Barcodes for genomes and applications

Abstract

Each genome has a stable distribution of the combined frequency for each k-mer and its reverse complement measured in sequence fragments as short as 1000 bps across the whole genome, for 1<k<6. The collection of these k-mer frequency distributions is unique to each genome and termed the genome's barcode.
We found that for each genome, the majority of its short sequence fragments have highly similar barcodes while sequence fragments with different barcodes typically correspond to genes that are horizontally transferred or highly expressed. This observation has led to new and more effective ways for addressing two challenging problems: metagenome binning problem and identification of horizontally transferred genes. Our barcode-based metagenome binning algorithm substantially improves the state of the art in terms of both binning accuracies and the scope of applicability. Other attractive properties of genomes barcodes include (a) the barcodes have different and identifiable characteristics for different classes of genomes like prokaryotes, eukaryotes, mitochondria and plastids, and (b) barcodes similarities are generally proportional to the genomes' phylogenetic closeness.
These and other properties of genomes barcodes make them a new and effective tool for studying numerous genome and metagenome analysis problems.

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BMC Bioinformatics
Open Access
Research article
Barcodes for genomes and applications
Fengfeng Zhou
†
, Victor Olman
†
and Ying Xu*
Address: Department of Biochemistry and Molecular Biology and Institute of Bioinformatics, and BioEnergy Science Center (BESC), University of
Georgia, Athens, GA 30602, USA
Email: Fengfeng Zhou - ffzhou@csbl.bmb.uga.edu; Victor Olman - olman@csbl.bmb.uga.edu; Ying Xu* - xyn@bmb.uga.edu
* Corresponding author †Equal contributors
Abstract
Background: Each genome has a stable distribution of the combined frequency for each k-mer
and its reverse complement measured in sequence fragments as short as 1000 bps across the whole
genome, for 1<k<6. The collection of these k-mer frequency distributions is unique to each
genome and termed the genome's barcode.
Results: We found that for each genome, the majority of its short sequence fragments have highly
similar barcodes while sequence fragments with different barcodes typically correspond to genes
that are horizontally transferred or highly expressed. This observation has led to new and more
effective ways for addressing two challenging problems: metagenome binning problem and
identification of horizontally transferred genes. Our barcode-based metagenome binning algorithm
substantially improves the state of the art in terms of both binning accuracies and the scope of
applicability. Other attractive properties of genomes barcodes include (a) the barcodes have
different and identifiable characteristics for different classes of genomes like prokaryotes,
eukaryotes, mitochondria and plastids, and (b) barcodes similarities are generally proportional to
the genomes' phylogenetic closeness.
Conclusion: These and other properties of genomes barcodes make them a new and effective
tool for studying numerous genome and metagenome analysis problems.
Background
The challenges being faced in sorting out short genomic
fragments generated by metagenome sequencing projects
[1] pose a fundamental question: "does each genome
have a unique signature imprinted on its short sequence
fragments so that fragments from the same genomes in a
metagenome can be identified accurately?" A positive
answer to this question could have significant implica-
tions to many important genome and metagenome anal-
ysis problems such as identification of genetic material
transferred from other organisms [2] or through virus
invasions [3,4], separation of short sequence fragments
generated by metagenome sequencing into individual
genomes [5] and phylogenetic analyses of genomes [6].
Understanding the intrinsic properties of genome
sequences, either general to all or specific to some classes
of genomes, has been the focus of many studies in the past
two decades. Earlier work includes the discovery of the
periodicity property of DNA sequences across both
prokaryotic and eukaryotic genomes [7] and the realiza-
tion that coding sequences follow Markov chain proper-
ties [8-10]. Karlin and colleagues have studied various
genome properties based on analyses of k-mer frequency
Published: 17 December 2008
BMC Bioinformatics 2008, 9:546 doi:10.1186/1471-2105-9-546
Received: 16 June 2008
Accepted: 17 December 2008
This article is available from: http://www.biomedcentral.com/1471-2105/9/546
© 2008 Zhou et al; licensee BioMed Central Ltd.
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/2.0
),
which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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distributions, and have observed that the di-nucleotide rel-
ative abundance, a normalized di-mer frequency with
respect to the mono-mer frequencies, is generally stable
across a genome measured on 50 K base-pair (bp) frag-
ments [11-13]. They even suggested that such normalized
di-mer frequency distributions can possibly serve as signa-
tures of genomes.
