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Vol. 12, Issue 10, 1466-1482, October 2002
Department of Molecular Biophysics and Biochemistry, Yale University, New Haven, Connecticut 06520, USA
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ABSTRACT |
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Mammals have 79 ribosomal proteins (RP). Using a systematic procedure based on sequence-homology, we have comprehensively identified pseudogenes of these proteins in the human genome. Our assignments are available at http://www.pseudogene.org/ or http://bioinfo.mbb.yale.edu/genome/pseudogene. In total, we found 2090 processed pseudogenes and 16 duplications of RP genes. In relation to the matching parent protein, each of the processed pseudogenes has an average relative sequence length of 97% and an average sequence identity of 76%. A small number (258) of them do not contain obvious disablements (stop codons or frameshifts) and, therefore, could be mistaken as functional genes, and 178 are disrupted by one or more repetitive elements. On average, processed pseudogenes have a longer truncation at the 5' end than the 3' end, consistent with the target-primed-reverse-transcription (TPRT) mechanism. Interestingly, on chromosome 16, an RPL26 processed pseudogene was found in the intron region of a functional RPS2 gene. The large-scale distribution of RP pseudogenes throughout the genome appears to result, chiefly, from random insertions with the numbers on each chromosome, consequently, proportional to its size. In contrast to RP genes, the RP pseudogenes have the highest density in GC-intermediate regions (41%-46%) of the genome, with the density pattern being between that of LINEs and Alus. This can be explained by a negative selection theory as we observed that GC-rich RP pseudogenes decay faster in GC-poor regions. Also, we observed a correlation between the number of processed pseudogenes and the GC content of the associated functional gene, i.e., relatively GC-poor RPs have more processed pseudogenes. This ranges from 145 pseudogenes for RPL21 down to 3 pseudogenes for RPL14. We were able to date the RP pseudogenes based on their sequence divergence from present-day RP genes, finding an age distribution similar to that for Alus. The distribution is consistent with a decline in retrotransposition activity in the hominid lineage during the last 40 Myr. We discuss the implications for retrotransposon stability and genome dynamics based on these new findings.
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INTRODUCTION |
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All of the proteins in the cell are synthesized by the ribosomes, large
complexes of RNA and protein molecules. A typical mammalian cell has
about 4 × 106 ribosomes, and each is composed of four RNA
molecules (rRNA) and 79 ribosomal proteins (RPs). In total,
ribosomes constitute about 80% of the RNA and 5%-10% of the protein
in a cell (Kenmochi et al. 1998). Great progress has been made in recent years in
elucidating the structure and mechanism of the ribosome. The peptide
sequence of the complete set of mammalian RPs was deduced by Wool
and colleagues (1995)
, and the genes encoding all human RPs have been
positioned on the human genetic map (Kenmochi et al. 1998
; Uechi et al. 2001
; Yoshihama et al. 2002
). Moreover, several high-resolution atomic structures
are now available for archaeal ribosomes (Ban et al. 2000
; Schluenzen et al. 2000
; Wimberly et al. 2000
; Yusupov et al. 2001
).
Although it is well recognized that rRNA catalyzes the basic biochemistry of
protein synthesis, ribosomal proteins are important in facilitating
rRNA folding, protecting them from nucleases, and coordinating the
multistep process of protein synthesis. Some RPs have substantial
extra-ribosomal functions as well (Wool 1996). It is believed that RPs from all three kingdoms of
life are related, probably having evolved from the same ancestral set
of proteins after the conversion of the ribosome from an RNA complex
to a ribonucleoprotein particle (RNP). Among eukaryotes, the
number and sequence of cytoplasmic RPs are fairly well conserved.
For instance, yeast and rat share all but one RP, and the
sequence identity of their RPs ranges from 40% to 88%, with an
average of 60%. Among mammals, the amino acid sequences of the RPs
are almost identical. For example, for the 72 RPs of which amino
acid sequences are available for both human and rat, the average
sequence identity is 99%, and 32 of them are perfectly identical
(Wool et al. 1995
).
In the yeast cell, the 78 RPs are encoded by 137 genes; 59 of
the genes are duplicated (Planta and Mager 1998). In all cases, both gene copies are transcribed
although their expression levels often differ considerably (Raue and
Planta 1991
). The proteins encoded by duplicated genes have
identical or virtually identical sequences and are functionally
indistinguishable. In contrast, it is widely recognized that in
mammals a single gene encodes each RP, although most if not all of
the RP genes have a number of processed pseudogenes located elsewhere
in the genome. The existence of these pseudogenes has greatly
hindered the sequencing and mapping efforts of human RP genes, so a
special intron-trapping strategy had to be undertaken to
differentiate the real transcribed RP gene and pseudogenes (Kenmochi
et al. 1998
; Uechi et al. 2001
). A number of RP genes have also been implicated in
various human diseases, such as RPS19 in Diamond-Blackfan anemia
(DBA; Draptchinskaia et al. 1999
), RPL6 in Noonan syndrome (Kenmochi et al. 2000
), and RPS4X gene in Turner's syndrome (Zinn et al.
1993
).
In general, pseudogenes are disabled copies of functional genes that do not
produce a functional, full-length protein (Vanin 1985; Mighell et al. 2000
). The disablements can take the form of premature stop
codons or frame shifts in the protein-coding sequence (CDS), or less
obviously, deleterious mutations in the regulatory regions that
control gene transcription or splicing. There are two main types of
pseudogenes: duplicated (nonprocessed) and processed. Duplicated
pseudogenes arise from genomic DNA duplication or unequal
crossing-over. They have the same general structure as functional
genes, with sequences corresponding to exons and introns in the usual
locations. Processed pseudogenes result from retrotransposition, that
is, reverse-transcription of mRNA transcript followed by integration
into genomic DNA, presumably in the germ line. Because of their
origin, processed pseudogenes are sometimes considered a special type
of retrotransposons just like Alu and long interspersed (LINE)
elements, and are sometimes referred to as retro-pseudogenes. They
are typically characterized by a complete lack of introns, the
presence of small flanking direct repeats, and a polyadenine tract
near the 3' end (provided that they have not decayed). Processed
pseudogenes in general are not transcribed, however in very rare
cases, transcripts of some pseudogene have been reported, although
the functional relevance of these pseudogene transcripts remains
unclear (McCarrey et al. 1996
; Fujii et al. 1999
; Olsen and Schechter 1999
).
