BACKGROUND
translational selection on synonymous codon use is indicated if frequencies of preferentially used, 'optimal', codons increase with expression level and correspond to the most abundant trna or to the trna with which they form the strongest binding - for several organisms, this seems to be the case .
additional support for a beneficial role of certain 'optimal' codons in translation comes from laboratory studies  <cit> .
translational selection may act to maximise the speed of elongation, minimize the costs of proofreading or maximise the accuracy of translation  <cit> , and depending on the selective target, one can test further distinct predictions.
under selection for translational accuracy we expect for example:  selection against translational errors to relate to the error's costs.
as costs of an erroneous protein should accrue with each added amino acid during protein synthesis, one may expect long genes to experience higher optimal codon use than short genes  <cit> .
supporting selection for translational accuracy, in e. coli and yeast, relative optimal codon use indeed increases with gene length  <cit> .
we also expect selection against translational errors to relate to the error's functional effect: translational errors for some amino acids may have no functional effects, while for other amino acids, translational errors render a protein non-functional.
the latter should be under stronger selection for translational accuracy.
as akashi  <cit>  points out, the functional importance of amino acid site may be approximated by its evolutionary conservation.
under translational selection for accuracy one may hence expect higher optimal codon frequencies at conserved than at non-conserved amino acid sites.
this is indeed the case in d. melanogaster, c. elegans, e. coli  <cit> ; a recent study  <cit>  indicates this pattern may also apply to mouse and human using a modified measure of optimal codons.
however, surprisingly, in d. melanogaster, c. elegans, a. thaliana, and humans, optimal codon use decreases with gene length, thereby opposing the prediction under selection for translational accuracy  <cit> .
this decrease is particularly surprising for species, in which selection for translational accuracy is indicated by the aforementioned higher optimal codon use at conserved amino acid sites.
the explanation may be that the negative correlation between optimal codon use and gene length simply is a side effect: highly expressed genes with high optimal codon use tend to be short, possibly to be more economic  <cit> .
yet, while control of expression level affects the correlation of optimal codon use with gene length in yeast, causing a change from negative to positive  <cit> , in d. melanogaster, c. elegans, a. thaliana or humans, the negative correlation of optimal codon use with gene length does not seem to be due to a correlation of gene length with expression level only  <cit> .
two explanations for the negative correlation have been proposed, both of which are based on translational selection.
first, under selection for translational efficiency, selection for optimal codons may decrease with gene length due to the decrease in the relative fitness effect per optimal codon  <cit> .
the second hypothesis invokes hill-robertson interference  <cit> , which considers the reduction in selective efficacy due to linkage among sites: weakly or strongly selected sites that evolve adaptively or under constraints may affect evolutionary dynamics of linked sites.
as comeron et al.
<cit>  suggest selection efficacy on optimal codons may decrease with gene length, as long genes with higher numbers of potentially interfering sites may experience a stronger hill-robertson effect.
the hill-robertson effect has been considered for various effects on synonymous codons .
as recombination breaks down linkage, the observed positive correlation of optimal codon use with recombination rate was taken as support for the hill-robertson effect reducing the efficacy of translational selection on optimal codons  <cit> .
yet, optimal codons in several metazoans, such as the ones for which the negative correlation was first reported for, i.e.
d. melanogaster, c. elegans and a. thaliana, but also for humans are mostly ending with g or c  , and compositionally biased mutation or repair processes may indirectly affect optimal codon use.
recombination-dependent repair  is indeed biased towards -gc in many organisms including yeast, mice, humans and drosophila  <cit> , and hence may be the potential force.
effects of gc-biased gene conversion will be most obvious at sites that evolve neutrally or under weak selection, and the substitution patterns it leaves resembles that of directional selection .
gc-biased gene conversion has been indicated to affect optimal codon use before: optimal codon frequencies increase with recombination rate, a patterns consistent with population genetic predictions under translational selection on optimal codons  <cit> .
however, in d. melanogaster and c. elegans not only optimal codon frequencies increase with recombination, but also non-optimal ones, as long as they end with -gc  <cit> .
the positive correlation of non-optimal gc-ending codon frequencies with recombination indicates the observed positive correlation optimal  codons - that was taken as evidence for reduced efficacy of translational selection due to hill-robertson interference - is likely affected by compositionally biased processes such gc-biased gene conversion  <cit> .
whether or not gc-biased gene conversion or hill-robertson effects the positive correlation between optimal codons and recombination attracted controversy , but with respect to the observed negative correlation of optimal codon use with gene length, gc-biased gene conversion has never been considered.
the negative correlation of optimal codon use with gene length is found in organisms whose optimal codons are biased towards gc-ending ones, and may hence be caused by forces acting on optimal codons or on base composition.
as translational selection affects optimal codons, while a compositional bias like gene conversion affects gc-ending codons, one may disentangle the effects by looking at optimal and non-optimal gc- and at-ending codons separately.
saccharomyces cerevisiae is a good organism to disentangle the two forces because translationally optimal codons are not biased towards gc-ending ones as in the above mentionned organisms.
furthermore, translational selection and gc-biased gene conversion are comparably well-studied and supported in s. cerevisiae .
results of this study demonstrate in s. cerevisiae the frequency of gc-ending  codons decreases with gene length and increases with recombination.
also a decrease of gc-ending codons along genes is indicated.
this distinction between at- and gc-ending codons cannot be explained by variation in strength and efficiency of translational selection, while gc-biased gene conversion may explain the observation.
substitutions at four-fold degenerated sites differ between at->gc and gc->at changes, further supporting an effect of gc-biased gene conversion.
initiation of gene conversion events in promoter regions and the presence of a gene conversion gradient most likely explain the observed decrease of gc-ending codons with gene length and gene position.
RESULTS
difference between optimal codons depending on whether they end with -at or -gc
to disentangle forces affecting base compositions  from translational selection on optimal codons, one can compare optimal gc-ending and optimal at-ending codons.
as expected under translational selection, all optimal codons independent of their third nucleotide increase with gene expression .
as expected under gc-biased gene conversion, only the frequency of gc-ending optimal codons increases with recombination, at-ending optimal codons however tend to be negatively or not significantly correlated with recombination .
crucially with respect to gene length, only the relative frequencies of at-ending optimal codons increase with gene length as one may expect under selection for translational accuracy.
in contrast, the relative frequencies of gc-ending optimal codons decrease with gene length.
this is true for individual amino acids, as well as for groups of amino acids with either at-or with gc-ending optimal codons .
this distinction between optimal at- and optimal gc-ending codons indicates an effect related to base composition.