In this paper, we present a barcoding scheme for all
sequenced genomes, and illustrate a number of interest-
ing and useful properties of the barcodes, which we can
take advantage to solve challenging genome analysis
problems. We highlight the power of this barcoding
scheme through addressing two application problems:
metagenome binning problem and identification of hori-
zontally transferred genes.
Results
Barcodes and their properties
We have calculated the barcode for each sequenced
prokaryotic genome, using the following procedure. For
each genome, we partition its sequence into a series of
non-overlapping and equal-sized fragments of M bps;
then for each k-mer (1 <k < 6 in this study), we calculate
the combined frequency of the k-mer and its reverse com-
plement within each partitioned fragment. The barcode for
each genome is a matrix of N(k) columns and
genome_length/M rows, with each element representing
the frequency of the corresponding k-mer within the cor-
responding sequence fragment, where N(k) is the number
of unique combined k-mers. Note that N(k) = 4
k
/2 or (4
k
+ 4
k/2
)/2, depending on whether k is odd or even. For
example, N(4) = 136. The portion of the barcode corre-
sponding to a fragment in a genome is called the frag-
ment's barcode. In this paper, barcodes are calculated
using M = 1000 and k = 4 unless stated otherwise. A dis-
cussion on our choices of the M and k values is given in
Additional file 1, where we can also see that the above
"equal-sized" requirement is not necessary.
For each barcode, we have created a grey-level image, a
barcode image, by mapping the k-mer frequencies to grey
levels using a procedure given in the METHODS section
so that darker grey levels are for lower frequencies. Figure
1 shows the barcode images for five prokaryotic genomes.
A key advantage of having barcode images is that they pro-
vide an intuitive, informative and global view of genomes,
from which various genomic features become immedi-
ately apparent. This view can be used to guide our rigor-
ous statistical analyses of genomes. We have calculated
the barcode images for all 586 sequenced prokaryotic
genomes, which are all accessible at [14], along with the
barcode images for other classes of genomes.
From these barcodes (e.g., Figure 1), we observed that (a)
all chromosomal genomes have remarkably stable 4-mer
frequency distributions essentially for all 4-mers, giving
rise to the vertical bands with consistent grey levels across
each barcode; (b) the small fraction of the fragments with
clearly different, abnormal, barcodes (horizontal stripes
in the barcodes) than the rest of the genome typically rep-
resent 2–3 special classes of genes (see discussion later);
(c) multiple chromosomes of the same organisms gener-
ally have highly similar barcodes (Figure 2(a)) but they
each have their unique patterns of abnormal fragments;
and (d) the barcodes similarities tend to be generally pro-
portional to the genomes' phylogenetic closeness (Figure
2(b)).
To understand why a genomic sequence has the barcode
property, we have examined random nucleotide
sequences generated using different models, including
Markov chain models of order from 0 to 6. We observed
that barcodes for random nucleotide sequences generated
using a third-order Markov chain model are the closest to
the barcodes of genomic sequences in terms of their
appearances (Additional file 1), and higher order Markov
chain models do not seem to add much to this property.
Hence we believe that the barcode property of prokaryotic
genomes is mainly due to the third-order Markov chain
property of the coding sequences in the genomes, which
count for 80–90% of a typical prokaryotic genome. It is
worth noting that barcodes for coding and non-coding
sequences of the same genome are generally different
though they share a weakly similar backbone structure
while each of these two classes of (composite) regions
generally has highly similar barcodes (Figure 3).
Extension to other genomes
In addition to prokaryotes, we have also calculated the
barcodes for the other classes of sequenced genomes,
namely eukaryotic, mitochondrial, plastid and plasmid
genomes. For eukaryotes, we studied the barcodes for four
key components in eukaryotic genomes, namely the
(composite) regions of repetitive sequences, promoter
sequences (the 1000-bp upstream region from each trans-
lation start), coding regions and introns, respectively (Fig-
ure 3(b)–(e)). We observed that (i) different regions in a
high-level eukaryotic genome (e.g., human) have similar
"backbone" structures in their barcodes, and (ii) the bar-
codes for the four types of regions have increasingly
higher complexity, going from repetitive sequences to
coding regions to introns and promoter sequences. This is
consistent with the belief that introns and promoter
sequences are probably the most information rich among
the four because of the possibly large numbers of regula-
tory elements they encode.