It is unclear how many pseudogenes exist in the human genome. Estimates for
the number of human genes range from ~22,000 to ~75,000 (Crollius et
al. 2000; Ewing and Green 2000
; Lander et al. 2001
; Venter et al. 2001
; Harrison et al. 2002b
). From previous reports, it is thought that up to 22%
of these gene predictions may be pseudogenic (Lander et al. 2001
; Yeh et al. 2001
). It is important to characterize the human pseudogene
population, as their existence interferes with gene identification
and annotation. They are also an important resource for the study of
the evolution of protein families, for example, studies on the human
olfactory receptor subgenome (Glusman et al. 2001
). Harrison et al. (2002a)
performed a detailed analysis of pseudogenes on human
chromosomes 21 and 22. It was discovered that the protein
family that has the largest number of processed pseudogenes is RPs, a
total of 43 of which were found on the two smallest human
chromosomes. This extrapolated to over 2000 RP pseudogenes in
the whole human genome.
We have developed a pipeline of mostly automatic procedures that enables us
to discover and characterize pseudogenes quickly and comprehensively.
Here we report the identification of over 2400 processed RP
pseudogenes and pseudogenic fragments on the latest human genome
draft sequence (Lander et al. 2001). Complete sequence and precise chromosomal location
have been obtained for each pseudogene. We provide a comprehensive
characterization of the human RP pseudogene population and discuss
its implications for retrotransposition and genome
dynamics.
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RESULTS |
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Human Genome Has 2090 RP Processed Pseudogenes
We have conducted a comprehensive search for cytosolic RP pseudogenes on the
August 2001 freeze of the human genome draft (Lander et al.
2001). Details of the annotation procedure are described in
the Methods section, and a flow chart is shown in Figure 8A below. Table
1 shows the
distribution of identified RP pseudogenes among 22 autosomes and
two sex chromosomes, together with the length of each chromosome and
the number of functional RP genes previously mapped onto it (Kenmochi
et al. 1998
; Uechi et al. 2001
; Yoshihama et al. 2002
). Some general statistics of the processed pseudogene
population are shown in Table 2. A total
of 2090 processed RP pseudogenes were identified in the whole
human genome. The substantial majority (1912) of these are termed
"intact" pseudogenes because they are continuous in sequence with
insertions shorter than 60 bp, whereas the remaining 178 are
disrupted by long insertions in the middle of their sequence. The
majority (146 of 178) of these disruptions are caused by the
insertions of one or more retrotransposons, Alu, or less often, LINE
elements.
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358 Pseudogenic Fragments
We also found 358 pseudogenic fragments, which are continuous in sequence but produce transcripts shorter than 70% of a full-length RP peptide. On average these fragments match 40% of the full-length RPs with an average amino acid sequence identity of 74.2% (see Table 2). There are three possible explanations for these short fragments. (1) They could have originally been individual exons of duplicated RP genes. (2) They could have been intact processed pseudogenes and later became truncated by spontaneous DNA deletion or retrotransposon insertion. (3) They could have been caused by premature termination of the reverse transcription process, which would lead to incomplete incorporation of cDNA into the chromosome. Because the reverse-transcription starts at the 3' end (poly-A tail), such premature truncation would tend to occur at the 5' end of the cDNA sequence. The first scenario involves duplicated RP genes, and the last two scenarios assume a processed origin for the pseudogenic fragments. We believe the last two are more likely because there is evidence for both hypotheses. For most of these pseudogenic fragments, we could locate a retrotransposon within 300 bp on the chromosome with the average distance between the fragments and the retrotransposon being 108 bp. This close proximity strongly indicates retrotransposon insertion events in past evolution, which caused the RP pseudogene truncation. Also, the average truncation at the 5' end for these fragments is almost twofold longer than at the 3' end (227 vs. 127 bp), which is consistent with the mechanism of target-primed reverse transcription (Table 2). Based on these arguments, we counted these pseudogenic fragments as processed when we computed pseudogene density (see Table 1 footnote), but in general these fragments were treated separately from the full-length processed pseudogene population. As the total number of these fragments is much smaller than the number of processed pseudogenes (358 vs. 2090), exclusion of them from the processed pseudogene counts does not affect the conclusions one way or another.
Kenmochi and colleagues sequenced most of the 80 human RP genes and
mapped them onto individual cytogenic bands (Kenmochi et al. 1998; Uechi et al. 2001
; Yoshihama et al. 2002
). In our present search for processed pseudogenes,
72 of these 80 RP genes were located and their cytogenic
locations were confirmed. In addition, 16 duplicated copies of
these RP genes were identified, mostly in the neighboring region of
the original RP genes.
Overall Statistics of the Processed Pseudogenes
Because the ribosomal proteins are of various lengths, we measure sequence
completeness by defining relative length as the ratio between the
length of translated pseudogene and the length of the corresponding
functional ribosomal proteins. In general, the RP pseudogenes are
well preserved, as they tend to be almost full-length in their coding
regions (96.5%), with high sequence identity in terms of both
translated amino acid sequence (76.2%) and also underlying
nucleotides (86.8%). Figure 1A
illustrates the distribution of the relative sequence length of
processed pseudogenes. Surprisingly, although we used 70% as a
threshold to separate the processed pseudogenes from pseudogenic
fragments, the CDSs of the majority of the processed pseudogenes
(>90% of the set) are practically full-length. It is known that
LINE1 reverse-transcriptase (RT) has a low efficiency that often
leads to 5' truncation and thus incomplete insertion of transcripts.
It is a little surprising that we have observed such a high
percentage of near-complete pseudogenes, but it is probably because
RT truncations mostly occurred in the 5' UTR instead of the
protein-coding region. Figure 1B shows the
distribution of DNA sequence identity between processed pseudogenes
and the RP cDNA sequences. Figure 1C shows the
distribution of number of disablements (premature stop codons and
frame shifts) per pseudogene, with the y-axis plotted in log
scale. Of the 1912 "intact" processed pseudogenes (Table 1),
258 (13%) do not contain any disablements; therefore they could
potentially be mistaken as functional genes by some automatic gene
prediction algorithms. The graph shows an exponential relationship. A
similar exponential relationship was observed in a smaller set of
human olfactory pseudogenes (~600; Glusman et al. 2001), and was interpreted in such a way to support an
alternative origin for olfactory receptor pseudogenes other than gene
duplication or retrotransposition.
