BACKGROUND
with the recent accumulation of complete bacterial genome sequences there has been increased attention to prokaryote chromosome organization.
one prominent aspect of most of these genomes is that several features, such as nucleotide composition and coding strand bias, display an organization that is centered on the origin of replication  <cit> .
in these chromosomes, as exemplified by escherichia coli  <cit> , replication initiates at a single origin  and proceeds bi-directionally to a terminus  where the two forks meet  <cit> .
this divides the chromosome into a replichore  <cit> , defined as a chromosome with two oppositely replicated halves , within each of which there is a leading and lagging strand such that one dna strand is leading within one replication arm but lagging within the other.
many bacterial genomes display a compositional asymmetry between the two dna strands within a replication arm meaning that parity rule  <dig>  which stipulates that the frequencies of a and t are equal as are the frequencies of g and c, is violated  <cit> .
observed strand asymmetry, or skew, in base composition is either a purine  or a keto  excess on one strand and the leading strand in one replication arm shows the same skew as the leading strand in the other despite the fact that they are opposite genome strands.
one issue that has arisen from these observations is the cause of the compositional asymmetry between strands, with evidence having been presented for contributions from both mutation and selection  <cit> .
many of the prokaryotes that have a replichore structure also have a bias towards coding genes, particularly 'essential' genes  <cit> , on the leading strand  <cit>  suggesting that composition asymmetry could result from selection and/or transcription-coupled mutation and repair processes  <cit> .
there is also evidence, though, that leading and lagging strands differ in mutation bias  <cit> , which has interesting and important implications for genome evolution  <cit> .
although there have been estimates of the contribution of mutation to skew in several genomes that suggest a role for selection  <cit>  the issue has not been studied within a statistical framework.
replichores with strand asymmetry have also been exploited to make inferences about the location of an origin of replication when the origin has not been mapped experimentally, which is the case in the vast majority of sequenced genomes.
the compositional difference between leading and lagging strands, and the replichore structure in general, means that the two dna strands have complementary composition biases in the two replication arms of these genomes.
plotting composition skew along a sliding window leads to a characteristic pattern in which the origin lies at a point where a given measurement of strand asymmetry switches between positive and negative values.
this type of graphical approach has been used frequently to infer the location of replication origins  <cit>  but these approaches have the disadvantage that determining the existence of skew and where it switches strand is subjective  <cit> .
a more objective linear discriminant analysis has also been developed  <cit> , but this method does not account for gene density nor does it utilize intergenic regions  <cit> .
we develop a simple bipartition model  that exploits the existence of a replichore structure with strand asymmetry and provides for analyses within a maximum likelihood  framework.
in the current study we will apply the model to bacterial chromosomes  in two analyses.
the first is the identification of two peaks on a likelihood surface, the locations of the putative origin and terminus of replication.
additional information, such as the organization of ribosomal rna  genes  <cit> , can then be used to infer which of the two locations is the origin.
in this study we assign the origin to maximize the arrangement of rrna genes on the resulting leading strands  <cit>  and then compare the location of our putative origin to "origin-associated" genes that are located at or close to the replication origin in certain genomes  <cit> .
the second application is a statistical analysis of the contribution of mutation to nucleotide composition skew across bacterial species.
1the two phyla with the largest sample sizes are shown sub-divided by class representation.
RESULTS
we applied the bipartition model to  <dig> fully sequenced bacterial chromosomes.
an assessment of the mutational  component of compositional skew  requires an identification of the origin and terminus of replication.
since these have not been empirically identified in most genomes we first use the model to generate a maximum likelihood estimation of the two loci and discuss the accuracy of this approach.
once the putative origin and terminus have been identified for each chromosome we use the model to quantify the degree to which the mutational difference between leading and lagging strands generates a skew.
replication arms comprise half of most bacterial chromosomes
we expect that if the unordered pair of sites identified by our model as the potential origin and terminus  is an accurate estimation of the replication origin and terminus then these two sites should divide the chromosome roughly in half.
the existence of such a physical balance is the basis of the adopt-adapt model  <cit> , which proposes that this balance would guarantee a synchronous completion of replication by the two forks.
the distribution of chromosome divisions, measured by the statistic cd  is shown in figure  <dig> for the  <dig> circular chromosomes in which the  <dig> percent confidence interval of cd was less than 20% of the chromosome.
linear chromosomes were also excluded since the method of calculating the confidence interval cannot be applied to them.
we took cd between  <dig> and  <dig>  as indicating a relatively equal division of chromosome arms and >  <dig>  as an arbitrary measure of an inequitable division: these are chromosome in which ml generated a replication arm less than 40% of the total length.
of the  <dig> chromosomes analyzed,  <dig>  had an inequitable division by our definition .
overall, this result agrees with the prediction of the 'adopt-adapt' model.
the advantage to such an arrangement would presumably be that it results in the shortest possible replication time, which would otherwise be limited by the time taken to replicate the longer of the two arms.
1one replication arm less than 40% of the total chromosome length .
2primary chromosome unless otherwise indicated.
3class is given only for firmicutes and proteobacteria as in table  <dig>
given an expectation for physical balance of chromosomes, it is possible that the  <dig> chromosomes with an inequitable division have undergone recent rearrangements.
large indels in either replication arm or inversions that include either the origin or the terminus could lead to deviations from equitable distribution.
this cannot be investigated for all  <dig> cases since many chromosomes have not been studied in great detail or do not have close relatives for comparison, but evidence suggests that at least some of these chromosomes have undergone the predicted rearrangements.
for example, pseudomonas aeruginosa pa <dig> has a large inversion encompassing about 1/ <dig> the genome  <cit> , yersinia pestis str.
