In order for the immune system to generate its vast numbers of receptors, B- and T-cell receptor genes are created by recombining preexisting gene segments. This well- coordinated set of reactions is explained

The immune system needs to be able to identify and ultimately destroy foreign invaders. To do so, it utilizes two major types of immune cells, T cells and B cells (or, collectively, lymphocytes). Lymphocytes display a large variety of cell surface receptors that can recognize and respond to an unlimited number of pathogens, a feature that is the hallmark of the “adaptive” immune system. To react to such a variety of invaders, the immune system needs to generate vast numbers of receptors. If the number of different types of receptors present on lymphocytes were encoded by individual genes, the entire human genome would have to be devoted to lymphocyte receptors. To establish the necessary level of diversity, B- and T-cell receptor (BCR and TCR, respectively) genes are created by recombining preexisting gene segments. Thus, different combinations of a finite set of gene segments give rise to receptors that can recognize unlimited numbers of foreign invaders. This is accomplished by a supremely well-coordinated set of reactions, starting with cleaving DNA within specific, well-conserved recombination signal sequences (RSSs). This highly regulated step is carried out by the lymphocyte-specific recombinationactivating genes ( RAG1  and  RAG2 ). The segments are then reassembled using a common cellular repair mechanism.RAG1RAG2For foreign invaders and their proteins (antigens) that are not part of the host to elicit an immune response, the immune system must be able to recognize countless numbers of antigens. For obvious reasons, an unlimited number of unique antigen receptors cannot be genetically encoded. Rather, the necessary diversity in receptors is achieved by creating variations in the antigen-recognition regions of the receptors of both B cells and T cells. These regions are created by the pairing of two different protein segments, called polypeptide chains (heavy [H] and light [L] chains in the case of the BCR and α and β chains in the case of the TCR), which form a cleft that provides a binding site for the antigen. The mechanism that generates variation in the antigen-binding pockets of these receptors involves mixing and matching variable (V), diversity (D), and joining (J) gene segments in a process called V(D)J recombination. To assemble a single functional receptor, preexisting V, D, and J gene segments are rearranged to yield a contiguous V(D)J region, just upstream of another element of the receptor, the constant (C) region ( Figure 1A ).The BCR H chain and the TCR β chain consist of V, D, and J segments, while BCR L chains and the TCR α chain are comprised of only V and J segments. The number of each type of segments within the chains allows for a large but finite combinatorial possibility in rearrangement, a phenomenon termed combinatorial diversity ( Table 1 ). However, variations generated by V(D)J recombination are uncountable because they do not simply rely on the number of gene segments. Further diversity is introduced because the junctions between rearranged gene segments contain small insertions and deletions (junctional diversity). Finally, both BCR and TCR are heterodimers (consisting of two unmatched polypeptides), so the possibilities of different pairing between the chains can also increase variation. Successful V(D)J rearrangement is clearly useful in terms of antigen recognition, and it is absolutely required for the development and survival of B and T cells.Diversification of BCRs and TCRs
Number of V, D, and J segments contributes to combinatorial diversity. Further changes are introduced by junctional diversity, to give the total number of BCR and TCR repertoiresV(D)J Recombination: A Cut-and-Paste Reaction In the first part of the “cut-and-paste” reaction, breaks within both strands of the DNA helix (double-stranded breaks) are made within the RSS sites; in the second part, the newly created breaks are repaired by the cell's general DNA repair pathway. In the initial phase, two lymphocyte-specific proteins that are encoded by the recombinationactivating genes ( RAG1  and  RAG2 ) work together to recognize and bind RSSs. The complex consisting of these two proteins, RAG1–RAG2 (henceforth RAG), cuts the DNA between the rearranging DNA segments and the adjacent RSS motifs ( Figure 1B ). The second step of the reaction glues together the ends of the chromosome containing the rearranging segments, which will ultimately code for the receptor and are called coding joints (CJs). The portion of DNA between the rearranged segments is shed from the genome, but it too gets glued together in a minicircle (a signal joint [SJ]). Typically, SJs are rapidly and precisely fused, but CJs are ligated more slowly, in part because their fusion is not precise—small insertions are present quite often, and even deletions can be detected. (For detailed reviews, see  Fugmann et al. 2000 ;  Gellert 2002 ). Both pasting reactions are necessary for creating the receptors as well as for preventing havoc within the genome.
