BACKGROUND
categorising organisms has always been a key activity in biology.
numerous methods exist, and each reflects particular properties of the organism studied  <cit> .
for microbial organisms, genome sequences are now commonly used as a basis for determining phylogenetic relationships.
the simple comparison of nucleotide content  between species is probably the most used and one of the easiest methods for whole genome comparisons.
at/gc content however, will not necessarily provide reliable information about phylogenetic relationships.
it has been proposed that the chromosomal average gc content is more reflective of the environment in which the organism lives, and sometimes less related to its taxonomic group  <cit> .
this is in part due to differences in codon usage, which has been presumed to be reflective of the environment in many ways, such as the organism's growth temperature  <cit> , size of the genome and optimal growth rate  <cit> , and anaerobic or aerobic growth conditions  <cit> .
thus, the amino acid composition and gc content of an organism seems to be related to its ecological niche  <cit> .
since oligonucleotide usage is influenced by gc content, the habitat of an organism may be largely responsible for the observed dna word frequencies in genomic dna.
in most bacteria, the distribution of guanine compared to cytosine on the same strand  varies along the chromosome  <cit> , with g's generally biased towards the replication leading strand for nearly all genomes studied so far.
skews in guanine compared to cytosine, or to a lesser extent adenine versus thymine, may indicate where and how dna replication is taking place and can help identifying the replication leading or lagging strands, as well as the origin and terminus of replication  <cit> .
although this method works for many prokaryotes some have skews that are much less pronounced or even undetectable.
worning and coworkers  <cit>  found that scoring strand bias frequencies of progressively larger oligonucleotides, from dinucleotides up to heptanucleotides, and their reverse complements, the chromosomal location of the origin and terminus of dna replication could be predicted for nearly all sequenced prokaryotic genomes.
weinel et al.
<cit>  have looked at the over- and under-representation of oligonucleotides up to 14-mers to compare two different species of pseudomonas.
abe and colleagues  <cit>  used an algorithm based on neural networks to classify dna of unknown source by focusing on tetranucleotide frequency distributions.
distributions of oligonucleotides can therefore be used as a more refined way of discriminating between different bacterial genomes.
samuel karlin and coworkers  <cit>  applied odds-ratios consisting of observed dinucleotide frequencies divided by expected, determined by genomic nucleotide content, to compare genomes to each other.
this method actually dates back to the 1960s  <cit> , but its use has become more popular due to the growing amount of sequenced data available.
these relative abundance patterns, or zero order markov distributions , were coined genomic signatures by karlin and coworkers  <cit> .
the reason for calling these distributions "genomic signatures" was that zoms were thought to reflect species-specific properties not directly found from gc content or oligonucleotide distributions.
further, zoms were found to vary much less within than between even closely related genomes, almost regardless of where dna was sampled from within the chromosome.
zoms indicate if oligonucleotides are over- or under-represented in dna sequences compared with what is expected from average genomic nucleotide content.
differences between observed and expected oligonucleotide distributions might reflect dna structural conformations, such as dna curvature, flexibility, and "meltable" regions, in addition to transcription/restriction and other protein binding sites  <cit> .
while karlin and others  <cit>  focused on dinucleotide zoms, pride and colleagues  <cit>  compared tetranucleotide zoms and tetranucleotide distributions predicted by a markov chain model  to 16s rrna based trees to investigate which of the methods had the strongest phylogenetic signal.
the markov chain method assumes that tetranucleotide frequencies have the same likelihood of occurrence, given trinucleotide frequencies, as trinucleotide frequencies have, given dinucleotide frequencies.
alternatively, this can be considered as a tetranucleotide frequency approximation with overlapping trinucleotide frequencies normalized with dinucleotide frequencies.
a thorough investigation of how markov chains approximate oligonucleotides in escherichia coli can be found in  <cit> .
even though the tetranucleotide mcm is calculated from observed di- and trinucleotide frequencies, the zom method, which only uses nucleotide content to approximate tetranucleotides, showed a better congruency towards the 16s rrna based trees than the mcm method  <cit> .
it was also demonstrated that tetranucleotide zoms differed in coding and non-coding areas in contrast to dinucleotide zoms  <cit> .
it is the goal of this paper to examine the strengths and weaknesses of a series of dna sequence comparison methods, based on statistical distributions of oligonucleotides.
these methods include relative oligonucleotide frequencies , di- to hexanucleotide zoms and tetranucleotide mcms.
in the literature the focus has mainly been on di-  <cit>  and tetranucleotide zoms  <cit> , and tetranucleotide rofs  <cit>  and mcms  <cit> .
in this work, tri-, penta- and hexanucleotide zoms are included additionally to see how they compare against the more popular measures and whether they have any useful differences.
the different measures are compared against each other, both as tools for dna profiling and sequence comparisons, and the most appropriate measure is used to look at plasmid-host relations as an application.
RESULTS
comparing the phylogenetic strength of the statistical measures using a random dna sequence
in the first test, all the measures mentioned above were used to compare  <dig> bacterial and archaeal chromosomes and plasmids with a completely random dna sequence with similar size and gc content to an e. coli chromosome, which for this case can be considered as a  <dig> mbp genome with 50% gc.
lower correlation values between genomes and the random dna sequences means that the method is more reliable with fewer false positives.
for all measures, correlation values above  <dig>  indicate some kind of relation.
from figure  <dig>  it can be observed that the dinucleotide zoms had, by far, the largest spread with respect to correlation scores ranging from - <dig>  for pseudoalteromonas haloplanktis strain tac <dig> to methanospirillum hungatei strain jf- <dig> with a correlation of  <dig> .
stepping up to trinucleotide zoms the spread decreased dramatically with p. haloplanktis strain tac <dig>  again having the lowest correlation value of - <dig> , while corynebacterium efficiens strain ys- <dig> had the highest value of  <dig> .
the tetranucleotide zoms were still better, with scores ranging from - <dig>  for p. haloplanktis strain tac <dig> to  <dig>  for leptospira interrogans serovar copenhageni.
pentanucleotide zom correlations ranged from - <dig>  to  <dig> , while hexanucleotide zoms were firmly placed with the lowest correlation scores, never going outside the interval  for all  <dig> dna sequences tested.
turning now to tetranucleotide rofs and mcms, as shown in figure  <dig>  the correlation scores were between , and , respectively.
for the rof measure mostly plasmids were found at the lower end of the correlation score interval.
xylella fastidiosa strain 9a5c and geobacter metallireducens strain gs- <dig> were the first chromosomes from the lower end of the correlation list, obtaining scores of - <dig>  and  <dig> , respectively.
tetranucleotide mcms found sulfolobus solfataricus strain p <dig> and acinetobacter sp.
adp <dig> at each end, respectively, in the correlation score interval .
comparing the measures using real genomes
we used bacillus subtilis subsp.
subtilis str.
<dig>  yersinia pestist biovar microtus str.