<dig> has significant inversions surrounding the putative origin  <cit>  and prochlorococcus marinus mit <dig> has several genome rearrangements relative to strain med <dig> and is also much larger  <cit> .
candidatus blochmannia pennsylvanicus str.
bpen has undergone significant gene loss relative to b. floridanus  <cit> , halobacterium sp.
nrc- <dig> contains  <dig> insertion sequences from  <dig> different families  <cit>  and candidatus pelagibacter ubique htcc <dig> has a very small genome that appears to have undergone numerous recent deletions  <cit> .
these rearrangements suggest the possibility that the origin and terminus in these chromosomes do, in fact, yield a noticeably inequitable division.
although it seems likely that selection would favor an equitably divided genome, it is not known how rapidly a chromosome would regain equitable division following such a rearrangement and the genomes in table  <dig> may be evolving towards a more equitable division.
alternatively, it could be that the genome assembly was performed incorrectly  or that in these cases skew is not at equilibrium as a result of genome rearrangement and ml does not represent the origin and terminus.
if this is the case then any method that utilizes composition skews to estimate the origin of replication, whether our ml approach or a graphical approach, would be misled.
locating the putative replication origins of bacterial chromosomes
we used ml to assign a putative origin/terminus pair  for the  <dig> chromosomes in our dataset.
as described in the methods we used several different methods to accomplish this; each are described separately.
where possible we can compare our results to empirically identified replication origins to assess the accuracy of our approach.
linear chromosomes
the five linear chromosomes are relatively simple since an origin has been annotated for each at the center of the genome and these annotations appear to be reliable: the annotations for borrelia burgdorferi and b. garnii are based on empirical evidence  <cit>  as are the annotations for the two streptomyces taxa  <cit> , and in the case of a. tumefaciens the annotation is based on an analysis of the repabc genes  <cit> .
therefore, we can assign poml and ptml for the linear chromosomes in the dataset using the annotated origins and assess our method.
we find a putative origin near the annotated origin in each of the five linear chromosomes ; in three it is within  <dig> % of the genome length of the annotated origin while in the other two it is within 3% of the genome length.
in each case the other site is near the end of the chromosome.
the data indicate that the bipartition model locates the origin and terminus accurately in these five chromosomes.
1location of the annotated origin as a fraction of chromosome length starting at the ncbi site  <dig>
2location of ml pair as a fraction of chromosome length.
3poml as inferred by which of s1ml or s2ml is closest to the annotated origin.
4distance between the annotated origin and poml.
ribosomal rna genes in circular chromosomes
there is strong evidence that circular chromosomes are organized such that the ribosomal rna  genes tend to be located on the leading strand of replication regardless of where they are distributed along the length of the chromosome  <cit> .
we used this as a basis for assigning ml in the  <dig> primary and  <dig> secondary circular chromosomes in our dataset.
if s1ml is assigned as the origin then in the chromosome portion s1ml → s2ml the + strand is the leading strand while in the s2ml → s1ml portion the – strand is leading.
assigning s2ml as the origin reverses this leading strand assignment.
we calculated the proportion of rrna coded on the leading strand in the two possible organizations and assigned the origin based on which of the two resulted in a majority of rrna genes on the leading strand.
in  <dig> chromosomes there was no annotation of rrna genes while in  <dig> others we could not assign an origin because both possibilities yielded 50% rrna genes on each strand.
for the remaining  <dig> chromosomes,  <dig> had 100% of the rrna genes on the putative leading strand,  <dig> others had > 75% of the rrna genes on the putative leading strand and the  <dig> others had 60% of the rrna genes on the putative leading strand.
an interesting point involves assignment of the origin to the middle of the linear borrelia chromosomes.
in borrelia garinii only 20% of the rrna genes are on the leading strand.
the 23s rrna genes in borrelia garinii are inverted with respect to borrelia burgdorferi where 97% of the rrna sites are on the leading strand.
evidence other than rrna genes
for the  <dig> circular chromosomes noted above for which an origin could not be assigned based on the distribution of rrna genes, we designated ml based on assigning the leading strand in each replication arm as the strand for which the replication-induced effect was inferred to make g > c at four-fold degenerate  sites.
the rationale for this is discussed in the methods and necessarily limits the conclusions we can draw about composition bias in these chromosomes.
identification of genes consistently located near the origin of bacterial chromosomes
one interesting feature of the circular chromosomes in our dataset is the existence of genes that may function in segregating the two replication products during cell division  <cit>  and which appear to be located near the origin of replication in many chromosomes.
in this section we compare the locations of poml in each chromosome to these genes in order to determine the degree of concurrence.
we will do this separately for the  <dig> secondary and  <dig> primary circular chromosomes; the  <dig> linear chromosomes will not be analyzed in this section.
this comparison is not essential for our identification of ml but it provides a way of both assessing our model as well as the proposal that these genes do tend to be located near the replication origin.
secondary chromosomes
in the secondary chromosomes, the segregation system involves either the para and parb genes, along with a co-localized cis element , which is bound by the parb protein, or the repa, repb  and repc genes.
we will refer to this generally as par/rep system; it is found in all of the secondary chromosomes in this study.
the location of the par/rep genes in each of the  <dig> secondary chromosomes was determined by annotation if possible, while for the chromosomes in which neither was annotated we used a blast search to locate the gene.
