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EVOLUTION high salinity. With all possible combinations of 13 mutations of various fitness effects at 6 positions, the presented landscape is not only uniquely large but also distinguishes itself from pre- viously published work regarding several other experimental features—namely, by its systematic and controlled experimen- tal setup using engineered mutations of various selective effects and by considering multiple alleles simultaneously. We begin by describing the landscape and identifying the global peak, which is reached through a highly positively epistatic combination of four mutations. Based on a variety of implemented statistical measures and models, we describe the accessibility of the peak, the pattern of epistasis, and the topography of the landscape. To accommodate our data, we extend several previously used models and statistics to the multiallelic case. Using subsets of the landscape, we discuss the predictive potential of such mod- eling and the problem of selecting nonrandom mutations when attempting to quantify local landscapes to extrapolate global features. Results and Discussion We used the EMPIRIC approach (24, 25) to assess the growth rate of 640 mutants in yeast Hsp90 (Materials and Methods). Based on previous screenings of fitness effects in different envi- ronments (26) and on different genetic backgrounds (20), and on expectations of their biophysical role, 13 amino acid-changing point mutations at 6 sites were chosen for the fitness landscape presented here (Fig. 1). The fitness landscape was created by assessing the growth rate associated with each individual muta- tion on the parental background and all possible mutational com- Fig. 2. (A) Empirical fitness landscape by mutational distance to parental binations. A previously described Monte Carlo Markov chain type. Each line represents a single substitution. Vertical lines appear when (MCMC) approach was used to assess fitness and credibility multiple alleles have been screened at the same position. There is a global intervals (ref. 27 and Materials and Methods). pattern of negative epistasis. The three focal landscapes are highlighted. (B) Close-up on the beneficial portion of the landscape. (C) Expected (“Exp.”) versus observed (“Obs.”) fitness for the focal landscapes, obtained from 1,000 posterior samples. We observe strong positive epistasis in the land- scape that contains the global optimum, whereas the other two are domi- nated by negative epistasis. In A–C, the y axis depicts growth rate as a proxy for fitness.

The Fitness Landscape and Its Global Peak. Fig. 2 presents the resulting fitness landscape, with each mutant represented based on its Hamming distance from the parental genotype and its median estimated growth rate. Lines connect single-step sub- stitutions, with vertical lines occurring when there are multiple mutations at the same position (Fig. 1). With increasing Ham- ming distance from the parental type, many mutational combina- tions become strongly deleterious. Thus, we observe strong neg- ative epistasis between the substitutions that, as single steps on the parental background, have small effects. This pattern is con- sistent with Fisher’s Geometric Model (28) when combinations of individually beneficial or small-effect mutations overshoot the optimum and with classic arguments predicting negative epistasis based on mutational load (29). It is also intuitively comprehen- sible on the protein level, where the accumulation of too many mutations is likely to destabilize the protein and render it dys- functional (30). Fig. 1. Individual amino acid substitutions and their effect on the parental The global peak of the fitness landscape is located four muta- background in elevated salinity, obtained from 1,000 samples from the pos- tional steps away from the parental type (Fig. 2B), with 98% terior distribution of growth rates. Boxes represent the interquartile range of posterior samples identifying the peak. The fitness advan- [i.e., the 50% confidence interval (CI)], whiskers extend to the highest/lowest tage of the global peak reaches nearly 10% over the parental data point within the box ±1.5 times the interquartile range, and circles type and is consistent between replicates (Materials and Meth- represent outliers; gray and white background shading alternates by amino ods and SI Appendix, Fig. S3 1). Perhaps surprising given the acid position. The box below indicates with colored dots which mutations degree of conservation of the studied genomic region (figure are involved in the focal landscapes discussed throughout the main text: the four mutations leading from the parental type to the global optimum S5 in ref. 24), it is important to note that these fitness effects (“opt”), the four individually most beneficial mutations on the parental are measured under highly artificial experimental conditions background (“best”), and the four mutations with the individually low- including high salinity, which are unlikely to represent a nat- est growth rates on the parental background (“worst”). (Inset) Parental ural environment of yeast. The effects of the individual muta- sequence at positions 582–590 and assessed amino acids by position. tions comprising the peak in a previous experiment without