The barcodes of the mitochondrial genomes are generally
unique compared to the barcodes of the other genomes as
they have a distinct overall appearance (e.g., Figure 3(h)–
(i)). Their similar appearance may be the result of all

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mitochondria originating from Proteobacteria. The bar-
codes of all plasmid genomes also tend to have similar
characteristics among themselves, possibly due to being
under similar selection pressure caused by their frequent
transferring among cell cultures. The barcodes of all the
plastid genomes are also generally unique compared to
the barcodes of the others (e.g., Figure 3(j)–(k)). For
example, a majority of them each consist of two dark hor-
izontal bends toward one end in their barcodes along the
genome axis, whose corresponding genomic regions con-
sist of RNA genes such as ribosomal RNAs and tRNAs,
plus ribosomal proteins. The fuzzier appearance of the
plastid barcodes indicates that their k-mer frequencies
along the genome axis are not as stable as in the other
genomes. The overall similar appearances of the plastid
barcodes may be due to all originating from the Cyanobac-
teria.
One interesting question is "do different classes of
genomes have their unique characteristics in their bar-
codes?" Our answer is yes, based on their highly separable
distributions in the feature space defined by two particu-
lar features, as shown in Figure 4, one of which measures
the overall frequency variation for all 4-mers across the
Barcodes for five prokaryotic genomesFigure 1
Barcodes for five prokaryotic genomes. (a) E. coli K-12; (b) E. coli O157; (c) chromosome 1 of B. pseudomallei K96243; (d)
archaean P. furiosus DSM 3638; and (e) a random nucleotide sequence generated using a zero
th
order Markov chain model. The
x-axis for each barcode is the list of all 4-mers arranged in the alphabetical order, and the y-axis is the genome axis with each
pixel representing a fragment of M bp long.

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Basic features of barcodesFigure 2
Basic features of barcodes. (a) Barcode distance distribution among chromosomes from the same organisms, across all
prokaryotic and eukaryotic chromosomal genomes. The x-axis is the barcode distance and the y-axis is the frequency of chro-
mosome pairs of the same organism having a particular barcode distance. (b) Genome barcode distances versus sequence simi-
larities among the corresponding 16S rRNAs (based on the multiple sequence alignment given in DeSantis TZ et al. [26]). The
y-axis represents the barcode distance, and the x-axis is the sequence identity axis between two 16S rRNAs grouped into nine
bins, where the sequence identity is calculated as the average sequence identity over all 16S pairs in each bin.

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genome's barcode, and the other measures the overall
similarity level among all the M-bp fragments of the
genome, each considered as a vector of 4-mer frequencies.
While Figure 2(b) indicates that barcodes generally pre-
serve sequence-level similarities, Figure 4 suggests that
barcodes also capture a higher-level similarity beyond
individual genome sequence similarities through the tex-
tures of their images, which are the common and unique
Barcodes of some organismsFigure 3
Barcodes of some organisms. Barcodes of (a) Human chromosome 1 (226.21 Mbps); major components of human chro-
mosome in a composite form: (b) repetitive sequence, (c) promoter sequence, (d) coding regions and (e) introns; and (f) cod-
ing and (g) non-coding regions of E. coli K-12. Only a 639-Kbp region of each sequence in (b) – (g) is displayed so each pixel
represents the same sequence length. 639 Kbps is used since this is the length of the shortest region among them all, i.e. the
total non-coding region of E. coli K-12. Mitochondrial genome barcodes of (h) C. elegans (13794 bps) and (i) Drosophila mela-
nogaster (19517 bps). Plastid genome barcodes of (j) aquatic plant Ceratophyllum demersum (156252 bps) and (k) land plant Pop-
ulus trichocarpa (157033 bps).

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characteristics of different classes of genomes. This prop-
erty indicates that barcodes are not just a simple visualiza-
tion tool, instead they have captured some fairly basic
information about genomes! From application point of
view, we believe that this feature will prove to be useful to
metagenome analyses as fragments from different classes
of genomes such as eukaryotes, prokaryotes or different
organelle genomes, have different characteristics in their
barcode images.
Identification of abnormal sequence fragments
Our procedure for identifying sequence fragments with
abnormal barcodes in a genome employs a clustering
strategy to divide all the sequence fragments in a genome
into two groups: (a) a large group of fragments with their
barcodes all similar to each other and (b) the rest (see
METHODS section).