in  <dig> of the  <dig> secondary chromosomes we find that poml is within 1% of the genome length of par/rep and in one of the other two chromosomes the distances is  <dig> % of the chromosome length .
in the remaining case, rhodobacter sphaeroides chromosome  <dig>  it is ptml and not poml that is near par/rep, although the assignation of po was based on it resulting in all of the rrna genes being on the leading strand .
therefore, either poml is near the par/rep location and none of the rrna genes are on the leading strand or ptml is near the par/rep location and all of the rrna genes are on the leading strand.
it is possible that a recent inversion or other chromosome rearrangement resulted in a separation of the segregation genes and the origin, leading to an incorrect assignment of the origin based on rrna distribution.
overall, the co-localization of ptml and the par/rep genes in all but this one case provides strong evidence that the bipartition model is accurately locating the replication origin.
1para or repa location , as a fraction of chromosome length starting at the ncbi site  <dig>
2poml as inferred from rrna sites or σgc >  <dig> .
3distance between para/repa location and poml.
primary chromosomes
for the analysis of the  <dig> primary, circular chromosomes we excluded  <dig> chromosomes for which the statistical significance of ml is uncertain;  <dig> of them because there was no evidence for a replication-induced effect on composition, and the other  <dig> because the confidence limit of the genome division parameter cd spanned more than 20% of the chromosome.
for the remaining  <dig> chromosomes we used what we will call an "origin gene" approach to assess the location of poml, an approach that is similar to what was applied to the secondary chromosomes.
unlike the secondary chromosomes, there is no single cluster of genes that can be used to locate the origin in all of the primary genomes in the dataset.
despite this lack of a universal gene cluster, evidence indicates that the origin of replication in these primary chromosomes is frequently located nearby any or all of several genes which may actually have formed an ancestral origin gene "cluster"  <cit> .
these genes, which we will refer to as "origin genes", are para, parb, gida, gidb, yidc, yidd, rnpa, rpmh, dnaa and dnan  <cit> .
these genes vary in location with respect to one another and thus cannot always be used to determine a single chromosome location, but despite this, evidence from chromosomes where these genes have been studied indicates that at least one of these genes is close to the origin in any given chromosome  <cit> .
we used these so-called origin genes to assess poml as follows.
ncbi annotations were used to locate all genes annotated with any of the  <dig> gene names.
since these genes are not located together across all chromosomes we treated them as  <dig> pairs that tend to be co-located; para and parb, gida and gidb, yidc and yidd, rnpa and rpmh, and dnaa and dnan.
a chromosome was scored as having a specific gene pair if both genes in that pair were annotated and the mid-points were within  <dig> kb of each other or if only one gene of the pair was annotated .
we then scored poml as being located near that specific pair if it was within 1% of the chromosome length of the midpoint between the two genes or from the mid-point of the single annotated gene.
of the  <dig> chromosomes,  <dig> had none of the  <dig> genes annotated and thus could not be assessed.
for the remaining  <dig>  table  <dig> shows the number of gene pairs that were scored for each chromosome along with how many chromosomes had poml near any pair.
overall  <dig> chromosomes  have the putative origin within 1% of the genome length of one of the pairs and of the  <dig> chromosomes that have  <dig> or more gene pairs,  <dig>  have the putative origin within 1% of the length from a gene pair.
of the  <dig> chromosomes with all  <dig> gene pairs located,  <dig> have poml near at least one pair and in the one exception , all  <dig> gene pairs were close to one another and the putative origin was between  <dig> % and  <dig> % of the pairs.
in addition, in cases where there was more than one gene pair annotated, the most common category in table  <dig> is that in which poml is located within 1% of all identified gene pairs.
this indicates that the origin genes were all clustered and very close to our putative origin.
the results confirm that the replication origin is frequently near one or more of the set of "origin genes".
1number of "origin gene" pairs found in any given chromosome, as defined in the text.
2number of chromosomes for which the specified number of origin gene pairs is found within 1% of the chromosome length from poml.
when multiple origin gene pairs are found near poml it indicates that the gene pairs are close together on the chromosome.
3total number of chromosomes with that number of annotated gene pairs regardless of whether or not any pair is close to poml.
r-dependent component of skew across bacterial chromosomes
once we have identified ml for each chromosome we can use our model to calculate the effect of leading vs lagging strand mutation differences, the r-dependent component of skew.
as discussed in the methods, the r-dependent component is best estimated by using sites least affected by selection.
the intergenic  regions and four fold degenerate  sites of cds regions are possible choices.
we used relative σ values  to compare the r-dependent component of skew across all  <dig> bacterial chromosomes.
these measures represent the proportional increase of g and t, respectively, on the leading strand as a result of mutational differences between the leading and lagging strands.
there is a strong correlation between ig and d <dig> for both rg  and rt , indicating that they give similar estimates of the relative contribution of the r-dependent mutation effect to skew.
it also suggests that transcription-coupled mutation effects are not strongly affecting the estimates of r-independent effects at d <dig> sites.
however, the data also show that for most chromosomes the absolute value of the skew is stronger for d <dig> sites than ig sites, for both rg and rt.
we propose, based on the compact nature of intergenic sites in bacterial genomes and the existence of regulatory sequences within these regions, that this is most likely due to selective constraints on many intergenic sites similar to recent findings from drosophila  <cit> , and that the d <dig> sites provide the more accurate estimation of the contribution of the r-dependent component.