<dig> , pseudomonas aeruginosa strain pao <dig> and staphylococcus areus subsp.
aureus strain mu <dig>  to compare the phylogenetic capabilities of the different statistical measures.
additionaly, the measures were used to assess possible phylogenetic relationships of t. maritima, which has been difficult to classify due to extensive horizontal transfer  <cit> .
starting with b. subtilis, see table  <dig> for details concerning strains, correlation scores, gc content and size, the dinucleotide zom measure found the γ-proteobacteria hahella chejuensis strain kctc  <dig>  and firmicutes bacillus licheniformis strain atcc  <dig>  bacillus cereus strain atcc  <dig>  bacillus anthracis strain 'ames ancestor', and bacillus thuringiensis subsp.
konkukian serotype h <dig> strain 97- <dig> ranked after plasmid phcm <dig> belonging to γ-proteobacterium salmonella enterica subsp.
enterica serovar typhi strain ct <dig>  the trinucleotide zom measure found b. licheniformis as the closest match, followed by a set of genomes and plasmids of proteobacteria.
b. licheniformis was the closest genome for tetra- to hexanucleotide zoms.
the penta- and hexanucleotide zoms ranked bacillus clausii strain ksm-k <dig> under b. licheniformis.
the same was observed for the tetranucleotide mcm measure, but in contrast to the zom measures, a set of bacillus species followed, and genera from other phyla obtained only low correlation scores with this measure.
b. licheniformis was also found on the top of the list for the tetranucleotide rof measure, followed by bacillus halodurans strain c- <dig> and geobacillus kaustophilus strain hta <dig>  bacteria from different phyla populated the list further down.
additional file  <dig> contains complete listings of comparisons between b.subtilis and all genomes for the measures discussed.
for p. aeruginosa, see table  <dig> , dinucleotide zoms found plasmids from ralstonia metallidurans strain ch <dig>  xanthomonas campestris pv.
vesicatoria strain 85- <dig> and azoarcus sp.
ebn <dig> as best matches.
the best matching chromosome with the dinucleotide zom measure was the actinobacteriumcorynebacterium jeikeium strain k <dig>
the zom measures from trinucleotides and up ranked pseudomonas entomophila strain l <dig> highest while the α-proteobacterium novosphingobium aromaticivorans strain dsm  <dig> was the third best match.
although all zom measures found the β-proteobacteria ralstonia sp.
relatively close to p. aeruginosa, only penta- and hexanucleotide zoms ranked pseudomonas fluorescens strain pf- <dig> as the third best match.
p. aeruginosa was found closest to p. entomophila and p. fluorescens with the mcm measure, while the β-proteobacterium ralstonia solanacearum strain gmi <dig> followed close behind.
other species of pseudomonas obtained relatively high correlation scores, but were more dispersed, with respect to ranking, than the results from the penta- and hexanucleotide zoms.
the rof measure found ralstonia eutropha strain h <dig> closest to p. aeruginosa, and, with the exception of p. entomophila, other species of pseudomonas were more dispersed for this measure than for any of the other tested.
soil bacteria in general obtained high correlation scores for all the measures tested.
other strains of s. aureus ranked as closest matches to s. aureus subsp.
aureus strain mu <dig>  see table  <dig> , with high correlation scores for all measures.
staphylococcus saprophyticus subsp.
saprophyticus strain atcc  <dig> ranks after all s. aureus strains for all zom measures, while staphylococcus haemolyticus strain jcsc  <dig> followed for tri- to hexanucleotide zoms.
two strains of staphylococcus epidermidis were only found together with s. aureus and s. haemolyticus for tetra- to hexanucleotide zoms.
the γ-proteobacterium acinetobacter sp.
adp <dig> was found closer to s. aureus than s. haemolyticus and s.epidermidis for the dinucleotide zom measure.
all zom measures ranked a set of proteobacteria like photobacterium profundum strain ss <dig> and vibrio fischerii strain es <dig> before other members of the firmicutes phyla.
s. aureus was found close together with other species and genera of firmicutes, just as b. subtilis was, with the mcm measure.
other species of staphylococcus ranked highest, followed by oceanobacillus iheyensis strain hte <dig>
members of the firmicutes phylum were also predominantly present as the best matching members when the rof measure was used, with only the second chromosome of v. fischerii breaking this trend.
v. fischerii, and vibrio sp.
in general, obtained high correlation scores for all measures except the mcm.
for y. pestis biovar microtus str.
<dig>  see table  <dig> , most measures found other "enterics" as closest matches, but with some variations in the rankings.
yersinia pseudotuberculosis strain ip <dig> correlated identically with the other yersinia species, and the relative photorhabdus luminescens subsp.
laumondii strain tto <dig> obtained high correlation scores for all measures.
the dinucleotide zom measure however, found the bacteroidete cytophaga hutchinsonii strain atcc  <dig> as the best match to the yersinia species.
other members of the proteobacteria phyla followed further down the list.
the number of "enterics" close to yersinia sp.
increased with word size for the zom measures.
alcanivorax borkumensis strain sk <dig> ranked highest after p. luminescens for tri- and tetranucleotide zoms while e. coli were closer for penta- and hexanucleotide zoms.
the mcm measure ranked erwinia carotovora subsp.
atroseptica strain scri  <dig> as best match to yersinia sp., followed closely by p. luminescens.
all "enterics" obtained relatively high correlation scores with the mcm measure.
the rof measure ranked sodalis glossinidius strain 'morsitans' as closest match to p. luminescens, and yersinia sp.
plasmids ranked higher with this measure than the others.
comparing the different measures using t. maritima, see table  <dig> , tetranucleotide zoms found the following bacteria closest: archaeoglobus fulgidus strain dsm  <dig>  geobacter metallireducens strain gs  <dig>  and thermococcus kodakaraensis strain kod <dig>  a  <dig> kb plasmid of salinibacter ruber strain dsm  <dig>  psr <dig>  ranked after t. kodakaraensis.
all tested oligonucleotide zoms ranked the thermophilic euryarchaeota t. kodakaraensis highest.
it is interesting to note that for t. maritima the dinucleotide zom measure seemed to be under-correlating much more than for the random genome mentioned above.
tetranucleotide rofs had a. fulgidus, aquifex aeolicus strain vf <dig> and chlamydia trachomatis strain a har- <dig> as closest matches.
the mcm measure ranked t. kodakaraensis strain kod <dig>  pelobacter carbinolicus strain dsm  <dig> and syntrophus aciditrophicus strain sb, both δ-proteobacteria, on top.
a. aeolicus, which is assumed to be one of t. maritima closest sequenced relatives  <cit> , was ranked progressively higher for di- to hexanucleotide zoms, achieving a  <dig>  place for dinucleotide zoms and a  <dig>  place for hexanucleotide zoms.
as was mentioned above, a. aeolicus has the second best correlation score for rofs while tetranucleotide mcms rank a. aeolicus as the  <dig>  closest match with t. maritima.
the markov measures, including both zom and mcm methods, seemed to be more similar to each other than to the rof measure.
considerably higher correlation scores were obtained, on average, for the dinucleotide zom measure, while the hexanucleotide zom and tetranucleotide mcm measures produced the lowest.
the rof measure seemed to have the most varied average correlation scores.
autocorrelation profiles
figures  <dig> and  <dig> illustrate some of the above mentioned measures in autocorrelation profiles of b. subtilis and t. maritima.
the b. subtilis genome is presumed to consist of large sections of horizontally acquired dna  <cit> , and was therefore used to compare the capabilities of the different statistical measures to detect foreign dna.
the autocorrelation profiles in figure  <dig> contain a set of dips that may be conserved and/or foreign dna.
blast  <cit>  searches against the ncbi nr database were used to get information about these special regions, while genes and proteins were examined further with the string database  <cit> .
the dips at  <dig> kbp and  <dig> kbp, see figure  <dig>  were presumed to be remnants of prophages, while the remaining visible dips just short of genomic position  <dig> mbp were conserved proteins and/or rrna genes according to blast.
the two dips just before and after position  <dig> mbp were found to be transcriptional regulators, possibly horizontally transferred  <cit> , while the large dips at positions  <dig>  and  <dig>  mbp are known prophages  <cit> .
it should be noted that blast identified an uvrx gene, involved in dna repair, together with the prophage at position  <dig>  mbp.
three more sections were examined more carefully, and they all turned out to contain rrna genes, except the dip found close to position  <dig>  mbp according to blast.
this dip was fairly easy to observe with the different zom measures, but harder with the rof and mcm measures.
