Accounting for Background Nucleotide Composition When Measuring Codon Usage Bias

Transcription

1 Letter to the Editor Accounting for Bcground Nucleotide Composition When Mesuring Codon Usge Bis John A. Novembre Deprtment of Integrtive Biology, University of Cliforni Bereley The phenomenon of codon usge bis hs been importnt in the study of evolution becuse it provides exmples of we selection woring t the moleculr level. During the lst two decdes, evidence hs ccumulted tht some exmples of codon usge bis re driven by selection, prticulrly for species of fungi (e.g., Bennetzen nd Hll 198; Iemur 1985), bcteri (e.g., Iemur 1981; Shrp nd Li 1987), nd insects (e.g., Ashi 1997; Moriym nd Powell 1997). This connection between codon usge bis nd selection hs been importnt in stimulting the development of lterntives to strictly neutrl theories of moleculr evolution (Oht nd Gillespie 1996; Kreitmn nd Antezn 000). Uncertinty persists, however, regrding the phylogenetic distribution of codon usge bis (such s whether selection-bsed codon usge bis is present in mmmls; e.g., Krlin nd Mrze 1996; Iid nd Ashi 000; Sueo nd Kwnishi 000; Smith nd Eyre- Wler 001; Urruti nd Hurst 001). Questions lso remin s to wht models of selection underlie codon preferences (Kreitmn nd Antezn 000), nd specificlly whether the presence of suboptiml codons is the result of muttion nd drift, vrition in selection pressure cross sites, or ntgonistic selection pressures (Smith nd Eyre-Wler 001b). For investigting certin questions regrding the evolution of codon usge bis, it is useful to hve summry sttistic describing the pttern of codon usge cross ll mino cids. Mny summry sttistics hve lredy been developed to describe the ptterns of codon usge. They cn be divided roughly into two clsses (Comeron nd Agude 1998). One clss summrizes the usge of certin preferred codons, nd the other compres every codon s usge to null distribution (typiclly uniform usge of synonymous codons). The former clss of methods hs the disdvntge tht it requires prior nowledge of the preferred codons. With summry sttistics one cn explore generl ptterns, such s the reltionship of codon usge bis to recombintion rte, gene length, or synonymous substitution rte. Observing brod ptterns such s these hs lredy provided insight into the evolutionry dynmics of codon usge bis (Klimn nd Hey 1993; Ashi nd Eyre-Wler 1998; Kreitmn nd Comeron 1999). Abbrevitions: ENC, effective number of codons. Key words: codon usge bis, bcground nucleotide composition, muttion bis. Address for correspondence nd reprints: John A. Novembre, Deprtment of Integrtive Biology, University of Cliforni Bereley, VLSB 3060, Bereley, Cliforni E-mil: novembre@ socrtes.bereley.edu. Mol. Biol. Evol. 19(8): by the Society for Moleculr Biology nd Evolution. ISSN: Of the summry sttistics tht do not require nowledge of preferred codons, the effective number of codons (ENC, or Nˆ c s proposed by Wright 1990) hs been found to be the most sttisticlly well behved, in tht it is the lest ffected by short gene lengths (Comeron nd Agude 1998). Nˆ c is inversely proportionl to the extent of nonuniform codon usge. It tes the vlue of 61 when ll codons re being used with equl frequency, nd its vlue decreses s codon usge becomes less uniform. It is intuitively ccessible becuse its vlue is intended to correspond to the number of codons being used in sequence. One limittion of Nˆ c is tht mesuring the deprtures from uniform codon usge is not lwys desirble. Knowledge of bcground nucleotide composition ptterns my suggest null distribution of codon usge tht is nonuniform. For instnce, in Drosophil, where the bcground nucleotide composition is 60% AT, one might lie to mesure how fr codon usge deprts from 60% usge of AT-ending codons. Indeed, ccounting for bcground nucleotide composition when studying codon usge hs been recognized s being importnt (Ashi, Klimn, nd Eyre-Wler 1998; Mris, Mouchiroud, nd Duret 001; Urruti nd Hurst 001). Ting composition into ccount is prticulrly importnt for phylogenetic studies of codon usge bis where comprisons re mde mong species with differing bcground nucleotide compositions or for studies of codon usge bis in genomic regions tht my differ in bcground nucleotide composition. If not ten into considertion, differences in bcground nucleotide composition might led one to conclude tht differences in codon preference exist when they do not. The deprture of Nˆ c from 61 becuse of vrition in bcground nucleotide composition ws recognized by Wright nd described s the following reltionship between the third position GC content (f GC ) nd Nˆ c: 9 ˆN c fgc. f (1 f ) Using this reltionship one cn plot the expected vlue of Nˆ c versus the GC content. Such plots re nown s Nˆ c-plots (e.g., see fig. in Wright 1990). Points tht fll below the bell-shped line suggest devitions from null model of no-codon preferences. Unfortuntely, studying such ptterns does not hve cler sttisticl bsis nd detrcts from the vlue of Nˆ c s quntittive summry sttistic. Other codon usge bis summry sttistics such s Ashi s scled (Ashi 1995), the mximum-lielihood codon bis sttistic (MCB; Urruti nd Hurst GC GC 1390