therefore, we will use these sites to examine this component of skew across bacterial chromosomes.
given that there is also a strong correlation between d <dig> sites coded on the + and - strands across the  <dig> bacterial chromosomes , we calculated the average of the two strands for both rg and rt to obtain a single estimate to assess the relative strength of replication-induced skew .
we also calculated a measure of overall skew sqrt and those chromosomes with the strongest and weakest overall skew are shown in table  <dig>  there are  <dig> chromosomes that have a significantly stronger g/c than t/a skew  and  <dig> that have a significantly stronger t/a than g/c skew .
rg and rt are not significantly different in the remaining  <dig>  this suggests that mutation bias tends to generate a stronger g/c skew across microbial chromosomes  <cit>  but a statistical analysis is confounded by the fact that the points are not independent due to shared ancestry as well as the fact that the species that have been sequenced have not been sampled randomly.
1overall skew given by sqrt
the g/c skew is almost exclusively biased towards g, which agrees with the observation of lobry and sueoka  <cit>  who found that g > c on the leading strand in almost all of the bacterial genomes they surveyed, the one exception being the linear chromosome of streptomyces coelicolor.
since we used the criterion of g > c on the leading strand to assign poml for  <dig> of the circular chromosomes, we excluded these from an assessment of the pattern of g/c bias.
of the remaining  <dig> chromosomes, only  <dig> show a significant leading strand skew towards c. these are bifidobacterium longum, thermobifida fusca yx, deinococcus radiodurans r <dig>  tropheryma whipplei tw08/ <dig>  t. whipplei str.
twist, mycoplasma mobile 163k and m. penetrans hf- <dig> as well as the two linear streptomyces chromosomes, streptomyces avermitilis ma- <dig> and s. coelicolor.
we also find that among those chromosomes with a significant t/a skew ,  <dig> have a significant skew towards t and  <dig> a significant skew towards a. overall, there were  <dig> chromosomes with a significant g&t bias,  <dig> with a g&a bias,  <dig> with a c&t bias and  <dig> with a c&a bias on the leading strand.
this analysis supports the finding of lobry and sueoka  <cit>  that the g&t  skew is more common than g&a  skew on the leading strand.
statistical analysis is again confounded by non-independence of points.
despite the limitations that arise from the non-independence of the chromosomes one conclusion that can be drawn from the data is that the chromosomes with a purine  skew are predominantly gram-positive bacteria .
lobry and sueoka  <cit>  previously noted the exception of the gram-positive lactococcus lactis and staphylococcus aureus to the general trend of keto skew.
we show that it is a common feature across the firmicutes, with the exception of the genus mycoplasma with  <dig> representative chromosomes, all of which show very little overall r-dependent effect.
of the  <dig> genomes that have significant strand average skew towards a in figure  <dig>   <dig> are firmicutes and only  <dig> of the  <dig> sequenced gram-positive chromosomes show significant strand average skew towards t .
these trends are difficult to assess without a general knowledge of how rapidly mutational biases change and the degree of relationship in the genomes being compared, but it does appear that the gram-positive chromosomes tend to show a different general pattern of skew than other prokaryotes.
the difference in composition bias between the firmicutes and the other bacterial lineages may be related to a general difference in the mode of replication.
it has been noted previously that those species that have a leading strand bias towards a over t have a polc homolog in addition to a dnae homolog  <cit> .
these authors point out that proofreading in species with only a dnae homolog involves an interaction of the Θ and α subunits while in species that also have a polc homolog proofreading involves only the α subunit.
this difference is probably sufficient to result in the general difference in mutation pattern but it is also the case that the firmicutes show a stronger tendency to code genes on the leading strand than do other lineages  <cit> .
this could conceivably contribute to an r-dependent mutation effect if there is a transcription-coupled repair system or if the lagging strand is more frequently in the single stranded state as a result, given the much greater tendency of ssdna than dsdna to undergo cytosine deamination  <cit> .
if we consider overall skew  there are some general points that are apparent, although these might partly reflect the non-random sample of genomes that have been sequenced.
the high degree of overall skew in borrelia noted by loby and sueoka  <cit>  is apparent in our data, and the other taxa they noted as having strong skew  rank in the  <dig> chromosomes with strongest skew .
the alphaproteobacteria  and the firmicutes are disproportionately represented in the high skew genomes  while the cyanobacteria tend to have low skew .
there are exceptions in each case  suggesting that mutational biases can vary dramatically and, perhaps, rapidly across lineages.
in a previous survey, rocha  <cit>  also reported a low general skew in cyanobacteria which is consistent with our finding, but also reported a low skew in the alphaproteobacteria.
the difference in the later case could be due to our use of an estimate from putatively neutral sites instead of a general composition bias.
CONCLUSIONS
the bipartition model allows us to quantify the contribution of the mutational difference between leading and lagging strands to nucleotide skew and also allows us to estimate the locations of the origin and terminus in chromosomes with bi-directional replication when the accumulation of skew is sufficiently strong.
the model has several advantages over other methods of analyzing genome skew.
first, using the model we can quantify the role of mutation in generating skew so that the effect on composition, for example codon bias, can be assessed.
second, it provides an objective method for locating origin and terminus that exploits composition bias.
finally, the model has the potential to be utilized in a maximum likelihood framework in order to analyze various aspects of genome structure, such as the effect of chromosome rearrangements on nucleotide composition.