a blast search resulted in a hit for a rodc gene that is active in cell synthesis.
focusing on the t. maritima genome, especially visible  are the two dips located at positions close to  <dig> and  <dig>  mbp, which are barely detectable from the dinucleotide zom profile.
turning to the other measures it can be seen that the tetranucleotide rof profile has a very high average autocorrelation score, yet the dip found in all autocorrelation zom profiles at position close to  <dig>  mbp is hardly visible.
a similar phenomenon was also observed in the tetranucleotide mcm autocorrelation profile.
this profile contained dips that were more pronounced than any of the other profiles, with the ones found close to positions  <dig> kbp and  <dig>  mbp standing particularly out.
selections starting from positions  <dig> kbp,  <dig> kbp,  <dig>  mbp, and  <dig>  mbp all gave hits related to an abc transporter system that is presumed to have been acquired horizontally from species belonging to the archaea kingdom  <cit> .
all the selections were  <dig> kbp except for the last which was  <dig> kbp.
the selections starting from positions  <dig>   <dig> kbp ,  <dig>  mbp, and  <dig>  mbp were all termed hypothetical proteins except for the last, which was termed laci family transcriptional regulator , and the first, position  <dig>  which matched cela and celb genes, which, according to  <cit> , encodes glycosyl hydrolases.
the biggest dip, found in all autocorrelation profiles above, starts at position  <dig> kbp and extends  <dig> kbp, encodes 16s, 23s, and 5s rrna genes according to blast.
at position  <dig>  mbp another large dip was clearly visible on all autocorrelation profiles, except for dinucleotide zom and the mcm measures.
blast listed a spc operon that encodes a set of ribosomial proteins according to  <cit> .
t. maritima is believed to have acquired large amounts of dna from other bacteria and archaea  <cit> .
estimations go as high as 24% from archaea alone and still more dna is presumed to have been acquired from other prokaryotes, and possibly eukaryotic species as well  <cit> .
homologues to all or parts of the extracted sequences at positions  <dig> kbp,  <dig>  mbp and  <dig>  mbp were found in pyrococcus furiosus dsm  <dig>  sinorhizobium meliloti, and clostridium thermocellum atcc  <dig>  respectively.
the hexanucleotide zom and tetranucleotide based mcm had the lowest average autocorrelation scores of the measures tested.
increasing the sliding window size from  <dig> kbp to  <dig> kbp, overlapping every  <dig> kbp, did increase average autocorrelation scores, but visual detail was poorer .
the zom measures were found to be similar, with the tetranucleotide zom possibly the best measure of all tested with respect to size and detail.
other differences include more pronounced dips for tetra- and hexanucleotide zoms, and fewer for rofs, mcms and dinucleotide zoms.
distance homology searches with large dna sequences
for the distant homology search the heptanucleotide frequencies of a  <dig> kbp dna sequence consisting of rrna genes taken from t. maritima were compared against heptanucleotide frequencies in the m. leprae chromosome  with the sliding window approach described in the methods section.
from figure  <dig>  a good hit can be observed that achieved a noticeable higher correlation score around position  <dig>  mbp than any other place in the genome.
blast reports the corresponding dna to be m. leprae 5s, 16s, 23s rrna genes with a 100% identity score.
the dna taken from t. maritima obtained only a 75% identity score with the m. leprae genome, indicating that the rof method can cope with both large and mutated dna sequences, while still being fairly fast.
plasmid-host similarity analysis
tetranucleotide zoms were used to compare plasmids sized  <dig> kbp and larger with corresponding host genomes, totalling  <dig> different bacteria and archaea with  <dig> chromosomes and  <dig> different plasmids.
a minimum plasmid size was used to make the comparisons as accurate as possible between plasmids and hosts using the tetranucleotide zom method.
our findings support the claim in  <cit>  that plasmids are, especially at rich genomes, more distantly related to their host  than what would be expected from their hosts average autocorrelation values based on correspondingly sized sliding windows , see figure  <dig>  and materials and methods section for details.
in addition, we found that plasmid similarity to host, yph, correlated well with host average autocorrelation values, xaac, and gc content, xgc,
yph = 1/ <dig>
r <dig> =  <dig>  , i.e.
higher gc content and chromosomal average zom autocorrelation  values means closer correlation with plasmids.
correlation between xaac and xgc was r <dig> =  <dig> .
this means that plasmid similarity to host tends to be connected with intra-chromosomal homogeneity and gc content.
the bacteria that obtained the highest plasmid-host correlation scores were predominantly soil/free-living, while host-associated and pathogenic typically had the lowest and most varied.
last, but not least, we calculated plasmid-host similarity based on plasmid size, see materials and methods for details.
in short, plasmid-host correlation values were compared to correspondingly sized host average autocorrelation values based on appropriately sized sliding windows.
we chose three different sizes for the sliding windows depending on the size of the plasmids.
for plasmids sized 10– <dig> kbp we used a  <dig> kbp sliding window, 30– <dig> kbp plasmid comparisons were based on a  <dig> kbp sliding window, while plasmids sized  <dig> kbp and above were compared to  <dig> kbp sliding windows.
for the first group, consisting of  <dig> plasmids sized 15– <dig> kbp and their respective hosts, we found that the average zom autocorrelation value was  <dig> .
the average of the respective plasmid-host correlations was  <dig> .
in the next group, consisting of  <dig> plasmids sized 30– <dig> kbp, the average zom autocorrelation value was  <dig> , while the average for the respective plasmid-host correlations was  <dig> .
for the largest plasmids, sized  <dig> kbp and above,  <dig> in total, we found that the average based on zom autocorrelation values was  <dig>  and the corresponding average plasmid-host correlation was  <dig> .
discussion
this paper has focused on comparing different statistical methods based on oligonucleotide frequencies.
we have paid particular attention to zoms by including word sizes from dinucleotides up to hexanucleotides while focusing on tetranucleotides for the rof and mcm based comparisons.
this choice was made because the zom method obtained large differences between observed and expected values, or departures  <cit> , which in turn can be regarded as information.
the markov based measures are presumed to give a composite picture of bacterial mechanisms reflected in the chromosome, and in this sense they can be considered to carry a stronger phylogenetic signal than other types of such measures  <cit> .
the over- and under-expression of certain oligonucleotides can be caused by dna structural conformations, dna base stacking energies, codon preference, and protein binding sites including transcription/restriction sites, dna replication and repair, etc.
<cit> .
while mcms are thought to be affected by similar pressures, they are likely to be much less so compared with zoms, since they approximate tetranucleotide frequencies based on observed transition probabilities from di- and trinucleotide distributions.
in other words, tetranucleotide mcms assume that tetranucleotide frequencies will have the same transition probabilities from trinucleotide frequencies as trinucleotide frequencies have from dinucleotide frequencies.
since large parts of bacterial dna codes for proteins the tetranucleotide mcm transition probabilities will, to a large extent, be affected by codon distributions.
differences between observed tetranucleotide frequencis and expected, based on mcms, will therefore reflect additional influences than codon preference.
phylogenetic comparisons based on tetranucleotide rofs are more directly affected by gc-content and codon usage than the other measures since they are only normalized by sequence size.
in other words, there is no assumption of discrepancy from any expected statistical distribution.
comparisons between archaea and bacteria based only on oligonucleotide frequencies are thus measuring differences in relative oligonucleotide occurences.
archaea and bacteria with similar genes and gc content might therefore be considered more alike regardless of phylogenetic relationship  <cit> .
the first part of this analysis was motivated by the observation that not much has been stated about possible errors for the different statistical measures mention above.
a fake genome was created with a uniform distribution of nucleotides comparable to e. coli in both size and gc content.