Using this procedure, we have identified 30,582 abnor-
mal fragments, covering 30,889 genes across all the com-
plete prokaryotic genomes. Specifically 28,460 such
fragments are identified in the 542 bacterial genomes,
covering 28,562 genes, and 2,122 such fragments are
identified in the 46 archaeal genomes, covering 2,327
genes. We found that the percentage of fragments with
abnormal barcodes ranges from 9.40% to 32.32% across
all the bacterial genomes, with the average being 12.85%.
Among the 46 sequenced archaeal genomes, the percent-
Barcodes in feature spaceFigure 4
Barcodes in feature space. The x-axis is the average of variations of the 4-mer frequencies across a whole genome across
all 4-mers, and the y-axis measures the similarity level among all 1000-bp partitioned fragments of the genome, each repre-
sented as a 136-dimensional vector of 4-mer frequencies; Specifically, for each genome, we build a minimum spanning tree [27]
based on the 4-mer frequency vectors for its sequence fragments and their distances. The y-axis is the averaged weight (dis-
tance) of all edges in the minimum spanning tree. The green dots represent prokaryotes (586 genomes), the blue ones for
eukaryotes (83 chromosomes), the red ones for plastids (101 genomes with lengths > 20,000 bps), the brown ones for plas-
mids of prokaryotic genomes (237 plasmids > 20,000 bps) and the black for mitochondria (120 genomes with lengths > 20,000
bps).

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age of fragments with abnormal barcodes ranges from
9.86% to 23.14%, with the average being 13.58%. Further
information can be found from Additional file 1. The
detailed frequency information for abnormal fragments
across different genomes is in Additional file 2[15].
While we found that it is generally more challenging to
study the abnormal fragments in eukaryotes, we did apply
the same procedure to different human chromosomes,
and found that the percentage of abnormal fragments
ranges from 10.08% to 31.32%, with the average being
12.10%.
We have analyzed the abnormal fragments across the
prokaryotic genomes, and found the following: ~30% of
the abnormal fragments can be explained in terms of (a)
horizontal gene transfers, (b) phage invasions and (c)
highly expressed genes, based on PHX-PA [16,17] and
Prophinder [18], respectively. Among the genes that fall
into this 30%, 6.99% are horizontally transferred genes,
4.97% bacteriophage genes and 18.90% highly expressed
genes, based on the above two prediction programs – note
that these numbers do not add up to exactly 30% since
there are overlaps among them. The genes falling into dif-
ferent categories are given in Additional file 3[15]. We
have carried out an enrichment analysis of such elements
in regions with abnormal versus normal barcodes. We
found that the highly expressed genes are enriched in the
abnormal fragments, with the enrichment ratio > 1 across
all the genomes and the average enrichment ratio being
1.90. Similar results hold for the horizontally transferred
genes and bacteriophage genes. All the detailed data can
be found in Additional file 2
We noted that our estimate of the percentages of "foreign
fragments" in bacterial genomes (after deducting the
"highly expressed genes") is in general agreement with the
previous estimates though different information and tech-
niques are used to derive the estimates [19].
We do not yet have an explanation for the remaining
~70% of abnormal fragments in prokaryotic genomes,
although we suspect that they mostly fall into the same
three categories – one reason that we could not explain
them now is possibly due to the limited coverage of the
current databases for horizontally transferred genes, bac-
teriophage genomes and highly expressed genes. We
believe that by using more sophisticated computational
procedures, one may be able to derive the level of abnor-
mality of a fragment's barcode in a genome, and possibly
link such information to when such fragments were hori-
zontally transferred [20].
Binning metagenome sequence
The ability to sequence a microbial community has led to
the sequencing of at least 7.04 Giga bps of metagenome
sequences, already 2.22 times the total complete genome
sequences accumulated in the past two decades [21].
These metagenome sequences have opened many doors
to new research possibilities, and have posed some chal-
lenging problems. One such problem is determining
which fragments are from the same organisms in a large
pool of metagenomic fragments [22], typically ~1000 bps
in lengths after the initial assembly using the Sanger
sequencing techniques.