 with the recent accumulation of complete bacterial genome sequences there has been increased attention to prokaryote chromosome organization. one prominent aspect of most of these genomes is that several features, such as nucleotide composition and coding strand bias, display an organization that is centered on the origin of replication. in these chromosomes, as exemplified by escherichia coli, replication initiates at a single origin and proceeds bi-directionally to a terminus where the two forks meet. this divides the chromosome into a replichore, defined as a chromosome with two oppositely replicated halves, within each of which there is a leading and lagging strand such that one dna strand is leading within one replication arm but lagging within the other. many bacterial genomes display a compositional asymmetry between the two dna strands within a replication arm meaning that parity rule which stipulates that the frequencies of a and t are equal as are the frequencies of g and c, is violated. observed strand asymmetry, or skew, in base composition is either a purine or a keto excess on one strand and the leading strand in one replication arm shows the same skew as the leading strand in the other despite the fact that they are opposite genome strands. one issue that has arisen from these observations is the cause of the compositional asymmetry between strands, with evidence having been presented for contributions from both mutation and selection. many of the prokaryotes that have a replichore structure also have a bias towards coding genes, particularly'essential' genes, on the leading strand suggesting that composition asymmetry could result from selection and/or transcription-coupled mutation and repair processes. there is also evidence, though, that leading and lagging strands differ in mutation bias, which has interesting and important implications for genome evolution. although there have been estimates of the contribution of mutation to skew in several genomes that suggest a role for selection the issue has not been studied within a statistical framework. replichores with strand asymmetry have also been exploited to make inferences about the location of an origin of replication when the origin has not been mapped experimentally, which is the case in the vast majority of sequenced genomes. the compositional difference between leading and lagging strands, and the replichore structure in general, means that the two dna strands have complementary composition biases in the two replication arms of these genomes. plotting composition skew along a sliding window leads to a characteristic pattern in which the origin lies at a point where a given measurement of strand asymmetry switches between positive and negative values. this type of graphical approach has been used frequently to infer the location of replication origins but these approaches have the disadvantage that determining the existence of skew and where it switches strand is subjective. a more objective linear discriminant analysis has also been developed, but this method does not account for gene density nor does it utilize intergenic regions. we develop a simple bipartition model that exploits the existence of a replichore structure with strand asymmetry and provides for analyses within a maximum likelihood framework. in the current study we will apply the model to bacterial chromosomes in two analyses. the first is the identification of two peaks on a likelihood surface, the locations of the putative origin and terminus of replication. additional information, such as the organization of ribosomal rna genes, can then be used to infer which of the two locations is the origin. in this study we assign the origin to maximize the arrangement of rrna genes on the resulting leading strands and then compare the location of our putative origin to "origin-associated" genes that are located at or close to the replication origin in certain genomes. the second application is a statistical analysis of the contribution of mutation to nucleotide composition skew across bacterial species. 1the two phyla with the largest sample sizes are shown sub-divided by class representation.  we applied the bipartition model to fully sequenced bacterial chromosomes. an assessment of the mutational component of compositional skew requires an identification of the origin and terminus of replication. since these have not been empirically identified in most genomes we first use the model to generate a maximum likelihood estimation of the two loci and discuss the accuracy of this approach. once the putative origin and terminus have been identified for each chromosome we use the model to quantify the degree to which the mutational difference between leading and lagging strands generates a skew. replication arms comprise half of most bacterial chromosomes we expect that if the unordered pair of sites identified by our model as the potential origin and terminus is an accurate estimation of the replication origin and terminus then these two sites should divide the chromosome roughly in half. the existence of such a physical balance is the basis of the adopt-adapt model, which proposes that this balance would guarantee a synchronous completion of replication by the two forks. the distribution of chromosome divisions, measured by the statistic cd is shown in figure for the circular chromosomes in which the percent confidence interval of cd was less than 20% of the chromosome. linear chromosomes were also excluded since the method of calculating the confidence interval cannot be applied to them. we took cd between and as indicating a relatively equal division of chromosome arms and > as an arbitrary measure of an inequitable division: these are chromosome in which ml generated a replication arm less than 40% of the total length. of the chromosomes analyzed, had an inequitable division by our definition. overall, this result agrees with the prediction of the'adopt-adapt' model. the advantage to such an arrangement would presumably be that it results in the shortest possible replication time, which would otherwise be limited by the time taken to replicate the longer of the two arms. 1one replication arm less than 40% of the total chromosome length. 2primary chromosome unless otherwise indicated. 