although most of the measures showed low correlation between the fake genome and the  <dig> real genomic dna sequences, dinucleotide zoms tended to give some very high correlation values.
for instance, m. hungatei strain jf- <dig> achieved a correlation value of  <dig>  with the completely random genome.
this is the same value obtained for mycoplasma pneumoniae strain m <dig>  compared with mycoplasma genitalium strain g <dig> .
for trinucleotide to hexanucleotide zoms the corresponding correlation values with the random genome were  <dig> ,  <dig> ,  <dig>  and  <dig>  respectively.
we believe that the high correlation values that dinucleotide zoms obtained are due to the small oligonucleotide size considered in the method.
using dinucleotides there are only  <dig> =  <dig> possible combinations which means that a smaller amount of dna is needed to get an understanding of how the dinucleotide distributions progresses.
for hexanucleotides there are  <dig> =  <dig> possible combinations resulting in large vectors containing far more detail, but also the requirement of substantially larger amounts of dna.
our conclusions are therefore that dinucleotide zoms can be used to give some limited inference of phylogenetic similarity, with an increased risk of false positives, between small dna sequences , whilst penta- and hexanucleotide zoms and the mcm measure are best-suited for whole genome comparisons due to the requirements of large amounts of dna.
we find that tetranucleotide zoms are good all-round measures that can be used to measure similarity between both relatively small dna sequences,  <dig> to  <dig> kbp in size, and larger, while still giving reliable comparison results and information.
comparing the statistical measures against real genomes, we found that the zom measures became increasingly ordered with larger oligonucleotide sizes, with the mcm measure performing comparable to the penta- and hexanucleotide zom measures for the genomes tested.
the mcm and rof measures produced the most reliable rankings of s. aureus and b. subtilis, with the mcm slightly better than the rof measure.
results obtained with the rof and dinucleotide zom measures were, in general, varied, and it is our impression that the mcm, and penta- and hexanucleotide zoms were the most robust measures in terms of phylogeny.
the mcm measure seemed to have a better ability to detect farther relatives than the other measures, although more genomes must be tested to confirm this claim.
presumed extensive dna exchange with species from all kingdoms of life  <cit>  has made phylogenetic characterization of the hyperthermophilic t. maritima difficult, which may explain the different results obtained with the statistical measures tested.
autocorrelation profiles are often used in whole genome analysis to search for regions of special interest.
these regions are thought to be composed of foreign or conserved dna.
we used b. subtilis and t. maritima in our examples since they are presumed to have undergone extensive horizontal transfer  <cit> .
the different zom autocorrelation profiles are similar though differences can be detected.
for instance, dinucleotide zoms contains far less detail than hexanucleotide zoms which, on the other hand, have low average autocorrelation values indicating that the sliding windows used  are too small for that particular measure.
the lack of detail for dinucleotide zoms may be due to the opposite reason, namely that the sliding window is too large.
as mentioned above, dinucleotides come in  <dig> different combinations and, assuming a uniform distribution, each dinucleotide will be repeated for every  <dig> base pairs.
hexanucleotides have  <dig> different combinations and each hexamer will therefore be expected to appear for every  <dig> base pairs, again assuming a uniform distribution.
this implies that the size of the oligonucleotide used for profiles should depend on the sliding window.
another possibility for the difference in detail with respect to autocorrelation profiles is that smaller oligonucleotides lack information present in larger ones.
turning now to tetranucleotide rofs and mcm based autocorrelation profiles, illustrated in figure  <dig>  we find that the profiles based on tetranucleotide rofs appear to be quite similar to zoms.
in these particular examples zoms seem to carry more detail even though tetranucleotides are used in both profile types.
similarly to the hexanucleotide zom profiles, the tetranucleotide mcm autocorrelation profiles have also low average autocorrelation scores.
as explained previously, this is thought to be caused by low departure or discrepancy values between expected and observed frequencies.
in other words, this could indicate that tetranucleotide mcms need larger sliding windows.
although most of the other dips were missing from the t. maritima profile some unique ones were also found, most notably at positions  <dig> kbp and  <dig>  mbp.
considering the fact that the dip located at position  <dig> kbp appeared to be linked with the abc transporter system, as shown above, we believe that tetranucleotide mcms presents complimentary information to the other measures used.
increasing the sliding window size from  <dig> kbp to  <dig> kbp for both the hexanucleotide zoms and tetranucleotide mcm based profiles, increased average autocorrelation scores, but reduced detail in the respective profiles noticeably, even though the sliding windows were overlapping every  <dig> kbp .
thus, the tetranucleotide zom measure with  <dig> kbp sliding windows, overlapping every  <dig>  kbp, seems to be the best measures in terms of sliding window size and detail.
rofs stand out from the other measures when it comes to homology searches.
large dna sequences, many kbp or mbp in size, can be used and since the methods are not seed-based homologous dna sequences with many mutations may still be detected.
this was demonstrated by taking the dna sequence in t. maritima containing a set of rrna genes .
since the sequence is close to  <dig> kbp we chose a  <dig> kbp sliding window and heptanucleotide frequencies.
in terms of homology searches based on rofs, fixed sized words larger than tetranucleotides have to be used in order to get sufficient precision.
actually, this process is exactly the same as the one used for the t. maritima autocorrelation profile  with the exceptions that the global vector now contains the dna word frequencies from the rrna genes taken from t. maritima, the sliding window is only  <dig> kbp long, and heptanucleotides are used instead of tetranucleotides.
the frequency-based search program used was only  <dig> lines of c++ code, and performed the search in less than  <dig> seconds on a  <dig> ghz pentium  <dig> computer.
although the method is relatively fast, easy to implement, and can handle sequences from 50– <dig> bp up to millions of bp, it suffers from the fact that the hit positions are never more accurate than the sliding window.
making the method more accurate means that the sliding windows must overlap more often, thereby removing the speed advantage gained in comparing large dna sequences.
this can be remedied by combining the rof method with a secondary method, like a seed based search algorithm.
while rofs may be the most appropriate measure for homology searches, zoms and the mcm measure may carry stronger phylogenetic signals due to reasons explained above.
tetranucleotide zoms were shown above to give reasonably good results in terms of size, reliability and detail.
we therefore used that measure to compare plasmids with their hosts.
as has been previously noted  <cit> , we find that plasmids are much less correlated with their hosts than what would be expected from autocorrelation scores based on similarly sized sliding windows .
large plasmids tend to be closer to their hosts, at least in terms of tetranucleotide zoms, than smaller plasmids.
whether this is due to the increased amount of dna available for the comparisons or that larger plasmids are, for some reason, more affected by host amelioration processes is not known.
the fact that gc rich bacteria and archaea with high tetranucleotide zom average autocorrelation values  attain better correlation scores with their plasmids may be caused by better dna maintenance in such bacteria and/or lower mutation rates  <cit> .
since many host-associated at rich bacteria tend to lose their dna replication and repair systems  <cit>  we believe that this may be one explanation for the lower plasmid-host correlation scores.
CONCLUSIONS
in this paper, we have investigated different statistical methods based on oligonucleotide frequencies, to compare microbial dna from various genomes.
dinucleotide zoms can, with care, be used for small dna sequences, while hexanucleotide zoms and mcms seems more reliable for large dna sequences and whole genome comparisons.
zom, mcm and rofs were found to be complimentary measures in terms of autocorrelation profiles.
the tetranucleotides zom measure was found to be the most versatile in terms of detail, error, and sliding window size when used for dna profiling.
the rof measure was the best of the measures for fast distant homology searches with large dna sequences.
finally, based on the findings from the autocorrelation profiles, tetranucleotide zoms were used to look at similarities between a selection of plasmids, sized  <dig> kbp and larger, and their corresponding hosts.
it was found that plasmid-host dna similarity correlated with intra-chromosomal homogeneity of the host, and gc content, i.e.
the more gc rich and homogeneous a genome was, the more similar were the corresponding plasmids.
plasmids were found to be more dissimilar to their hosts than expected, and similarity seemed also to be related to plasmid size.