We have applied a clustering algorithm (see METHODS
section) for binning sequence fragments together based
on their barcode similarities, and tested the clustering
strategy on three sets of simulated metagenome data cre-
ated by cutting actual bacterial genomes into fragments
and mixing them together. The three test sets consist of all
sequence fragments from three sets of genomes, respec-
tively, extracted from the GenBank. The first set consists of
11 genomes randomly selected from the same genus but
from 11 different species (the genus has only 11
sequenced species) while the last two sets each consist of
30 and 100 genomes randomly selected from 30 and 100
different bacterial genera, respectively. The genome
names are given in Additional file 4[15].
To assess the binning ability of our algorithm as a func-
tion of the fragment size, we have considered fragment
size M = 1000, 2000, 5000 and 10000. To test the limit of
our binning algorithm, we have also considered M = 500.
For each set of genomes, we partitioned each genome into
fragments of size M, and then mixed the fragments of the
same length into one pool. We then calculated the bar-
code for each fragment, and did a clustering analysis,
assuming that the number of genomes in each pool is
known (this information is derivable from the 16S
rRNAs). We have carried out binning predictions, one
directly on the generated fragments and one on a reduced
set of generated fragments, in which we remove 10% of
the fragments from each genome whose barcodes are
most different from the average barcode of the genome.
The consideration is that each bacterial genome has ~13%
of fragments with abnormal barcodes on average, which
are not expected to be binned correctly with the rest of
their host genome. This way we can more accurately assess
the binning ability of our algorithm. Table 1 gives the bin-
ning results on the three sets of synthetic metagenome
data, both the original set and the reduced set.
From the table, we can see that the binning accuracy (into
the correct genomes) is high for fragment size M = 1000
and above, at both the species and the genus level. From
the table, we see that there is a drop in the binning accu-
racy when the number of the underlying genomes is
increased from 30 to 100. This indicates the increased
complexity of the problem as a function of the number of
underlying genomes.

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We have compared our binning performance with the
published results by the best available algorithm PhyloPy-
thia [5]. Our comparison indicates that our algorithm
gives consistently more accurate and more specific bin-
ning results across different fragment sizes. For example,
at the species level, our algorithm has better than 50%
accuracy on our test set when the fragment size is at least
2000 bps while no binning results at the species level is
given in McHardy et al. [5]. At the genus level, the accu-
racy (the average of binning specificity and sensitivity,
extracted from Figure 1(a) and 1(b) in McHardy et al. [5])
by PhyloPythia is 45.5% for fragment size 1000, 56% for
2000, 74% for 5000 and 82.5% for 10000 (no data is pro-
vided for 500), all measured in terms of putting fragments
into the correct genera while ours is to the correct
genomes and with more accurate binning results. It
should be noted that the test set used by PhyloPythia is
different than ours, which may affect the performance sta-
tistics somewhat though we suspect that will be insignifi-
cant, considering the sizes of the test sets. Another key
difference between the two algorithms is that while Phy-
loPythia is a supervised learning algorithm, which
requires a training set, our algorithm does not require a
training set, and hence it is more general.
One thing worth noting is that a prokaryotic genome, on
average, has ~13–14% of abnormal sequence fragments,
when the fragment size is M = 1,000, suggesting that the
theoretical limit for binning accuracy should be no better
than 86–87%. Similarly we expect that the theoretical lim-
its of binning accuracy for 2,000, 5,000 and 10,000 frag-
ments-based binning should, in general, be no better than
87.36%, 87.58% and 88.4%, respectively.
Discussion and Conclusion
A natural question is "do all nucleotide sequences have
the barcode property like genome sequences have?" The
answer is no, based on the large number of randomly gen-
erated sequences that we have examined. Figure 1(e)
shows a typical barcode of a random sequence generated
using a zero
th
order Markov chain model. We found that
none of the so generated nucleotide sequences has the ver-
tical band structures as in genomes barcodes. More gener-
ally, barcodes for genomes and the randomly generated
nucleotide sequences have different characteristics as
shown in Figure 5.
The barcode analyses in this paper are mainly based on
data from prokaryotes. Though we have applied the same
barcode model to eukaryotes and made interesting obser-
vations, we suspect that the current barcoding scheme is
rich enough to capture all the complexity of eukaryotes.
Further studies along this direction are clearly needed.