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We also checked the existence of a polyadenine tail for our processed
pseudogene set. Of the 2090 processed pseudogenes,
952 (45.5%) have no obvious polyadenine tail of at least
30 bp detected (see Methods section), 176 (8%) have both a
poly-A tail and a polyadenylation signal (mostly AATAAA) within
50 bp of the poly-A tail. Thirty-two pseudogenes (1.5%) have a
poly-A tail and a polyadenylation signal 50-100 bp upstream;
903 pseudogenes (44.5%) only have a poly-A tail with no
detectable polyadenylation signal. We are confident in our assignment
of processed pseudogenes; lack of a poly-A tail for about half of the
assigned processed pseudogenes can be explained as decay in genome
sequence and nucleotide substitutions. Harrison et al. (2002a) found polyadenylation for only 52% of the processed
pseudogenes on chromosomes 21 and 22, which is similar to
the ratio we found here for RP pseudogenes.
Distribution of Pseudogenes Among Chromosomes
Unlike in prokaryotes, where the RP genes are organized into operons, the
distribution of RP genes among human chromosomes is dispersed but not
random (Feo et al. 1992; Kenmochi et al. 1998
; Uechi et al. 2001
; Yoshihama et al. 2002
). Every human chromosome except chromosomes 7 and
21 contains at least one or more RP genes. Chromosome
19, one of the smallest chromosomes, contains as many as
13 RP genes (Table 1). Such high
density of RP genes on chromosome 19 can be explained by the
high chromosome GC content, which results in unusual high gene
density (Mouchiroud et al. 1991
; Lander et al. 2001
; Venter et al. 2001
). The distribution of processed RP pseudogenes in the
human genome appears more random and uniform than their functional
counterparts (Fig. 2). It is
obvious that the abundance of processed pseudogenes on each
chromosome is proportional to the chromosome length (Fig. 3A), with a
correlation coefficient of 0.89 (P<1E-8). Including
pseudogenic fragments in the set has no noticeable effect on this
result.
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We further calculated the RP pseudogene density (number of pseudogenes per
Mb) for each chromosome and plotted them against chromosomal GC
content (Fig. 3B), which shows
a weak positive correlation (correlation
coefficient = 0.51, P<0.01). The outlier on the
bottom of the graph is the sex chromosome Y, which has the lowest
pseudogene density even for its relatively low GC content. Chromosome
Y is unusual in many ways, as it also has the lowest density for Alu
repeats (Lander et al. 2001); those authors suggested that these phenomena might be
related to the high tolerance for DNA insertion and deletion and
rapid gene turnover rate on this chromosome. If we weight the
chromosome length by its GC content, then the correlation with the
pseudogene density increases from 0.89 to
0.91 (P<1E-9). It is likely that the chromosomal GC content
reflects the relative stability of the chromosome; that is,
pseudogenes are more likely to be preserved on the chromosomes that
have a slower gene turnover rate.
Genomic Distribution of Processed Pseudogenes
Using a 100-Kb-long nonoverlapping window, we divided the human genome into
more than 30,000 segments and assigned them to five classes
according to their average GC content. For each class, we also
calculated the gene or pseudogene density by dividing the number of
genes or pseudogenes by the amount of DNA in that class (Table 3). It is well
established that in the human genome, gene density is strongly
correlated with local GC content, with the GC-rich regions being
mostly gene-dense (Mouchiroud et al. 1991; Lander et al. 2001
; Venter et al. 2001
). This is clearly the case for functional RP genes, as
the GC-rich classes (>46%) contain the majority of the RP genes
and have higher RP gene density. In contrast, the RP pseudogenes are
enriched in classes with lower GC content; they have the highest
density in the genomic region with intermediate GC content (41-46%).
In fact, the class that has the highest local GC content (>52%)
contains the fewest number of pseudogenes, although it has the
highest RP gene density. Similar genomic distributions have been
reported for chromosome 22 with a smaller set of
114 pseudogenes (Pavlicek et al. 2001
). Our results suggest that this is probably a general
rule for all processed pseudogenes in the human genome.
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It has been proposed that the protein machinery encoded by the LINE1 element
is involved in the arising of both the Alu repeats and LINE repeats
(Feng et al. 1996; Jurka 1997
; Weiner 1999
) and the processed pseudogenes (Weiner 1999
; Esnault et al. 2000
). LINEs and Alus are the most frequent retrotransposons
found in the human genome, each occupying about 15% and 10% of the
genome respectively. LINEs (long interspersed
elements) are about 6-kb long and encode two open reading
frames (ORFs). Alus are a major class of SINEs (short
interspersed elements), approximately 280 bp in
length. Despite their common origin, the Alus in the human genome are
predominantly found in GC-rich regions, whereas LINEs and processed
pseudogenes are more prevalent in relatively GC-poor regions. In this
sense, the distribution of Alus is more similar to that of genes than
pseudogenes. In Figure 4A, we plotted
the RP pseudogene density along with the densities of functional
RP genes, Alus, and LINEs. [The data for Alus and LINEs are from
the results of Pavlicek et al. (2001)
]. It is obvious that both the functional RP genes and
the Alus are enriched in the GC-rich regions and depleted in the
GC-poor regions. LINEs are predominantly found in genomic regions
with the lowest local GC content. The distribution of RP pseudogenes
falls between these extremes, as they have the highest density in the
regions with intermediate GC content (41%-46%).
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Negative Selection Theory
The puzzling contrast between the genomic distribution of Alus and LINEs was
recently explained by comparing the distribution of repeats of
different age groups (Lander et al. 2001; Pavlicek et al. 2001
). It has been observed that young Alus, similar to
LINEs, were more frequently found in the GC-poor region compared
to the more ancient Alu elements. Based on such findings, Pavlicek
et al. (2001)
proposed a negative selection theory, which hypothesized
that the enrichment of Alus in the GC-rich region was the result
of their higher stability in the compositionally matching
environment. It is believed that when the retrotransposons were first
integrated into the nuclear genome, both Alus and LINEs preferred a
GC-poor (AT-rich) region because the LINE1
reverse-transcriptase/endonuclease specifically targets the TT|AAA
insertion site. Because of the conspicuously higher GC content of
Alus (~57%), their existence in GC-poor regions would destabilize the
chromosome. Therefore, these Alus would be selected against to be
either lost or, perhaps more likely, their nucleotide composition
would have drifted towards a lower GC level and decayed into
background genomic DNA and become unrecognizable.