 categorising organisms has always been a key activity in biology. numerous methods exist, and each reflects particular properties of the organism studied. for microbial organisms, genome sequences are now commonly used as a basis for determining phylogenetic relationships. the simple comparison of nucleotide content between species is probably the most used and one of the easiest methods for whole genome comparisons. at/gc content however, will not necessarily provide reliable information about phylogenetic relationships. it has been proposed that the chromosomal average gc content is more reflective of the environment in which the organism lives, and sometimes less related to its taxonomic group. this is in part due to differences in codon usage, which has been presumed to be reflective of the environment in many ways, such as the organism's growth temperature, size of the genome and optimal growth rate, and anaerobic or aerobic growth conditions. thus, the amino acid composition and gc content of an organism seems to be related to its ecological niche. since oligonucleotide usage is influenced by gc content, the habitat of an organism may be largely responsible for the observed dna word frequencies in genomic dna. in most bacteria, the distribution of guanine compared to cytosine on the same strand varies along the chromosome, with g's generally biased towards the replication leading strand for nearly all genomes studied so far. skews in guanine compared to cytosine, or to a lesser extent adenine versus thymine, may indicate where and how dna replication is taking place and can help identifying the replication leading or lagging strands, as well as the origin and terminus of replication. although this method works for many prokaryotes some have skews that are much less pronounced or even undetectable. worning and coworkers found that scoring strand bias frequencies of progressively larger oligonucleotides, from dinucleotides up to heptanucleotides, and their reverse complements, the chromosomal location of the origin and terminus of dna replication could be predicted for nearly all sequenced prokaryotic genomes. weinel et al. have looked at the over- and under-representation of oligonucleotides up to 14-mers to compare two different species of pseudomonas. abe and colleagues used an algorithm based on neural networks to classify dna of unknown source by focusing on tetranucleotide frequency distributions. distributions of oligonucleotides can therefore be used as a more refined way of discriminating between different bacterial genomes. samuel karlin and coworkers applied odds-ratios consisting of observed dinucleotide frequencies divided by expected, determined by genomic nucleotide content, to compare genomes to each other. this method actually dates back to the 1960s, but its use has become more popular due to the growing amount of sequenced data available. these relative abundance patterns, or zero order markov distributions, were coined genomic signatures by karlin and coworkers. the reason for calling these distributions "genomic signatures" was that zoms were thought to reflect species-specific properties not directly found from gc content or oligonucleotide distributions. further, zoms were found to vary much less within than between even closely related genomes, almost regardless of where dna was sampled from within the chromosome. zoms indicate if oligonucleotides are over- or under-represented in dna sequences compared with what is expected from average genomic nucleotide content. differences between observed and expected oligonucleotide distributions might reflect dna structural conformations, such as dna curvature, flexibility, and "meltable" regions, in addition to transcription/restriction and other protein binding sites. while karlin and others focused on dinucleotide zoms, pride and colleagues compared tetranucleotide zoms and tetranucleotide distributions predicted by a markov chain model to 16s rrna based trees to investigate which of the methods had the strongest phylogenetic signal. the markov chain method assumes that tetranucleotide frequencies have the same likelihood of occurrence, given trinucleotide frequencies, as trinucleotide frequencies have, given dinucleotide frequencies. alternatively, this can be considered as a tetranucleotide frequency approximation with overlapping trinucleotide frequencies normalized with dinucleotide frequencies. a thorough investigation of how markov chains approximate oligonucleotides in escherichia coli can be found in. even though the tetranucleotide mcm is calculated from observed di- and trinucleotide frequencies, the zom method, which only uses nucleotide content to approximate tetranucleotides, showed a better congruency towards the 16s rrna based trees than the mcm method. it was also demonstrated that tetranucleotide zoms differed in coding and non-coding areas in contrast to dinucleotide zoms. it is the goal of this paper to examine the strengths and weaknesses of a series of dna sequence comparison methods, based on statistical distributions of oligonucleotides. these methods include relative oligonucleotide frequencies, di- to hexanucleotide zoms and tetranucleotide mcms. in the literature the focus has mainly been on di- and tetranucleotide zoms, and tetranucleotide rofs and mcms. in this work, tri-, penta- and hexanucleotide zoms are included additionally to see how they compare against the more popular measures and whether they have any useful differences. the different measures are compared against each other, both as tools for dna profiling and sequence comparisons, and the most appropriate measure is used to look at plasmid-host relations as an application.  comparing the phylogenetic strength of the statistical measures using a random dna sequence in the first test, all the measures mentioned above were used to compare bacterial and archaeal chromosomes and plasmids with a completely random dna sequence with similar size and gc content to an e. coli chromosome, which for this case can be considered as a mbp genome with 50% gc. lower correlation values between genomes and the random dna sequences means that the method is more reliable with fewer false positives. for all measures, correlation values above indicate some kind of relation. from figure it can be observed that the dinucleotide zoms had, by far, the largest spread with respect to correlation scores ranging from - for pseudoalteromonas haloplanktis strain tac to methanospirillum hungatei strain jf- with a correlation of. stepping up to trinucleotide zoms the spread decreased dramatically with p. haloplanktis strain tac again having the lowest correlation value of -, while corynebacterium efficiens strain ys- had the highest value of. the tetranucleotide zoms were still better, with scores ranging from - for p. haloplanktis strain tac to for leptospira interrogans serovar copenhageni. pentanucleotide zom correlations ranged from - to, while hexanucleotide zoms were firmly placed with the lowest correlation scores, never going outside the interval for all dna sequences tested. turning now to tetranucleotide rofs and mcms, as shown in figure the correlation scores were between, and, respectively. for the rof measure mostly plasmids were found at the lower end of the correlation score interval. xylella fastidiosa strain 9a5c and geobacter metallireducens strain gs- were the first chromosomes from the lower end of the correlation list, obtaining scores of - and, respectively. tetranucleotide mcms found sulfolobus solfataricus strain p and acinetobacter sp. adp at each end, respectively, in the correlation score interval. comparing the measures using real genomes we used bacillus subtilis subsp. subtilis str. yersinia pestist biovar microtus str., pseudomonas aeruginosa strain pao and staphylococcus areus subsp. aureus strain mu to compare the phylogenetic capabilities of the different statistical measures. additionaly, the measures were used to assess possible phylogenetic relationships of t. maritima, which has been difficult to classify due to extensive horizontal transfer. starting with b. subtilis, see table for details concerning strains, correlation scores, gc content and size, the dinucleotide zom measure found the γ-proteobacteria hahella chejuensis strain kctc and firmicutes bacillus licheniformis strain atcc bacillus cereus strain atcc bacillus anthracis strain'ames ancestor', and bacillus thuringiensis subsp. konkukian serotype h strain 97- ranked after plasmid phcm belonging to γ-proteobacterium salmonella enterica subsp. enterica serovar typhi strain ct the trinucleotide zom measure found b. licheniformis as the closest match, followed by a set of genomes and plasmids of proteobacteria. b. licheniformis was the closest genome for tetra- to hexanucleotide zoms. the penta- and hexanucleotide zoms ranked bacillus clausii strain ksm-k under b. licheniformis. the same was observed for the tetranucleotide mcm measure, but in contrast to the zom measures, a set of bacillus species followed, and genera from other phyla obtained only low correlation scores with this measure. b. licheniformis was also found on the top of the list for the tetranucleotide rof measure, followed by bacillus halodurans strain c- and geobacillus kaustophilus strain hta bacteria from different phyla populated the list further down. additional file contains complete listings of comparisons between b.subtilis and all genomes for the measures discussed. for p. aeruginosa, see table, dinucleotide