V(D)J Recombination: A Cut-and-Paste Reaction
In the first part of the “cut-and-paste” reaction, breaks within both strands of the DNA helix (double-stranded breaks) are made within the RSS sites; in the second part, the newly created breaks are repaired by the cell's general DNA repair pathway. In the initial phase, two lymphocyte-specific proteins that are encoded by the recombinationactivating genes ( RAG1  and  RAG2 ) work together to recognize and bind RSSs. The complex consisting of these two proteins, RAG1–RAG2 (henceforth RAG), cuts the DNA between the rearranging DNA segments and the adjacent RSS motifs ( Figure 1B ). The second step of the reaction glues together the ends of the chromosome containing the rearranging segments, which will ultimately code for the receptor and are called coding joints (CJs). The portion of DNA between the rearranged segments is shed from the genome, but it too gets glued together in a minicircle (a signal joint [SJ]). Typically, SJs are rapidly and precisely fused, but CJs are ligated more slowly, in part because their fusion is not precise—small insertions are present quite often, and even deletions can be detected. (For detailed reviews, see  Fugmann et al. 2000 ;  Gellert 2002 ). Both pasting reactions are necessary for creating the receptors as well as for preventing havoc within the genome.RAG1RAG2RAGs: Indispensable for V(D)J Recombination RAG proteins carry out the first enzymatic step of the reaction—site-specific cleavage of DNA ( van Gent et al. 1995 ). Artificial expression of RAGs in mammalian cells other than B- or T-lymphocytes suggests that RAG is the only lymphocyte-specific factor required for this recombination event to occur ( Schatz and Baltimore 1988 ). Indeed, in mice whose  RAG  genes have been deleted ( RAG
 −/− ), V(D)J recombination is completely abolished, and these mice have neither mature B nor T cells ( Mombaerts et al. 1992 ;  Shinkai et al. 1992 ). A similar type of immunodeficiency, called Omenn syndrome, is seen in people with mutations in their  RAG  genes ( Villa et al. 1998 ). In test-tube experiments, purified RAG proteins are sufficient for cleavage of a synthetic DNA containing the appropriate RSS ( McBlane et al. 1995 ). This reaction can be subdivided into two stages. First, a nick is made in the DNA, at a specific site within the RSS, leaving specific chemical modifications at the ends ( Figure 1B ). Then, one free end with a specific (3′-hydroxyl) group forms a new chemical (diester) bond with a different chemical (phosphoryl) group on the complementary nucleotide of the opposite strand (this is called a transesterification reaction). This results in the formation of a hairpin at the coding end, while leaving the signal end blunt ( McBlane et al. 1995 ).
RAGs: Indispensable for V(D)J Recombination
RAG proteins carry out the first enzymatic step of the reaction—site-specific cleavage of DNA ( van Gent et al. 1995 ). Artificial expression of RAGs in mammalian cells other than B- or T-lymphocytes suggests that RAG is the only lymphocyte-specific factor required for this recombination event to occur ( Schatz and Baltimore 1988 ). Indeed, in mice whose  RAG  genes have been deleted ( RAG
 −/− ), V(D)J recombination is completely abolished, and these mice have neither mature B nor T cells ( Mombaerts et al. 1992 ;  Shinkai et al. 1992 ). A similar type of immunodeficiency, called Omenn syndrome, is seen in people with mutations in their  RAG  genes ( Villa et al. 1998 ).RAGRAGRAGIn test-tube experiments, purified RAG proteins are sufficient for cleavage of a synthetic DNA containing the appropriate RSS ( McBlane et al. 1995 ). This reaction can be subdivided into two stages. First, a nick is made in the DNA, at a specific site within the RSS, leaving specific chemical modifications at the ends ( Figure 1B ). Then, one free end with a specific (3′-hydroxyl) group forms a new chemical (diester) bond with a different chemical (phosphoryl) group on the complementary nucleotide of the opposite strand (this is called a transesterification reaction). This results in the formation of a hairpin at the coding end, while leaving the signal end blunt ( McBlane et al. 1995 ).RSSs: The Targets of the Reaction RSSs are found next to every variable (V), diversity (D), and joining (J) segment. They consist of three distinct elements: a heptamer and a nonamer sequence, separated by a spacer element—either 12 or 23 bp long ( Figure 2 ) ( Tonegawa 1983 ;  Akira et al. 1987 ). Although the two RAG proteins work together