ala
nco:- <dig> ns
spo11:- <dig> ***
dmc1:- <dig> *
mre110:+ <dig> ns
arg
nco:+ <dig> ns
spo11:+ <dig> ns
dmc1:+ <dig> ns
mre110:+ <dig> ns
cys
nco:- <dig> ns
spo11:- <dig> ns
dmc1:+ <dig> ns
mre110:+ <dig> ns
gln
nco:- <dig> *
spo11:- <dig> ns
dmc1:- <dig> ***
mre110:- <dig> ns
glu
nco:- <dig> *
spo11:- <dig> **
dmc1:- <dig> ***
mre110:- <dig> ns
gly
nco:+ <dig> ns
spo11:+ <dig> ns
dmc1:+ <dig> ns
mre110:+ <dig> **
pro
nco:- <dig> ns
spo11:+ <dig> ns
dmc1:- <dig> ns
mre110:+ <dig> ns
grouped
n =  <dig> codons
r <dig> =  <dig> ***
p***,p***,
mco:- <dig> *
spo11:- <dig> ***
dmc1:- <dig> ***
mre110:- <dig> *
leu
nco:+ <dig> ***
spo11:+ <dig> ***
dmc1:+ <dig> ***
mre110:+ <dig> ***
asn
nco:+ <dig> ***
spo11:+ <dig> ***
dmc1:+ <dig> ***
mre110:+ <dig> ***
asp
nco:+ <dig> ***
spo11:+ <dig> ***
dmc1:+ <dig> ***
mre110:+ <dig> ***
tyr
nco:+ <dig> ***
spo11:+ <dig> ***
dmc1:+ <dig> ***
mre110:+ <dig> ***
phe
nco:+ <dig> ***
spo11:+ <dig> ***
dmc1:+ <dig> ***
mre110:+ <dig> ***
lys
nco:+ <dig> ***
spo11:+ <dig> ***
dmc1:+ <dig> ***
mre110:+ <dig> ***
his
nco:+ <dig> ***
spo11:+ <dig> ***
dmc1:+ <dig> ***
mre110:+ <dig> ***
grouped
n =  <dig> codons r <dig> =  <dig> ,
p***,p***
nco:+ <dig> ***
spo11:+ <dig> ***
dmc1:+ <dig> ***
mre110:+ <dig> ***
spearman rank correlations between optimal codon use, gene length, expression, and various recombination measures for amino acids and groups of amino acids with either at- or with gc-ending optimal codons.
<dig> genes for which all amino acids were present at least four times were used.
presented for grouped variables are also mr results of variables whose log-transformation did not grossly deviate from a normal distribution.
*p <  <dig> , **p <  <dig> ,***p <  <dig> , ns = not significant.
interrelated variables such as expression level may affect correlations between codon use and gene length.
to control for all possible interrelated variables, and especially for noisy variables such as expression level is not easy  <cit> .
however, as the same genes were used for comparing at- and gc-ending optimal codons, a control of other variables is not necessary to highlight their difference.
at- and gc-ending optimal codons are sampled from the same distributions of other potentially affecting variables such as expression level.
the effect of gene expression  should hence affect them both similarly.
the major difference between at- and gc-ending optimal codons can hence be demonstrated by simple spearman rank correlation analyses: expression level should affect all  optimal codons similarly, while clearly, gc-ending codons differ from at-ending codons in their correlation with gene length and with recombination .
the opposing correlation of at- and gc-ending optimal codons with gene length and recombination indicates another force unrelated to translational selection is acting.
multiple regression  analysis between log-transformed fopgc or fopat estimates, gene length, expression and two different measures of recombination confirms independent effects of expression, recombination and gene length .
please be aware however that both, recombination and expression measures will be noisy and as plotkin and fraser  <cit>  highlight, one should not compare the explanatory power of predictors with standard regression techniques when the predictors contain different amounts of measurement noise.
effect of base composition independent of translational selection
for amino acids with at least two optimal or with at least two non-optimal codons, one can estimate the relative gc-content of either optimal or at non-optimal codons separately.
for amino acids which have two optimal codons, i estimate the frequency of gc-ending optimal codons relative to all optimal codons ; for amino acids which have at least two non-optimal codons, i estimate the frequency of gc-ending non-optimal codons relative to all non-optimal .
to look at optimal and non-optimal codons separately controls for translational selection.
the analysis supports an effect of base composition: relative frequencies of gc-ending codons  consistently decrease with gene length and increase with recombination .
for all but arg, the correlations are significant per amino acid; when grouped across respective amino acids, the decrease is significant for both fgcopt and fgcnon-opt .
ile
nco:+ <dig> ***
spo11:+ <dig> ***
dmc1:+ <dig> ***
mre110:+ <dig> ***
ser
nco:+ <dig> ***
spo11:+ <dig> ***
dmc1:+ <dig> ***
mre110:+ <dig> ***
thr
nco:+ <dig> ***
spo11:+ <dig> ***
dmc1:+ <dig> ***
mre110:+ <dig> **
val
nco:+ <dig> ***
spo11:+ <dig> ***
dmc1:+ <dig> ***
mre110:+ <dig> ***
grouped
n =  <dig> codons
r <dig> =  <dig> ***
nco:+ <dig> ***
spo11:+ <dig> ***
dmc1:+ <dig> ***
mre110:+ <dig> ***
ala
nco:+ <dig> ***
spo11:+ <dig> ***
dmc1:+ <dig> ***
mre110:+ <dig> ***
arg
nco:+ <dig> *
spo11:+ <dig> ***
dmc1:+ <dig> ***
mre110:+ <dig> *
gly
nco:+ <dig> ***
spo11:+ <dig> ***
dmc1:+ <dig> ***
mre110:+ <dig> ***
leu
nco:+ <dig> ***
spo11:+ <dig> ***
dmc1:+ <dig> ***
mre110:+ <dig> ***
pro
nco:+ <dig> ***
spo11:+ <dig> ***
dmc1:+ <dig> ***
mre110:+ <dig> **
thr
nco:+ <dig> ***
spo11:+ <dig> ***
dmc1:+ <dig> ***
mre110:+ <dig> **
ser
nco:+ <dig> ***
spo11:+ <dig> ***
dmc1:+ <dig> ***
mre110:+ <dig> ***
val
nco:+ <dig> ***
spo11:+ <dig> ***
dmc1:+ <dig> ***
mre110:+ <dig> ***
grouped
n =  <dig> codons
r <dig> =  <dig> ***
p***,p***
p***,
nco:+ <dig> ***
spo11:+ <dig> ***
dmc1:+  <dig> ***
mre110:+  <dig> ***
spearman rank correlations between the frequency of gc-ending optimal or non-optimal codons with gene length, expression, and various recombination measures.
for each amino acid, only genes were used for which at least  <dig> optimal or  <dig> non-optimal codons were present respectively.
presented for grouped variables are also mr results of variables whose log-transformation did not grossly deviate from a normal distribution.