zoms found plasmids from ralstonia metallidurans strain ch xanthomonas campestris pv. vesicatoria strain 85- and azoarcus sp. ebn as best matches. the best matching chromosome with the dinucleotide zom measure was the actinobacteriumcorynebacterium jeikeium strain k the zom measures from trinucleotides and up ranked pseudomonas entomophila strain l highest while the α-proteobacterium novosphingobium aromaticivorans strain dsm was the third best match. although all zom measures found the β-proteobacteria ralstonia sp. relatively close to p. aeruginosa, only penta- and hexanucleotide zoms ranked pseudomonas fluorescens strain pf- as the third best match. p. aeruginosa was found closest to p. entomophila and p. fluorescens with the mcm measure, while the β-proteobacterium ralstonia solanacearum strain gmi followed close behind. other species of pseudomonas obtained relatively high correlation scores, but were more dispersed, with respect to ranking, than the results from the penta- and hexanucleotide zoms. the rof measure found ralstonia eutropha strain h closest to p. aeruginosa, and, with the exception of p. entomophila, other species of pseudomonas were more dispersed for this measure than for any of the other tested. soil bacteria in general obtained high correlation scores for all the measures tested. other strains of s. aureus ranked as closest matches to s. aureus subsp. aureus strain mu see table, with high correlation scores for all measures. staphylococcus saprophyticus subsp. saprophyticus strain atcc ranks after all s. aureus strains for all zom measures, while staphylococcus haemolyticus strain jcsc followed for tri- to hexanucleotide zoms. two strains of staphylococcus epidermidis were only found together with s. aureus and s. haemolyticus for tetra- to hexanucleotide zoms. the γ-proteobacterium acinetobacter sp. adp was found closer to s. aureus than s. haemolyticus and s.epidermidis for the dinucleotide zom measure. all zom measures ranked a set of proteobacteria like photobacterium profundum strain ss and vibrio fischerii strain es before other members of the firmicutes phyla. s. aureus was found close together with other species and genera of firmicutes, just as b. subtilis was, with the mcm measure. other species of staphylococcus ranked highest, followed by oceanobacillus iheyensis strain hte members of the firmicutes phylum were also predominantly present as the best matching members when the rof measure was used, with only the second chromosome of v. fischerii breaking this trend. v. fischerii, and vibrio sp. in general, obtained high correlation scores for all measures except the mcm. for y. pestis biovar microtus str. see table, most measures found other "enterics" as closest matches, but with some variations in the rankings. yersinia pseudotuberculosis strain ip correlated identically with the other yersinia species, and the relative photorhabdus luminescens subsp. laumondii strain tto obtained high correlation scores for all measures. the dinucleotide zom measure however, found the bacteroidete cytophaga hutchinsonii strain atcc as the best match to the yersinia species. other members of the proteobacteria phyla followed further down the list. the number of "enterics" close to yersinia sp. increased with word size for the zom measures. alcanivorax borkumensis strain sk ranked highest after p. luminescens for tri- and tetranucleotide zoms while e. coli were closer for penta- and hexanucleotide zoms. the mcm measure ranked erwinia carotovora subsp. atroseptica strain scri as best match to yersinia sp., followed closely by p. luminescens. all "enterics" obtained relatively high correlation scores with the mcm measure. the rof measure ranked sodalis glossinidius strain'morsitans' as closest match to p. luminescens, and yersinia sp. plasmids ranked higher with this measure than the others. comparing the different measures using t. maritima, see table, tetranucleotide zoms found the following bacteria closest: archaeoglobus fulgidus strain dsm geobacter metallireducens strain gs and thermococcus kodakaraensis strain kod a kb plasmid of salinibacter ruber strain dsm psr ranked after t. kodakaraensis. all tested oligonucleotide zoms ranked the thermophilic euryarchaeota t. kodakaraensis highest. it is interesting to note that for t. maritima the dinucleotide zom measure seemed to be under-correlating much more than for the random genome mentioned above. tetranucleotide rofs had a. fulgidus, aquifex aeolicus strain vf and chlamydia trachomatis strain a har- as closest matches. the mcm measure ranked t. kodakaraensis strain kod pelobacter carbinolicus strain dsm and syntrophus aciditrophicus strain sb, both δ-proteobacteria, on top. a. aeolicus, which is assumed to be one of t. maritima closest sequenced relatives, was ranked progressively higher for di- to hexanucleotide zoms, achieving a place for dinucleotide zoms and a place for hexanucleotide zoms. as was mentioned above, a. aeolicus has the second best correlation score for rofs while tetranucleotide mcms rank a. aeolicus as the closest match with t. maritima. the markov measures, including both zom and mcm methods, seemed to be more similar to each other than to the rof measure. considerably higher correlation scores were obtained, on average, for the dinucleotide zom measure, while the hexanucleotide zom and tetranucleotide mcm measures produced the lowest. the rof measure seemed to have the most varied average correlation scores. autocorrelation profiles figures and illustrate some of the above mentioned measures in autocorrelation profiles of b. subtilis and t. maritima. the b. subtilis genome is presumed to consist of large sections of horizontally acquired dna, and was therefore used to compare the capabilities of the different statistical measures to detect foreign dna. the autocorrelation profiles in figure contain a set of dips that may be conserved and/or foreign dna. blast searches against the ncbi nr database were used to get information about these special regions, while genes and proteins were examined further with the string database. the dips at kbp and kbp, see figure were presumed to be remnants of prophages, while the remaining visible dips just short of genomic position mbp were conserved proteins and/or rrna genes according to blast. the two dips just before and after position mbp were found to be transcriptional regulators, possibly horizontally transferred, while the large dips at positions and mbp are known prophages. it should be noted that blast identified an uvrx gene, involved in dna repair, together with the prophage at position mbp. three more sections were examined more carefully, and they all turned out to contain rrna genes, except the dip found close to position mbp according to blast. this dip was fairly easy to observe with the different zom measures, but harder with the rof and mcm measures. a blast search resulted in a hit for a rodc gene that is active in cell synthesis. focusing on the t. maritima genome, especially visible are the two dips located at positions close to and mbp, which are barely detectable from the dinucleotide zom profile. turning to the other measures it can be seen that the tetranucleotide rof profile has a very high average autocorrelation score, yet the dip found in all autocorrelation zom profiles at position close to mbp is hardly visible. a similar phenomenon was also observed in the tetranucleotide mcm autocorrelation profile. this profile contained dips that were more pronounced than any of the other profiles, with the ones found close to positions kbp and mbp standing particularly out. selections starting from positions kbp, kbp, mbp, and mbp all gave hits related to an abc transporter system that is presumed to have been acquired horizontally from species belonging to the archaea kingdom. all the selections were kbp except for the last which was kbp. the selections starting from positions kbp, mbp, and mbp were all termed hypothetical proteins except for the last, which was termed laci family transcriptional regulator, and the first, position which matched cela and celb genes, which, according to, encodes glycosyl hydrolases. the biggest dip, found in all autocorrelation profiles above, starts at position kbp and extends kbp, encodes 16s, 23s, and 5s rrna genes according to blast. at position mbp another large dip was clearly visible on all autocorrelation profiles, except for dinucleotide zom and the mcm measures. blast listed a spc operon that encodes a set of ribosomial proteins according to. t. maritima is believed to have acquired large amounts of dna from other bacteria and archaea. estimations go as high as 24% from archaea alone and still more dna is presumed to have been acquired from other prokaryotes, and possibly eukaryotic species as well. homologues to all or parts of the extracted sequences at positions kbp, mbp and mbp were found in pyrococcus furiosus dsm sinorhizobium meliloti, and clostridium thermocellum atcc respectively. the hexanucleotide zom and tetranucleotide based mcm had the lowest average autocorrelation scores of the measures tested. increasing the sliding window size from kbp to kbp, overlapping every kbp, did increase average autocorrelation scores, but visual detail was poorer. the zom measures were found to be similar, with the tetranucleotide zom possibly the best measure of all tested with respect to size and detail. other differences include more pronounced dips for tetra- and hexanucleotide zoms, and fewer for rofs, mcms and dinucleotide