2 Letter to the Editor ), nd B*() (Krlin nd Mrze 1996) ccount for bcground nucleotide composition. However, s presented below, these sttistics re ffected strongly by the sequence lengths being studied. Clerly, it would be useful to hve sttistic similr to Nˆ c tht hs low sequence-length effects but tht relxes the ssumption of equl usge of ll synonymous codons. Here, sttistic ( ˆN c ) is presented tht ccounts for bcground nucleotide composition nd is minimlly ffected by sequence length. The sttistic is bsed on Person s X sttistics nd describes the deprture of the observed codon usge from some expected distribution. The expected distribution cn be derived from nowledge of the bcground nucleotide composition. When uniform usge of codons is expected, ˆN c reduces to Nˆ c. Lie Nˆ c, ˆN c is reltively insensitive to sequence length. The properties of ˆN c re tested on simulted sequences, nd compred with relted summry sttistics. The results suggest tht ˆN c is useful for studying codon usge mong sequences tht vry in bcground nucleotide composition. To understnd the construction of ˆN, c it is first necessry to provide bcground on Nˆ c. Nˆ c, or the ENC (Wright 1990), is derived by ming n nlogy with the effective number of lleles n e t locus (Kimur nd Crow 1964). An estimte of n e is nˆe 1/Fˆ, where Fˆ is n estimte of the expected heterozygosity t the locus. For quntifying codon usge bis t n mino cid, Wright defined n estimte of the homozygosity of codon usge s follows: i i1 ˆF n p 1 (n 1) (1) Here, p i is the frequency of the ith codon, is the number of synonymous codons for the mino cid of interest, nd n is the observed number of codons for the mino cid. The verge of the Fˆ for ech r-fold redundncy clss (e.g., onefold, twofold, threefold, fourfold, sixfold) is then computed: 1 ˆF F ˆ r () n RC RC where n RC is the number of mino cids in the RC redundncy clss. Finlly, Nˆ c is computed s follows: Nˆ (9/ ˆF ) (1/ ˆF ) (5/ ˆF ) (3/ ˆF c 3 5 6). (3) The clcultion of Nˆ c cn lso be expressed more generlly s Nˆ n / ˆF (4) c r r r ARC where ARC is the set of ll redundncy clsses, nd n r is the number of mino cids in the redundncy clss. For ny prticulr mino cid we cn lso compute n Nˆ c vlue tht is simply 1/Fˆ, where Fˆ is the homozygosity of codon usge for tht prticulr mino cid. To derive ˆN c nd show its reltionship to Nˆ c, I use Person s X sttistics to quntify the deprture of ech codon s usge (p i ) from some expected usge (e i ) for ech mino cid. The expected usge of codons cn be clculted in number of wys, including using mono-, di-, or trinucleotide frequencies. The sttistic for ech mino cid,, is clculted s n (p e ) i i i1 ei X F ˆ X n X. Using the X vlues, is defined s follows: ˆF. (5) (n 1) The clcultions from here on mirror those of Nˆ c. The F ˆ vlues re verged for ech redundncy clss ( ˆF r) nd used to clculte ˆN: c N ˆ n / ˆF. (6) c r r r ARC Note tht becuse X is distributed, the expected vlue of Fˆ will be 1/ when the codon usge mtches the expected usge pttern. Using the -method, it cn lso be shown tht the expected vlue of ˆN c will be equl to 61 for the stndrd genetic code. Notbly, ˆN c simplifies to Nˆ c when synonymous codons re expected to be in equl frequency. In this cse the e i re ll 1/, nd the X sttistic for ech mino cid reduces to i i1 X n p n. (7) Substitution of this X into the eqution for F (eq. 5) produces ˆ i i1 ˆF n p 1 (n 1). (8) This vlue of ˆF is equl to the Fˆ used by Wright in the clcultion of Nˆ c (eq. 1). Becuse the clcultion of N ˆ mtches tht of Nˆ c once ˆ is obtined, ˆ c F Nc is equivlent to Nˆ c when uniform usge is expected. This derivtion shows tht ˆN c is generliztion of Nˆ c to the cse in which expected codon usge is not uniform. Wheres Nˆ c is implicitly bsed on n expected distribution of uniform usge, ˆN c cn hve the expected proportions of synonymous codon usge given by the bcground nucleotide composition. ˆN c will decrese from 61 when the codon usge does not mtch the distribution predicted by nucleotide composition. In contrst, Nˆ c will decrese from 61 whenever the codon usge deprts from uniform usge of ech synonymous codon. The result is tht the vlue of ˆN c should be less dependent on nucleotide composition nd more dependent on the codon preferences tht go beyond those cused by unequl nucleotide composition. In the prcticl implementtion of both Nˆ c nd ˆN c, cre must be ten to exclude Fˆ vlues tht re undefined or equl to zero, which occurs when mino cids re rre or missing (see Wright 1990). The clcultions presented subsequently follow Wright s suggestion tht if no threefold redundnt codons re observed, one should verge ˆF nd to obtin ˆF 4 ˆF 3. If other -fold redundncy clsses re unobserved, ˆF is ssumed to equl 1/. Such

