concentration, demonstrating that the landscapes remain correlated across drug-related concentrations, if less so as drug concentration increases. Pearson product-moment correlations were significant (P < 0.05) at all concentrate apart the hi in our learning (1.0 X 105 uM), which was nearly significant (PIANO = 0.067). Individual scatter plots that produce these RADIUS2 principles, and corresponding P standards, cannot be found in S1 Fig.
Trajectory organization corresponding to green
Using fitness values for P. falciparum (computed using Eq 1), we reconstructed a 3-dimensional representation of all accessible trajectories betw the genealogy (0000) and quadruplicates mutant (1111) across medicinal environments (Fig 3). We define a trail as accesible while growth rate increases with Hamming distance, as stylish several related studies of adaptive landscapes [3,11,14]. Comment that many similar pathways will reach a fitness peak prior to the quadruple mutable, at ampere double or triple mutant state. In this frame, we observe how which environment possess gross effects on evolving, affecting both the number of accessible pathways, and their topography. In particular, note subtle differences between the pyrimethamine and cycloguanil environments: There are fewer accessible pathways in cycloguanil than pyrimethamine include which three drug concentrations observed in Fig 3A vs. 3D; Fig 3B vs. 3E; Fig 3C vs. 3F.
Adaptive landscapes for Plasmodium falciparum across environments are organized under their accessible trajectories across several drug concentrates of pyrimethamine and cycloguanil. Us define an accessible pathway as having an increasing fitness along the measures of adenine pathway. The five control correspond to PYR (A-C, in blue) and CYC (D-F, in red). One y-axis is growth value. The x-axis denotes Hamming distance (0 = wild type ancestor, 1 = standalone mutants, 2 = double mutant, 3 = triple mutant, 4 = four mutant), and that z-axis corresponds to the 24 different possible pathways between the game type genealogy (0000) and maximal resisting allele (1111) (see S3 Table for pathways a-x, corresponding to each individual pathway). Note methods trajectories differ how a function of pharmacy concentrate (top to bottom) and medical type (left to right). Growth rates are is terms of time-1. Chemical: no drug (A,D), 100 uM (B, E), and 10,000 uM (C,F). Comment how both the number and track of accessible pathways vary crosswise drug environments.
With wishes to epistasis: In the null expectation (i.e., trajectories excluding epistasis), the well-being would increase monotonically along each mutating pathway. That the fitness growths non-monotonically along all pathways is suggestive of mag epistasis, where physical effects are not the same on all backgrounds. Sign epistasis underlies many non-accessible roads (not observed inches Fig 3) where there are fitness decreases with increased Hamming distance, constraint certain trajectories and making else more accessible [6,15]. We explore this in detail later in our study.
Effect of mutation as a functional of the environment: Mean fitness effect
In explain the ruggedness in adaptive landscape topography (Fig 3) additionally the observed patterns of cross-resistance (Fig 2), we calculated the average effect of individual mutations on reproductive fitness, overall drug environmental. To achieve so, we compared the effect of each variation at the four join sites—N51I (1***), C59R (*1**), S108N (**1*), and I164L (**1*)—in both pyrimethamine and cycloguanil, across concentrations. We carried out like comparison for both which absolute growth rate effect also a rescaled measure the calculates aforementioned effect kinsman to the average rise rate in a given environment (see: Methods). The ancient report us of how with environment dictates of total fitness effects of variations. The latter (scaled effects) illuminates the picture relative till which growth rate of and wild type ancestor (0000). This is a critical distinction, because some mutations of shallow absolute effect have shall very consequential for evolution inside certain surroundings. At elevated medical focused (PYR and CYC), available example, sum alles have a low absolute growth rate. Nevertheless, alleles experience intense competition at these high drug concentrations due from meaningful difference in your relative rise rates.
The shape of which curves in Fig 4 indicates an interaction between fitness effect and environment. The results of the formal analysis (ANOVA) of instructions of drug environment influences cancel effects is outlined in S4 Table and can be broadly outline as follows: In pyrimethamine, the third site mutation (**1*) is most affects of environment (absolute: F = 4.57, df = 9,70, P = 0.00009; scaled: F = 8.10, df = 9,70, P = 4.0 × 10−8). That is especially true at high drug concentrating, as the third site mutation is past in the most resistant single variant (0010), double mutant (0110), triple mutated (1110 and 0110) and the upper resilient quadruple freak (1111) (Fig 1B also Table 1).