2 of 6 | www.pnas.org/cgi/doi/10.1073/pnas.1612676113 Bank et al. Downloaded by guest on September 24, 2021 Downloaded by guest on September 24, 2021 ake al. et Bank S3 Fig. Appendix, simi- (SI a epistasis shows positive optima growth local of of beneficial signature five lar terms the of in each type fact, In parental individu- rate). the are back- from that indistinguishable mutations parental beneficial (i.e., ally one mutations the of “neutral” combination three synergistic on and highly a mutations via but single-step ground beneficial also most see 20; with ref. associated from (data adaptation 26). environment ref. of salinity cost increased the potential respectively, the M589A, and emphasizing N588L, A587P, W585L, mutations for h oa n lbllnsaeptenmyb ut ifrn,an different, quite be may pattern that landscape indicates to global observation likely and This local is peak. the landscape fitness suboptimal studied a the at 26% on probability stall the higher adaptation only much from Hence, a with 47%. with away reached reached of substitutions is is 3C) two (Fig. it type optimum parental optimum, adap- local an global A in included the probability. are to vertices all walk of 78% tive type and edges parental all the of 73% from restricting and initiating when 3 walks changes (Fig. adaptive picture to the of The analysis accessibility 3). the high (Fig. indicating optimum - points global from starting probability of high with majority reached a is starting and of landscape, 95% the almost in from points probability nonzero with reached be land- the in and mutant 3 given (Fig. reach any scape to from probability starting the optimum particular and a Information Methods), Supporting and Materials Appendix, Extended (SI steps 1: optimum of fitness number the a of reach variance to and mean the for solutions lytical mutations Methods neighboring and the (Materials by the attainable to increases correspond absorbing fitness probabilities the relative transition the to which correspond in absorbing and optima an states, mutation local as weak where dynamics resulting selection chain, the Markov strong express can the until we landscape, In (34), the limit reached. in is mutant optimum any an of from length the starting the evaluated walks we of adaptive addition, accessibility In the optima. local studied observed pro- and six walks recently landscape, adaptive empirical simulated the framework Given we (33). a Plotkin and Draghi within by posed Landscape. landscape Fitness fitness the empirical on Walks Adaptive interact effects individual 13). their (4, for antagonistically synergistically, interact selected to beneficial mutations tend and combined whereas background their wild-type (13) a for mutations on selected effect small-effect were that of more mutations landscape be that to the tends than mutations large-effect rugged of landscape that such fitness TEM-1 mutations the small-effect than enzyme strongly more resistance interact tions antibiotic (32). in the found al. β recently underlying et pattern Visser gene the de the support by results predicted our between been Furthermore, epistasis has positive mutations epista- and negative neutral mutations in fact, beneficial particularly In between 31), evolution. sis (18, compensatory occasionally of epista- context observed the positive been also frequently, has more sis reported been epistasis. during has background mutations negative adaptation com- beneficial parental strong between actual exhibits epistasis the negative thus the on Although and Notably, mutations deleterious 6%. highly four is of posi- these per benefit of mutation a bination one predicts most only at in tion) (considering background (best) advantage. parental dataset the fitness most- the on individually 4% mutations four a the single-step only of beneficial, combination predicts a (opt) even peak Furthermore, involved mutations global four the the in of combination a that demonstrates were NaCl added lcaaein -lactamase uiul,tegoa eki o ece ycmiigthe combining by reached not is peak global the Curiously, sn hsfaeok efidta h lblotmmcan optimum global the that find we framework, this Using is S3 Figs. 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Intro- extension Main Models brief analytical Landscape the for Fitness in Different (14); duced of see landscapes Overview 2: terms, egg-box mation these (41), with (36–38), of HoC them [NK definitions 40), compared models (39, and landscape RMF 14) theoretical 11, from gamma (10, expectations proposed Methods ) recently and the Materials and epistasis, statistics; of fraction ratio, acid-specific. amino or shape site- the are in landscape changes the whether of study opportunity. may contained we this are landscape, site the with same within the us at alleles provides statistics. multiple because here landscape Moreover, consis- of studied the potential landscape for predictive tests The the preventing into hence 12), divided and and be 10 tency refs. to see small (but too cre- subsets are were of landscapes majority landscapes complete the Furthermore, published studied criteria. conclusions different the to drawing according because ated However, difficult (10). proven similar landscape capturing has the hence and of been correlated have features land- them ruggedness fitness of and the most epistasis proposed, of Landscape. of topography Fitness measures global Various the scape. the of considered Topography we the Next, and Measures Epistasis experi- of contribution the of see discussion interaction error, additive a mental purely for no alleles; is between there to attributed (i.e., are epistasis 62% magnitude remaining sign the reciprocal whereas and (35), (30%) epistasis sign alle- (8%) pervasive of show pairs loci that different find at we les peaks, fitness local multiple of existence below detail more in discussed (see and confirmed is that observation accessible. but poorly probability, is high it very which a from The with points starting sequence. reached are general, parental there in the is, to from (B) corresponds optimum starting geno- line global red when given The a probability dataset. from respective the starting in the genotypes optimum all specific for a computed reach type to probability the is, h e ieidctsma ahlnt o dpiewlsfo the from walks adaptive for length chain). path Markov the mean (B of indicates times genotype. absorbing parental line (i.e., red landscape full The the in type any 3. Fig. ABC efidta h eea oorpyo h teslandscape fitness the of topography general the that find We (roughness-to-slope statistics landscape various computed We .I iewt the with line In Statistics). Landscape of Potential Predictive itiuino vrg egh faatv ak trigfrom starting walks adaptive of lengths average of Distribution (A) IApni,Spotn nomto :Extended 1: Information Supporting Appendix, SI i.S3 Fig. Appendix, SI and C itiuino bobn rbblte,that probabilities, absorbing of Distribution ) IAppendix SI IApni,Spotn Infor- Supporting Appendix, SI o diinlrsls(e.g., results additional for 5 ). NSEryEdition Early PNAS A and .Weesthe Whereas B). | f6 of 3