We believe that the aforementioned negative selection theory can also explain
the pseudogene density distribution illustrated in Figure 4A. The GC
content of RP CDS ranges from 42% to 63% with the median at 51%,
which is not as high as Alus, but still much higher than the LINE
repeats (~42%) and the genome-wide average (~41%). The average GC
content for the RP pseudogene sequences is 47%, which is intermediate
between those of the functional RP genes and genomic DNA. Therefore,
at least for RP pseudogenes, we have observed the drift in their GC
content, which supports the negative selection hypothesis. We further
divided RP processed pseudogenes into four groups according to the
average GC content in the 100-Kb genomic region surrounding each
pseudogene. For each group, we calculated the average GC content for
both the pseudogene sequences and also the CDS of the functional RP
genes they originated from. The results are plotted in Figure 4B, which
clearly shows a greater drift for pseudogenes in the GC-poor region
than in the GC-rich region; therefore, the pseudogenes in GC-poor
region appear more decayed than those in the GC-rich region. Such
drift in nucleotide composition was previously reported for silent
mutation sites in mammalian MHC gene sequences (Eyre-Walker 1999) and interspersed repeats in the human genome (Lander
et al. 2001
). In both studies, significantly more single nucleotide
substitutions from G/C to A/T than from A/T to G/C have been
observed. Despite the drift in composition, the majority of the
processed RP pseudogenes still have GC content higher than their
surrounding genomic sequences.
Age Distribution of Processed Pseudogenes
When mRNA transcripts were reverse-transcribed to become pseudogenes, they
were immediately released from selection pressure. Therefore the
amount of mutations they accumulated during evolution could be used
to infer their ages. Because mammalian RP sequences have stayed
almost unchanged since rodents and primates diverged over
100 millions of years (Myr) ago (99% sequence identity between
rats and human), we can safely use the present-day human RP sequence
as the ancient RP gene sequences to calculate the divergence rate
for the processed pseudogenes. The percentage of sequence divergence
was converted into approximate age in Myr by using a constant
substitution rate of 1.5 × 109 per site per year (Li 1997
). It is known that substitution rate varies during
evolution (Goodman et al. 1998
; Lander et al. 2001
); however we believe that such simplified treatment is
sufficient for our purpose.
The age distribution of human repetitive sequences has been analyzed (Smit
1999; Lander et al. 2001
). Figure 5 shows the
distribution of sequence divergences for RP pseudogenes together with
LINE1 and Alu repeats; each increment in divergence represents
roughly 6.7 Myr. The repeats data are from Arian Smit (pers.
comm.). It is obvious that processed pseudogenes have an age
distribution much more similar to Alu elements than to LINE1
elements, although they were all processed by the same LINE1
machinery. Note that LINE1s are mammalian-specific and Alus are
primate-specific. The distribution for RP pseudogenes peaks at an
evolutionary age corresponding to 8%-10% sequence divergence, whereas
Alus peak at 7% and LINE1 elements peak at both 4% and 21%.
Interestingly, RP pseudogenes also have a shoulder at 17%-18%, which
could have been the consequence of the surge of LINE1
retrotransposition activity just a few million years before that. The
rate of new processed pseudogenes generated in the human genome has
slowed down since ~40 Myr ago, which was about the time when human
species diverged from gibbons. This coincides with the decline of new
LINE1 elements and Alus in the genome. It has been proposed that the
structure and dynamics of hominid populations are responsible for
such decline in retrotransposon activity (Lander et al. 2001
).
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GC-Poor RP Genes Have More Processed Pseudogenes
Table 4
lists the number of processed pseudogenes among 79 RPs, sorted in the
descending order. The first two columns list the SWISSPROT ID
(Bairoch and Apweiler 2000) for the human RPs, and the standard mammalian RP gene
nomenclature (Mager et al. 1997
). Also listed are the lengths of RP mRNA transcripts, coding
sequence (CDS), and the CDS GC content, all retrieved from GenBank.
On average, 26 processed pseudogenes are found for each RP gene;
however, different RP genes have clearly very different propensities
for generating processed pseudogenes. The distribution of numbers
of processed pseudogenes among RP genes is strikingly skewed,
although presumably for each RP only one functional gene exists
(Wool et al. 1995
). RPL21 has the most copies of processed pseudogenes at
145, which is about 50% more than that of RPL23A, which has the
second-most at 85. Meanwhile, 24 RP genes have less than ten
copies of processed pseudogenes each, and MRPL14 has the fewest
at three. Regarding the RP genes that have the greatest numbers
of processed pseudogenes, we also checked their chromosomal locations
to make sure that they were not created from genomic duplication;
that is, these processed pseudogenes arose mostly independently.
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We were curious as to whether the differing processed pseudogene abundance among RP genes is correlated with the recent decline in retrotransposition activity. We further divided the processed pseudogenes originated from the same RP gene into three groups according to their ages: <40 Myr, 40-80 Myr, and >80 Myr (Fig. 6A). It is obvious that the age distribution of processed pseudogenes is similar for all 79 RP genes, that is, there were no preferences for a certain group of RP genes in different evolution periods. The correlation between the number of young pseudogenes (<40 Myr) and number of mid-age pseudogenes (40-80 Myr) per RP gene is 0.73 (P<1E-13); the correlation between mid-age pseudogenes and old pseudogenes (>80 Myr) is 0.68 (P<1E-11).
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It is also plausible that the differences in pseudogene abundance merely
reflect the different ages for individual RP genes, as presumably
genes that have been around longer will have more chance being
reverse-transcribed to generate pseudogenes. To check this, we
grouped RP genes into three groups according to their phylogenetic
profile, that is, some RP genes are unique to eukaryotes while others
have homologs in eubacterial and archaebacterial kingdoms (Wool et
al. 1995). There appears to be no correlation between processed
pseudogene abundance and the degree of ubiquity. Within eukaryotes,
we also looked at the sequence identity between yeast RPs and human
RPs; no correlation was found there as well. The pseudogene abundance
also has no correlation with the extra-ribosomal function of some of
the RP genes (Wool 1996
).
