Software for the analysis and visualization of deep mutational scanning data

Transcription

1 Bloom BMC Bioinfomatics :168 DOI /s SOFTWARE Open Access Softwae fo the analysis and visualization of deep mutational scanning data JesseDBloom Abstact Backgound: Deep mutational scanning is a technique to estimate the impacts of mutations on a gene by using deep sequencing to count mutations in a libay of vaiants befoe and afte imposing a functional selection. The impacts of mutations must be infeed fom changes in thei counts afte selection. Results: I descibe a softwae package, dms_tools, to infe the impacts of mutations fom deep mutational scanning data using a likelihood-based teatment of the mutation counts. I show that dms_tools yields moe accuate infeences on simulated data than simply calculating atios of counts pe- and post-selection. Using dms_tools, one can infe the pefeence of each site fo each amino acid given a single selection pessue, o assess the extent to which these pefeences change unde diffeent selection pessues. The pefeences and thei changes can be intuitively visualized with sequence-logo-style plots ceated using an extension to weblogo. Conclusions: dms_tools implements a statistically pincipled appoach fo the analysis and subsequent visualization of deep mutational scanning data. Keywods: Deep mutational scanning, Sequence logo, Amino-acid pefeences Backgound Deep mutational scanning is a high-thoughput expeimental technique to assess the impacts of mutations on a potein-coding gene [1]. Figue 1 shows a schematic of deep mutational scanning. A gene is mutagenized, and the libay of esulting vaiants is intoduced into cells o viuses, which ae then subjected to an expeimental selection that eniches fo functional vaiants and depletes non-functional ones. Deep sequencing of the vaiants peand post-selection povides infomation about the functional impacts of mutations. Since the oiginal desciption of deep mutational scanning by Fowle et al. [2], the technique has been applied to a wide ange of genes [3-15], both to measue mutational toleance given a single selection pessue as in Figue 1A, o to identify mutations that have diffeent effects unde altenative selections as in Figue 1B. New techniques to ceate compehensive codon-mutant libaies of genes make it possible to pofile all amino-acid mutations [8-10,15-17], while Coespondence: jbloom@fedhutch.og Division of Basic Sciences and Computational Biology Pogam, Fed Hutchinson Cance Reseach Cente, 1100 Faiview Ave N, Seattle, WA, USA new techniques fo tageted mutagenesis of mammalian genomes enable deep mutational scanning to be applied acoss the biological spectum fom viuses and bacteia to human cells [18]. A key component of deep mutational scanning is analysis of the data: Fist, aw eads fom the deep sequencing must be pocessed to count mutations pe- and postselection. Next, the biological effects of mutations must be infeed fom these counts. The fist task of pocessing the eads is idiosyncatic to the specific sequencing stategy used. But the second task of infeing mutational effects fom sequencing counts is amenable to moe geneal algoithms. Howeve, only a few such algoithms have been descibed [19,20]. Hee I pesent use-fiendly softwae, dms_tools, that infes mutational effects fom sequencing counts. Befoe descibing the algoithms implemented in dms_tools and illustating its use on existing and simulated data, I fist discuss issues associated with infeing mutational effects fom sequencing counts. The natue of deep mutational scanning data. The data consist of counts of vaiants pe- and postselection. The appoach pesented hee teats each site 2015 Bloom; licensee BioMed Cental. This is an Open Access aticle distibuted unde the tems of the Ceative Commons Attibution License which pemits unesticted use, distibution, and epoduction in any medium, povided the oiginal wok is popely cedited. The Ceative Commons Public Domain Dedication waive applies to the data made available in this aticle, unless othewise stated.