*p <  <dig> , **p <  <dig> ,***p <  <dig> , ns = not significant.
notably, the analysis also indicates expression may affect the frequencies of gc-ending codons: controlling for translational selection, gc-ending codons, fgcopt and fgcnon-opt, increase with expression level.
this may be a side effect: first, in yeast, recombination and gene expression seem coupled  <cit>  and secondly, highly expressed genes tend to be short  <cit> .
however, it may also reveal some selective force: gc-ending codons affect for example thermodynamic stability and hence mrna secondary structures which may be under selection  <cit>  .
mr analysis between log-transformed variables supports independent effects of gene length, expression and recombination for the grouped data .
effect of gene position on relative codon frequencies
intragenic variation in codon use exists: optimal codons may for example increase along genes due to selection against non-sense errors  <cit> ; also a decrease of gc-content along genes has been described  <cit> .
to investigate an effect of gene position, i look at the four different measures of tables  <dig> and  <dig> for grouped amino acids:
fopgc = frequency of optimal codons relative to all synonymous codons, but only for amino acids which have optimal codons that end with g or c;
fopat = frequency of optimal codons relative to all synonymous codons, but only for amino acids which have optimal codons that end with a or t;
fgcopt = frequency of gc-ending optimal codons relative to all optimal codons; only for amino acids which have two optimal codons, one ending with g or c the other with a or t;
fgcnon-opt = frequency of gc-ending non-optimal codons relative to all non-optimal; only for amino acids which have at least two non-optimal codons, one ending with g or c and one with a or t.
results show that optimal codons  tend to increase with gene position, and gc-ending ones  tend to decrease .
the result remains excluding the first  <dig> codons that often appear to be under different pressures  <cit> .
the non-significant result for fopgc may be due to conflicting pressures: optimal codons tend to increase while gc-ending codons tend to decrease.
the non-significant result of fgcopt may be due to dominant selection on optimal codons that is stronger than additional compositional forces.
fopat
fopgc
fgcopt
fgcnon-opt
spearman rank analysis of frequencies of optimal and gc-ending codons with gene position for position numbers 1- <dig> and 49- <dig>  *p <  <dig> , **p <  <dig> ,***p <  <dig> , ns = not significant.
an increase  of certain codons along genes will as a side effect cause a positive  correlation of these codons with gene length  <cit> .
to control for this effect of gene position, i take genes that are greater than  <dig> codons and only consider the level of bias in those codons from number  <dig> up to codon number  <dig>  <cit> .
i repeat the two previous analyses  for the grouped data.
the general patterns that gc-ending codons tend to decrease with gene length and increase with recombination remains, but becomes non-significant for the correlation between fgcnon-opt and gene length .
the positive correlation between fopat and gene length disappears indicating selection for translational accuracy may mainly act against non-sense errors .
the two measures that showed no significant effect of gene position, fopgc and fgcopt  remain significantly negative correlated after the control of gene position .
mr analysis of log-transformed variables indicates no independent effect of gene length for any codon class after controlling for position .
the results hence support that gc-ending codons tend to decrease along genes, and that this decrease along genes contributes considerably to the negative correlation of gc-ending codons with gene length.
fopat
n =  <dig> codons
r <dig> =  <dig> ***
pns,p***,
nco:- <dig> ***
spo11:- <dig> ns
dmc1:- <dig> ***
mre110:- <dig> *
fopgc
n =  <dig> codons
r <dig> =  <dig> ***
pns, p***,
p*,
nco:+ <dig> ***
spo11:+ <dig> ***
dmc1:+ <dig> ***
mre110:+2648***
fgcopt
n =  <dig> codons
r <dig> =  <dig> ***
nco:+ <dig> ***
spo11:+ <dig> ***
dmc1:+ <dig> ***
mre110:+ <dig> ***
fgcnon-opt
n =  <dig> codons
r <dig> =  <dig> ***
pns, p***
nco:+ <dig> ***
spo11:+ <dig> ***
dmc1:+ <dig> ***
mre110:+ <dig> ***
spearman rank correlations between frequencies of optimal and gc-ending codons with gene length, expression, and various recombination measures after controlling for a potential effect of gene position.
the same  <dig> genes were used for all measures.
presented are also mr results of variables whose log-transformation did not grossly deviate from a normal distribution.
*p <  <dig> , **p <  <dig> ,***p <  <dig>
substitution rates and patterns
for both, gc-biased gene conversion as well as translational selection, we may not only expect relative codon frequencies to mirror the respective forces, but also substitution patterns.
to disentangle the effect of gene conversion from translational selection, i take four-fold degenerated changes that do not change the non-optimal codon status and estimate four rates of substitutions at->gc, gc->at, at->at, and gc->gc.
under gc-biased gene conversion, we expect an increase of at->gc  with recombination.
as for the relative frequencies, the same genes are used for comparison, so a control of other variables should not be necessary to highlight their differences.
however, while differences with respect to recombination can indeed be observed, a general decrease of all substitution rates with gene expression  confounds the observation .
higher expressed  genes appear more constraint even at non-optimal sites and indicate again beneficial roles of non-optimal codons for gene expression.
at -> gc
n =  <dig> conserved,  <dig> changes
r <dig> =  <dig> ***
p***,p**
nco:+ <dig> ns
spo11:+ <dig> ns
dmc1:+ <dig> ns
mre110:+ <dig> ns
gc -> at
n =  <dig> conserved,  <dig> changes
r <dig> =  <dig>  068***
p***,p**
nco:- <dig> **
spo11:- <dig> ***
dmc1:- <dig> ***
mre0:- <dig> ***
gc -> gc
n =  <dig> conserved,  <dig> changes
r <dig> =  <dig> ***
p***,pns,
nco: + <dig> ns
spo: + <dig> ns
dmc1:- <dig> ns
mre0:+ <dig> ns
at -> at
n =  <dig> conserved,  <dig> changes
r <dig> =  <dig> ***
p***,p***,
nco:- <dig> *
spo:- <dig> **
dmc1:- <dig> ***
mre110:- <dig> ns
nco:+ <dig>  ns
spo11: + <dig> ***
dmc1:+ <dig> ***
mre110:+ <dig> ***
at-> gc
n =  <dig> conserved,  <dig> changes
r <dig> =  <dig> **
pns,pns,
nco:- <dig> ns
spo11:+ <dig> ns
dmc1:+ <dig> ns
mre110:+ <dig> ns
gc-> at
n =  <dig> conserved,  <dig> changes
r <dig> =  <dig> ***
nco:- <dig> ***
spo11:- <dig> ***
dmc1:- <dig> ***
mre110:- <dig> ***
gc-> gc
nco:+ <dig> ns
spo11:+ <dig> *
dmc1:+ <dig> ns
mre110:+ <dig> ns
at-> at
nco:- <dig> **
spo:- <dig> *
dmc1:- <dig> ns
mre110:+ <dig> ns
nco:+ <dig> **
spo11:+ <dig> **
dmc1:+ <dig> ***
mre110:+ <dig> **
spearman rank correlations of directed substitutions at four-fold degenerated sites  and of the proportion of at->gc substitutions with gene length, expression, and various recombination measures, with and without controlling for an effect of gene position.
presented are also mr results of variables whose log-transformation did not grossly deviate from a normal distribution.