Goncalves et al. (2000) analyzed 249 processed pseudogenes, which correspond to
181 functional genes, and concluded that human genes that gave
rise to processed pseudogenes in general share four features. They
are (1) widely expressed, especially in germ line, (2) highly
conserved, (3) short, and (4) GC-poor. The first two criteria are
trivial for ribosomal proteins, as RPs are ubiquitous in all cell
types, and they are also the most highly conserved among eukaryotes
and mammals (Wool et al. 1995
). In general, RP genes have short mRNAs and short CDS
as seen in Table 4, although
there is no significant correlation between the number of processed
pseudogenes and the mRNA length (correlation
0.01, P<0.93) (Fig. 6B) or the CDS
length (correlation 0.04, P<0.73). We would like to
emphasize the lack of obvious correlation between gene length and
pseudogene abundance, as it demonstrates that our pseudogene
searching procedure did not systematically miss out short
pseudogenes; that is, the skewed pseudogene distribution is not an
artifact. However, there is a significant inverse correlation between
the number of processed pseudogenes and the GC-content of RP
gene CDS (correlation
0.41, P<0.0002) as shown in Figure 6C; that
is, relatively GC-poorer RP genes tend to have more processed
pseudogenes than GC-richer ones. It is not immediately obvious
what is the mechanism behind the enrichment for the relatively
GC-poor RP genes, since the arising of a processed pseudogene
involves multiple steps and the selection for GC-poor RP genes
could have occurred at any step along the way. More on this topic
will be discussed in the Discussion section.
Nonprocessed Pseudogenes and Duplicated RP Genes
We found only 16 duplicated RP genes in the human genome (Table 5), which share
identical exon structure with previously characterized RP genes
(Kenmochi et al. 1998; Uechi et al. 2001
). This is in sharp contrast to the yeast genome, where
most RP genes are duplicated and the duplicated genes are also
transcribed and functional. Only one duplicated gene in the human
genome (RPL13A) has an obvious disablement in the coding region; it
is possible that other duplicated RP genes may have hard-to-detect
disablements in the UTR regions or introns. It is not clear whether
these duplicated RP genes are transcribed in the cell, although it is
generally assumed that only one gene is functional for each ribosomal
protein (Wool et al. 1995
; Kenmochi et al. 1998
). The majority of the duplicated genes are in the
vicinity of the original genes, and therefore could not have been
resolved from the original genes in the hybridization experiments.
There are notable exceptions: RPL26, RPS27, and RPL3 have duplicated
copies on separate chromosomes, and RPS4Y has a duplicated copy on
the opposite end of chromosome Y. Interestingly, the duplicated
copies for RPL26, RPS27, and RPL3 genes have much longer introns than
the mapped genes, which were caused by insertion of Alu or LINE
repeats (with the exception of RPS27). It is likely that the sequence
difference in intron region is the reason that they were missed out
in the hybridization experiments, even though they are far apart from
the mapped RP genes. Detailed analysis of these duplicated genes will
be described in subsequent reports.
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Our homology matching procedure located at least one intron-containing functional gene for all but eight RP genes: RPP2, RPL4, RPL30, RPL35A, RPL38, RPL41, RPS7, and RPS27A. We did, however, find processed pseudogenes for these RP genes in the genome. These genes either consist of short exons or their protein sequences are predominantly low-complexity, making them difficult to find by homology matching.
It was surprising to discover a processed RPL26 pseudogene in the intron region of the functional RPS2 gene on chromosome 16 (band p13.3, Contig AC005363.1.1.75108, Ensembl ID ENSG00000140988). RPS2 gene has seven exons; the pseudogene resides in the third intron (1015 bp long), between residues 89 and 90 in the RPS2 protein sequence. Interestingly, there is also an Alu element at the 3' end of the pseudogene, about 100 bp away. The pseudogene itself is 357 bp long, corresponding to residues 14 to 141 of RPL26, having amino acid sequence identity of 49% and nucleotide sequence identity of 73% (Fig. 7). It appears to be very ancient, has already lost its poly-A tail, and has sequence divergence of 0.28, which corresponds to more than 100 Myr old. Figure 7 shows the alignment of RPL26 sequences from several eukaryotic organisms together with this pseudogene. At 11 positions, the pseudogene has the same residue with the mammalian sequences but not with the invertebrates. Note that rat and human sequences are almost identical except at residue 100, where rat has an arginine and human has a histidine. Interestingly, this RPL26 pseudogene also has a Histidine at that position; this suggests that the pseudogene became part of the intron before the divergence of rodent and hominid species. It has been known that some RP genes contain Alu or LINE elements in the 3' or 5' UTR; to our knowledge this is the first case where a processed pseudogene is found in the intron region of another functional gene. This has implications for the origin and evolution of introns.
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Online Database
The data and results discussed in this report can be accessed online at http://www.pseudogene.org/ or http://bioinfo.mbb.yale.edu/genome/pseudogene/.
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DISCUSSION |
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Significance of RP Pseudogenes
Characterizing ribosomal protein pseudogenes is valuable in many ways. (1) It
will be tremendously useful in the study of functional RP genes. RP
genes are implicated in many human genetic diseases such as
Diamond-Blackfan anemia (Draptchinskaia et al. 1999), Noonan syndrome (Kenmochi et al. 2000
), and Turner`s syndrome (Zinn et al. 1993
). The precise nucleotide sequence and chromosomal
location of RP pseudogenes will certainly help researchers in
designing probes specific to functional genes. (2) Pseudogenes
can also serve as genomic milestones, as they provide snapshots
of RP sequences existing millions of years back in evolution.
Such information will be valuable in studying ribosome biogenesis
and the phylogenetic relationships between organisms. The discovery
of an RPL26 pseudogene in the intron region of a functional RPS2
gene could certainly shed light on the evolution of both RP genes.
(3) From the perspective of studying retrotransposition, processed
pseudogenes are just a special type of repetitive elements like
Alus. However, processed pseudogenes are much more diverse in
terms of sequence length, GC content, and other features than
traditional retrotransposons, which makes them useful in studying
evolution and dynamics of genomes. To our knowledge, our RP
pseudogenes are the largest set ever studied.
Comparing With Ensembl Annotations
The Ensembl database (http://www.ensembl.org/) is an automated
system for genome-wide gene prediction and annotation, which has
direct links to primary HGP data sources (Birney et al. 2001; Hubbard et al. 2002
). The annotation process relies on matching genomic DNA
sequence and GenScan peptides (Burge and Karlin 1997
) with known proteins, mRNAs, and other sequence
information. All of the genes were checked to be transcribed before
they were included into the database (Daniel Barker, pers. comm.). As
of the end of February 2002, there were approximately
47,000 annotated genes in Ensembl, of which 549 were
annotated as ribosomal protein genes. Some of these have more
detailed annotations associating them with a particular RP such as
"60S RIBOSOMAL PROTEIN L7", and others were described more loosely
such as "60S RIBOSOMAL PROTEIN". After re-aligning these genes with
human RP protein sequences and removing some dubious matches, we
derived a set of 481 Ensembl RP entries.