2 Bloom BMC Bioinfomatics :168 Page 2 of 13 A B Figue 1 A deep mutational scanning expeiment. A A gene is mutagenized to ceate a libay that contains all single codon mutations. The mutant libay is intoduced into cells o viuses and subjected to a functional selection that eniches beneficial mutations and depletes deleteious ones. Deep sequencing is used to count mutations in a sample of the vaiants pesent pe- and post-selection. Using dms_tools, the data can be analyzed to infe the pefeence of each site fo each amino acid; in the visualization, lette heights ae popotional to the pefeence fo that amino acid. B The expeiment can be extended by subjecting the libay of functional vaiants to two diffeent selection pessues, and using deep sequencing to assess which vaiants ae favoed in one condition vesus the othe. Using dms_tools, the data can be analyzed to infe the diffeential pefeence of each site fo each amino acid in the altenative selection s2 vesus the contol selection s1;in the visualization,lette heights above o below the line ae popotional to the diffeential pefeence fo o against that amino acid. in the gene sepaately, ignoing epistatic coupling among mutations. This aspect of the appoach should not be constued as a suggestion that inteactions among mutations ae unimpotant; indeed, seveal studies have used deep mutational scanning to examine paiwise epistasis [14,21,22], and techniques have been descibed to obtain linkage between distant sites [23,24]. Howeve, the exploding combinatoics of multiple mutations a 500-esidue potein has only single mutants, but double mutants and ! 3! 500! tiple mutants make it cuently plausible to compehensively chaacteize only single mutations to all but the shotest genes. Teating sites independently is theefoe not a majo limitation fo most cuent datasets. Eventually the appoach hee might be extended to include coupling among mutations. The data fo each site is chaacteized by the sequencing depth total numbe of counts; let N pe, N post, N s1, and N s2 denote the depth at fo each of the fou libaies in Figue 1 pe-selection, post-selection, selection s1, and selection s2. Typical depths fo cuent expeiments ae N Denote the counts of chaacte x chaactes mightbenucleotides,aminoacids,ocodonsat as n pe,x, n post,x, n s1,x,andns2,x. The values of n,x fo chaactes x that diffe fom the wildtype identity wt depend on both the depth N and the aveage pe-site mutation ate μ. Since the mutations ae intentionally intoduced into the mutant libay by the expeimentalist, in pinciple μ could have any value. But typically, deep mutational scanning expeiments aim to intoduce about one mutation pe gene to avoid filling the mutant libay with highly mutated genes so the aveage mutation ate is usually μ 1/L whee L is the length of the gene. Theefoe, if a 500-codon gene is sequenced at depth N 10 6, we expect Nμ 2000 counts of non-wildtype codons at each site. Since thee ae 63 mutant codons, the aveage pe-selection counts fo a mutation to a specific x = wt will be n pe,x 30, with counts fo most mutations deviating fom this aveage due to biases in ceation of the mutant libay and andomness in which molecules ae sequenced. Counts in the post-selection libaies will futhe deviate fom this aveage due to selection. Theefoe, even at depths N 10 6, the actual counts of most mutations will be quite modest.

3 Bloom BMC Bioinfomatics :168 Page 3 of 13 The est of this pape assumes that the sequencing depth is less than the numbe of unique molecules in the mutant libay, such that the deep sequencing andomly subsamples the set of molecules. If this assumption is false i.e. if the numbe of unique molecules is substantially less than the sequencing depth, then the accuacy of infeences about mutational effects will be fundamentally limited by this aspect of the expeimental design. Popely done expeiments should quantify the numbe of unique molecules in the libay so that it is obvious whethe this assumption holds. In the absence of such infomation, the analysis can be epeated using only a andom faction of the deep sequencing data to assess whethe infeences ae limited by sequencing depth o the undelying molecula divesity in the mutant libay. The goal: infeing site-specific amino-acid pefeences Thegoalistoestimatetheeffectsofmutationsfom changes in thei counts afte selection. Let μ,x, f,x, f,x s1, and f,x s2 denote the tue fequencies at site of all mutant chaactes x = wt that would be obseved fo the fou libaies in Figue 1 if we sampled at infinite depth in both the actual expeiment and the sequencing. The definition of these fequencies fo the wildtype chaacte wt depends on how the mutant libay is constucted. If the mutant libay is constucted so that thee is a Poisson distibutionofthenumbeofmutationspegeneasis the case fo eo-pone PCR o the codon-mutagenesis in [9,11], then μ,wt, f,wt, f,wt s1,andfs2,wt ae defined