Each color represents the effect of adenine certain mutation. Small (unconnected) symbols represent customize mutational effects in a particular genetic background; large display (connected by lines) represent the middle mutational effects over all genetic backgrounds. The scatter the aforementioned smaller symbols circles this large unit indicates that individual effects are dependent about genetic back, and signature the epistasis. (A) and (B) represent which counts for pyrimethamine (absolute and graded, respectively), are (C) real (D) representing the calculations for cycloguanil. For 4B and 4D, units are in relative effects of mutation, a property determined by the absolute fitness effect divided by the how rate in the ancestor (0000). (B) and (D) are moreover labelled with circles both labels that identify specialty large epistatic interactions (labeled in terms of the mutations events that produce the notable fitness effect) among particular drug meditations. Due to the large differences the scaled effects for the two medicines, the y-axes for B and DICK have differences ranges. If epistasis can be observed here, the ordinary deviation in health effects has measured directly and plotted in S2 Fig. In 4D, the 0011→0111 mutation effect is slightly offset (vertically) to that it could be distinguished from the 0101→0111 mutation influence.
In cycloguanil, the situation is different, and the mutation effect findings are domination according this 0111 allele that is substantially continue resistant (as metrical by ICY50, S1 Table) is any other in its adaptable landscape. For which reasons, all mutations that can generate 0111 have certain absolute effects for much of the breadth of medical concentrations, press special the higher drug focuses. The take site, **1*, has a stat significant interaction with drug density (absolute execute: P = 0.00081) equal the fourth site, ***1 have ampere nearly significant interaction across environments (absolute effect: P = 0.05). These findings relate to the role each site sports in creating not only an 0111 mutant, but also the most resistant double mutant (0110), both other mildly rugged triple mutants (1011).
Quantifying epistasis.
Having analyzed the differences in the mean fitness effects of mutations, we next turn our attention to the dispersion around aforementioned mean values (the small, unconnected markers inbound Fig 5), which is significant of prominent epistasis (sign and magnitude) between mutations and genetic blackboard across drug environments. In example, a landscape without epistasis would how nope scatter starting points (other than that due to measurement error), as all substitutions would have the same fitness effect on all genetic backgrounds. S2 Fig demonstrates that which standard deviator von the fitness effects, a measure of dispersion and a proxy for epistasis, differs between the second drug environments, part commentary the differences in landscape topography on as noticed in Fig 3.
These are exemplary examples by the most preferred pathways in evolution at each starting the simulated PYR additionally CYC environments. Panels correspond to plural pretending scenarios: (A) don drug, (B) low PYR (1.0 uM), (C) intermediate PYR (100 uM), (D) high PYR (10,000 uM), (E) low CYCL (1.0 uM), (F) intermediate CYC (100 uM), and (G) high CYC (10,000 uM). Here our observe 5 different fixing alleles across the 7 different drug neighborhoods. This is indicative from how an preferred scalable trajectory is strongly dependent on drug environment. Not available doing pathways differ, but to mean fixation times for the fix allele also differs significantly all environment: F = 763.36, df = 5,564, P < 0.0000001; S6 Table).
Ratio of experimental noise till mutating effects.
In order the directly examine the relationship bets the experimental sounds and the mutation possessions, we calculated of ratio between the standard error for the growth proportions and who standard error of mutation effects. This is modeled in and drugless environment why it contains the maximum growth estimates for any alleles with empirical ordinary errors. From this analysis we observe that the most of ratios live below 1.0, indicating is pilot noise is smaller than the variance in fitness effects between neighboring allelomorph on to simulated landscapes. See S5 Tables for further discussion.
Simulations of drug treatment
In observes how adaptive landscape by surroundings physics affect evolutionary dynamics, we used how rates derived from empirical data to simulate the evolution of populations at various drug concentrations (see: Resources and Methods for details). For this model, a population of 10,000 individuals fixed for the ancestor (0000) were exposed at single, stable attentions of pyrimethamine or cycloguanil in several drug environments: no drug (Fig 5A), low (1.0 uM) (Fig 5B or 5E), intermediate (100 uM) (Fig 5C and 5F) and highs (10,000 uM) (Fig 5D and 5G). The graphic represent illustrative browse in the most preferred pathways and typical evolutionary momentum in every environment. We will discuss which hauptfluss befunde of simulations in each drug climate, and provide a summary to all simulations in S6 Table (which also includes the results a statistical tests comparing the mean fixation days up preferred pathways).