*p <  <dig> , **p <  <dig> ,***p <  <dig> , ns = not significant.
to look at the proportion of the rates of at->gc substitutions from all at <->gc substitutions will control for this general increase in substitution rates.
according to sueoka  <cit> , one may estimate the equilibrium of gc content, gc*, to which a sequence is evolving to by gc* = u/, with u = rate at->gc, and v = rate gc->at.
sueoka's model assumes that all sites within a sequence evolve independently and as cpg do not appear hyper-mutable in yeast  <cit>  one may use this simple approach.
to control for translational selection, i again only consider four-fold degenerate changes that do not change the non-optimal codon status and estimate the proportion of at->gc.
this confirms an increase of the proportion of at->gc substitutions with recombination as expected under gc-biased gene conversion and a decrease with gene length .
the proportion at->gc further slightly increases with expression level ; this may be due to coupling of recombination and expression in yeast or indicate again a selective force favouring gc.
after control for gene position, the decrease with expression, and the opposing effects of recombination on rates of gc->at and at->gc remain .
interestingly, the general increase of substitution rates with gene length disappears.
also, the proportion of at->gc changes does not correlate with gene length anymore, indicating again the effect of gene position.
why the rate of at->at changes decreases with gene length after control of gene position is unclear .
mr analysis of log-transformed variables confirms independent effects of gene length, recombination and expression for at->gc and gc->at changes; independent effects of gene length disappear after controlling for gene position .
only little of the overall variation for at->gc and gc->at changes is explained by the variables .
recombination measures
the different recombination measures all tend to be conform in their general result; just for the substitution analysis, not all recombination measures support the finding.
in general, dmc <dig> double-strand break  data tends to correlate strongest with gc-ending codons, followed by spo <dig>  dsb and crossing-over  events.
but also non-crossing over events  and mre <dig> dsb data before and after meiosis and recombination  confirms the finding.
for the mr analysis, only dmc <dig> and mre <dig> were considered as their log-transformation deviated the least from the bell-shaped normal distribution.
discussion
separating translational selection from base composition indicates that in yeast frequency of gc-ending  codons decreases with gene length and increases with recombination.
this effect of base composition cannot be explained by variation in strength and efficiency of translational selection.
gc-biased gene conversion appears the most likely explanation for the correlations with gene length and recombination.
a decrease of gc-ending codons along genes is indicated and contributes to the decrease with gene length.
patterns of synonymous substitutions at four-fold degenerated sites support differences between at->gc and gc->at substitutions related to recombination, as expected under gc-biased gene conversion.
selection on gc-ending codons, for instance due to selection mrna secondary structures may also contribute.
in models of homologous recombination that relate to double-strand break  repair, mismatches in the formed heteroduplex may be repaired by gene conversion, i.e.
the conversion of one dna strand into another, and the formed holliday junction can then either be resolved with or without crossing-over  <cit> .
gene-conversion is biased towards -gc in yeast as in several other organisms and has been suggested before to affect synonymous codon use .
however in studies investigating the effect of gene conversion on codon use or on patterns of divergence and polymorphism effects of gene length and gene position have not been considered before.
an effect of gene position and length may arise as gene conversion events are not randomly distributed across the genome; the number of gene conversion events should for example relate to the number of initiating dsbs and interestingly the number of dsbs already decreases with gene length in the yeast data assembled here .
it is known that dsbs are often located in promoters with highest conversion numbers near the initiating dsbs  <cit> .
especially with short conversion tract lengths, the probability of gene conversion will hence decrease with distance from the dsb, i.e.
from the promoter.
if gc-biased, gene conversion could hence cause the negative correlation of gc-ending codons with gene position and thereby gene length.
gene conversion gradients, the decrease of gene conversion from one end of the gene to the other, have been observed in s. cerevisiae and other fungi .
this decrease further seems often uni-directional in the 5'->3' direction, which may be due to various reasons including a gradient in heteroduplex formation or a gradient in the relative repair with gene conversion   <cit> .
three recent studies in yeast are interesting with respect to the results of this study and gc- biased gene conversion.
noor  <cit>  looks at the correlation of intergenic and intronic substitution rates with recombination to test for mutagenic effects of recombination on substitution rates; the lack of an increase of substitution rates with recombination however suggests mutagenic effects of recombination do not affect the substitution rates in yeast very much.
the decrease noor  <cit>  observes instead is conform with gc-biased gene conversion; however surprisingly, he finds no difference between gc->at and at->gc substitutions associated with dsbs.
weber and hurst  <cit>  find a decrease of non-synonymous substitution rates with recombination, and interestingly not only with crossover but also with non-crossover events, which again is conform with gc-biased gene conversion.
referring to noor's  <cit>  lack of difference between gc->at and at->gc, they do not discuss gc-biased gene conversion further.
harrisson and charlesworth  <cit>  investigate the effect of gc-biased gene conversion in much detail, but do not consider the negative correlation between optimal codons and gene position and length.
the potential contribution and importance of gc-biased gene conversion to observed patterns of substitutions for primates and humans have been highlighted much recently  and in humans gene conversion tracts are short and steep  <cit> .
it would be interesting whether an effect of gene position and length may be observed.
besides a compositional bias in repair, such as gc-biased gene conversion, a negative correlation of gc-content at synonymous sites with gene length could also be due to a compositional bias in selection or mutation.
selection alternative to translational selection may differentiate among gc- and at-ending codons, and its strength or efficiency could correlate with gene length and position.
one selective target related to gene length and gc-content is the stability of secondary structures.
thermodynamic stability of mrna structures increases with gene length and gc-content as the absolute thermodynamic stability of a sequence will depend on the absolute number paired bases, and their strength of bonds, which is highest for pairs of g and c. laboratory studies suggest too stable secondary structures within the protein coding part interfere with translation  <cit> , in which case selection should dis-favour too stable structures.
especially in genes that are more stable through their length, lower level of gc may be beneficial and selected for.
this could theoretically lead to the observed negative correlation of gc-ending codons with gene length.
it may also explain a negative correlation of the gc-content with expression level : first, selection on thermodynamic stability may vary with expression, and secondly, higher expressed genes will be shorter, and if the absolute stability would be under selection, their gc-content may be higher.
whether selection favours or dis-favours stability in protein coding regions however is a controversial issue , for yeast, selection may indeed act against too stable structures  <cit> .
however, even under selection against too stable secondary structures in coding mrnas, it is not obvious why there should be a decrease of gc with gene position.
variation in rate or bias of mutations may also contribute to the observed patterns, and mutations appears to be biased towards at in yeast  <cit> .
in this case however, polymorphism data should show the same patterns as divergence.
note that in contrast to yeast, in e. coli, relative optimal codon use of all amino acids increases in frequency with gene length; this is independent of whether the optimal codon ends in at- or gc-  <cit> .
a possibly related difference between prokaryotes and eukaryotes is indicated in a separate line of studies: in prokaryotes gc-content increases with gene length  <cit> , while in eukaryotes it mainly decreases  <cit> .
it will be interesting to check other organisms for a decrease of gc-ending codons with gene length and gene position, and evaluate the effect of base composition - and gc-biased gene conversion - on synonymous  codon use and sequence evolution.
gc-biased gene conversion may contribute to the negative correlation of  optimal codons with gene length described in various organisms, which so far has been explained only by variation in the strength or efficacy of translational selection.
hill-robertson interference has been suggested to cause the negative correlation between optimal codon use and gene length, and while hill-robertson interference may contribute to several patterns of synonymous codon use , it cannot easily explain the here described compositional correlations for yeast that affect both optimal and non-optimal codons.
loewe and charlesworth  <cit>  included gene conversion in their model of intragenic background selection and highlight its contribution in breaking down linkage.
it will be interesting to set up models that include also current knowledge on gene conversion bias towards gc, distribution of dsbs, e.g.
the relation to promoters, the conversion lengths and dependencies on homology.