We believe that for many genome analysis problems, par-
ticularly for prokaryotic genomes, the barcodes provide a
natural, intuitive, information-rich and unified frame-
work for studying them. Further applications of this capa-
bility to numerous genome analysis problems can be
envisioned, such as phylogeny studies, particularly for
genomes without obvious marker genes such as viruses,
more thorough examination of different types of genomic
regions in eukaryotes, their structures and organization,
further studies of horizontal gene transfers, assisting in
genome assembly of higher-order organisms (e.g., populus
which we are currently working on) and possibly many
more. We believe that we have only begun exploring the
true power of this new capability for genome studies.
Methods
Mapping frequencies to grey levels
The frequency of each k-mer is mapped to a grey level as
follows. We first count the frequency of each k-mer across
all prokaryotic genomes, and sort the frequency list S
[1:N(k)] in the increasing order of the frequencies with
N(k) being the number of k-mers. We then find an integer
L, L > 0, and partition S [1:N(k)] into L sub-lists so that the
following function is minimized: , where S
i
is
()SS
i
i
iL
−
=
=
∑
1
Table 1: Binning accuracies of our barcode-based clustering algorithm.
11 genomes 30 genomes 100 genomes
Original genomes Filtered genomes Original genomes Filtered genomes Original genomes Filtered genomes
FS = 500 bps 71.10% 77.30% 51. 6% 55.70% 40.50% 41.10%
FS = 1000 bps 79.90% 85.90% 65.30% 70.30% 51.10% 52.60%
FS = 2000 bps 86.30% 91.70% 74.80% 80.60% 61.00% 68.53%
FS = 5000 bps 91.10% 98.10% 86.60% 93.20% 79.40% 81.90%
FS = 10000 bps 95.80% 99.30% 91.90% 97.50% 86.60% 89.18%
The binning accuracy is defined as (prediction specificity + prediction sensitivity)/2, and FS is for fragment size, where both the specificity and sensitivity
are measured in terms of putting the fragments into the correct bin corresponding to each genome, defined by the majority of the fragments in the
bin. The column "Original genomes" lists the binning accuracy of our algorithm on all the non-overlapping fragments in each group of genomes, and
the column "Filtered genomes" gives the accuracy after removing the 10% fragments with the most abnormal barcodes from each genome.

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the sum of all frequencies in the i
th
sub-list, is the aver-
age of S, and L is a parameter to be determined by the
minimization result. For M = 1000 and k = 4, we found L
= 14 gives the best value for the above objective function.
The computed partition of S gives a mapping of frequen-
cies to the grey levels. Note that this mapping is genome-
independent so each grey level in the barcodes has the
same meaning in different genomes.
Barcode similarity calculation
We define the distance (or dissimilarity) between two bar-
codes based on their simplified representations, each of
which is a matrix having the same number of columns of
the barcode and the number of grey levels, L, used in bar-
code images as the number of rows; each element in the
matrix represents the frequency of the corresponding grey
level across each column in the barcode. For two such
matrices M
1
and M
2
with K columns and L rows, we define
their barcode distance as
Clearly this is a generalization of the Euclidean distance
between two vectors of the averaged k-mer frequencies
across each genome, widely used for genome comparisons
as in the work of Karlin and colleagues [13,16,23,24] and
many others. This is equivalent to the special case of our
barcode distance when L = 1. Figure S4 in Additional file
1 provides a comparison between the two distances.
S
((,) (,)).Mij Mij
j
K
i
L
1
11
2
2
==
∑∑
−
Distribution of ratios between barcode variations of all prokaryotic genomes and their corresponding randomly generated nucleotide sequencesFigure 5
Distribution of ratios between barcode variations of all prokaryotic genomes and their corresponding ran-
domly generated nucleotide sequences. For each genome, a corresponding random nucleotide sequence is defined as a
random sequence of the same length and with the same mono-nucleotide frequencies as those of the genome, generated using
a zero
th
order Markov chain model. The variation of a barcode is defined as the standard deviation of the list of the averaged
frequencies of all the k-mers along the genome. The x-axis is the ratio of the barcode variations between a genome and a cor-
responding random sequence, and the y-axis represents the frequency of cases with a particular variation ratio.