asfoallothechaactesx, and denote the fequencies of wt at site that would be obseved if sampling at infinite depth. The eason we can make this definition fo libaies containing genes with Poisson-distibuted numbes of mutations is that fo any easonable-length gene L 1, the maginal distibution of the numbe of mutations in a gene is vitually unchanged by the knowledge that thee is a mutation at site. On the othe hand, if the mutant libay is constucted so that thee is exactly zeo o one mutation pe gene as in [8,10,15], then the maginal distibution of the total numbe of mutations in a gene is changed by the knowledge that thee is a mutation at. In this case, the wildtype-chaacte fequencies μ,wt, f,wt, f,wt s1,andfs2,wt ae coectly defined as the fequency of unmutated genes in the libay, and the counts n pe,wt, etc. ae defined as the numbe of eads at attibutable to unmutated genes. In this case, measuement of these counts equies sequencing with linkage as in [15,23,24]. The pope analysis of libaies containing only unmutated and singly mutated clones sequenced without linkage is beyond the scope of this pape. If we knew the fequencies μ,x, f,x, f,x s1,andfs2,x,we could calculate paametes that eflect the effects of mutations. One paamete that chaacteizes the effect of mutating fom wt to x fo the expeiment in Figue 1A is the enichment atio, which is the elative fequency of mutations to x afte selection vesus befoe selection: φ,x = f,x/f,wt. 1 μ,x /μ,wt Beneficial mutations have φ,x > 1, while deleteious ones have φ,x < 1. A elated paamete is the pefeence π,x of fo x. At each site, the pefeences ae simply the enichment atios escaled to sum to one: π,x = φ,x y φ = f,x/μ,x,y y f, 2,y/μ,y o equivalently f,x = π,x μ,x y π,y μ,y, 3 whee y is summed ove all chaacte identities all nucleotides, codons, o amino acids. The pefeences can be intuitively visualized Figue 1A and intepeted as the equilibium fequencies in substitution models fo gene evolution [9,25] afte accounting fo uneven mutational ates [26,27]. The challenge of statistical infeence fom finite counts Equations 1 and 2 ae in tems of the tue fequencies μ,x, f,x, etc. But in pactice, we only obseve the counts in the finite sample of sequenced molecules. The computational challenge is to estimate the pefeences o enichment atios fom these counts. The most naive appoach is to simply substitute the counts fo the fequencies, eplacing Equation 1 with φ,x = n post,x +P n post,wt +P n pe,x +P n pe,wt +P 4 whee P often chosen to be one is a pseudocount added to each count to avoid atios of zeo o infinity. Howeve, Equation 4 involves atios of counts with values 10 to 100 and as oiginally noted by Kal Peason [28,29], atios estimated fom finite counts ae statistically biased, with the bias inceasing as the magnitude of the counts decease. This bias can popagate into subsequent analyses, since many statistical tests assume symmetic eos. The poblems caused by biases in uncoected atios have been noted even in applications such as isotope-atio mass spectomety [30] and fluoescent imaging [31], whee the counts usually fa exceed those in deep mutational scanning. Taking atios also abogates ou ability to use the magnitude of the counts to assess ou cetainty about conclusions. Fo instance, imagine that at a fixed depth, the counts of a mutation incease fom a pe-selection value of 5 to a post-selection value of 10. While this doubling suggests that the mutation might be beneficial, the small

4 Bloom BMC Bioinfomatics :168 Page 4 of 13 counts make us somewhat uncetain of this conclusion. But if the counts inceased fom 20 to 40 we would be substantially moe cetain, and if they inceased fom 100 to 200 we would be quite sue. So only by an explicit statistical teatment of the counts can we fully leveage the data. HeeIdescibeasoftwaepackage,dms_tools, that infes mutational effects in a Bayesian famewok using a likelihood-based teatment of the counts. This softwae can be used to infe and visualize site-specific pefeences fom expeiments like Figue 1A, and to infe and visualize diffeences in pefeences unde altenative selections fom expeiments like Figue 1B. Implementation and esults Algoithm to infe site-specific pefeences dms_tools uses a Bayesian appoach to infe sitespecific pefeences fom expeiments like those in Figue 1A. The algoithm calculates the likelihoods of the counts given the unknown pefeences and mutation/eo ates, placing plausible pios ove these unknown paametes. The pios coespond to the assumption that all possible identities e.g. amino acids have equal pefeences, and that the mutation and eo ates fo each site ae equal to the oveall aveage fo the gene. MCMC is used to calculate the posteio pobability of the pefeences given the counts. This algoithm is a slight modification of that in the Methods of [9]; hee the algoithm is descibed anew to explain the implementation in dms_tools. Optional