in a protein complex, they do have unique functions. RAG1 binds both the 12- and 23-RSSs with equal affinities, while RAG2 does not bind either RSS sequence. This suggests that RAG1 forms the initial complex with DNA, which then recruits and is stabilized by RAG2 ( Fugmann et al. 2000 ). Figure 2 RSSs Consist of a Fairly Conserved Heptamer and Nonamer Sequence, Separated by a Spacer Element Heptamer is shown in red and nonamer in green. Conserved nucleotides are shown in bold. The spacer is either 12 or 23 bp long. Both the heptamer and the nonamer contain nucleotides that are absolutely required for efficient V(D)J recombination. The first three nucleotides within the heptamer are conserved, whereas mutations in the next four positions affect but do not abolish the reaction. Within the nonamer, positions 5 and 6 are conserved, while variations are tolerated elsewhere in the sequence ( Figure 2 ). The length of the spacer (but not its sequence) was thought to play an important role in regulating which elements could be recombined ( Gellert 2002 ): a 12mer differs from a 23mer by a single turn of the DNA helix, providing for the proteins that bind RSSs to remain in the same rotational phase ( Gellert 2002 ). The paper in this issue of  PLoS Biology  by  Lee et al. (2003)  now challenges this paradigm. They report that not only the length of the spacer but also its sequence are important, so that changes in the spacer sequence directly affect rates of recombination. Based on these data, they have developed an algorithm that accurately predicts the relative efficiencies of RSS binding, cleavage, and rearrangement based on nucleotide sequence.
RSSs: The Targets of the Reaction
RSSs are found next to every variable (V), diversity (D), and joining (J) segment. They consist of three distinct elements: a heptamer and a nonamer sequence, separated by a spacer element—either 12 or 23 bp long ( Figure 2 ) ( Tonegawa 1983 ;  Akira et al. 1987 ). Although the two RAG proteins work together in a protein complex, they do have unique functions. RAG1 binds both the 12- and 23-RSSs with equal affinities, while RAG2 does not bind either RSS sequence. This suggests that RAG1 forms the initial complex with DNA, which then recruits and is stabilized by RAG2 ( Fugmann et al. 2000 ).Both the heptamer and the nonamer contain nucleotides that are absolutely required for efficient V(D)J recombination. The first three nucleotides within the heptamer are conserved, whereas mutations in the next four positions affect but do not abolish the reaction. Within the nonamer, positions 5 and 6 are conserved, while variations are tolerated elsewhere in the sequence ( Figure 2 ). The length of the spacer (but not its sequence) was thought to play an important role in regulating which elements could be recombined ( Gellert 2002 ): a 12mer differs from a 23mer by a single turn of the DNA helix, providing for the proteins that bind RSSs to remain in the same rotational phase ( Gellert 2002 ). The paper in this issue of  PLoS Biology  by  Lee et al. (2003)  now challenges this paradigm. They report that not only the length of the spacer but also its sequence are important, so that changes in the spacer sequence directly affect rates of recombination. Based on these data, they have developed an algorithm that accurately predicts the relative efficiencies of RSS binding, cleavage, and rearrangement based on nucleotide sequence.PLoS BiologyBreaks: Necessary Precursors of Recombination After RAG cuts the DNA at the RSS, the two sides of the break are different. The coding ends are closed to resemble hairpins, while the RSS ends are open and blunt. These blunt RSS ends are rejoined rapidly, forming SJs, but before the coding ends can be fused, the hairpins must be opened ( Gellert 2002 ). Normally, hairpins are opened either at the tip or on the side. In either case, an enzyme called terminal deoxynucleotidyl transferase can add a small amount of random (nontemplated) nucleotides to freed ends, and this phenomenon of N-nucleotide addition contributes to junctional diversity of the CJs ( Bassing et al. 2002 ). When the hairpin is opened on the side, the reaction leaves a short overhang on one strand. When the overhangs are filled, palindromic sequences are generated, and these modifications are referred to as “P-nucleotides” ( Bassing et al. 2002 ). These, too, contribute to the diversity of the CJs and ultimately, when the rearranged gene produces protein, to more variability in the antigen-binding pocket of the receptor.