EVOLUTION Fig. 4. (A) Expected pattern of landscape-wide epis-

tasis measure γd (SI Appendix, Eq. S1 15) with muta- tional distance for theoretical fitness landscapes with

6 loci from ref. 14. (B) Observed decay of γd with mutational distance under the drop-one approach is quite homogenous, except when hot spot mutation 588P is removed; 95% CIs are contained within the lines for the global landscape. (C) Observed decay of

γd for all diallelic six-locus sublandscapes. Depend-

ing on the underlying mutations, γd is vastly differ- ent, suggesting qualitative differences in the topog- raphy of the underlying fitness landscape and in the extent of additivity in the landscape. Three focal

landscapes representative of different types and γd for the full landscape have been highlighted. (D)

Observed decay of γd for all diallelic four-locus sub- landscapes containing the parental type, indicative of locally different landscape topographies. High- lighted are the three focal landscapes. (Insets) His- tograms of the roughness-to-slope ratio r/s for the respective subset, with horizontal lines indicating

values for highlighted landscapes [r/s for global landscape (blue) is significantly different from HoC expectation, p = 0.01]. Similar to γd, there is a huge variation in r/s for subparts of the fitness landscape, especially when considering the four-locus subsets.

Predictive Potential of Landscape Statistics. When computed based reflected in the corresponding roughness-to-slope ratio (inset of on the whole landscape and on a drop-one approach, the land- Fig. 4C and D), further emphasizing heterogeneity of the fitness scape appears quite homogeneous, and the gamma statistics landscape with local epistatic hotspots. show relatively little epistasis (Figs. 4B and 5B). At first sight, Finally, the 1,570 di-allelic four-locus landscapes containing this result contradicts our earlier statement of strong negative the parental genotype, although highly correlated genetically, and positive epistasis but can be understood, given the differ- reflect a variety of possible landscape topographies (Fig. 4D), ent definitions of the epistasis measures used: above, we have ranging from almost additive to egg-box shapes, accompanied by measured epistasis based on the deviation from the multiplica- an extensive range of roughness-to-slope ratios. The three focal tive combination of the single-step fitness effects of mutations on landscapes discussed above are not strongly different compared the parental background. Because these effects were small, epis- with the overall variation and yet show diverse patterns of epis- tasis was strong in comparison. Conversely, the gamma measure tasis between substitutions (Fig. 5). is independent of a reference genotype and captures the fitness decay with a growing number of substitutions as a dominant and quite additive component of the landscape. Only mutation 588P has a pronounced effect on the global ABCD landscape statistics and seems to act as an epistatic hotspot by making a majority of subsequent mutations (of individually small effect) on its background strongly deleterious (clearly vis- ible in Figs. 4B and 5C). This finding can be explained by look- ing at the biophysical properties of this mutation. In wild-type Hsp90, amino acid 588N is oriented away from solvent and forms hydrogen bond interactions with neighboring amino acids (24). Proline lacks an amide proton, which inhibits hydrogen bond interactions. As a result, substituting 588N with a proline could disrupt hydrogen bond interactions with residues that may be involved in main chain hydrogen bonding and destabilize the protein. In addition, the pyrrolidine ring of proline is extremely rigid and can constrain the main chain, which may restrict the conformation of the residue preceding it in the protein Fig. 5. (A) Epistasis measure γ (SI Appendix, Eq. S1 8; (A , B ) on (Ai,Bi)→(Aj,Bj) i i sequence (43). the x axis) between any two substitutions, averaged across the entire land- The variation between inferred landscape topographies in- scape. The majority of interactions are small to moderate (blue). Parts of the creases dramatically for the 360 diallelic, 6-locus sublandscapes fitness landscape show highly localized and mutation-specific epistasis, rang- (Fig. 4C). Whereas all sublandscapes are largely compatible with ing from strong magnitude epistasis (white) to sign and reciprocal sign epis- tasis (yellow). (B) The average epistatic effect γ (SI Appendix, Eq. S1 10) an RMF landscape, the decay of landscape-wide epistasis with Ai→ mutational distance (as measured by γd ) shows a large variance, of a mutation occurring on any background is always small. (C) The aver- age epistatic effect γ (SI Appendix, Eq. S1 13) of a background on any suggesting large differences in the degree of additivity. Interest- →Aj ingly, various sublandscapes, typically carrying mutation *588P, new mutation is usually small, except for mutations to *588P, which shows a show a relaxation of epistatic constraint with increasing muta- strong magnitude effect. (D) Locus-specific gamma for the four mutations leading to the global optimum (Top), the four largest single-effect mutations tional distance (i.e., increasing γd ) that is not captured by any (Middle), and the single-effect mutations with the lowest fitness (Bottom). of the proposed theoretical fitness landscape models, sugges- The opt landscape exhibits strong sign epistasis between loci 587 and 588 and tive of systematic compensatory interactions (but see the egg-box between loci 588 and 589. Also, the best landscape exhibits pervasive epista- model for an explicit example featuring nonmonotonicity in γd ). sis with sign epistasis between locus 588 and loci 585 and 586, respectively. The variation in the shape of the fitness (sub)landscapes is also We observe almost no epistasis in the worst landscape.