contols to quantify eo ates Some sequencing eads that epot a mutation may actually eflect an eo intoduced duing sequencing o PCR athe than an actual mutation that expeienced selection. Eos can be quantified by sequencing an unmutated gene, so that any counts at of x = wt fo this contol eflect eos. In some cases e.g. sequencing an RNA vius whee the post-selection libaies must be evese-tanscibed, eo ates fo the pe- and postselection libaies may diffe and so be descibed by diffeent contols. Let N epe and n epe,x and n epost,x and N epost be the depth be the counts of x in the peselection and post-selection eo contols, espectively. Define ɛ,x and ρ,x to be the tue fequencies of eos at fom wt to x in the pe- and post-selection contols, espectively. Likelihoods of obseving specific mutational counts Define vectos of the counts and fequencies fo all chaactes at each site, i.e.n pe =, n pe,x,, n post =, n post,x,, μ =, μ,x,, f =, f,x,, etc. Also define π =, π,x, of the pefeences fo each, noting that Equation 3 implies f = μ π μ π whee is the Hadamad poduct. The likelihoods of some specific set of counts ae: P n epe Multi n epe P n epost Multi P n pe N epe, ɛ = ; N epe, ɛ 5 N epost, ρ = n epost N pe, μ, ɛ = ; N epost, ρ 6 Multi n pe ; N pe 7, μ + ɛ δ P n post N post, μ, π, ρ = Multi n post ; N post, μ π 8 + ρ δ μ π whee Multi is the multinomial distibution, δ =, δx,wt, is a vecto with the element coesponding to wt equal to one and all othe elements zeo δ xy is thekoneckedelta,andwehaveassumedthatthepobability that a site expeiences both a mutation and an eo is negligibly small. Pios ove the unknown paametes We specify Diichlet pios ove the paamete vectos: P π = Diichlet π ; α π 1 9 P μ = Diichlet μ ; α μ N x a,μ 10 P ɛ = Diichlet ɛ ; α ɛ N x a,ɛ 11 P ρ = Diichlet ρ ; α ρ N x a,ρ 12 whee 1 is a vecto of ones, N x is the numbe of chaactes 64 fo codons, 20 fo amino acids, 4 fo nucleotides, the α s ae scala concentation paametes > 0 by default dms_tools sets the α s to one. Fo codons, the eo ate depends on the numbe of nucleotides being changed. The aveage eo ates ɛ m and ρ m fo codon mutations with m nucleotide changes ae estimated as ɛ m = 1 1 L N epe 1 x n epe,x δ m,dx,wt 13 ρ m = 1 L N epost n epost,x δ m,dx,wt 14 x whee D x,wt is the numbe of nucleotide diffeences between x and wt. Given these definitions, a,ɛ =, ɛ m δ m,dx,wt, 15 C m m a,ρ =, ρ m δ m,dx,wt, 16 C m m whee C m is the numbe of mutant chaactes with m changes elative to wildtype fo nucleotides C 0 = 1and C 1 = 3; fo codons C 0 = 1, C 1 = 9, C 2 = C 3 = 27.

5 Bloom BMC Bioinfomatics :168 Page 5 of 13 Ou pio assumption is that the mutagenesis intoduces all mutant chaactes at equal fequency this assumption is only plausible fo codons if the mutagenesis is at the codon level as in [8-10,15-17]; if mutations ae made at the nucleotide level such as by eo-pone PCR then chaactes should be defined as nucleotides. The aveage pe-site mutagenesis ate is estimated as μ = 1 1 L N pe n pe,x ɛ m, 17 m 1 so that a,μ = x =wt μ, N x 1 + δ x,wt [1 μ],. 18 Chaacte types: nucleotides, amino acids, o codons dms_tools allows fou possibilities fo the type of chaacte fo the counts and pefeences. The fist thee possibilities ae simple: the counts and pefeences can both be fo any of nucleotides, amino acids, o codons. The fouth possibility is that the counts ae fo codons, but the pefeences fo amino acids. In this case, define a function mapping codons to amino acids, A w =, δ a,ax w x, 19 x whee w is a 64-element vecto of codons x, A w is a 20- o 21-element depending on the teatment of stop codons vecto of amino acids a, anda x is the amino acid encoded by x. The pio ove the pefeences π is still a symmetic Diichlet now only of length 20 o 21, but the pios fo μ, ɛ,andρ ae now Diichlets paameteized by A a,μ, A a,ɛ and A a,ρ athe than a,μ, a,ɛ,anda,ρ. The likelihoods ae computed in tems of these tansfomed vectos afte similaly tansfoming the counts to A n pe, A n post A. n epost, A n epe,and Implementation The pogam dms_infepefs in the dms_tools package infes the pefeences by using pystan [32] to pefom MCMC ove the posteio defined by the poduct of the likelihoods and pios in Equations 5, 6, 7, 8, 9, 10, 11, and 12. The pogam uns fou chains fom diffeent initial values, and checks fo convegence by ensuing that the Gelman-Rubin statistic ˆR [33] is < 1.1 and the effective sample size is > 100; the numbe of MCMC iteations is inceased until convegence is achieved. The pogam dms_logoplot in the dms_tools package visualizes the posteio mean pefeences via an extension to weblogo [34]. The pogam dms_mege can be used to aveage pefeences infeed fom diffeent expeimental eplicates that have individually been analyzed by dms_infepefs, andthepogamdms_coelate can be used to compute the coelations among infeences fom diffeent eplicates. Infeing pefeences with dms_tools Application to actual datasets