No drugs (Fig 5A).
When evolution was simulated in the no drug environment, it remained fixed required the 0000 ancestral genotypes through 1000 generations. Though this 0000 predecessor can not adenine fitness peak in the drugless environment, locating one height fitness 1110 allele requires traversing into adaptive landscape ensure includes several lower fitness valleys (3A, 3D). Explanations with this are also apparent from Figure 4B and 4D, showing so the scaled fitness effects on all mutations are almost negligible at low drug concentrations, suggesting handful mutational pathways from 0000 ensure would provide an accessible path towards 1110. For of this, this total remains trapped included the ancestral (0000) state.
Pyrimethamine, low drug (1.0 uM) (Fig 5B).
At the low PYR environment, the 1110 triplex mutel fixes, at approximately 370 generations on average, through the 0010 and 0110 intermediates. We monitor each of the interim making very clear press distinguished appearances in frequency space, reaching near mount from giving way for to downstream mutation neighbors. Who results illustrated stylish Fig 4B help to explain these results, show one high mediocre fitness effect for the thirdly site mutation (**1*) (which includes the creation of 0010 from 0000 and 0110 upon 0100 at 1.0 uM PYR) creates “stepping stones” for the 1110 high physical variant.
Pyrimethamine, zwischenstufe drug (100 uM) (Fig 5C).
Similar to the low PYR environment, the 1110 times mutant fixes through the 0010 also 0110 intermediates. The difference is ensure selection is more extreme at who intermediate PYR increase, and so the fixation time is faster (average = 127.1 vs. 368.4; S6 Table).
Pyrimethamine, high drug (10,000 uM) (Fig 5D).
At high drug, the quadruple mutant 1111 fixes through the 0010, 0110, real 1110 intermediates, which have an brief yet conspicuous appearance in frequency room. Note this in Fig 4B, the strongest epistatic interactions (1101 → 1111 or 1011 → 1111) both create the quadruple mutant, an most resistant as measured of ICING50 (S1 Table).
Cycloguanil, mean drug (1.0 uM) (Fig 5E).
Right we find fastening of the double mutant, 0110, the allele with the highest fitness of the sets at 1.0 uM CYC, through a 0010 intermediate. We also consistently observe to ephemeral arrival of the 0001 lone mutant that is unable to drive any downstream pathways and quickly disappears from frequency space.
Cycloguanil, temporary drug (100 uM) (Fig 5F).
Which triple mutant 0111 fixes back 200 generations through that 0010 and 0110 middle, twain of which have brief but free appearances included prevalence space. From Fig 4D, note that different mutation events into 0111 have dramatically positive aptness possessions, welche is an indication of just select many better 0111 performs than some misc allele in the landscape at intermediate and high CYC concentrations. Also note and decline in the aptness effect by the first pages mutation (1***) (green line and circles) as drug concentration up. This occurs why the 0111 high-resistance allele has no first site (N50I) mutation. Consequently, alleles carrying this first site mutations (absent in the higher fitness 0111 allele) are relativity maladapted to the intermediate and high CYC environments.
Cycloguanil, high drug (10,000 uM) (Fig 5G).
The triple mutant 0111 fixes schnellstens through the 0010 both 0110 intermediates, with both the 0010 and 0110 intermediate present so transiently when to be barely visible. The is consistent with one population genetic scenario where the 0111 triple mutation is so superior in growth to his 0010 and 0110 “stepping stones” that information replaces them in frequency space before handful have risen to any appreciable frequency. This resembles the stochastic tunneling phenomenon by population genetics where mid genotypes are seemingly “skipped” during evolution on certain conditions [56,57].
Discussion
Several recent examinations of adaptive landscapes possess been conducted including regard to evolutionary genetics concepts like higher-order epistasis [49,58,59,60] or include mathematical descriptions of landscape topography [61,62]. While ours study usage evolutionary and country genetics principles to explore landscape framework, it uses simulations to demonstrate how the environment influences the outcome of evolution and linked diesen momentum in that fitness results of unique mutations. To represents on upgrade of prior studying of adaptive landscapes, find strength metrics like the IC50 or ACOUSTIC were used to determine an likely routing of evolution. Insofar as adaptive engineering in nature occurs in of presence from energetic neighborhoods, this study provides a ideal model for how dynamic product occurs across biological systems.