Breaks: Necessary Precursors of Recombination
After RAG cuts the DNA at the RSS, the two sides of the break are different. The coding ends are closed to resemble hairpins, while the RSS ends are open and blunt. These blunt RSS ends are rejoined rapidly, forming SJs, but before the coding ends can be fused, the hairpins must be opened ( Gellert 2002 ).Normally, hairpins are opened either at the tip or on the side. In either case, an enzyme called terminal deoxynucleotidyl transferase can add a small amount of random (nontemplated) nucleotides to freed ends, and this phenomenon of N-nucleotide addition contributes to junctional diversity of the CJs ( Bassing et al. 2002 ).When the hairpin is opened on the side, the reaction leaves a short overhang on one strand. When the overhangs are filled, palindromic sequences are generated, and these modifications are referred to as “P-nucleotides” ( Bassing et al. 2002 ). These, too, contribute to the diversity of the CJs and ultimately, when the rearranged gene produces protein, to more variability in the antigen-binding pocket of the receptor.Resolution: The Final Step As mentioned,  RAG
 −/−  mice do not have mature B and T cells. This causes a severe combined immunodeficiency syndrome (SCID) characterized by a complete block in B- and T-cell development, but no other defects ( Mombaerts et al. 1992 ;  Shinkai et al. 1992 ). However, there are other molecular deficiencies that also have a SCID phenotype. One of these is mapped to the enzyme DNA protein kinase (DNA-PKcs), which is required for the proper joining of DNA ends ( Bosma et al. 1988 ). Mice deficient in DNA-PKcs can initiate V(D)J recombination, but cannot form the CJs ( Gao et al. 1998 ). These mice are also sensitive to processes that induce DNA double-stranded breaks, such as ionizing radiation ( Gao et al. 1998 ). Hence, the repair pathway responsible for fixing DNA breaks caused by radiation also creates CJs. Indeed, along with DNA-PKcs, other proteins of this nonhomologous end-joining repair pathway are important for the completion of V(D)J recombination (such as Ku70 and Ku80, Artemis, XRCC4, and DNA ligase IV) ( Bassing et al. 2002 ).
Resolution: The Final Step
As mentioned,  RAG
 −/−  mice do not have mature B and T cells. This causes a severe combined immunodeficiency syndrome (SCID) characterized by a complete block in B- and T-cell development, but no other defects ( Mombaerts et al. 1992 ;  Shinkai et al. 1992 ). However, there are other molecular deficiencies that also have a SCID phenotype. One of these is mapped to the enzyme DNA protein kinase (DNA-PKcs), which is required for the proper joining of DNA ends ( Bosma et al. 1988 ). Mice deficient in DNA-PKcs can initiate V(D)J recombination, but cannot form the CJs ( Gao et al. 1998 ). These mice are also sensitive to processes that induce DNA double-stranded breaks, such as ionizing radiation ( Gao et al. 1998 ). Hence, the repair pathway responsible for fixing DNA breaks caused by radiation also creates CJs. Indeed, along with DNA-PKcs, other proteins of this nonhomologous end-joining repair pathway are important for the completion of V(D)J recombination (such as Ku70 and Ku80, Artemis, XRCC4, and DNA ligase IV) ( Bassing et al. 2002 ).RAGAn Evolutionary Model of V(D)J Recombination From the discovery of the  RAG  genes on, investigators have suspected that V(D)J recombination may be the result of the landing of a transposable genetic element (a “jumping gene” or transposon) into the vertebrate genome. The clues were many. Firstly, the compact organization of the  RAG  locus resembles a transposable element ( Schatz et al. 1989 ). Secondly, RAGs cut the DNA after binding RSSs throughout the BCR and TCR loci ( Gellert 2002 ). RSSs resemble the ends of other transposable elements. Biochemically, the reaction shares characteristics with enzymes found in other transposable elements ( Gellert 2002 ). Finally, these genes appear abruptly in evolution: they are present in the jawed vertebrates (like the shark), but not in more ancient organisms ( Schluter et al. 1999 ). A current model is that an ancient transposon containing the  RAG  genes flanked by RSS ends “jumped” into an area of the vertebrate lineage containing a primordial antigen receptor gene, separating it into pieces. When the transposon lifted off, it left the RSSs behind. Multiple rounds of transposition and duplication eventually gave rise to our TCR and BCR loci. Mechanistically, transposition could happen even now, if the DNA segment containing the SJs is not ligated into a minicircle. These unsealed SJs are able to insert into heterologous sequences in vitro, and if they are allowed to float free in the cell, they have the potential to invade the genome. This phenomenon could give rise to certain types of chromosomal translocations prevalent in some types of B- and T-cell cancers ( Shih et al. 2002 ). Generally, repair processes in the cell actively suppress this phenomenon by rapidly ligating SJs.