Figues 2 and 3 illustate application of dms_tools to two existing datasets [10,11]. The pogams equie as input only simple text files listing the counts of each chaacte identity at each site. As the figues show, the dms_infepefs and dms_logoplot pogams can pocess these input files to infe and visualize the pefeences with a few simple commands. Eo contols can be included when available they ae not fo Figue 2, but ae fo Figue 3. The untime fo the MCMC depends on the gene length and chaacte type codons ae slowest, nucleotides fastest but if the infeence is paallelized acoss multiple CPUs using the -ncpus option of dms_infepefs, the infeence should take no moe than a few hous. As shown in Figues 2 and 3, the visualizations can ovelay infomation about potein stuctue onto the pefeences. Figues 2 and 3 also illustate use of dms_coelate to assess the coelation between pefeences infeed fom diffeent biological eplicates [35] of the expeiment. The inclusion and analysis of such eplicates is the only sue way to fully assess the souces of noise associated with deep mutational scanning. Testing on simulated data To test the accuacy of pefeence-infeence by dms_tools, I simulated deep mutational scanning counts using the pefeences in Figue 2, both with and without eos quantified by appopiate contols. Impotantly, the eo and mutation ates fo these simulations wee not unifom acoss sites and chaactes, but wee simulated to have a level of unevenness compaable to that obseved in eal expeiments. I then used dms_tools to infe pefeences fom the simulated data, and also made simila infeences using simple atio estimation Equation 4. Figue 4 shows the infeed pefeences vesus the actual values used to simulate the data. Fo simulations with mutation counts quantified by the poduct Nμ of the depth and aveage pe-site mutation ate 1000 to 2000, the infeences ae quite accuate. Infeences made by dms_tools ae always moe accuate than those obtained by simply taking atios of mutation counts. Is the Bayesian infeence wothwhile? The foegoing sections explain why the Bayesian infeence of pefeences implemented in dms_tools is conceptually pefeable to estimating mutational effects via diect atio estimation using Equation 4. Howeve, do

6 Bloom BMC Bioinfomatics :168 Page 6 of 13 Figue 2 Site-specific pefeences fom deep mutational scanning of a Tn5 tansposon. Melnikov et al. [10] pefomed deep mutational scanning on a Tn5 tansposon using kanamycin selection, and epoted the counts of amino-acid mutations fo two biological eplicates of the expeiment. Hee I have used dms_tools to infe the pefeences. A Visualization of the pefeences aveaged acoss the two eplicates. B Coelation between the pefeences infeed fom each of the two eplicates. Given files containing the mutation counts, the plots can be geneated as logoplot.pdf and co.pdf with the following commands: dms_infepefs pe_counts_1.txt post_counts_1.txt pefs_1.txt --excludestop --ncpus -1 --chatype aa dms_infepefs pe_counts_2.txt post_counts_2.txt pefs_2.txt --excludestop --ncpus -1 --chatype aa dms_coelate pefs_1.txt pefs_2.txt co -name1 "eplicate 1" -name2 "eplicate 2" --co_on_plot dms_mege pefs.txt aveage pefs_1.txt pefs_2.txt dms_logoplot pefs.txt logoplot.pdf -npeline 53 --ovelay1 RSAs.txt RSA "elative solvent accessibility" --ovelay2 SSs.txt SS "seconday stuctue". the pactical benefits of this Bayesian infeence justify its inceased complexity? The simulations in the pevious section show that the Bayesian infeence is moe accuate, but in the absence of backgound eos Figue 4A the magnitude of the impovement becomes negligible once the mutation counts pe site Nμ stat to exceed When thee is a need to coect fo backgound eos Figue 4B, meaningful benefits of the Bayesian infeence ove enichment atios extend to somewhat highe sequencing depths. Oveall, it appeas that Bayesian infeence will always pefom as well o bette than atio estimation, but that the tangible benefit becomes negligible at high sequencing depth. In that case, the use will have to decide if the inceased computational untime and complexity of the Bayesian infeence is woth a small impovement in accuacy. Simple atio estimation can be pefomed using the -atio_estimation option of dms_infepefs o using an altenative pogam such as Enich [19]. When applying atio estimation to data whee some mutations have low counts, it is impotant to include pseudocounts denoted by P in Equation 4 as a fom of egulaization to avoid estimating excessively high o low pefeences at sites with limited counts. Algoithm to infe diffeential pefeences As shown in Figue 1B, a useful extension to the expeiment in Figue 1A is to subject the functional vaiants to two diffeent selection pessues to identify mutations favoed by one pessue vesus the othe. While this expeiment could in pinciple by analyzed by simply compaing the initial unselected mutants to the final vaiants afte the