Ensembl does not explicitly differentiate between functional genes and pseudogenes, nor does it aim to (D. Barker, pers. comm.). Consequently, most of these 481 Ensembl RP entries turned out to be pseudogenes instead of functional genes, as only 260 (54%) translate to peptides longer than 95% of full-length ribosomal proteins. For instance, a gene ENSG00000150624 on chromosome 2 was annotated as "60S RIBOSOMAL PROTEIN L17", but produced a transcript that was only 51.6% of the full-length RPL17, and had sequence identity of 56.2%. Moreover, only 170 of these genes have introns; most of these Ensembl RP genes (64.6%) are single exons. We checked the overlap between our RP pseudogene sets with these Ensembl RP entries: 474 of 481 (98.5%) Ensembl RP entries have significant overlaps with our pseudogenes, and in most cases our pseudogenes were longer than the Ensembl entries. Five RPL41 single-exon processed pseudogenes from Ensembl were the only ones missed by our procedure. The RPL41 is the shortest ribosomal protein, with only 25 amino acids; it also contains 17 near-consecutive Arginine and Lysine residues. It is likely that short length and low complexity caused BLAST to fail to detect these pseudogenes. Note that Ensembl is a database in flux, that is, the sequence and annotation are continuously updated and improved. Therefore some of the examples and statistics given above will probably be out of date when this report is published. Nonetheless, the overlap in annotation of genes and pseudogenes documented above is important as it demonstrates the need to systematically include pseudogene identification in genome annotation efforts.
Automatic gene prediction programs alone do not have the ability to
differentiate between functional genes and pseudogenes, especially if
the pseudogenes do not contain obvious disablements in the coding
sequence (CDS). Furthermore, for those pseudogenes that contain
disablements, gene prediction programs either discard them or stop at
the disablement and predict the pseudogene as a functional gene but
with truncated length. We think this is the reason that so many RP
pseudogenes were passed into the Ensembl database as functional
genes. The number of genes in the human genome has long been a matter
of debate, as different methods such as EST analysis and GenScan
(Burge and Karlin 1997) gave different estimates (Harrison et al. 2002b
). It is probably not appropriate to extrapolate the
overestimation for RP genes onto the whole human proteome, as
ribosomal proteins are a very unique protein family in many ways.
Nevertheless, special care should be taken in interpreting outputs
from automatic gene prediction programs.
Pseudogene Abundance per RP Cannot Be Explained by Positive Selection
As mentioned previously, we found an inverse correlation between RP gene GC
content and the pseudogene abundance for that gene (Fig. 6C); that is,
the relatively GC-poor RP genes tend to have more processed
pseudogenes. Before we further discuss the possible mechanism behind
this correlation, it would be well to give a brief overview of the
LINE1-mediated retrotransposition process, which is believed to be
responsible for generating processed pseudogenes (Kazazian and Moran
1998). LINE1-mediated retrotransposition can be divided into
four steps. (1) First, a retrotransposon or gene is transcribed in
the nucleus to produce an mRNA transcript. (2) Second, the mRNA
transcripts are transported into cytoplasm, and LINE1 mRNA
transcripts are translated into two proteins: ORF1 (also known as
p40), and ORF2, which is a reverse-transcriptase/endonuclease. (3)
Human ORF1 has been demonstrated to be a sequence-specific
single-strand RNA binding protein, which binds specifically but
not exclusively to LINE1 transcript to form a ribonucleoprotein
particle (RNP) which also includes ORF2 protein (Leibold et al.
1990
; Martin 1991
; Hohjoh and Singer 1996
, 1997b
; Moran et al. 1996
; Kazazian and Moran 1998
). (4) Lastly, the RNP particle migrates into the
nucleus and undergoes target-primed reverse-transcription, which give
rise to a new retrotransposon or processed pseudogene.
If the GC-poor RP genes were selected favorably in retrotransposition (i.e.,
there is a positive selection for them), it must have occurred in one
of the four steps described above. However, we cannot find any
evidence for such positive selection in any of the steps. In relation
to step 1, we have compared the processed pseudogene abundance
per gene with the mRNA expression level in human and yeast cells (see
Methods). No significant correlation between the datasets was found,
suggesting that the selection could not have occurred at the step of
gene transcription. In relation to step 2, the lack of
correlation between mRNA length and pseudogene abundance also
suggested that the transportation of RP transcript in and out of the
nucleus had no effect on retrotransposition. This is based on the
idea that longer mRNAs are harder to transport. In relation to step
3, the forming of RNP particle, it has been demonstrated that
the binding between ORF1 and mRNA transcript has a
cis-preference; that is, ORF1 has higher affinity to wild-type
LINE1 transcripts that encode it. However at a much lower level,
ORF1 or ORF1 and ORF2 together can also act in trans to
retrotranspose mutant LINEs and other mRNA transcripts (Hohjoh and
Singer 1997a,b
; Esnault et al. 2000
; Wei et al. 2001
). It is not clear what sequence or structural features
on the mRNA transcripts constitute the cis and trans
preference, though it is unlikely that the overall GC content is
the deciding factor, because Alu elements and LINE elements, the two
most populous retrotransposons in human genome, have very different
GC content (56.8% for Alus and 42.3% for LINEs). Following the same
reasoning, it is also unlikely that the reverse transcription in the
fourth step has a preference for GC-poor transcripts.
Negative Selection for GC-Poor RP Genes in Retrotransposition
In the above analysis we found no evidence of a positive selection mechanism in retrotransposition of GC-poor RP genes; however, a negative selection mechanism can readily explain the skewed distribution. In this mechanism, the accumulation of GC-poor RP pseudogenes can be interpreted as the indirect result of a faster decay rate for GC-rich RP pseudogenes in the GC-poor genome region where they were originally inserted.
Analogous to the mechanism of enrichment of Alu elements in the GC-rich
region, which we described earlier in this report, the existence of
GC-rich RP pseudogenes in the GC-poor genomic region was more
unfavorable than GC-poor RP pseudogenes. Thus there would be greater
selection pressure against these GC-rich pseudogenes. Pavlicek et al.