3class is given only for firmicutes and proteobacteria as in table given an expectation for physical balance of chromosomes, it is possible that the chromosomes with an inequitable division have undergone recent rearrangements. large indels in either replication arm or inversions that include either the origin or the terminus could lead to deviations from equitable distribution. this cannot be investigated for all cases since many chromosomes have not been studied in great detail or do not have close relatives for comparison, but evidence suggests that at least some of these chromosomes have undergone the predicted rearrangements. for example, pseudomonas aeruginosa pa has a large inversion encompassing about 1/ the genome, yersinia pestis str. has significant inversions surrounding the putative origin and prochlorococcus marinus mit has several genome rearrangements relative to strain med and is also much larger. candidatus blochmannia pennsylvanicus str. bpen has undergone significant gene loss relative to b. floridanus, halobacterium sp. nrc- contains insertion sequences from different families and candidatus pelagibacter ubique htcc has a very small genome that appears to have undergone numerous recent deletions. these rearrangements suggest the possibility that the origin and terminus in these chromosomes do, in fact, yield a noticeably inequitable division. although it seems likely that selection would favor an equitably divided genome, it is not known how rapidly a chromosome would regain equitable division following such a rearrangement and the genomes in table may be evolving towards a more equitable division. alternatively, it could be that the genome assembly was performed incorrectly or that in these cases skew is not at equilibrium as a result of genome rearrangement and ml does not represent the origin and terminus. if this is the case then any method that utilizes composition skews to estimate the origin of replication, whether our ml approach or a graphical approach, would be misled. locating the putative replication origins of bacterial chromosomes we used ml to assign a putative origin/terminus pair for the chromosomes in our dataset. as described in the methods we used several different methods to accomplish this; each are described separately. where possible we can compare our results to empirically identified replication origins to assess the accuracy of our approach. linear chromosomes the five linear chromosomes are relatively simple since an origin has been annotated for each at the center of the genome and these annotations appear to be reliable: the annotations for borrelia burgdorferi and b. garnii are based on empirical evidence as are the annotations for the two streptomyces taxa, and in the case of a. tumefaciens the annotation is based on an analysis of the repabc genes. therefore, we can assign poml and ptml for the linear chromosomes in the dataset using the annotated origins and assess our method. we find a putative origin near the annotated origin in each of the five linear chromosomes; in three it is within % of the genome length of the annotated origin while in the other two it is within 3% of the genome length. in each case the other site is near the end of the chromosome. the data indicate that the bipartition model locates the origin and terminus accurately in these five chromosomes. 1location of the annotated origin as a fraction of chromosome length starting at the ncbi site 2location of ml pair as a fraction of chromosome length. 3poml as inferred by which of s1ml or s2ml is closest to the annotated origin. 4distance between the annotated origin and poml. ribosomal rna genes in circular chromosomes there is strong evidence that circular chromosomes are organized such that the ribosomal rna genes tend to be located on the leading strand of replication regardless of where they are distributed along the length of the chromosome. we used this as a basis for assigning ml in the primary and secondary circular chromosomes in our dataset. if s1ml is assigned as the origin then in the chromosome portion s1ml → s2ml the + strand is the leading strand while in the s2ml → s1ml portion the – strand is leading. assigning s2ml as the origin reverses this leading strand assignment. we calculated the proportion of rrna coded on the leading strand in the two possible organizations and assigned the origin based on which of the two resulted in a majority of rrna genes on the leading strand. in chromosomes there was no annotation of rrna genes while in others we could not assign an origin because both possibilities yielded 50% rrna genes on each strand. for the remaining chromosomes, had 100% of the rrna genes on the putative leading strand, others had > 75% of the rrna genes on the putative leading strand and the others had 60% of the rrna genes on the putative leading strand. an interesting point involves assignment of the origin to the middle of the linear borrelia chromosomes. in borrelia garinii only 20% of the rrna genes are on the leading strand. the 23s rrna genes in borrelia garinii are inverted with respect to borrelia burgdorferi where 97% of the rrna sites are on the leading strand. evidence other than rrna genes for the circular chromosomes noted above for which an origin could not be assigned based on the distribution of rrna genes, we designated ml based on assigning the leading strand in each replication arm as the strand for which the replication-induced effect was inferred to make g > c at four-fold degenerate sites. the rationale for this is discussed in the methods and necessarily limits the conclusions we can draw about composition bias in these chromosomes. identification of genes consistently located near the origin of bacterial chromosomes one interesting feature of the circular chromosomes in our dataset is the existence of genes that may function in segregating the two replication products during cell division and which appear to be located near the origin of replication in many chromosomes. in this section we compare the locations of poml in each chromosome to these genes in order to determine the degree of concurrence. we will do this separately for the secondary and primary circular chromosomes; the linear chromosomes will not be analyzed in this section. this comparison is not essential for our identification of ml but it provides a way of both assessing our model as well as the proposal that these genes do tend to be located near the replication origin. secondary chromosomes in the secondary chromosomes, the segregation system involves either the para and parb genes, along with a co-localized cis element, which is bound by the parb protein, or the repa, repb and repc genes. we will refer to this generally as par/rep system; it is found in all of the secondary chromosomes in this study. the location of the par/rep genes in each of the secondary chromosomes was determined by annotation if possible, while for the chromosomes in which neither was annotated we used a blast search to locate the gene. in of the secondary chromosomes we find that poml is within 1% of the genome length of par/rep and in one of the other two chromosomes the distances is % of the chromosome length. in the remaining case, rhodobacter sphaeroides chromosome it is ptml and not poml that is near par/rep, although the assignation of po was based on it resulting in all of the rrna genes being on the leading strand. therefore, either poml is near the par/rep location and none of the rrna genes are on the leading strand or ptml is near the par/rep location and all of the rrna genes are on the leading strand. it is possible that a recent inversion or other chromosome rearrangement resulted in a separation of the segregation genes and the origin, leading to an incorrect assignment of the origin based on rrna distribution. overall, the co-localization of ptml and the par/rep genes in all but this one case provides strong evidence that the bipartition model is accurately locating the replication origin. 1para or repa location, as a fraction of chromosome length starting at the ncbi site 2poml as inferred from rrna sites or σgc >. 