An Evolutionary Model of V(D)J Recombination
From the discovery of the  RAG  genes on, investigators have suspected that V(D)J recombination may be the result of the landing of a transposable genetic element (a “jumping gene” or transposon) into the vertebrate genome. The clues were many. Firstly, the compact organization of the  RAG  locus resembles a transposable element ( Schatz et al. 1989 ). Secondly, RAGs cut the DNA after binding RSSs throughout the BCR and TCR loci ( Gellert 2002 ). RSSs resemble the ends of other transposable elements. Biochemically, the reaction shares characteristics with enzymes found in other transposable elements ( Gellert 2002 ). Finally, these genes appear abruptly in evolution: they are present in the jawed vertebrates (like the shark), but not in more ancient organisms ( Schluter et al. 1999 ).RAGRAGA current model is that an ancient transposon containing the  RAG  genes flanked by RSS ends “jumped” into an area of the vertebrate lineage containing a primordial antigen receptor gene, separating it into pieces. When the transposon lifted off, it left the RSSs behind. Multiple rounds of transposition and duplication eventually gave rise to our TCR and BCR loci.RAGMechanistically, transposition could happen even now, if the DNA segment containing the SJs is not ligated into a minicircle. These unsealed SJs are able to insert into heterologous sequences in vitro, and if they are allowed to float free in the cell, they have the potential to invade the genome. This phenomenon could give rise to certain types of chromosomal translocations prevalent in some types of B- and T-cell cancers ( Shih et al. 2002 ). Generally, repair processes in the cell actively suppress this phenomenon by rapidly ligating SJs.Conclusion V(D)J recombination is absolutely crucial for the adaptive immune response. In its absence, our immune system is compromised. When it is not properly controlled, it gives rise to chromosomal translocations and B-and T-cell cancers. The elucidation of all steps of the reaction and attempts to understand exactly how these steps are regulated to avoid disastrous side effects are areas of study that have occupied researchers in the past and will continue to do so in the future.
Conclusion
V(D)J recombination is absolutely crucial for the adaptive immune response. In its absence, our immune system is compromised. When it is not properly controlled, it gives rise to chromosomal translocations and B-and T-cell cancers. The elucidation of all steps of the reaction and attempts to understand exactly how these steps are regulated to avoid disastrous side effects are areas of study that have occupied researchers in the past and will continue to do so in the future.


Background A significant portion (about 8% in the human genome) of mammalian mRNA sequences contains AU (Adenine and Uracil) rich elements or AREs at their 3' untranslated regions (UTR). These mRNA sequences are usually stable. However, an increasing number of observations have been made of unstable species, possibly depending on certain elements such as Alu repeats. ARE motifs are repeats of the tetramer AUUU and a monomer A at the end of the repeats ((AUUU) n A). The importance of AREs in biology is that they make certain mRNA unstable. Proto-oncogene, such as c-fos, c-myc, and c-jun in humans, are associated with AREs. Although it has been known that the increased number of ARE motifs caused the decrease of the half-life of mRNA containing ARE repeats, the exact mechanism is as of yet unknown. We analyzed the occurrences of AREs and Alu and propose a possible mechanism for how human mRNA could acquire and keep AREs at its 3' UTR originating from Alu repeats.