zoms. distance homology searches with large dna sequences for the distant homology search the heptanucleotide frequencies of a kbp dna sequence consisting of rrna genes taken from t. maritima were compared against heptanucleotide frequencies in the m. leprae chromosome with the sliding window approach described in the methods section. from figure a good hit can be observed that achieved a noticeable higher correlation score around position mbp than any other place in the genome. blast reports the corresponding dna to be m. leprae 5s, 16s, 23s rrna genes with a 100% identity score. the dna taken from t. maritima obtained only a 75% identity score with the m. leprae genome, indicating that the rof method can cope with both large and mutated dna sequences, while still being fairly fast. plasmid-host similarity analysis tetranucleotide zoms were used to compare plasmids sized kbp and larger with corresponding host genomes, totalling different bacteria and archaea with chromosomes and different plasmids. a minimum plasmid size was used to make the comparisons as accurate as possible between plasmids and hosts using the tetranucleotide zom method. our findings support the claim in that plasmids are, especially at rich genomes, more distantly related to their host than what would be expected from their hosts average autocorrelation values based on correspondingly sized sliding windows, see figure and materials and methods section for details. in addition, we found that plasmid similarity to host, yph, correlated well with host average autocorrelation values, xaac, and gc content, xgc, yph = 1/ r =, i.e. higher gc content and chromosomal average zom autocorrelation values means closer correlation with plasmids. correlation between xaac and xgc was r =. this means that plasmid similarity to host tends to be connected with intra-chromosomal homogeneity and gc content. the bacteria that obtained the highest plasmid-host correlation scores were predominantly soil/free-living, while host-associated and pathogenic typically had the lowest and most varied. last, but not least, we calculated plasmid-host similarity based on plasmid size, see materials and methods for details. in short, plasmid-host correlation values were compared to correspondingly sized host average autocorrelation values based on appropriately sized sliding windows. we chose three different sizes for the sliding windows depending on the size of the plasmids. for plasmids sized 10– kbp we used a kbp sliding window, 30– kbp plasmid comparisons were based on a kbp sliding window, while plasmids sized kbp and above were compared to kbp sliding windows. for the first group, consisting of plasmids sized 15– kbp and their respective hosts, we found that the average zom autocorrelation value was. the average of the respective plasmid-host correlations was. in the next group, consisting of plasmids sized 30– kbp, the average zom autocorrelation value was, while the average for the respective plasmid-host correlations was. for the largest plasmids, sized kbp and above, in total, we found that the average based on zom autocorrelation values was and the corresponding average plasmid-host correlation was. discussion this paper has focused on comparing different statistical methods based on oligonucleotide frequencies. we have paid particular attention to zoms by including word sizes from dinucleotides up to hexanucleotides while focusing on tetranucleotides for the rof and mcm based comparisons. this choice was made because the zom method obtained large differences between observed and expected values, or departures, which in turn can be regarded as information. the markov based measures are presumed to give a composite picture of bacterial mechanisms reflected in the chromosome, and in this sense they can be considered to carry a stronger phylogenetic signal than other types of such measures. the over- and under-expression of certain oligonucleotides can be caused by dna structural conformations, dna base stacking energies, codon preference, and protein binding sites including transcription/restriction sites, dna replication and repair, etc.. while mcms are thought to be affected by similar pressures, they are likely to be much less so compared with zoms, since they approximate tetranucleotide frequencies based on observed transition probabilities from di- and trinucleotide distributions. in other words, tetranucleotide mcms assume that tetranucleotide frequencies will have the same transition probabilities from trinucleotide frequencies as trinucleotide frequencies have from dinucleotide frequencies. since large parts of bacterial dna codes for proteins the tetranucleotide mcm transition probabilities will, to a large extent, be affected by codon distributions. differences between observed tetranucleotide frequencis and expected, based on mcms, will therefore reflect additional influences than codon preference. phylogenetic comparisons based on tetranucleotide rofs are more directly affected by gc-content and codon usage than the other measures since they are only normalized by sequence size. in other words, there is no assumption of discrepancy from any expected statistical distribution. comparisons between archaea and bacteria based only on oligonucleotide frequencies are thus measuring differences in relative oligonucleotide occurences. archaea and bacteria with similar genes and gc content might therefore be considered more alike regardless of phylogenetic relationship. the first part of this analysis was motivated by the observation that not much has been stated about possible errors for the different statistical measures mention above. a fake genome was created with a uniform distribution of nucleotides comparable to e. coli in both size and gc content. although most of the measures showed low correlation between the fake genome and the real genomic dna sequences, dinucleotide zoms tended to give some very high correlation values. for instance, m. hungatei strain jf- achieved a correlation value of with the completely random genome. this is the same value obtained for mycoplasma pneumoniae strain m compared with mycoplasma genitalium strain g. for trinucleotide to hexanucleotide zoms the corresponding correlation values with the random genome were,, and respectively. we believe that the high correlation values that dinucleotide zoms obtained are due to the small oligonucleotide size considered in the method. using dinucleotides there are only = possible combinations which means that a smaller amount of dna is needed to get an understanding of how the dinucleotide distributions progresses. for hexanucleotides there are = possible combinations resulting in large vectors containing far more detail, but also the requirement of substantially larger amounts of dna. our conclusions are therefore that dinucleotide zoms can be used to give some limited inference of phylogenetic similarity, with an increased risk of false positives, between small dna sequences, whilst penta- and hexanucleotide zoms and the mcm measure are best-suited for whole genome comparisons due to the requirements of large amounts of dna. we find that tetranucleotide zoms are good all-round measures that can be used to measure similarity between both relatively small dna sequences, to kbp in size, and larger, while still giving reliable comparison results and information. comparing the statistical measures against real genomes, we found that the zom measures became increasingly ordered with larger oligonucleotide sizes, with the mcm measure performing comparable to the penta- and hexanucleotide zom measures for the genomes tested. the mcm and rof measures produced the most reliable rankings of s. aureus and b. subtilis, with the mcm slightly better than the rof measure. results obtained with the rof and dinucleotide zom measures were, in general, varied, and it is our impression that the mcm, and penta- and hexanucleotide zoms were the most robust measures in terms of phylogeny. the mcm measure seemed to have a better ability to detect farther relatives than the other measures, although more genomes must be tested to confirm this claim. presumed extensive dna exchange with species from all kingdoms of life has made phylogenetic characterization of the hyperthermophilic t. maritima difficult, which may explain the different results obtained with the statistical measures tested. autocorrelation profiles are often used in whole genome analysis to search for regions of special interest. these regions are thought to be composed of foreign or conserved dna. we used b. subtilis and t. maritima in our examples since they are presumed to have undergone extensive horizontal transfer. the different zom autocorrelation profiles are similar though differences can be detected. for instance, dinucleotide zoms contains far less detail than hexanucleotide zoms which, on the other hand, have low average autocorrelation values indicating that the sliding windows used are too small for that particular measure. the lack of detail for dinucleotide zoms may be due to the opposite reason, namely that the sliding window is too large. as mentioned above, dinucleotides come in different combinations and, assuming a uniform distribution, each dinucleotide will be repeated for every base pairs. hexanucleotides have different combinations and each hexamer will therefore be expected to appear for every base pairs, again assuming a uniform distribution. this implies that the size of the oligonucleotide used for profiles