(2001) divided Alu and LINE elements into different age groups
and studied their distribution in genome regions of different GC
content. They showed that the young Alus (divergence <2% from
consensus sequence) are indeed less depleted in the GC-poor region.
This effect is not evident for older Alus (sequence divergence
>4%). We did a similar age segmentation analysis on RP
pseudogenes, with the results shown in Table 6. (The
numbers in the table were not normalized by amount of DNA.) We found
different results for young pseudogenes than described above for
young Alus. For young pseudogenes, there is no indication of
enrichment in the GC-poor region (where "young" here is defined as
sequence divergence less than 2% from their parents, the same cutoff
as used in the study of the Alus). Note, however, that there is
a slight enrichment for the youngest pseudogenes, which have
sequence divergence less than 1%, corresponding to roughly
6.7 Myr old. We think that the reason we did not observe the
same behavior for young pseudogenes as for young Alus is because of
the much smaller sample size for pseudogenes. In addition, the recent
decline in retrotransposition activity in the human genome (Fig. 5; Lander
et al. 2001
) could have further complicated the situation, as fewer
fresh pseudogenes were generated in the human genome.
|
In conclusion, the precise mechanism behind the negative correlation between gene GC content and processed pseudogene abundance remains unsettled until more pseudogene sequences from other protein families are available. As of this writing, based on the analysis of Alu elements and the elimination of positive selection mechanisms for RP pseudogenes, the negative selection mechanism appears attractive.
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METHODS |
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Six-Frame BLAST Search for Raw Fragment Homologies
Figure 8A
is a flow chart describing our basic procedure for finding RP pseudogenes. We
used the August 6, 2001 freeze of the human genome draft,
downloaded from the Ensembl Web site (http://www.ensembl.org/).
Subsequently, all of the chromosomal coordinates were based on
these sequences. The amino acid sequences of the 79 ribosomal
proteins were extracted from SWISSPROT (Bairoch and Apweiler 2000). Because the sequence identity between the two RPS4
isoforms (RS4_HUMAN and RS4Y_HUMAN) is very high (91%), only protein
RS4_HUMAN was used in the BLAST search. Each human chromosome was
split into smaller overlapping chunks of 5.1 million bp, and the
tblastn program of the BLAST package 2.0 (Altschul et al. 1997
) was run on these sequences. The genome sequence was
not repeat-masked (A. Smit and P. Green, unpubl.) because
we were concerned that some of the RP pseudogenes may reside in
repetitive regions. Default SEG (Wootton and Federhen 1993
) low-complexity filter parameters
(12 2.2 2.5) were used in the homology search. We then
picked the significant homology matches (e-value <1E-4), and
reduced them for mutual overlap by selecting the matches in
decreasing order of significance and removing any matches that
overlap substantially with a picked match (i.e., more than ten amino
acids or 30 base pairs).
|
Merging Adjacent Fragment Homologies Into Single RP Matches
After sorting the BLAST matches according to their starting coordinates on the chromosomes, we found many neighboring matches on the same chromosome that match the same RP. Some of these adjacent matches obviously were separate genes or pseudogenes, whereas others appeared to be part of the same gene or pseudogene. A two-step procedure was developed to determine (1) whether the neighboring matches belong to the same gene structure and (2) whether they should be merged together into a longer homology match.
Step (1): Consider two adjacent homology fragments, M1 and M2, which are on the same chromosomal strand and match the same RP (Fig. 8B). M1 has chromosomal coordinates (c11, c12) and matches amino acid sequence (q11, q12) on the query RP protein. Similarly, M2 has chromosomal coordinates (c21, c22) and matches amino acids (q21, q22) on the query protein. By convention, q21 is always greater than q11 and c21 is always greater than c12. If M1 and M2 satisfy the following two criteria, then we decide they belong to the same gene structure; that is, they are either two exons of the same gene or two fragments of the same pseudogene interrupted by insertions.
(1) | q21q12 |
max
(20, 0.2xL) and (2) c21
c12
5000 (L denotes the length of the query RP peptide
sequence). The reasoning behind criterion (1) is that if the two
homology fragments have too much overlap or have too long a gap
between them on the query protein sequence, then they should be
considered two separate and independent matches. Criterion (2) sets
the maximum length of insertions in the middle of a pseudogene. We
checked that the introns in the RP genes are all shorter than
5000 bp, so we would not have accidentally split a gene
into two.
Step (2): If two homology fragments are determined to be part of the same
gene or pseudogene structure in step (1), then in step (2) the
fragments were merged only if the chromosomal distance between the
matches was shorter than 60 bp; that is, c22c21
60. The rationale behind such treatment was that if the
gap between the matches were too long, then merging them together
would generate errors in the Smith-Waterman realignment procedure
described below. In addition, it has been shown that more than 95% of
the introns in human are longer than 60 bp (Lander et al. 2001
), and thus we would not have accidentally merged two
exons together or included introns into the coding
sequence.
Optimization From Smith-Waterman Alignment of Merged Matches
After merging, each match was extended on both sides to equal the length of
the RP they matched, plus a buffer of 30 bp. For each extended
match, the corresponding SWISSPROT protein sequences were then
realigned to the genomic DNA sequence following the Smith-Waterman
algorithm (Smith and Waterman 1981) by using the program FASTA (Pearson 1997
). The reason for such an extension procedure is that
BLAST may have skipped low-complexity segments in the query RP
sequence; also, BLAST does not recognize frame shifts. After the
realignment, the matches are "cleaned up": any redundant matches were
removed, and matches that contain gaps longer than 60 bp were
split up into two individual matches. Because sequence alignment
programs sometimes tend to pick up some extra residues at the ends of
the alignment, each alignment was filtered to remove dubious matches
at the ends. At this step, we had a total of 2531 pseudogene
candidates in the whole genome that matched the human RPs. Most of
these were potential pseudogenes, but there could also be real
functional RP genes in this set, because we did not exclude any
matches based on disablement.
Deriving a Set of RP Genes From the Ensembl Database
We wanted to compare our pseudogene sets with the RP genes from the Ensembl
database (http://www.ensembl.org/; Birney
et al. 2001; Hubbard et al. 2002
). As of the end of February 2002, there were
approximately 47,000 confirmed genes, each with an annotated
function. (Details regarding the Ensembl annotation procedure
can be found in the aforementioned references.) We searched the
Ensembl database and picked out 549 genes that have been
annotated as ribosomal proteins. We then reannotated these genes by
aligning them pairwise with human RP protein sequences, and picked
out those Ensembl genes that had FASTA e-values lower than
0.0001. After removing a few remaining mitochondrial ribosomal
protein genes, we had a set of 481 Ensembl nuclear RP
genes.