Background
A significant portion (about 8% in the human genome) of mammalian mRNA sequences contains AU (Adenine and Uracil) rich elements or AREs at their 3' untranslated regions (UTR). These mRNA sequences are usually stable. However, an increasing number of observations have been made of unstable species, possibly depending on certain elements such as Alu repeats. ARE motifs are repeats of the tetramer AUUU and a monomer A at the end of the repeats ((AUUU) n A). The importance of AREs in biology is that they make certain mRNA unstable. Proto-oncogene, such as c-fos, c-myc, and c-jun in humans, are associated with AREs. Although it has been known that the increased number of ARE motifs caused the decrease of the half-life of mRNA containing ARE repeats, the exact mechanism is as of yet unknown. We analyzed the occurrences of AREs and Alu and propose a possible mechanism for how human mRNA could acquire and keep AREs at its 3' UTR originating from Alu repeats.Results Interspersed in the human genome, Alu repeats occupy 5% of the 3' UTR of mRNA sequences. Alu has poly-adenine (poly-A) regions at its end, which lead to poly-thymine (poly-T) regions at the end of its complementary Alu. It has been found that AREs are present at the poly-T regions. From the 3' UTR of the NCBI's reference mRNA sequence database, we found nearly 40% (38.5%) of ARE (Class I) were associated with Alu sequences (Table  1 ) within one mismatch allowance in ARE sequences. Other ARE classes had statistically significant associations as well. This is far from a random occurrence given their limited quantity. At each ARE class, random distribution was simulated 1,000 times, and it was shown that there is a special relationship between ARE patterns and the Alu repeats. Table 1 Defined ARE classes. (Symbol marks are used in this study instead of full sequences.) Symbol ARE sequence Class I (AUUU)5A AUUUAUUUAUUUAUUUAUUUA Class II (AUUU)4A AUUUAUUUAUUUAUUUA Class III U(AUUU)3AU UAUUUAUUUAUUUAU Class IV UU(AUUU)2AUU UUAUUUAUUUAUU Class V U4AUUUAU4 UUUUAUUUAUUUU Class VI W3UAUUUAUW3 WWWUAUUUAWWW
Results
Interspersed in the human genome, Alu repeats occupy 5% of the 3' UTR of mRNA sequences. Alu has poly-adenine (poly-A) regions at its end, which lead to poly-thymine (poly-T) regions at the end of its complementary Alu. It has been found that AREs are present at the poly-T regions. From the 3' UTR of the NCBI's reference mRNA sequence database, we found nearly 40% (38.5%) of ARE (Class I) were associated with Alu sequences (Table  1 ) within one mismatch allowance in ARE sequences. Other ARE classes had statistically significant associations as well. This is far from a random occurrence given their limited quantity. At each ARE class, random distribution was simulated 1,000 times, and it was shown that there is a special relationship between ARE patterns and the Alu repeats.Defined ARE classes. (Symbol marks are used in this study instead of full sequences.)Conclusion AREs are mediating sequence elements affecting the stabilization or degradation of mRNA at the 3' untranslated regions. However, AREs' mechanism and origins are unknown. We report that Alu is a source of ARE. We found that half of the longest AREs were derived from the poly-T regions of the complementary Alu.
Conclusion
AREs are mediating sequence elements affecting the stabilization or degradation of mRNA at the 3' untranslated regions. However, AREs' mechanism and origins are unknown. We report that Alu is a source of ARE. We found that half of the longest AREs were derived from the poly-T regions of the complementary Alu.