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Identification of abnormal fragments in a genome
We have used the following procedure to identify frag-
ments in a genome with substantially different barcodes
than the average barcode of the genome. The procedure
consists of two key steps. First, for each k-mer, we select
the fragments in the genome that have the highest or the
lowest X% of this k-mer's frequency among all fragments,
with X being a parameter. Then we sort all the fragments
in the increasing order of the number of times they are
selected in the first step, termed function F(p), with p
being the index of a fragment. Let p
0
be the fragment index
having the highest second-order derivative of F(p). We
consider all fragments p with F(p) > F(p
0
) to be the non-
native fragments of the genome as they have used the
most number of k-mers with frequencies that are substan-
tially different than the typical k-mer frequencies through-
out the genome. We found that the abnormal fragment
prediction is not very sensitive to the detailed value of X
within the range from 5 to 20. So we have chosen X = 10
as the default value of our program.
The rationale for this procedure is that fragments with
higher F(p) values represent fragments that have more
"abnormal" k-mer frequencies compared to the average k-
mer frequencies in the genome, and hence are more prob-
able to be non-native fragments. By examining the curve
of the F(p) function, we found that it is convex with one
sharp transition point p
0
, indicating a transition point
from the typical fragments to the "abnormal" fragments
in the genome (see Additional file 1). Hence we have used
this point as the separation point between the normal (or
native) fragments and the "abnormal"fragments.
Metagenome binning algorithm
Our binning procedure starts with an application of the
CLUMP program [25] to a given pool of fragments (not
necessarily of the same lengths) to be clustered based on
their barcode similarities. A unique feature of CLUMP is
that it is quite accurate in identifying the core elements of
each cluster as we have previously demonstrated [25],
though a weakness of the algorithm could be that it does
not always handle the boundary elements accurately.
Hence we have combined CLUMP with a K-means based
clustering approach that we implemented. After identify-
ing the initial clusters formed by CLUMP based on bar-
code similarities, assuming that we know the number of
clusters to be identified, we pick a seed from each pre-
dicted cluster randomly according to the density distribu-
tion of the cluster. Then we run the K-means algorithm,
using the selected seeds. For each pool of fragments, we
run this two-step clustering algorithm multiple times,
using a different set of seeds for each run. In deciding the
number of runs, our rule of thumb based on our experi-
ence working on the metagenome data is to use 500 * (the
number of clusters),. For each given set of seeds, we run the
K-means algorithm 10000 iterations. Among all the com-
puted clustering results for each pool, we choose the clus-
tering result C
1
, C
2
,..., C
K
that minimizes the following
function as the final binning result:
where C
1
, C
2
,..., C
K
is a partition of a given pool of metage-
nomic fragments with each C
i
being a subset of the pool
and being the average of the barcodes of all fragments
in C
i
, i = 1,..., K.
Authors' contributions
Y.X. conceived the project. F.Z. and V.O. analyzed the data
and performed the experiments. Y.X. supervised this
project as P.I. and wrote the manuscript.
Additional material
Acknowledgements
This work was supported by National Science Foundation (DBI-0354771,
ITR-IIS-0407204, DBI-0542119, CCF0621700), a U.S. Department of
Energy "BioEnergy Research Center" grant from the Office of Biological and
Environmental Research in the DOE Office of Science, and a Distinguished
Scholar grant from the Georgia Cancer Coalition. We would like to thank
Additional file 1
Supplementary material. Supplementary material 1–3.
Click here for file
[http://www.biomedcentral.com/content/supplementary/1471-
2105-9-546-S1.doc]
Additional file 2
Supplementary Table 1. HX is highly expressed gene, HT is horizontally
transferred gene, and PH is the phage gene. UnknownGene consists of
genes within fragments of abnormal barcodes but do not belong to the
above three categories.
Click here for file
[http://www.biomedcentral.com/content/supplementary/1471-
2105-9-546-S2.xls]
Additional file 3
Supplementary Table 2. Gene classifications of all the prokaryotic
genomes.
Click here for file
[http://www.biomedcentral.com/content/supplementary/1471-
2105-9-546-S3.zip]
Additional file 4
Supplementary Table 3. Genomes used in the binning section.
Click here for file
[http://www.biomedcentral.com/content/supplementary/1471-
2105-9-546-S4.xls]
(),XXi
XCi
K
i
−
∈=
∑∑
2
1
X
i

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BMC Bioinformatics 2008, 9:546 http://www.biomedcentral.com/1471-2105/9/546
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(page number not for citation purposes)
the two anonymous reviewers for their helpful comments on our work.
We would also like to thank Ms Joan Yantko for preparing the manuscript.
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