CONCLUSIONS
separating translational selection from base composition indicates that in yeast frequencies of gc-ending  codons decrease with gene length and position and increase with recombination.
gc-biased gene conversion appears the most likely explanation.
substitution patterns support effects of gc-biased gene conversion.
these results are of interest for our understanding of the process of gene conversion and its implications, but also for interpreting the negative correlation between optimal codon use and gene length observed in various organisms whose optimal codons tend to end with -gc.

 translational selection on synonymous codon use is indicated if frequencies of preferentially used,'optimal', codons increase with expression level and correspond to the most abundant trna or to the trna with which they form the strongest binding - for several organisms, this seems to be the case. additional support for a beneficial role of certain'optimal' codons in translation comes from laboratory studies. translational selection may act to maximise the speed of elongation, minimize the costs of proofreading or maximise the accuracy of translation, and depending on the selective target, one can test further distinct predictions. under selection for translational accuracy we expect for example: selection against translational errors to relate to the error's costs. as costs of an erroneous protein should accrue with each added amino acid during protein synthesis, one may expect long genes to experience higher optimal codon use than short genes. supporting selection for translational accuracy, in e. coli and yeast, relative optimal codon use indeed increases with gene length. we also expect selection against translational errors to relate to the error's functional effect: translational errors for some amino acids may have no functional effects, while for other amino acids, translational errors render a protein non-functional. the latter should be under stronger selection for translational accuracy. as akashi points out, the functional importance of amino acid site may be approximated by its evolutionary conservation. under translational selection for accuracy one may hence expect higher optimal codon frequencies at conserved than at non-conserved amino acid sites. this is indeed the case in d. melanogaster, c. elegans, e. coli; a recent study indicates this pattern may also apply to mouse and human using a modified measure of optimal codons. however, surprisingly, in d. melanogaster, c. elegans, a. thaliana, and humans, optimal codon use decreases with gene length, thereby opposing the prediction under selection for translational accuracy. this decrease is particularly surprising for species, in which selection for translational accuracy is indicated by the aforementioned higher optimal codon use at conserved amino acid sites. the explanation may be that the negative correlation between optimal codon use and gene length simply is a side effect: highly expressed genes with high optimal codon use tend to be short, possibly to be more economic. yet, while control of expression level affects the correlation of optimal codon use with gene length in yeast, causing a change from negative to positive, in d. melanogaster, c. elegans, a. thaliana or humans, the negative correlation of optimal codon use with gene length does not seem to be due to a correlation of gene length with expression level only. two explanations for the negative correlation have been proposed, both of which are based on translational selection. first, under selection for translational efficiency, selection for optimal codons may decrease with gene length due to the decrease in the relative fitness effect per optimal codon. the second hypothesis invokes hill-robertson interference, which considers the reduction in selective efficacy due to linkage among sites: weakly or strongly selected sites that evolve adaptively or under constraints may affect evolutionary dynamics of linked sites. as comeron et al. suggest selection efficacy on optimal codons may decrease with gene length, as long genes with higher numbers of potentially interfering sites may experience a stronger hill-robertson effect. the hill-robertson effect has been considered for various effects on synonymous codons. as recombination breaks down linkage, the observed positive correlation of optimal codon use with recombination rate was taken as support for the hill-robertson effect reducing the efficacy of translational selection on optimal codons. yet, optimal codons in several metazoans, such as the ones for which the negative correlation was first reported for, i.e. d. melanogaster, c. elegans and a. thaliana, but also for humans are mostly ending with g or c, and compositionally biased mutation or repair processes may indirectly affect optimal codon use. recombination-dependent repair is indeed biased towards -gc in many organisms including yeast, mice, humans and drosophila, and hence may be the potential force. effects of gc-biased gene conversion will be most obvious at sites that evolve neutrally or under weak selection, and the substitution patterns it leaves resembles that of directional selection. gc-biased gene conversion has been indicated to affect optimal codon use before: optimal codon frequencies increase with recombination rate, a patterns consistent with population genetic predictions under translational selection on optimal codons. however, in d. melanogaster and c. elegans not only optimal codon frequencies increase with recombination, but also non-optimal ones, as long as they end with -gc. the positive correlation of non-optimal gc-ending codon frequencies with recombination indicates the observed positive correlation optimal codons - that was taken as evidence for reduced efficacy of translational selection due to hill-robertson interference - is likely affected by compositionally biased processes such gc-biased gene conversion. whether or not gc-biased gene conversion or hill-robertson effects the positive correlation between optimal codons and recombination attracted controversy, but with respect to the observed negative correlation of optimal codon use with gene length, gc-biased gene conversion has never been considered. the negative correlation of optimal codon use with gene length is found in organisms whose optimal codons are biased towards gc-ending ones, and may hence be caused by forces acting on optimal codons or on base composition. as translational selection affects optimal codons, while a compositional bias like gene conversion affects gc-ending codons, one may disentangle the effects by looking at optimal and non-optimal gc- and at-ending codons separately. saccharomyces cerevisiae is a good organism to disentangle the two forces because translationally optimal codons are not biased towards gc-ending ones as in the above mentionned organisms. furthermore, translational selection and gc-biased gene conversion are comparably well-studied and supported in s. cerevisiae. results of this study demonstrate in s. cerevisiae the frequency of gc-ending codons decreases with gene length and increases with recombination. also a decrease of gc-ending codons along genes is indicated. this distinction between at- and gc-ending codons cannot be explained by variation in strength and efficiency of translational selection, while gc-biased gene conversion may explain the observation. substitutions at four-fold degenerated sites differ between at->gc and gc->at changes, further supporting an effect of gc-biased gene conversion. initiation of gene conversion events in promoter regions and the presence of a gene conversion gradient most likely explain the observed decrease of gc-ending codons with gene length and gene position.  