3 139 Novembre Tble 1 Nucleotide Compositions Used for the Simulted Sequences None Low-1 Low- Med-1 Med- High-1 High- f A... f G... f C... f T FIG. 1. Summry sttistic vlues reltive to their vlues when nucleotide compositions re equl. n ssumption is conservtive with regrd to mesuring strong codon usge bis. Finlly, in the clcultion of ˆF we exclude mino cids tht re observed fewer thn five times. Here, these methods of deling with missing dt re pplied eqully to the clcultion of both Nˆ c nd ˆN c. To explore the properties of the sttistics Nˆ c nd ˆN, c pseudorndomly generted coding sequences were generted for vrious lengths nd nucleotide compositions. Amino cids were chosen uniformly, nd codon usge ws ssumed to be multinomil with proportions determined by the nucleotide composition. The bcground nucleotide composition estimtes re given s f A, f C,f G, nd f T for denine, cytosine, gunine, nd thymine, respectively. For exmple, for codon i tht hs the sequence CAT, the expected frequency ws clculted s e i f C f A f T /K, where K is renormliztion constnt for ensuring the e i for n mino cid sum to one. A rnge of nucleotide compositions were used to generte the sequences (Tble 1). The nucleotide compositions re modeled fter those used in study by Comeron nd Agude (1998) nd contin conditions corresponding to different levels of bcground GC-AT content. The compositions lso vry in their degree of GC sew (Lobry 1996; Shioiri nd Tht 001). The Low-, Med-, nd High- hve higher GC sew reltive to Low-1, Med-1, nd High-1, respectively. For ech composition nd gene length, 10,000 sequences were generted. The men nd vrince of the Nˆ c nd ˆN c sttistics were clculted for ech set of sequences. To compre the performnce of Nˆ c nd ˆN c with other summry sttistics tht incorporte the effects of bcground nucleotide composition, Ashi s scled sttistic (Ashi 1995), the MCB sttistic of Urruti nd Hurst (001), s well s the B*() mesure proposed by Krlin nd Mrze (1996) were lso computed for ech sequence. Ech of these mesures ttempts to ccount for bcground nucleotide composition. In the implementtion of these clcultions the sme expected vlues tht re used for clculting ˆN c re used for the scled nd B*() mesures. For clculting MCB the expected vlues were generted ccording to the method given by Urruti nd Hurst (001). For the sequence lengths of 150 nd 10 bp, there ws insufficient dt for the Urruti nd Hurst expecttions to be computed, nd so MCB ws not clculted for these sequence lengths. Figure 1 shows the men vlues of the vrious bis sttistics for sequences of 7,500 bp for the vrious bcground nucleotide compositions. The men vlues re shown reltive to their men vlues with uniform nucleotide composition. As expected when the nucleotide frequencies re uniform, Nˆ c nd ˆN c re equl, nd both shre vlue of 61. However, s the unevenness in the bcground nucleotide composition increses, the men vlue of Nˆ c decreses, wheres tht of ˆN c remins reltively constnt. The vlue of ˆN c is nerly 61 for ll nucleotide composition conditions, wheres tht of Nˆ c rnges from 61 with equl nucleotide compositions to nerly 6 when the compositions re highly nonuniform. It is lso worth noting tht Nˆ c is prticulrly sensitive to GC sew. The vlue of Nˆ c is on verge nine units smller for the composition sets with high GC sew thn for those with none. Lie ˆN, c scled nd MCB remin constnt over vrious nucleotide composition sets. The B*() sttistic remins nerly constnt for modest levels of unevenness in nucleotide composition but increses for the medium nd high levels. The sttistics were lso studied over rnge of gene lengths to observe the effects of gene length. Figure represents the vlues of ech sttistic reltive to their vlues t 7,500 bp. At short sequence lengths (less FIG.. Summry sttistic vlues reltive to their vlues t 7,500 bp. Sequences were generted with the Medium- composition set. Results for other composition sets re qulittively similr.