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Growth of Estimation sequencing (26). of described Analysis previously 49). as (48, performed scoring were PHRED data on based position read Elim each by performed produced was and Sequencing Biopharmaceuticals (25). described previously as performed at stored and points time specific gen- at 12 taken for were NaCl M Samples 0.5 erations. containing medium The selective to dextrose. 30 shifted then (wt/vol) at and h Hsp90 2% 8 with for replaced grown are was culture Gal and Gal to raffinose similar but medium selective medium ampli- to After transferred Gal). was 1% culture and library raffinose leucine, the 1% g/L with fication, uracil 0.1 g/L methionine, 0.01 and g/L lysine, g/L 0.02 0.1 g/L 0.03 hemisulfate, 0.03 sulfate, phenylalanine, adenine g/L g/L 0.05 ammonium 0.04 isoleucine, tyrosine, g/L g/L g/L 0.03 0.4 threonine, acid, 5 glutamic g/L g/L 0.2 0.1 acids, valine, serine, g/L 0.03 arginine, amino g/L 30 0.02 acid, without aspartic at g/L base transfor- h 100 nitrogen 12 Following with :pgals- yeast medium for (47). (Gal) : amplified galactose method using ho: was conditions acetate :leu2 library hsc82: lithium the :leu2 mation, the hsp82: using ura3-1 hsp82-his3) trp1-1 leu2-3,12 his3-11,15 the into introduced h arxo psai fet ewe ifrn ar falleles of calculated pairs geno- different we between all (14), effects theory over epistatic recent of averaged Extending matrix background, landscape. the fitness genetic the altered different is of mutation a types focal onto a of put effect selective when mutations the of how effects quantifies fitness which of (14), correlation the Mutations. calculating by of assessed were Effects Fitness of Correlation dataset. full the from obtained those all to comparing and statistics recalculating and unobserved) as delet- mutation in by corresponding rows assessed and were columns mutations corresponding specific the of ing influence the proba- and the results calculate the of to and optimum the optimum reach in any to variance bility reaching the before and steps expectation the of determine number to allows then matrix tal neighbors one-mutant matrix adaptive, transition all genotype over current sum the the of by normalized 53) (52, ity mutant any from j A ( (g) arigamtn leea locus at allele mutant a carrying A j es yi,DAioain n rprto o luiasqecn were sequencing Illumina for preparation and isolation, DNA lysis, Yeast were combinations mutation Hsp90 of libraries expressed Constitutively ,B i S1 S1 ,B = j i
) w ihHmigdistance Hamming with 15) ,adtedcyo orlto ffins effects fitness of correlation of decay the and 12), → termed (g Eq. Appendix, (SI g [ j [i ] k ) ] − and bobn ie,otm)and optima) (i.e., absorbing γ w w ntesrn eeto ekmtto ii 5) adapta- (51), limit mutation weak selection strong the In (A P stefins fgenotype of fitness the as (g) g i ,sc httetasto probabilities transition the that such (g), , g 5)i t aoia omadcmuigtefundamen- the computing and form canonical its in (54) B [ oaymutant any