In our examination of these Ensembl RP entries, it became obvious that most of these were pseudogenes other than real functional RP genes, because they do not contain introns. We found that 474 (98.5%) of the 481 Ensembl RP genes have significant overlaps with our pseudogene sets. Five single-exon RPL41 pseudogenes from Ensembl were added to our pseudogene sets.
Assessing for Processing by Checking for Exon Structures
We divided our pseudogene population into two subsets based on whether they
contained long gaps in the middle of the sequence (Fig. 8A). We labeled
those pseudogenes as "processed" if they met two criteria: (1) they
contained gaps of shorter than 60 bp, that is,
c21c12
60
in Figure 8B,
and (2) they produced transcripts longer than 70% of the ribosomal
protein they matched. Venter et al. (2001)
also used the last criterion. We also checked in
GenBank that all 79 ribosomal protein genes contain introns
longer than 60 bp. The remaining single-exon pseudogenes, which
are shorter than 70% of the full-length protein, were labeled
"fragments". A total of 1912 "intact" processed pseudogenes and
358 pseudogenic fragments were identified at this
step.
For those pseudogene candidates that contained multiple segments separated by
gaps longer than 60 bp (total of 266), it was not
straightforward to determine whether they were of processed or
nonprocessed origin because the gaps could be either introns or
repeat insertions. It is also likely that there were real functional
ribosomal protein genes in this group. The cytogenetic locations
of the 80 human RP genes (including the isoform gene RPS4Y on
chromosome Y) were previously mapped (Kenmochi et al. 1998; Uechi et al. 2001
; Yoshihama et al. 2002
). Using the cytogenetic map as reference and comparing
the position of the gaps in the sequence with the exon structure of
the functional RP genes, we identified 72 functional RP genes
and 16 duplicated genes, and assigned the remaining 178 as
"disrupted" processed pseudogenes. In summary, at the end of this
process we had 2090 processed pseudogenes, 358 pseudogenic
fragments, 72 functional RP genes, and 16 duplicated
RP genes.
Further Verification of Processing by Poly-A Signal
When processed pseudogenes were integrated into genome from mRNA, a
polyadenine tail at the 3' end would also be included (Vanin 1985; Mighell et al. 2000
). This polyadenine tail is at least 15-20 nucleotides
long and is preceded by a polyadenylation signal (mostly AATAAA; Wool
et al. 1995
). We were interested to survey how many of the
ribosomal pseudogenes still had the polyadenine tail. Following the
procedure described by Harrison et al. (2001)
, we searched a 1000-bp region that was 3' to the
pseudogene homology segment, with a sliding window of
50 nucleotides for a region of elevated polyadenine content
(>30 bp), and picked the most adenine-rich 50-bp segment as the
most likely candidate. An interval of 1000 nucleotides was used
because of the possible existence of 3'-untranslated regions
(3'-UTRs); 90% of 3'-UTRs are of length less than 942 bp
(Makalowski et al. 1996
). In addition, we searched in the same 1000-bp region
for candidate AATAAA or other polyadenylation signals and checked
whether they were upstream of the candidate polyadenine tail
site.
Dating Processed Pseudogenes
Processed pseudogene sequences are aligned together with the corresponding
functional RP gene sequences using program ClustalW (Thompson et al.
1994). For each pseudogene, we calculated sequence
divergence from the present-day RP gene with the program MEGA2
(Kumar et al. 2001
), using the Kimura two-parameter model and pairwise
deletion. Kimura's two-parameter model (Kimura 1980
) corrects for transitional and transversional
substitution rates while assuming that the four nucleotide
frequencies are the same and rates of substitution do not vary among
sites. Evolutionary ages were calculated by the formula
T = D/k, where D is the corrected divergence rate
and k is the mutation rate per year per site for nonfunctional
sequences. A mutation rate of 1.5 × 10-9 per site per year
(Li 1997
) was used.
Calculating Pseudogene Density In Different GC Regions
Each human chromosome was divided into consecutive 100K bp-long,
nonoverlapping segments. The GC content for each segment was
calculated and the segment was assigned to one of the five groups
according to their GC content: <37%, 37%-41%, 41%-46%, 46%-52% and
>52%. The number of processed pseudogenes in each group was
counted, and the pseudogene density for each group was calculated.
Note that we used the same GC content that was used for isochore
classification (Macaya et al. 1976; Bernardi 2000
), although the validity of the isochore definition has
been under debate (Bernardi 2001
; Lander et al. 2001
).
Expression Analysis
To investigate the possible correlation between the pseudogene abundance and
the mRNA expression level, we compared the number of processed
pseudogenes for each functional RP gene with its cellular mRNA
expression level in the human cell (Yuval Kluger, pers. comm.) and
the yeast cell (Cho et al. 1998). No significant correlation was found. Ribosomal
protein genes are the most highly expressed genes in the cell; it is
likely, in this case, that the overabundance of mRNA transcripts has
made the expression level a nondeciding factor for RP pseudogene
retrotransposition.
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WEB SITE REFERENCES |
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http://www.pseudogene.org/; Pseudogene database.
http://bioinfo.mbb.yale.edu/genome/pseudogene; Pseudogene database.
http://www.ensembl.org/; Ensembl database.
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ACKNOWLEDGMENTS |
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We thank Adam Pavlicek for carefully reading the manuscript and Arian Smit for providing the data on Alu/LINE sequence divergence. Mark Gerstein acknowledges NIH CEGS grant (P50 HG02357-01) for financial support. Zhaolei Zhang acknowledges Ted Johnson for doing the BLAST runs and thanks Paul Bertone, Ronald Jansen, Nick Luscombe, Yuval Kluger, and Jiang Qian for helpful discussions.
The publication costs of this article were defrayed in part by payment of page charges. This article must therefore be hereby marked "advertisement" in accordance with 18 USC section 1734 solely to indicate this fact.
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FOOTNOTES |
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1 Corresponding author.
E-MAIL Mark.Gerstein@yale.edu; FAX (360) 838-7861.
Article and publication are at http://www.genome.org/cgi/doi/10.1101/gr.331902.
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REFERENCES |
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Received April 3, 2002; accepted in revised form August 12, 2002.
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