difference between optimal codons depending on whether they end with -at or -gc to disentangle forces affecting base compositions from translational selection on optimal codons, one can compare optimal gc-ending and optimal at-ending codons. as expected under translational selection, all optimal codons independent of their third nucleotide increase with gene expression. as expected under gc-biased gene conversion, only the frequency of gc-ending optimal codons increases with recombination, at-ending optimal codons however tend to be negatively or not significantly correlated with recombination. crucially with respect to gene length, only the relative frequencies of at-ending optimal codons increase with gene length as one may expect under selection for translational accuracy. in contrast, the relative frequencies of gc-ending optimal codons decrease with gene length. this is true for individual amino acids, as well as for groups of amino acids with either at-or with gc-ending optimal codons. this distinction between optimal at- and optimal gc-ending codons indicates an effect related to base composition. ala nco:- ns spo11:- *** dmc1:- * mre110:+ ns arg nco:+ ns spo11:+ ns dmc1:+ ns mre110:+ ns cys nco:- ns spo11:- ns dmc1:+ ns mre110:+ ns gln nco:- * spo11:- ns dmc1:- *** mre110:- ns glu nco:- * spo11:- ** dmc1:- *** mre110:- ns gly nco:+ ns spo11:+ ns dmc1:+ ns mre110:+ ** pro nco:- ns spo11:+ ns dmc1:- ns mre110:+ ns grouped n = codons r = *** p***,p***, mco:- * spo11:- *** dmc1:- *** mre110:- * leu nco:+ *** spo11:+ *** dmc1:+ *** mre110:+ *** asn nco:+ *** spo11:+ *** dmc1:+ *** mre110:+ *** asp nco:+ *** spo11:+ *** dmc1:+ *** mre110:+ *** tyr nco:+ *** spo11:+ *** dmc1:+ *** mre110:+ *** phe nco:+ *** spo11:+ *** dmc1:+ *** mre110:+ *** lys nco:+ *** spo11:+ *** dmc1:+ *** mre110:+ *** his nco:+ *** spo11:+ *** dmc1:+ *** mre110:+ *** grouped n = codons r =, p***,p*** nco:+ *** spo11:+ *** dmc1:+ *** mre110:+ *** spearman rank correlations between optimal codon use, gene length, expression, and various recombination measures for amino acids and groups of amino acids with either at- or with gc-ending optimal codons. genes for which all amino acids were present at least four times were used. presented for grouped variables are also mr results of variables whose log-transformation did not grossly deviate from a normal distribution. *p <, **p <,***p <, ns = not significant. interrelated variables such as expression level may affect correlations between codon use and gene length. to control for all possible interrelated variables, and especially for noisy variables such as expression level is not easy. however, as the same genes were used for comparing at- and gc-ending optimal codons, a control of other variables is not necessary to highlight their difference. at- and gc-ending optimal codons are sampled from the same distributions of other potentially affecting variables such as expression level. the effect of gene expression should hence affect them both similarly. the major difference between at- and gc-ending optimal codons can hence be demonstrated by simple spearman rank correlation analyses: expression level should affect all optimal codons similarly, while clearly, gc-ending codons differ from at-ending codons in their correlation with gene length and with recombination. the opposing correlation of at- and gc-ending optimal codons with gene length and recombination indicates another force unrelated to translational selection is acting. multiple regression analysis between log-transformed fopgc or fopat estimates, gene length, expression and two different measures of recombination confirms independent effects of expression, recombination and gene length. please be aware however that both, recombination and expression measures will be noisy and as plotkin and fraser highlight, one should not compare the explanatory power of predictors with standard regression techniques when the predictors contain different amounts of measurement noise. effect of base composition independent of translational selection for amino acids with at least two optimal or with at least two non-optimal codons, one can estimate the relative gc-content of either optimal or at non-optimal codons separately. for amino acids which have two optimal codons, i estimate the frequency of gc-ending optimal codons relative to all optimal codons; for amino acids which have at least two non-optimal codons, i estimate the frequency of gc-ending non-optimal codons relative to all non-optimal. to look at optimal and non-optimal codons separately controls for translational selection. the analysis supports an effect of base composition: relative frequencies of gc-ending codons consistently decrease with gene length and increase with recombination. for all but arg, the correlations are significant per amino acid; when grouped across respective amino acids, the decrease is significant for both fgcopt and fgcnon-opt. ile nco:+ *** spo11:+ *** dmc1:+ *** mre110:+ *** ser nco:+ *** spo11:+ *** dmc1:+ *** mre110:+ *** thr nco:+ *** spo11:+ *** dmc1:+ *** mre110:+ ** val nco:+ *** spo11:+ *** dmc1:+ *** mre110:+ *** grouped n = codons r = *** nco:+ *** spo11:+ *** dmc1:+ *** mre110:+ *** ala nco:+ *** spo11:+ *** dmc1:+ *** mre110:+ *** arg nco:+ * spo11:+ *** dmc1:+ *** mre110:+ * gly nco:+ *** spo11:+ *** dmc1:+ *** mre110:+ *** leu nco:+ *** spo11:+ *** dmc1:+ *** mre110:+ *** pro nco:+ *** spo11:+ *** dmc1:+ *** mre110:+ ** thr nco:+ *** spo11:+ *** dmc1:+ *** mre110:+ ** ser nco:+ *** spo11:+ *** dmc1:+ *** mre110:+ *** val nco:+ *** spo11:+ *** dmc1:+ *** mre110:+ *** grouped n = codons r = *** p***,p*** p***, nco:+ *** spo11:+ *** dmc1:+ *** mre110:+ *** spearman rank correlations between the frequency of gc-ending optimal or non-optimal codons with gene length, expression, and various recombination measures. for each amino acid, only genes were used for which at least optimal or non-optimal codons were present respectively. presented for grouped variables are also mr results of variables whose log-transformation did not grossly deviate from a normal distribution. *p <, **p <,***p <, ns = not significant. notably, the analysis also indicates expression may affect the frequencies of gc-ending codons: controlling for translational selection, gc-ending codons, fgcopt and fgcnon-opt, increase with expression level. this may be a side effect: first, in yeast, recombination and gene expression seem coupled and secondly, highly expressed genes tend to be short. however, it may also reveal some selective force: gc-ending codons affect for example thermodynamic stability and hence mrna secondary structures which may be under selection. mr analysis between log-transformed variables supports independent effects of gene length, expression and recombination for the grouped data. effect of gene position on relative codon frequencies intragenic variation in codon use exists: optimal codons may for example increase along genes due to selection against non-sense errors; also a decrease of gc-content along genes has been described. to investigate an effect of gene position, i look at the four different measures of tables and for grouped amino acids: fopgc = frequency of optimal codons relative to all synonymous codons, but only for amino acids which have optimal codons that end with g or c; fopat = frequency of optimal codons relative to all synonymous codons, but only for amino acids which have optimal codons that end with a or t; fgcopt = frequency of gc-ending optimal codons relative to all optimal codons; only for amino acids which have two optimal codons, one ending with g or c the other with a or t; fgcnon-opt = frequency of gc-ending non-optimal codons relative to all non-optimal; only for amino acids which have at least two non-optimal codons, one ending with g or c and one with a or t. results show that optimal codons tend to increase with gene position, and gc-ending ones tend to decrease. the result remains excluding the first codons that often appear to be under different pressures. the non-significant result for fopgc may be due to conflicting pressures: optimal codons tend to increase while gc-ending codons tend to decrease. the non-significant result of fgcopt may be due to dominant selection on optimal codons that is stronger than additional compositional forces. fopat fopgc fgcopt fgcnon-opt spearman rank analysis of frequencies of optimal and gc-ending codons with gene position for position numbers 1- and 49- *p <, **p <,***p <, ns = not significant. an increase of certain codons along genes will as a side effect cause a positive correlation of these codons with gene length. to control for this effect of gene position, i take genes that are greater than codons and only consider the level of bias in those codons from number up to codon number. i repeat the two previous analyses for the grouped data. the general patterns that gc-ending codons tend to decrease with gene length and increase with recombination remains, but becomes non-significant for the correlation between fgcnon-opt and gene length. the positive correlation between fopat and gene length disappears indicating selection for translational accuracy may mainly act against non-sense errors. the two measures that showed no significant effect of gene position, fopgc and fgcopt remain significantly negative correlated after the control of gene position. mr analysis of log-transformed