to i olwn es 5ad5,w unie hte spe- whether quantified we 56, and 35 refs. Following .cerevisiae S. )→(A j ] (with g If g. j ,B hnsatn rmgenotype from starting when S1 j niiulgot ae eeetmtdaccord- estimated were rates growth Individual ) i Eq. , Appendix (SI g 6 = ,tevco feittcefcsbtenall between effects epistatic of vector the 9), ◦ sa(oa)optimum, (local) a is oalwsuofo h idtp oyof copy wild-type the of shutoff allow to C j ihrsett ie eeec geno- reference given a to respect with ) htf tanDY8 cn-0 ade2-1 (can1-100 DBY288 strain shutoff 0mlinraso 9 ofiec at confidence 99% of reads million ≈30 i d h eeto ofceti eoe by denoted is coefficient selection the , g [i vrgdoe l genotypes all over averaged ] A r ie ytefiainprobabil- fixation the by given are j (A , B n n j i P
, − teghadtp fepistasis of type and Strength ifrn tts(.. mutants), (i.e., states different ie,b setal raigthe treating essentially by (i.e., B termed k i ) S1 rnin tts(.. nonop- (i.e., states transient and g, nalohrpiso alleles of pairs other all on NSEryEdition Early PNAS ,tevco fepistatic of vector the 8), /Lapcli 17g/L (1.7 ampicillin µg/mL ◦ γ p ne nonselective under C →(A g, g g [i ] 0 j = γ ,B stegenotype the as 5) Robustness (55). p d j g, ) .Ptigthe Putting 1. IAppendix, (SI IAppendix, (SI [i (A ] −80 o going for i g ,B | fthe of i ) f6 of 5 ◦ C. and γ

EVOLUTION type g over the entire fitness landscape. There was no epistatic interaction if variance and, thus, a very large roughness-to-slope ratio (as in the HoC −6 |si(g[ j]) − si(g)| < ε = 10 , magnitude epistasis if sj(g)sj(g[i]) ≥ 0 and model). In addition, we calculated a test statistic Zρ by randomly shuffling si(g)si(g[ j]) ≥ 0, reciprocal sign epistasis if sj(g)sj(g[i]) < 0 and si(g)si(g[ j]) < fitness values in the sequence space to evaluate the statistical significance 0, and sign epistasis in all other cases (58). of the obtained roughness-to-slope ratio from the dataset ρdata given by ρdata−E[ρRSL] Zρ = √ . Var[ρ ] Roughness-to-Slope Ratio. Following ref. 11, we calculated the roughness- RSL to-slope ratio ρ by fitting the fitness landscape to a multidimensional lin- ear model using the least-squares method. The slope of the linear model ACKNOWLEDGMENTS. We thank Dan Bolon, Brian Charlesworth, Pamela Cote, Inesˆ Fragata, and Hermina Ghenu for helpful comments and dis- corresponds to the average additive fitness effect (10, 23), whereas the cussion. This project was funded by grants from the Swiss National roughness is given by the variance of the residuals. Generally, the bet- Science Foundation and a European Research Council Starting Grant ter the linear model fit, the smaller the variance in residuals such that (to J.D.J.). Computations were performed at the Vital-IT Center the roughness-to-slope ratio approaches 0 in a perfectly additive model. (www.vital-it.ch) for high-performance computing of the Swiss Institute of Conversely, a very rugged fitness landscape would have a large residual Bioinformatics.

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