3distance between para/repa location and poml. primary chromosomes for the analysis of the primary, circular chromosomes we excluded chromosomes for which the statistical significance of ml is uncertain; of them because there was no evidence for a replication-induced effect on composition, and the other because the confidence limit of the genome division parameter cd spanned more than 20% of the chromosome. for the remaining chromosomes we used what we will call an "origin gene" approach to assess the location of poml, an approach that is similar to what was applied to the secondary chromosomes. unlike the secondary chromosomes, there is no single cluster of genes that can be used to locate the origin in all of the primary genomes in the dataset. despite this lack of a universal gene cluster, evidence indicates that the origin of replication in these primary chromosomes is frequently located nearby any or all of several genes which may actually have formed an ancestral origin gene "cluster". these genes, which we will refer to as "origin genes", are para, parb, gida, gidb, yidc, yidd, rnpa, rpmh, dnaa and dnan. these genes vary in location with respect to one another and thus cannot always be used to determine a single chromosome location, but despite this, evidence from chromosomes where these genes have been studied indicates that at least one of these genes is close to the origin in any given chromosome. we used these so-called origin genes to assess poml as follows. ncbi annotations were used to locate all genes annotated with any of the gene names. since these genes are not located together across all chromosomes we treated them as pairs that tend to be co-located; para and parb, gida and gidb, yidc and yidd, rnpa and rpmh, and dnaa and dnan. a chromosome was scored as having a specific gene pair if both genes in that pair were annotated and the mid-points were within kb of each other or if only one gene of the pair was annotated. we then scored poml as being located near that specific pair if it was within 1% of the chromosome length of the midpoint between the two genes or from the mid-point of the single annotated gene. of the chromosomes, had none of the genes annotated and thus could not be assessed. for the remaining table shows the number of gene pairs that were scored for each chromosome along with how many chromosomes had poml near any pair. overall chromosomes have the putative origin within 1% of the genome length of one of the pairs and of the chromosomes that have or more gene pairs, have the putative origin within 1% of the length from a gene pair. of the chromosomes with all gene pairs located, have poml near at least one pair and in the one exception, all gene pairs were close to one another and the putative origin was between % and % of the pairs. in addition, in cases where there was more than one gene pair annotated, the most common category in table is that in which poml is located within 1% of all identified gene pairs. this indicates that the origin genes were all clustered and very close to our putative origin. the results confirm that the replication origin is frequently near one or more of the set of "origin genes". 1number of "origin gene" pairs found in any given chromosome, as defined in the text. 2number of chromosomes for which the specified number of origin gene pairs is found within 1% of the chromosome length from poml. when multiple origin gene pairs are found near poml it indicates that the gene pairs are close together on the chromosome. 3total number of chromosomes with that number of annotated gene pairs regardless of whether or not any pair is close to poml. r-dependent component of skew across bacterial chromosomes once we have identified ml for each chromosome we can use our model to calculate the effect of leading vs lagging strand mutation differences, the r-dependent component of skew. as discussed in the methods, the r-dependent component is best estimated by using sites least affected by selection. the intergenic regions and four fold degenerate sites of cds regions are possible choices. we used relative σ values to compare the r-dependent component of skew across all bacterial chromosomes. these measures represent the proportional increase of g and t, respectively, on the leading strand as a result of mutational differences between the leading and lagging strands. there is a strong correlation between ig and d for both rg and rt, indicating that they give similar estimates of the relative contribution of the r-dependent mutation effect to skew. it also suggests that transcription-coupled mutation effects are not strongly affecting the estimates of r-independent effects at d sites. however, the data also show that for most chromosomes the absolute value of the skew is stronger for d sites than ig sites, for both rg and rt. we propose, based on the compact nature of intergenic sites in bacterial genomes and the existence of regulatory sequences within these regions, that this is most likely due to selective constraints on many intergenic sites similar to recent findings from drosophila, and that the d sites provide the more accurate estimation of the contribution of the r-dependent component. therefore, we will use these sites to examine this component of skew across bacterial chromosomes. given that there is also a strong correlation between d sites coded on the + and - strands across the bacterial chromosomes, we calculated the average of the two strands for both rg and rt to obtain a single estimate to assess the relative strength of replication-induced skew. we also calculated a measure of overall skew sqrt and those chromosomes with the strongest and weakest overall skew are shown in table there are chromosomes that have a significantly stronger g/c than t/a skew and that have a significantly stronger t/a than g/c skew. rg and rt are not significantly different in the remaining this suggests that mutation bias tends to generate a stronger g/c skew across microbial chromosomes but a statistical analysis is confounded by the fact that the points are not independent due to shared ancestry as well as the fact that the species that have been sequenced have not been sampled randomly. 1overall skew given by sqrt the g/c skew is almost exclusively biased towards g, which agrees with the observation of lobry and sueoka who found that g > c on the leading strand in almost all of the bacterial genomes they surveyed, the one exception being the linear chromosome of streptomyces coelicolor. since we used the criterion of g > c on the leading strand to assign poml for of the circular chromosomes, we excluded these from an assessment of the pattern of g/c bias. of the remaining chromosomes, only show a significant leading strand skew towards c. these are bifidobacterium longum, thermobifida fusca yx, deinococcus radiodurans r tropheryma whipplei tw08/ t. whipplei str. twist, mycoplasma mobile 163k and m. penetrans hf- as well as the two linear streptomyces chromosomes, streptomyces avermitilis ma- and s. coelicolor. we also find that among those chromosomes with a significant t/a skew, have a significant skew towards t and a significant skew towards a. overall, there were chromosomes with a significant g&t bias, with a g&a bias, with a c&t bias and with a c&a bias on the leading strand. this analysis supports the finding of lobry and sueoka that the g&t skew is more common than g&a skew on the leading strand. statistical analysis is again confounded by non-independence of points. despite the limitations that arise from the non-independence of the chromosomes one conclusion that can be drawn from the data is that the