variables indicates no independent effect of gene length for any codon class after controlling for position. the results hence support that gc-ending codons tend to decrease along genes, and that this decrease along genes contributes considerably to the negative correlation of gc-ending codons with gene length. fopat n = codons r = *** pns,p***, nco:- *** spo11:- ns dmc1:- *** mre110:- * fopgc n = codons r = *** pns, p***, p*, nco:+ *** spo11:+ *** dmc1:+ *** mre110:+2648*** fgcopt n = codons r = *** nco:+ *** spo11:+ *** dmc1:+ *** mre110:+ *** fgcnon-opt n = codons r = *** pns, p*** nco:+ *** spo11:+ *** dmc1:+ *** mre110:+ *** spearman rank correlations between frequencies of optimal and gc-ending codons with gene length, expression, and various recombination measures after controlling for a potential effect of gene position. the same genes were used for all measures. presented are also mr results of variables whose log-transformation did not grossly deviate from a normal distribution. *p <, **p <,***p < substitution rates and patterns for both, gc-biased gene conversion as well as translational selection, we may not only expect relative codon frequencies to mirror the respective forces, but also substitution patterns. to disentangle the effect of gene conversion from translational selection, i take four-fold degenerated changes that do not change the non-optimal codon status and estimate four rates of substitutions at->gc, gc->at, at->at, and gc->gc. under gc-biased gene conversion, we expect an increase of at->gc with recombination. as for the relative frequencies, the same genes are used for comparison, so a control of other variables should not be necessary to highlight their differences. however, while differences with respect to recombination can indeed be observed, a general decrease of all substitution rates with gene expression confounds the observation. higher expressed genes appear more constraint even at non-optimal sites and indicate again beneficial roles of non-optimal codons for gene expression. at -> gc n = conserved, changes r = *** p***,p** nco:+ ns spo11:+ ns dmc1:+ ns mre110:+ ns gc -> at n = conserved, changes r = 068*** p***,p** nco:- ** spo11:- *** dmc1:- *** mre0:- *** gc -> gc n = conserved, changes r = *** p***,pns, nco: + ns spo: + ns dmc1:- ns mre0:+ ns at -> at n = conserved, changes r = *** p***,p***, nco:- * spo:- ** dmc1:- *** mre110:- ns nco:+ ns spo11: + *** dmc1:+ *** mre110:+ *** at-> gc n = conserved, changes r = ** pns,pns, nco:- ns spo11:+ ns dmc1:+ ns mre110:+ ns gc-> at n = conserved, changes r = *** nco:- *** spo11:- *** dmc1:- *** mre110:- *** gc-> gc nco:+ ns spo11:+ * dmc1:+ ns mre110:+ ns at-> at nco:- ** spo:- * dmc1:- ns mre110:+ ns nco:+ ** spo11:+ ** dmc1:+ *** mre110:+ ** spearman rank correlations of directed substitutions at four-fold degenerated sites and of the proportion of at->gc substitutions with gene length, expression, and various recombination measures, with and without controlling for an effect of gene position. presented are also mr results of variables whose log-transformation did not grossly deviate from a normal distribution. *p <, **p <,***p <, ns = not significant. to look at the proportion of the rates of at->gc substitutions from all at <->gc substitutions will control for this general increase in substitution rates. according to sueoka, one may estimate the equilibrium of gc content, gc*, to which a sequence is evolving to by gc* = u/, with u = rate at->gc, and v = rate gc->at. sueoka's model assumes that all sites within a sequence evolve independently and as cpg do not appear hyper-mutable in yeast one may use this simple approach. to control for translational selection, i again only consider four-fold degenerate changes that do not change the non-optimal codon status and estimate the proportion of at->gc. this confirms an increase of the proportion of at->gc substitutions with recombination as expected under gc-biased gene conversion and a decrease with gene length. the proportion at->gc further slightly increases with expression level; this may be due to coupling of recombination and expression in yeast or indicate again a selective force favouring gc. after control for gene position, the decrease with expression, and the opposing effects of recombination on rates of gc->at and at->gc remain. interestingly, the general increase of substitution rates with gene length disappears. also, the proportion of at->gc changes does not correlate with gene length anymore, indicating again the effect of gene position. why the rate of at->at changes decreases with gene length after control of gene position is unclear. mr analysis of log-transformed variables confirms independent effects of gene length, recombination and expression for at->gc and gc->at changes; independent effects of gene length disappear after controlling for gene position. only little of the overall variation for at->gc and gc->at changes is explained by the variables. recombination measures the different recombination measures all tend to be conform in their general result; just for the substitution analysis, not all recombination measures support the finding. in general, dmc double-strand break data tends to correlate strongest with gc-ending codons, followed by spo dsb and crossing-over events. but also non-crossing over events and mre dsb data before and after meiosis and recombination confirms the finding. for the mr analysis, only dmc and mre were considered as their log-transformation deviated the least from the bell-shaped normal distribution. discussion separating translational selection from base composition indicates that in yeast frequency of gc-ending codons decreases with gene length and increases with recombination. this effect of base composition cannot be explained by variation in strength and efficiency of translational selection. gc-biased gene conversion appears the most likely explanation for the correlations with gene length and recombination. a decrease of gc-ending codons along genes is indicated and contributes to the decrease with gene length. patterns of synonymous substitutions at four-fold degenerated sites support differences between at->gc and gc->at substitutions related to recombination, as expected under gc-biased gene conversion. selection on gc-ending codons, for instance due to selection mrna secondary structures may also contribute. in models of homologous recombination that relate to double-strand break repair, mismatches in the formed heteroduplex may be repaired by gene conversion, i.e. the conversion of one dna strand into another, and the formed holliday junction can then either be resolved with or without crossing-over. gene-conversion is biased towards -gc in yeast as in several other organisms and has been suggested before to affect synonymous codon use. however in studies investigating the effect of gene conversion on codon use or on patterns of divergence and polymorphism effects of gene length and gene position have not been considered before. an effect of gene position and length may arise as gene conversion events are not randomly distributed across the genome; the number of gene conversion events should for example relate to the number of initiating dsbs and interestingly the number of dsbs already decreases with gene length in the yeast data assembled here. it is known that dsbs are often located in promoters with highest conversion numbers near the initiating dsbs. especially with short conversion tract lengths, the probability of gene conversion will hence decrease with distance from the dsb, i.e. from the promoter. if gc-biased, gene conversion could hence cause the negative correlation of gc-ending codons with gene position and thereby gene length. gene conversion gradients, the decrease of gene conversion from one end of the gene to the other, have been observed in s. cerevisiae and other fungi. this decrease further seems often uni-directional in the 5'->3' direction, which may be due to various reasons including a gradient in heteroduplex formation or a gradient in the relative repair with gene conversion. three recent studies in yeast are interesting with respect to the results of this study and gc- biased gene conversion. noor looks at the correlation of intergenic and intronic substitution rates with recombination to test for mutagenic effects of recombination on substitution rates; the lack of an increase of substitution rates with recombination however suggests mutagenic effects of recombination do not affect the substitution rates in yeast very much. the decrease noor observes