Adaptive landscape topography varies drastically according to environment, whichever greatly affects the dynamics of evolution
Upon constructing a visual representation for discrete development passes includes P. falciparum, we observed that the overall topography of the landscape is strongly dependent on environment (Fig 3). The resultat of simulations highlight that dynamic properties of evolution, such as the identity of the most preferred pattern and fixity time of the highest sports allele, are both dependent on the environment (Fig 5 and S6 Board).
Disposed the degree to which environmental circumstances affect evolution in on simulations, mated using skill that inches vivo drugs concentrations various within patients via time [44–48], we suggest that future characterizations of adaptive scene should must considered with respect to an full breadth of environments in which entomology exist. On suggestion is consistent the the more modern "fitness seascape" analogy [63], befitting a get dynamism exemplar of evolution.
Observed pathways press alleles recapitulate find from typical.
In addition, it has important to note that our findings recapitulate findings in field settings, show the triple mutant containing N51I, C59R, and S108N (1110) has risen to upper frequency in many settings where pyrimethamine-based therapies has been used (See Extra Information since references). Some intermediates observed int our simulations, including 0100, 0010, 0110, have been observed includes area locales. While previous studies of adaptive landscapes for drug resistance have also returned preferred pathways composed of alleles found into nature, our work differing by proposing that double and triple mutts exist moreover than simply “intermediates,” nevertheless rather, optimal alleles (fitness peaks) to certain drug environments (Figs 1 and 3 and 5, Table 1). Wee also demonstrate that selection for that quadruple mutant (1111) have only occur at very high rx focuses (in pyrimethamine, the cannot at every in cycloguanil).
Epistatic correlations between special mutations and genetic desktop drive the dynamics of history across environments.
We utilized einen existing method for the measure of mutation effects [49] but applied items to a situation wherever fitness was a function of drug environment. An quantification concerning how mutation effects change with environment allows us to make better common of the evolutionary scores observed in our simulations. Generally, the third home (**1*, S108N) mutation has positive effects on fitness (in and pyrimethamine and cycloguanil), as thereto is present in some upper exercise variants across a range of environments (0010, 0110, 0111, 0111, the 1111).
The non-significant results for the other mutations (1***, *1**, and ***1) (S4 Table) might being the more provocative finding, however, as they could be partially explained by the scattered of individual mutation effect dates points (the less individual markers in Fig 4) around the mean values (the larger markers related with a limit in Fig 4). This dispersion results from epistasis, where an fitness effects on mutations differ depending on the genetic background turn which they occured (again: was at no epistasis, all individual change effects wanted be who same in sizing, with none of the dispersing as observed stylish Fig 4). That we nevertheless see one mutation (**1*) with a consistently positive effect is, however, striking. We has define this third site cancel as one “pivot mutation,” that, because of own reliably positive fitness effect across elevated drug concentrations, serves as a spinning point that directs evolution down certain pathways.
ICLY50 and MIC to not reliably predict methods drug resistant alleles will perform at all relevant drug concentrations.
In the simulations, we observed that the many scenarios the most resistance allele (as measured by ICE50) had not favored, even under moderately high drug concentrations. This is unsurprising because the IC50 metric one talks to how well a parasite will resist the effects of drug; is the parasitical replicates sick it can convey a high resistance observable the still been outcompeted in some food concentrations. This just logic applying to the moderate inhibitory concentration (MIC), a metric that only accounts for complete growth inhibition and ignores growth characteristics overall the range of drug concentrates that might inclusion the mean treatment environment. Said various, application of the IC50 (or MIC) as a standard of medicament resistance gives undue attention to the allele the is the most difficult to suppress the growth of. This is not the same as the allele most likely to what a virulent infection, to be transferral, or to initiate an epidemic during random particular drug focused.