4 Letter to the Editor 1393 FIG. 3. CVs for the vrious summry sttistics pplied to sequences generted with the Medium- composition set. Results for other composition sets re qulittively similr. thn 600 bp), the vlues of Nˆ c nd ˆN c re higher thn their symptotic vlues. In generl, however, the symptotic vlue is well pproximted when the gene length reches 600 bp. In contrst, the vlues of scled, MCB, nd B*() do not closely mtch their symptotic vlues even t long sequence lengths (3,000 bp). Figure 3 shows the coefficients of vrition (CVs) for the vrious summry sttistics. For sequence lengths of bove 600 bp the order of the sttistics in terms of incresing CV is ˆN, c Nˆ c, B*(), scled, nd MCB. Below 600 bp the behvior of ech method s CV becomes complicted by the wys in which ech mesure hndles the missing vlues. These results show tht the sttistic ˆN c performs well in terms of ccounting for nucleotide composition, being the lest ffected by gene length nd hving low CV. Although ˆN c differs from Nˆ c, they re similr enough in some cses so tht using ˆN c rther thn Nˆ c my not lwys produce different results. For exmple, renlysis with ˆN c of dt from Dunn, Bielwsi, nd Yng (001) on the reltionship between Drosophil substitution rtes nd codon usge bis produced results tht re qulittively similr to those from the originl nlysis with Nˆ c (dt not shown). However, in other cses the difference between Nˆ c nd ˆN c will be importnt. For exmple, difference in Nˆ c of 10 my be seen s biologiclly significnt (e.g., Moriym nd Powell 1997, 1998). At tht resolution the results presented here show tht using ˆN c with nonuniform expecttions will result in considerble difference if the GC or AT content is on the order of 85%. Such nucleotide composition is extreme in nture nd is found genome-wide in protozon species, such s Plsmodium flciprum (Grdner et l. 1998), or in mitochondril genomes of rthropods, such s Drosophil, Anopheles, Bombyx, nd Apis (Shioiri nd Tht 001). In ddition, the results presented here show tht the presence of nucleotide composition sew will ffect the vlue of Nˆ c, to chnge it even more from tht of ˆN. c If differences of less thn 10 in the vlue of Nˆ c re of interest, then using ˆN c rther thn Nˆ c is importnt for even lower levels of unevenness in nucleotide composition. For instnce, nucleotide composition of pproximtely 35% GC or AT cn cuse the vlue of Nˆ c to chnge by five units reltive to equl usge. In ddition, modest levels of GC sew, such s in composition set Low-, cn cuse the vlue of Nˆ c to chnge by five units reltive to no sew. Using ˆN c with nonuniform expecttions will be prticulrly dvntgeous when compring codon usge bis mong sequences from genomic regions tht vry significntly in bcground nucleotide composition. Such vrition is especilly notble in mmmls nd birds, where vrition in nucleotide composition is structured into isochores (Bernrdi et l. 1985). In ddition, ˆN c my lso be useful in comprtive studies of codon usge bis in which the species being studied hve substntilly different nucleotide compositions. In summry, this pper hs introduced summry sttistic of codon usge bis ( ˆN c ) tht incorportes vrition in bcground nucleotide composition mong sequences. Simultions show tht reltive to the vilble sttistics, ˆN c effectively djusts for bcground nucleotide composition, is the lest ffected by gene length, nd hs low CV. With its use the nlysis of codon usge bis cn be ccomplished without the confounding effects of vrition in nucleotide composition. A freely distributble progrm tht clcultes both Nˆ c nd ˆN c is vilble on the Web pge: bereley.edu/lbs/sltin/softwre.html. Acnowledgments The uthor thns Josh Herbec nd Montgomery Sltin for helpful discussions, Arxi Urruti for discussion nd for providing the script to clculte MCB, nd two reviewers for their comments. The reserch ws supported by Howrd Hughes Medicl Institute Predoctorl Fellowship nd the Ntionl Institutes of Helth (NIH GM-408 to M. Sltin). LITERATURE CITED AKASHI, H Inferring we selection from ptterns of polymorphism nd divergence t silent sites in Drosophil DNA. Genetics 139: Distinguishing the effects of muttionl bises nd nturl selection on DNA sequence vrition. Genetics 147: AKASHI, H., nd A. EYRE-WALKER Trnsltionl selection nd moleculr evolution. Curr. Opin. Genet. Dev. 8: AKASHI, H., R. KLIMAN, nd A. EYRE-WALKER Muttion pressure, nturl selection, nd the evolution of bse composition in Drosophil. Genetic : BENNETZEN, J., nd B. HALL Codon selection in yest. J. Biol. Chem. 57: BERNARDI, G., B. OLOFSSON, J. FILIPSKI, M. ZERIAL, J. SALI- NAS, G.CUNY, M.MEUNIER-ROTIVAL, nd F. RODIER

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