instead is conform with gc-biased gene conversion; however surprisingly, he finds no difference between gc->at and at->gc substitutions associated with dsbs. weber and hurst find a decrease of non-synonymous substitution rates with recombination, and interestingly not only with crossover but also with non-crossover events, which again is conform with gc-biased gene conversion. referring to noor's lack of difference between gc->at and at->gc, they do not discuss gc-biased gene conversion further. harrisson and charlesworth investigate the effect of gc-biased gene conversion in much detail, but do not consider the negative correlation between optimal codons and gene position and length. the potential contribution and importance of gc-biased gene conversion to observed patterns of substitutions for primates and humans have been highlighted much recently and in humans gene conversion tracts are short and steep. it would be interesting whether an effect of gene position and length may be observed. besides a compositional bias in repair, such as gc-biased gene conversion, a negative correlation of gc-content at synonymous sites with gene length could also be due to a compositional bias in selection or mutation. selection alternative to translational selection may differentiate among gc- and at-ending codons, and its strength or efficiency could correlate with gene length and position. one selective target related to gene length and gc-content is the stability of secondary structures. thermodynamic stability of mrna structures increases with gene length and gc-content as the absolute thermodynamic stability of a sequence will depend on the absolute number paired bases, and their strength of bonds, which is highest for pairs of g and c. laboratory studies suggest too stable secondary structures within the protein coding part interfere with translation, in which case selection should dis-favour too stable structures. especially in genes that are more stable through their length, lower level of gc may be beneficial and selected for. this could theoretically lead to the observed negative correlation of gc-ending codons with gene length. it may also explain a negative correlation of the gc-content with expression level: first, selection on thermodynamic stability may vary with expression, and secondly, higher expressed genes will be shorter, and if the absolute stability would be under selection, their gc-content may be higher. whether selection favours or dis-favours stability in protein coding regions however is a controversial issue, for yeast, selection may indeed act against too stable structures. however, even under selection against too stable secondary structures in coding mrnas, it is not obvious why there should be a decrease of gc with gene position. variation in rate or bias of mutations may also contribute to the observed patterns, and mutations appears to be biased towards at in yeast. in this case however, polymorphism data should show the same patterns as divergence. note that in contrast to yeast, in e. coli, relative optimal codon use of all amino acids increases in frequency with gene length; this is independent of whether the optimal codon ends in at- or gc-. a possibly related difference between prokaryotes and eukaryotes is indicated in a separate line of studies: in prokaryotes gc-content increases with gene length, while in eukaryotes it mainly decreases. it will be interesting to check other organisms for a decrease of gc-ending codons with gene length and gene position, and evaluate the effect of base composition - and gc-biased gene conversion - on synonymous codon use and sequence evolution. gc-biased gene conversion may contribute to the negative correlation of optimal codons with gene length described in various organisms, which so far has been explained only by variation in the strength or efficacy of translational selection. hill-robertson interference has been suggested to cause the negative correlation between optimal codon use and gene length, and while hill-robertson interference may contribute to several patterns of synonymous codon use, it cannot easily explain the here described compositional correlations for yeast that affect both optimal and non-optimal codons. loewe and charlesworth included gene conversion in their model of intragenic background selection and highlight its contribution in breaking down linkage. it will be interesting to set up models that include also current knowledge on gene conversion bias towards gc, distribution of dsbs, e.g. the relation to promoters, the conversion lengths and dependencies on homology.  separating translational selection from base composition indicates that in yeast frequencies of gc-ending codons decrease with gene length and position and increase with recombination. gc-biased gene conversion appears the most likely explanation. substitution patterns support effects of gc-biased gene conversion. these results are of interest for our understanding of the process of gene conversion and its implications, but also for interpreting the negative correlation between optimal codon use and gene length observed in various organisms whose optimal codons tend to end with -gc. 
yeast is a good organism to study this as equal numbers of optimal codons end in -gc and -at and one may hence compare frequencies of optimal gc- with optimal at-ending codons to disentangle the forces. results of this study demonstrate in yeast frequencies of gc-ending codons decrease with gene length and increase with recombination. while suggested explanations focus on variation in strength and efficiency of translational selection, it has rarely been noticed that the negative correlation is reported only in organisms whose optimal codons are biased towards codons that end with g or c. correlations with recombination and gene expression differentiate between gc-ending and optimal codons, and also substitution patterns support effects of gc-biased gene conversion. surprisingly, in several multi-cellular eukaryotes optimal codon use correlates negatively with gene length. this raises the question whether forces that affect base composition - such as gc-biased gene conversion - contribute to the negative correlation between optimal codon use and gene length. a decrease of gc-ending codons along genes contributes to the negative correlation with gene length. while the general effect of gc-biased gene conversion is well known, the negative correlation of optimal codon use with gene length has not been considered in this context before. initiation of gene conversion events in promoter regions and the presence of a gene conversion gradient most likely explain the observed decrease of gc-ending codons with gene length and gene position. gc-biased gene conversionoptimal codon usecause of correlation this contrasts with the expectation under selection for translational accuracy.
 surprisingly, in several multi-cellular eukaryotes optimal codon use correlates negatively with gene length. this contrasts with the expectation under selection for translational accuracy. while suggested explanations focus on variation in strength and efficiency of translational selection, it has rarely been noticed that the negative correlation is reported only in organisms whose optimal codons are biased towards codons that end with g or c. this raises the question whether forces that affect base composition - such as gc-biased gene conversion - contribute to the negative correlation between optimal codon use and gene length.  yeast is a good organism to study this as equal numbers of optimal codons end in -gc and -at and one may hence compare frequencies of optimal gc- with optimal at-ending codons to disentangle the forces. results of this study demonstrate in yeast frequencies of gc-ending codons decrease with gene length and increase with recombination. a decrease of gc-ending codons along genes contributes to the negative correlation with gene length. correlations with recombination and gene expression differentiate between gc-ending and optimal codons, and also substitution patterns support effects of gc-biased gene conversion.  while the general effect of gc-biased gene conversion is well known, the negative correlation of optimal codon use with gene length has not been considered in this context before. initiation of gene conversion events in promoter regions and the presence of a gene conversion gradient most likely explain the observed decrease of gc-ending codons with gene length and gene position. gc-biased gene conversionoptimal codon usecause of correlation 