should depend on the sliding window. another possibility for the difference in detail with respect to autocorrelation profiles is that smaller oligonucleotides lack information present in larger ones. turning now to tetranucleotide rofs and mcm based autocorrelation profiles, illustrated in figure we find that the profiles based on tetranucleotide rofs appear to be quite similar to zoms. in these particular examples zoms seem to carry more detail even though tetranucleotides are used in both profile types. similarly to the hexanucleotide zom profiles, the tetranucleotide mcm autocorrelation profiles have also low average autocorrelation scores. as explained previously, this is thought to be caused by low departure or discrepancy values between expected and observed frequencies. in other words, this could indicate that tetranucleotide mcms need larger sliding windows. although most of the other dips were missing from the t. maritima profile some unique ones were also found, most notably at positions kbp and mbp. considering the fact that the dip located at position kbp appeared to be linked with the abc transporter system, as shown above, we believe that tetranucleotide mcms presents complimentary information to the other measures used. increasing the sliding window size from kbp to kbp for both the hexanucleotide zoms and tetranucleotide mcm based profiles, increased average autocorrelation scores, but reduced detail in the respective profiles noticeably, even though the sliding windows were overlapping every kbp. thus, the tetranucleotide zom measure with kbp sliding windows, overlapping every kbp, seems to be the best measures in terms of sliding window size and detail. rofs stand out from the other measures when it comes to homology searches. large dna sequences, many kbp or mbp in size, can be used and since the methods are not seed-based homologous dna sequences with many mutations may still be detected. this was demonstrated by taking the dna sequence in t. maritima containing a set of rrna genes. since the sequence is close to kbp we chose a kbp sliding window and heptanucleotide frequencies. in terms of homology searches based on rofs, fixed sized words larger than tetranucleotides have to be used in order to get sufficient precision. actually, this process is exactly the same as the one used for the t. maritima autocorrelation profile with the exceptions that the global vector now contains the dna word frequencies from the rrna genes taken from t. maritima, the sliding window is only kbp long, and heptanucleotides are used instead of tetranucleotides. the frequency-based search program used was only lines of c++ code, and performed the search in less than seconds on a ghz pentium computer. although the method is relatively fast, easy to implement, and can handle sequences from 50– bp up to millions of bp, it suffers from the fact that the hit positions are never more accurate than the sliding window. making the method more accurate means that the sliding windows must overlap more often, thereby removing the speed advantage gained in comparing large dna sequences. this can be remedied by combining the rof method with a secondary method, like a seed based search algorithm. while rofs may be the most appropriate measure for homology searches, zoms and the mcm measure may carry stronger phylogenetic signals due to reasons explained above. tetranucleotide zoms were shown above to give reasonably good results in terms of size, reliability and detail. we therefore used that measure to compare plasmids with their hosts. as has been previously noted, we find that plasmids are much less correlated with their hosts than what would be expected from autocorrelation scores based on similarly sized sliding windows. large plasmids tend to be closer to their hosts, at least in terms of tetranucleotide zoms, than smaller plasmids. whether this is due to the increased amount of dna available for the comparisons or that larger plasmids are, for some reason, more affected by host amelioration processes is not known. the fact that gc rich bacteria and archaea with high tetranucleotide zom average autocorrelation values attain better correlation scores with their plasmids may be caused by better dna maintenance in such bacteria and/or lower mutation rates. since many host-associated at rich bacteria tend to lose their dna replication and repair systems we believe that this may be one explanation for the lower plasmid-host correlation scores.  in this paper, we have investigated different statistical methods based on oligonucleotide frequencies, to compare microbial dna from various genomes. dinucleotide zoms can, with care, be used for small dna sequences, while hexanucleotide zoms and mcms seems more reliable for large dna sequences and whole genome comparisons. zom, mcm and rofs were found to be complimentary measures in terms of autocorrelation profiles. the tetranucleotides zom measure was found to be the most versatile in terms of detail, error, and sliding window size when used for dna profiling. the rof measure was the best of the measures for fast distant homology searches with large dna sequences. finally, based on the findings from the autocorrelation profiles, tetranucleotide zoms were used to look at similarities between a selection of plasmids, sized kbp and larger, and their corresponding hosts. it was found that plasmid-host dna similarity correlated with intra-chromosomal homogeneity of the host, and gc content, i.e. the more gc rich and homogeneous a genome was, the more similar were the corresponding plasmids. plasmids were found to be more dissimilar to their hosts than expected, and similarity seemed also to be related to plasmid size. 
advantages with these statistical methods include measurements of phylogenetic relationship with relatively small pieces of dna sampled from almost anywhere within genomes, detection of foreign/conserved dna, and homology searches. tests were performed on distant homology searches with large dna sequences, detection of foreign/conserved dna, and plasmid-host similarity comparisons. rofs were best suited for distant homology searches, whilst the hexanucleotide zom and mcm measures were more reliable measures in terms of phylogeny. the dinucleotide zom method produced high correlation values when used to compare real genomes to an artificially constructed random genome with similar %gc, and should therefore be used with care. our aim was to explore the reliability and best suited applications for some popular methods, which include relative oligonucleotide frequencies, di- to hexanucleotide zero'th order markov methods and order markov chain method. these methods compare observed genomic frequencies of fixed-sized oligonucleotides with expected values, which can be determined by genomic nucleotide content, smaller oligonucleotide frequencies, or be based on specific statistical distributions. the tetranucleotide zom measure was a good measure to detect horizontally transferred regions, and when used to compare the phylogenetic relationships between plasmids and hosts, significant correlation was found with genomic gc content and intra-chromosomal homogeneity.
 the increasing number of sequenced prokaryotic genomes contains a wealth of genomic data that needs to be effectively analysed. a set of statistical tools exists for such analysis, but their strengths and weaknesses have not been fully explored. the statistical methods we are concerned with here are mainly used to examine similarities between archaeal and bacterial dna from different genomes. these methods compare observed genomic frequencies of fixed-sized oligonucleotides with expected values, which can be determined by genomic nucleotide content, smaller oligonucleotide frequencies, or be based on specific statistical distributions. advantages with these statistical methods include measurements of phylogenetic relationship with relatively small pieces of dna sampled from almost anywhere within genomes, detection of foreign/conserved dna, and homology searches. our aim was to explore the reliability and best suited applications for some popular methods, which include relative oligonucleotide frequencies, di- to hexanucleotide zero'th order markov methods and order markov chain method. tests were performed on distant homology searches with large dna sequences, detection of foreign/conserved dna, and plasmid-host similarity comparisons. additionally, the reliability of the methods was tested by comparing both real and random genomic dna.  our findings show that the optimal method is context dependent. rofs were best suited for distant homology searches, whilst the hexanucleotide zom and mcm measures were more reliable measures in terms of phylogeny. the dinucleotide zom method produced high correlation values when used to compare real genomes to an artificially constructed random genome with similar %gc, and should therefore be used with care. the tetranucleotide zom measure was a good measure to detect horizontally transferred regions, and when used to compare the phylogenetic relationships between plasmids and hosts, significant correlation was found with genomic gc content and intra-chromosomal homogeneity.  the statistical methods examined are fast, easy to implement, and powerful for a number of different applications involving genomic sequence comparisons. however, none of the measures examined were superior in all tests, and therefore the choice of the statistical method should depend on the task at hand. 