7 Bloom BMC Bioinfomatics :168 Page 7 of 13 Figue 3 See legend on next page.

8 Bloom BMC Bioinfomatics :168 Page 8 of 13 See figue on pevious page. Site-specific pefeences fom deep mutational scanning of influenza hemagglutinin. Thyagaajan and Bloom [11] pefomed deep mutational scanning on influenza hemagglutinin, and epoted the counts of codon mutations fo thee biological eplicates of the expeiment. Hee I have used dms_tools to infe the pefeences. A Visualization of the pefeences aveaged acoss the thee eplicates. B Coelations between the pefeences fom each pai of eplicates. Given files containing the mutation counts, the plots can be geneated as logoplot.pdf, co_1_2.pdf, co_1_3.pdf, and co_2_3.pdf with the following commands: dms_infepefs mutdna_1.txt mutvius_1.txt pefs_1.txt --epe DNA_1.txt --epost vius_1.txt --ncpus -1 dms_infepefs mutdna_2.txt mutvius_2.txt pefs_2.txt --epe DNA_2.txt --epost vius_2.txt --ncpus -1 dms_infepefs mutdna_3.txt mutvius_3.txt pefs_3.txt --epe DNA_3.txt --epost vius_3.txt --ncpus -1 dms_coelate pefs_1.txt pefs_2.txt co_1_2 -name1 "eplicate 1" -name2 "eplicate 2" --co_on_plot dms_coelate pefs_1.txt pefs_3.txt co_1_3 --name1 "eplicate 1" -name2 "eplicate 3" --co_on_plot dms_coelate pefs_2.txt pefs_3.txt co_2_3 -name1 "eplicate 2" -name2 "eplicate 3" --co_on_plot dms_mege pefs.txt aveage pefs_1.txt pefs_2.txt pefs_3.txt dms_logoplot pefs.txt logoplot.pdf --npeline 71 --ovelay1 RSAs.txt RSA "elative solvent accessibility" -ovelay2 SSs.txt SS "seconday stuctue" --excludestop Note that unlike in Figue 2, no --chatype option is specified since the dms_infepefs default is aleady codon_to_aa. two altenative selections, this appoach is non-ideal. In expeiments like Figue 1A, many mutations ae eniched o depleted to some extent by selection, since a lage faction of andom mutations affect potein function [36-40]. Theefoe, the assumption that all mutations ae equally toleated i.e. the pefeences fo a site ae all equal, o the enichment atios ae all one is not a plausible null hypothesis fo Figue 1A. Fo this eason, dms_tools simply infes the pefeences given a unifom Diichlet pio athe than tying to pinpoint some subset of sites with unequal pefeences. But in Figue 1B, the assumption that most mutations will be similaly selected is a plausible null hypothesis, since we expect altenative selections to have makedly diffeent effects on only a small subset of mutations typically, majo constaints elated to potein folding and stability will be conseved acoss diffeent selections on the same potein. Theefoe, dms_tools uses a diffeent algoithm to infe the diffeential pefeences unde the two selections. This algoithm combines a pio that mildly favos diffeential pefeences of zeo with a likelihood-based analysis of the mutation counts to estimate posteio pobabilities ove the diffeential pefeences. Definition of the diffeential pefeences Given an expeiment like Figue 1B, let f,x stat be the tue fequency of chaacte x at site in the stating libay equivalent to the fequency f,x post in the figue, and let f,x s1 and f s2,x be the fequencies afte selections s1 ands2, espectively. The diffeential pefeence π,x fo x at in s2vesuss1isdefinedby: f s1,x = f s2,x = f,x stat y f,y stat f,x stat π s1,x y f stat,y π s1,y 20 π,x s1 + π,x π,y s1 + π 21,y whee π,x s1 is the contol pefeence and is teated as a nuisance paamete, and we have the constaints 0 = x π,x 22 0 π,x s1 + π,x If thee is no diffeence in the effect of x at between selections s1 ands2, then π,x = 0. If x at is moe pefeed by s2 thans1, then π,x > 0; convesely if x at is moe pefeed by s1thans2, then π,x < 0seeFigue5A. Likelihoods of obseving specific mutational counts Define vectos of the counts as n stat =, n stat,x, fo the post-selection functional vaiants that ae subjected to the futhe selections, and as n s1 =, n s1,x, and n s2 =, n s2,x, fo selections s1 and s2. We again allow an eo contol, but now assume that the same contol applies to all thee libaies since they ae all sequenced afte a selection, and define the counts fo this contol as n e =, n e,x, ; the tue eo fequencies ae denoted by ξ,x.definevectos of the fequencies, eos, contol pefeences, and diffeential pefeences: f stat =, f,x stat,, f s1 =, f s1,x,, f s2 =, f,x s2,, ξ =, ξ,x,, π s1 =, π,x s1,, and π =, π,x,.