Background Varying more than ten-fold, messenger RNA degradation is essential for the regulation of gene expression [ 1 , 2 ]. Differential mRNA decay rates were determined by specific  cis -acting sequences within mRNA. For example, the mRNA sequences of yeast, many mammalians, and other eukaryotes contain AU-rich elements or AREs at their 3' untranslated regions (UTR) [ 3 , 4 ]. For example, in yeast, AREs stimulated the shortening of poly adenine (poly A), and two kinds of degradation pathways followed. One is 5'-to-3' exonuclease access by removal of the 5' cap structure. The other is 3'-to-5' digestion by a complex of exonucleases called exosome [ 5 , 6 ]. Genes required for these steps have been identified in yeast and were found to be conserved among eukaryotes. Although the mechanisms of AREs enhanced mRNA degradation are unknown, several groups provided evidence that 3'-to-5' degradation by the exosome may be the major pathway of decay for at least some mammalian mRNAs, including ARE-containing mRNA sequences [ 7 - 9 ]. The length of AREs also affected the half-life of mRNA. The nonamer UUAUUUAUU is a typical ARE, and the simple repeats, (AUUU) n A motif, is the well-known pattern of AREs. It has been shown that the number of ARE motifs correlated with the turnover of ARE-mRNAs such as GM-CSF [ 10 , 11 ]. Because of this, AREs are usually classified according to the number of the repeats [ 12 ]. It is known that the stabilization factor, such as HuD, is able to bind to AREs [ 13 ] and most AREs seem to function as destablizing factors. The overall importance of AREs in biology is that they can make certain critical gene products unstable. They include proto-oncogenes such as c-fos [ 14 ], c-myb [ 15 ], c-myc [ 16 ], and Pim-1 [ 17 ]. Another class of ARE-associated genes are immune response genes such as interferon [ 15 , 18 ] and interleukin [ 15 , 19 - 21 ]. Growth factors, such as Gro-α [ 22 ] and the vascular endothelial factor [ 23 ] in humans, are also known to be associated with AREs. AREs consist of a great number of thymine (or uracil) and a few adenines. Alu repeats can be a source of poly-T regions in mRNA. Therefore, there is a possible link between ARE and Alu repeats. Alu repeats are sequences of approximately 300 nucleotides (nt) transcribed by RNA polymerase III. The Alu region is then reverse-transcribed and inserted into a new location in the genome [ 24 ]. It can reach a copy number in excess of 500,000 in the human genome [ 25 ]. Alu repeats were thought to be inserted very early in primate evolution, approximately 65 million years ago (mya). Alu amplification appears to have reached a maximum rate between 35 and 60 mya, and is currently amplifying at only 1% of the maximum rate [ 26 ]. Statistical analyses have identified key diagnostic nucleotide positions in Alu sequences that define 12 subfamilies. J class is the oldest one, S class is intermediate, and Y class is the newest. The majority of Alu retrotranspositions were completed at least 30 mya when the Alu-Sx subfamily, which accounts for half of all human Alu sequences, and the Alu-Sp and Alu-Sq subfamilies became unable to replicate [ 27 - 30 ]. Alu repeats account for 6–13% of the human genome [ 31 ] and were identified in 5% of 1,616 human full-length cDNA. Of the 5%, 82% were found in the 3' UTR, while 14% were located in the 5' UTR, and very rarely in the coding region [ 32 ]. The common role of Alu at 3' UTR has not been reported, although there is one specific case that the chemical, PMA, can bind to Alu at 3' UTR and increased mRNA half-life [ 43 ]. We investigated the link between Alu sequence and the potential AREs (that have not been experimentally verified but contain ARE sequence patterns), and suggest that the complementary poly-adenine regions of Alu is one of the sources of AREs at the 3' UTR of mRNA. Figure  1A  shows that the poly-adenine regions of Alu contained in the anti-sense strand on DNA complemented the poly-thymine regions in the sense strand; therefore, the poly-thymine regions on DNA transcribed the poly-uracil regions on mRNA (Figure  1B ). We propose a mechanism on how Alu has been converted to AREs gradually. When adenine was inserted at a regular interval in the poly-T(U) regions, it eventually led to the generation of potential AREs. It is not clear why such a regular insertion occurs, but the phenomenon has also been found in other ARE-like sequences. Figure  1C  shows transcribed ARE on mRNA [ 33 , 34 ]. Figure 1 The schematic diagram of poly-thymine (poly-T) generation by Alu. (A) Alu contains poly-adenine (poly-A) region at the end. It is shown as 'aaaaaaaa'. The poly-A of Alu at anti-sense becomes poly-T (complement of poly-A) at sense strand on DNA. It is shown as 'tttttttt'. (B) mRNA now contains a poly-uracile (poly-U) region after the transcription of poly-T region. (C) AU-rich elements are found in this poly-U region in (B).