chromosomes with a purine skew are predominantly gram-positive bacteria. lobry and sueoka previously noted the exception of the gram-positive lactococcus lactis and staphylococcus aureus to the general trend of keto skew. we show that it is a common feature across the firmicutes, with the exception of the genus mycoplasma with representative chromosomes, all of which show very little overall r-dependent effect. of the genomes that have significant strand average skew towards a in figure are firmicutes and only of the sequenced gram-positive chromosomes show significant strand average skew towards t. these trends are difficult to assess without a general knowledge of how rapidly mutational biases change and the degree of relationship in the genomes being compared, but it does appear that the gram-positive chromosomes tend to show a different general pattern of skew than other prokaryotes. the difference in composition bias between the firmicutes and the other bacterial lineages may be related to a general difference in the mode of replication. it has been noted previously that those species that have a leading strand bias towards a over t have a polc homolog in addition to a dnae homolog. these authors point out that proofreading in species with only a dnae homolog involves an interaction of the Θ and α subunits while in species that also have a polc homolog proofreading involves only the α subunit. this difference is probably sufficient to result in the general difference in mutation pattern but it is also the case that the firmicutes show a stronger tendency to code genes on the leading strand than do other lineages. this could conceivably contribute to an r-dependent mutation effect if there is a transcription-coupled repair system or if the lagging strand is more frequently in the single stranded state as a result, given the much greater tendency of ssdna than dsdna to undergo cytosine deamination. if we consider overall skew there are some general points that are apparent, although these might partly reflect the non-random sample of genomes that have been sequenced. the high degree of overall skew in borrelia noted by loby and sueoka is apparent in our data, and the other taxa they noted as having strong skew rank in the chromosomes with strongest skew. the alphaproteobacteria and the firmicutes are disproportionately represented in the high skew genomes while the cyanobacteria tend to have low skew. there are exceptions in each case suggesting that mutational biases can vary dramatically and, perhaps, rapidly across lineages. in a previous survey, rocha also reported a low general skew in cyanobacteria which is consistent with our finding, but also reported a low skew in the alphaproteobacteria. the difference in the later case could be due to our use of an estimate from putatively neutral sites instead of a general composition bias.  the bipartition model allows us to quantify the contribution of the mutational difference between leading and lagging strands to nucleotide skew and also allows us to estimate the locations of the origin and terminus in chromosomes with bi-directional replication when the accumulation of skew is sufficiently strong. the model has several advantages over other methods of analyzing genome skew. first, using the model we can quantify the role of mutation in generating skew so that the effect on composition, for example codon bias, can be assessed. second, it provides an objective method for locating origin and terminus that exploits composition bias. finally, the model has the potential to be utilized in a maximum likelihood framework in order to analyze various aspects of genome structure, such as the effect of chromosome rearrangements on nucleotide composition. 
finally, the model has the potential to be utilized in a maximum likelihood framework in order to analyze the effect of chromosome rearrangements on nucleotide composition. this indicates that our model provides an accurate, objective method of determining the replication arms and also provides support for the hypothesis that these genes represent an ancestral cluster of origin-associated genes. second, it provides an objective method for locating origin and terminus, one that is based on chromosome-wide accumulation of leading vs lagging strand nucleotide differences. we find that our estimations for the origin and terminus agree very well with the location of genes that are thought to be associated with the replication origin. mutational differences between these strands result in an overall pattern of skew that is centered about the origin of replication. we describe a model to quantify the contribution of mutational differences between the leading and lagging strands in producing replication-induced skew. first, it quantifies the role of mutation in generating skew so that its effect on composition, for example codon bias, can be assessed. the relative contributions of selection and mutation in producing compositional skew are largely unknown. the model may also be implemented in a maximum likelihood framework to estimate the locations of origin and terminus. the model has several advantages over other methods of analyzing genome skew. when the origin and terminus of replication are known, the model can be used to estimate the relative accumulation of g over c and of a over t on the leading strand due to replication effects in a chromosome with bidirectional replication arms.
 many bacterial chromosomes display nucleotide asymmetry, or skew, between the leading and lagging strands of replication. mutational differences between these strands result in an overall pattern of skew that is centered about the origin of replication. such a pattern could also arise from selection coupled with a bias for genes coded on the leading strand. the relative contributions of selection and mutation in producing compositional skew are largely unknown.  we describe a model to quantify the contribution of mutational differences between the leading and lagging strands in producing replication-induced skew. when the origin and terminus of replication are known, the model can be used to estimate the relative accumulation of g over c and of a over t on the leading strand due to replication effects in a chromosome with bidirectional replication arms. the model may also be implemented in a maximum likelihood framework to estimate the locations of origin and terminus. we find that our estimations for the origin and terminus agree very well with the location of genes that are thought to be associated with the replication origin. this indicates that our model provides an accurate, objective method of determining the replication arms and also provides support for the hypothesis that these genes represent an ancestral cluster of origin-associated genes.  the model has several advantages over other methods of analyzing genome skew. first, it quantifies the role of mutation in generating skew so that its effect on composition, for example codon bias, can be assessed. second, it provides an objective method for locating origin and terminus, one that is based on chromosome-wide accumulation of leading vs lagging strand nucleotide differences. finally, the model has the potential to be utilized in a maximum likelihood framework in order to analyze the effect of chromosome rearrangements on nucleotide composition. 