9 Bloom BMC Bioinfomatics :168 Page 9 of 13 Figue 4 Accuacy of pefeence infeence on simulated data. Deep mutational scanning counts wee simulated using the pefeences in Figue 2A and ealistic mutation and eo ates that wee uneven acoss sites and chaactes as in actual expeiments. The simulations wee done A without o B with sequencing eos quantified by contol libaies. Plots show the coelation between the actual and infeed pefeences as a function of the poduct of the sequencing depth N and the aveage pe-site mutation ate μ; eal expeiments typically have Nμ 1000 to 2000 depending on the sequencing depth and gene length. Pefeences ae infeed using the full algoithm in dms_tools toppanelso by simply calculating atios of counts bottom panels using Equation 4 and its logical extension to include eos, both with a pseudocount of one. The dms_tools infeences ae moe accuate than the simple atio estimation, with both methods conveging to the actual values with inceasing Nμ. Given files withthe mutationcounts, the plots in this figuecan be geneated aspefs_co.pdf and atio_co.pdf with commands such as: dms_infepefs pe.txt post.txt infeed_pefs.txt --ncpus -1 dms_infepefs pe.text post.text atio_pefs.txt --atio_estimation 1 dms_coelate actual_pefs.txt infeed_pefs.txt pefs_co --name1 "actual" --name2 "infeed" --co_on_plot --2 dms_coelate actual_pefs.txt atio_pefs.txt atio_co --name1 "actual" --name2 "infeed" --co_on_plot --2. Equations 20 and 21 imply f s1 f stat f stat π s1+ π π s1. + π = f stat π s1 f stat π s1 and f s2 = The likelihoods of the counts will be multinomially distibuted aound the tue fequencies, so P n e N e, ξ = Multi n e ; N e, ξ 24 P n stat Multi n stat P n s1 Multi N stat, f stat, ξ = ; N stat, f stat N s1, f stat n s1 ; Ns1 + ξ δ 25, π s1, ξ =, f stat f stat π s1 π s1 + ξ δ 26

10 Bloom BMC Bioinfomatics :168 Page 10 of 13 A B Figue 5 Infeence of diffeential pefeences on simulated data. To illustate and test the infeence of diffeential pefeences, the expeiment in Figue 1B was simulated at the codon level stating with the post-selection libay that yielded the pefeences in Figue 2. In the simulations, 20% of sites had diffeent pefeences between the contol and altenative selection. A, dms_tools was used to infe the diffeential pefeences fom the data simulated at N = 10 7, and the esulting infeences wee visualized. The ovelay bas indicate which sites had non-zeo diffeential pefeences in the simulation. B The coelations between the infeed and actual diffeential pefeences as a function of Nμ show that the infeed values convege to the tue ones. Given files with the mutation counts, the plots in this figue can be geneated as logoplot.pdf and co.pdf with the following commands: dms_infediffpefs stat.txt s1.txt s2.txt diffpefs.txt --ncpus -1 dms_logoplot diffpefs.txt logoplot.pdf --npeline 53 --ovelay1 actually_nonzeo.txt " = 0?" "Is actual diffeential pefeence non-zeo?" --diffpefheight 0.45 dms_coelate actual_diffpefs.txt diffpefs.txt co --name1 "actual" --name2 "infeed" --co_on_plot--2 Note that no --chatype option is specified because the default fo dms_infediffpefs is aleady codon_to_aa. P n s2 N s2, f stat, π s1, π, ξ = Multi n s2 ; Ns2, f stat π + π s1 27 f stat π + π s1 + ξ δ whee we have assumed that the pobability that a site expeiences a mutation and an eo in the same molecule is negligibly small. Pios ove the unknown paametes We specify Diichlet pios ove the paamete vectos: P π s1 = Diichlet π s1 ; α π s P ξ = Diichlet ξ ; α ξ N x a,ξ 29 P f stat = Diichlet f stat ; α stat N x a,stat 30

11 Bloom BMC Bioinfomatics :168 Page 11 of 13 P π π s1 = Diichlet π ; α π N x π s1 π s1 31 whee dms_tools by default sets all the scala concentation paametes α s to one except α π, which is set to two coesponding to a weak expectation that the π values ae close to zeo. The aveage eo ate ξ m fo mutations with m nucleotide changes is ξ m = 1 L 1 N e and so a,ξ =, m x n e,x δ m,d x,wt, 32 ξ m δ m,dx,wt,. 33 C m Ou pio assumption is that all mutations ae at equal fequency in the stating libay this assumption is unlikely Figue 6 Diffeential pefeences following selection of influenza NS1 in the pesence o absence of intefeon. Wu et al. [13]geneated libaies of influenza viuses caying nucleotide mutations in the NS segment. They passaged these viuses in the pesence o absence of intefeon pe-teatment. Hee, dms_tools was used to analyze and visualize the data to identify sites whee diffeent nucleotides ae pefeed in the pesence vesus the absence of intefeon. Because the mutations wee made at the nucleotide level, the data must also be analyzed at that level unlike in Figues 2, 3, and 5, whee codon mutagenesis means that the data can be analyzed at the amino-acid level. The plot can be geneated as logoplot.pdf with the following commands: dms_infediffpefs input.txt contol.txt intefeon.txt diffpefs.txt --ncpus -1 --chatype DNA dms_logoplot diffpefs.txt logoplot.pdf --npeline 68 --diffpefheight 0.4.