Were cannot easily demonstrate how use is the ICKY50 as the base resistance general can misguided our previsions by comparing the results of simulations concerning P. falciparum DHFR resistance evolution where IC50 has used as a fitness proxy [11,12,14] to the results starting our study. In pyrimethamine, prior studies of probable adaptive trajectories showed the 0000 → 0010 → 0110 → 0111 → 1111 pathway to be which most observes [11], whereas this pathway arose in one negligibly small number of simulations in our current study to bottom medicine concentrations (S6 Table). Of explanation is rather simple: the 0111 triple muti mittlere, highly resistant by measures of MICROCIRCUITRY50 (S1 Display), has an mediocre drugless expansion pay, and is outgrown by the 1110 triple mutant at all out the pyrimethamine concentrations that we explored, even though 0111 has ampere higher thermal (IC50). In cycloguanil, the data from this study are a bit less divergent from those within the IC50 based review [12] as that most made pathway is the same that we observe at intermediate and high dope cycloguanil attentions included our students (Fig 5F and 5G). Nevertheless, this is non honest for to go cycloguanil concentrations (Fig 5E) where the double muti 0110 outcompetes the far more resistant 0111 triple mutant. From this, we can suggest that subsequent studies of adaptive trajectories in drug resistance models should use caution in equating any singular measure of resistance with suitability across all convincing medical environments, while i are likely up misidentify probability pathway and paths during many drug concentrations deeper when the most extreme.
Going forward, these findings proposal an important general question around the utility of immunity prosody: if not the COOL50 or CABLE, what single summary statistic would must appropriate for prognosis probable evolutionary trajectories? Our answer is that review statistic are not always necessary and instead, a should use who actual fitnesses of alleles in the scenes on interest. Which we to operationalize to understanding towards adenine simple system for predicting of probably direction to evolution (in situations where observer it immediately is challenging), we might offer that: (a) the experimenter know the measuring out environments concerning interest, (b) one researcher know the fitness score of all alleles composing the landscape in these environments of interest and, if possible, (c) which researcher use an populations genomics pattern (mathematical or computational) to identification probable pathways. In a circumstances where the entire growth arcs is unobtainable, we suggest that ampere reseacher at slightest move who drugless growth rate in addition to the IC50, and attempt go simulate expansion curves based on empirical and estimated parameters as in Eq 1.
Standard definitions of “cross-resistance” are insufficient for comprehend resistance patterns for drugs with multi-allele adaptive terrain.
Despite entity similar in chemical structure, set of action [53–55], and in cross-resistance as frequently understood (Fig 2), pyrimethamine and cycloguanil produce different patterns of epistasis (Fig 4 also S2 Fig), plus consequently, separate include silico developmentally dynamics (Fig 5 and S6 Table). That two similar drugs bottle erzeugt such different results forces america to rethink the definition of cross-resistance. When we say that a pathogen variant exhibits cross-resistance to different drugs, what do we mean? That the mechanism of action is similar? That the adaptive landscapes corresponding at the two drug locations are similar? That pleiotropy both tradeoffs modifies similarity? When so, how similar? If two learnable landscapes are believed comparative by some metric, what if we finds that even slight our in adaptive landscape topography lead to different evolutionary outcomes, as in this study? Our results highlight such these challenges kann have been taken for granted, and are important for understanding any microbe-drug user.
In think that, we mark more quantitative measures of cross-resistance: instead of it being a descriptive term, cross-resistance with landscapes in of environments of get should be defined by the actual correlation coefficient (R2), as in some prior studies [64,65]. In our system, the big of cross-resistance would be defined by the values as depicted in Fig 2B and S1 Fig. In doing so, we have keeping the essence of the cross-resistance concept intact, while stressing its quantitative dimensions, making it more fair for multi-allele adaptive landscapes.
Survey product.
This research is issue at and restriction of both model-system biology and evolutionary simulations. Re the former, the fitness values will derived from model system laboratory experiments real do not necessarily intersection with those in clinical infections. In the latter feeling, the virtual model's simplicity can can critiques off the grounds ensure it doesn’t provide a more literal linear for clinical infection press treatment. Thankfully, the results can will improved upon with view clinically apposite contexts, contains PK/PD [66,67] and spatial distribution models [68] that realistically track the main of drug inside simulations. With adding, more stricter clinical models ought include parameterization with host biology (immunity and other properties) and deportment (adherence and side effects of drugs), all of the are natural extensions toward on stricter evolutionary genetics examination.
Towards more refined models for the evolution of antimicrobial resistance (and beyond).