12 Bloom BMC Bioinfomatics :168 Page 12 of 13 to be tue if the stating libay has aleady been subjected to some selection, but we lack a ationale fo a moe infomative pio. The aveage mutation fequency in the stating libay is f stat = 1 1 L N stat n stat,x ξ m, m 1 34 x =wt and so f a,stat =, stat ] N x 1 + δ x,wt [1 f stat,. 35 Implementation The pogam dms_infediffpefs in the dms_ tools package infes the diffeential pefeences by pefoming MCMC ove the posteio defined by the poduct of the likelihoods and pios in Equations 24, 25, 26, 27, 28, 29, 30, and 31. The MCMC is pefomed as descibed fo the pefeences, and chaactes can again be any of nucleotides, amino acids, o codons. The pogam dms_logoplot visualizes the posteio mean diffeential pefeences via an extension to weblogo [34]. In addition, dms_infediffpefs ceates text files that give the posteio pobability that π,x > 0o< 0. Theseposteiopobabilitiesaenot coected to account fo the fact that multiple sites ae typically being examined, although by default the infeences ae made using the egulaizing pio in Equation 31. Infeing diffeential pefeence with dms_tools To test the accuacy of diffeential pefeence infeence by dms_tools, I simulated an expeiment like that in Figue 1B with the stating counts based on Melnikov et al. s actual deep mutational scanning data of a Tn5 tansposon [10]. As shown by Figue 5, dms_infediffpefs accuately infes the diffeential pefeences at typical expeimental depths. The esults ae easily visualized with dms_logoplot. To povide a second illustation of diffeential pefeences, Figue 6 shows an analysis of the data obtained by Wu et al. when they pefomed an expeiment like that in Figue 1B on nucleotide mutants of the influenza NS gene in the pesence o absence of intefeon teatment. Conclusions dms_tools is a feely available softwae package that uses a statistically pincipled appoach to analyze deep mutational scanning data. This pape shows that dms_tools accuately infes pefeences and diffeential pefeences fom data simulated unde ealistic paametes. As the figues illustate, dms_tools can also be applied to actual data with a few simple commands. The intuitive visualizations ceated by dms_tools assist in intepeting the esults. As deep mutational scanning continues to polifeate as an expeimental technique [1], dms_tools can be applied to analyze the data fo puposes such as guiding potein engineeing [3,10], undestanding sequence-stuctue-function elationships [4,5,7,14,21], infoming the development of bette evolutionay models fo sequence analysis [9,25], and pobing the biology of viuses and cells [6,8,11-13,18]. Availability and equiements Poject name: dms_tools Poject home page: Documentation and installation instuctions: Souce code: tools Opeating systems: Linux Pogamming language: Python Othe equiements: pystan, weblogo License: GNU GPLv3 Restictions to use by non-academics: None Data and code fo figues in this pape The data and compute code used to geneate the figues ae invesion 1.01of thedms_tools souce code which is tagged on Github at tools/tee/1.0.1 in the examples subdiectoy. The LaTex souce fo this pape is in the pape subdiectoy. Competing inteests The autho declaes that he has no competing inteests. Authos contibutions JDB designed the algoithms, wote the softwae, pefomed the analyses, and wote the pape. Acknowledgements Thanks to Alec Hecket fo assistance in testing dms_tools, to Eick Matsen fo the excellent suggestion to use pystan fo MCMC, to Nicholas Wu fo poviding the mutational counts data fom [13], and to O Ashenbeg and Hugh Haddox fo helpful comments on the manuscipt. This wok was suppoted by the NIGMS of the NIH unde gant R01GM Received: 9 Januay 2015 Accepted: 22 Apil 2015 Refeences 1. Fowle DM, Fields S. Deep mutational scanning: a new style of potein science. Nat Methods. 2014;118: Fowle DM, Aaya CL, Fleishman SJ, Kellogg EH, Stephany JJ, Bake D, et al. High-esolution mapping of potein sequence-function elationships. Nat Methods. 2010;79: Taxlmay MW, Hasenhindl C, Hackl M, Stadlmay G, Rybka JD, Both N, et al. Constuction of a stability landscape of the CH3 domain of human IgG1 by combining diected evolution with high thoughput sequencing. J Mol Biol. 2012;423: McLaughlin J RN, Poelwijk FJ, Raman A, Gosal WS, Ranganathan R. The spatial achitectue of potein function and adaptation. Natue. 2012; :138.

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