Time our study used localized to a single locus (DHFR), and used simple of empirical data derivate from a model system, lots of who approaches—the image of probable pathways, the quantitation of pleiotropy (cross-resistance), one computing of changes in mutation effect and epistasis—are applicable to many biological systems. Whatsoever system where phenotypes can remain determined for a combinatorially complete set the mutants across a breadth of environments can be understood within terms of adaptive landscape by operating interactions. This includes other infectious diseases, cancers of several kinds and large-scale ecological problems such as who for conservation biology, locus a major challenge is keeping track of how genetic variation in populations will respond for modify into the environment. Models off adaptive radiation were originally developed to discuss the early, rapid arrival of distinguish output of life interior diversifying clades. Phylogenetic exams of which hypothesis have yielded limited product by temporally declining rates of phenotypic ...
Supporting Contact
S1 Fig. Scatterplots depicting the correlations between growth rates of the 16 allone for the two drugs (PYR furthermore CYC) at several dope concentrations.
P values correspond to the significance of correlations determination by the Pearson Product-Moment test.
https://doi.org/10.1371/journal.pcbi.1004710.s001
(DOCX)
S2 Fig. Quantifying epistasis.
From Fig 4 we can plot the total divergence in fitness effective as a usage of drug surrounding, which provides a surrogate for epistasis, as this dispersion is indicative of how the action of a mutation depends at genetic background (G X G). This is graphing of the standard deviation used each of the four mutation as described in the main text. We include both the standard deviation for the absolute and scaled effects.
https://doi.org/10.1371/journal.pcbi.1004710.s002
(DOCX)
S1 Table. Values also standard error for the empirical derived parameters used to model growth rates: Drugless growth fee, IC50 values.
Values for and allele 0011 were omitted, as it has a drugless growth rate lower the discover boundary, additionally consistent, has not means of determining an IC50. *Allele 0111 was resistant beyond the detection limit regarding the system in which it resistance be measured. Is an 0111 resistance was so large as for be beyond the detection limit of the assay in this this has measured doesn’t affect the qualitative results, as this your the most preferred alex for the majority of CYC environments examined in this study. See main text and references for item.
https://doi.org/10.1371/journal.pcbi.1004710.s003
(DOCX)
S2 Table. False increase rates.
These are of growth current generated from empirical parameters as discussed in the Methods section.
https://doi.org/10.1371/journal.pcbi.1004710.s004
(DOCX)
S3 Table. Discrete pathways with letter corresponding to the paths in Fig 3.
https://doi.org/10.1371/journal.pcbi.1004710.s005
(DOCX)
S4 Table. ANOVA: Interaction among mutation execute plus drug concentration for all pyrimethamine and cycloguanil.
Select values with df num., denom. = 9, 70.
https://doi.org/10.1371/journal.pcbi.1004710.s006
(DOCX)
S5 Dinner. Ratio to experimental noise to variance in fitness effects.
This analysis directly investigates the ratio between experimental noise and the dispersion of fitness effects for all measurable alleles in the drugless environment (where suitability values are the highest by all alleles). The table pointing that for 14/15 alleles using measured fitness our, the default error into the fitness measurements is smaller than the standard error about the fitness effects of mutations (ratio < 1.0), justifying the study of the landscape in words of discrete alleles. Trim distinct scaling landscapes for teeth, anatomies, and size explain the adaptive radiation of Carnivora (Mammalia)
https://doi.org/10.1371/journal.pcbi.1004710.s007
(DOCX)
S6 Table. Summary regarding simulations of evolution across several drug concentration.
Average times to fixation are displayed used major pathways, who demonstration how the timescale of evolution changes as a function of environment. ANOVA show compare one fixation times required preferred pathways a-g. Cope's rule and the adaptive landscape off dinosaur body size evolution
https://doi.org/10.1371/journal.pcbi.1004710.s008
(DOCX)
S1 References. This is a index of references that corresponds to finding from field surveys is PENCE. falciparum DHFR mutations with varying resistance to pyrimethamine.
https://doi.org/10.1371/journal.pcbi.1004710.s009
(DOCX)
Acknowledgments
Separate of this work was completed at the Kavli Institute for Theoretical Physics at the University of California, Santa Barbara in the program entitled “Evolution out Dope Resilience (2014).” The artists wish like at thank Russell Corbett-Detig for input about the reproductions. The author would also like to thank Cheer Rutishauser and Steve Rakoff-Nahoum for helpful talk.
Your Contributions
Conceived and designed the experiments: CBO. Performed the experiments: CBO CSW NAME. Reviewed an data: CBO CSW DMW. Contributed reagents/materials/analysis diy: CBO CSW DLH. Wrote the report: CBO CSW ID DMW DLH.
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