Background
Varying more than ten-fold, messenger RNA degradation is essential for the regulation of gene expression [ 1 , 2 ]. Differential mRNA decay rates were determined by specific  cis -acting sequences within mRNA. For example, the mRNA sequences of yeast, many mammalians, and other eukaryotes contain AU-rich elements or AREs at their 3' untranslated regions (UTR) [ 3 , 4 ]. For example, in yeast, AREs stimulated the shortening of poly adenine (poly A), and two kinds of degradation pathways followed. One is 5'-to-3' exonuclease access by removal of the 5' cap structure. The other is 3'-to-5' digestion by a complex of exonucleases called exosome [ 5 , 6 ]. Genes required for these steps have been identified in yeast and were found to be conserved among eukaryotes. Although the mechanisms of AREs enhanced mRNA degradation are unknown, several groups provided evidence that 3'-to-5' degradation by the exosome may be the major pathway of decay for at least some mammalian mRNAs, including ARE-containing mRNA sequences [ 7 - 9 ]. The length of AREs also affected the half-life of mRNA. The nonamer UUAUUUAUU is a typical ARE, and the simple repeats, (AUUU) n A motif, is the well-known pattern of AREs. It has been shown that the number of ARE motifs correlated with the turnover of ARE-mRNAs such as GM-CSF [ 10 , 11 ]. Because of this, AREs are usually classified according to the number of the repeats [ 12 ].cisIt is known that the stabilization factor, such as HuD, is able to bind to AREs [ 13 ] and most AREs seem to function as destablizing factors. The overall importance of AREs in biology is that they can make certain critical gene products unstable. They include proto-oncogenes such as c-fos [ 14 ], c-myb [ 15 ], c-myc [ 16 ], and Pim-1 [ 17 ]. Another class of ARE-associated genes are immune response genes such as interferon [ 15 , 18 ] and interleukin [ 15 , 19 - 21 ]. Growth factors, such as Gro-α [ 22 ] and the vascular endothelial factor [ 23 ] in humans, are also known to be associated with AREs.AREs consist of a great number of thymine (or uracil) and a few adenines. Alu repeats can be a source of poly-T regions in mRNA. Therefore, there is a possible link between ARE and Alu repeats.Alu repeats are sequences of approximately 300 nucleotides (nt) transcribed by RNA polymerase III. The Alu region is then reverse-transcribed and inserted into a new location in the genome [ 24 ]. It can reach a copy number in excess of 500,000 in the human genome [ 25 ]. Alu repeats were thought to be inserted very early in primate evolution, approximately 65 million years ago (mya). Alu amplification appears to have reached a maximum rate between 35 and 60 mya, and is currently amplifying at only 1% of the maximum rate [ 26 ]. Statistical analyses have identified key diagnostic nucleotide positions in Alu sequences that define 12 subfamilies. J class is the oldest one, S class is intermediate, and Y class is the newest. The majority of Alu retrotranspositions were completed at least 30 mya when the Alu-Sx subfamily, which accounts for half of all human Alu sequences, and the Alu-Sp and Alu-Sq subfamilies became unable to replicate [ 27 - 30 ]. Alu repeats account for 6–13% of the human genome [ 31 ] and were identified in 5% of 1,616 human full-length cDNA. Of the 5%, 82% were found in the 3' UTR, while 14% were located in the 5' UTR, and very rarely in the coding region [ 32 ]. The common role of Alu at 3' UTR has not been reported, although there is one specific case that the chemical, PMA, can bind to Alu at 3' UTR and increased mRNA half-life [ 43 ].We investigated the link between Alu sequence and the potential AREs (that have not been experimentally verified but contain ARE sequence patterns), and suggest that the complementary poly-adenine regions of Alu is one of the sources of AREs at the 3' UTR of mRNA. Figure  1A  shows that the poly-adenine regions of Alu contained in the anti-sense strand on DNA complemented the poly-thymine regions in the sense strand; therefore, the poly-thymine regions on DNA transcribed the poly-uracil regions on mRNA (Figure  1B ). We propose a mechanism on how Alu has been converted to AREs gradually. When adenine was inserted at a regular interval in the poly-T(U) regions, it eventually led to the generation of potential AREs. It is not clear why such a regular insertion occurs, but the phenomenon has also been found in other ARE-like sequences. Figure  1C  shows transcribed ARE on mRNA [ 33 , 34 ].Results The results from the method are shown in Figure  2 . In the ARE class I, marked as (AUUU)5A pattern in Table  1 , 26 AREs were found in all 21,121 mRNA 3' UTR. 38.5% of 26 AREs included in the class I, were detected in Alu sequences at 3' UTR. When we did a simulation test for the 26 AREs and 1,504 Alu sequences by 1,000 times, with a 95% confidence interval (C.I.) threshold, it was statistically significant (see the statistical analysis of the search results in the Methods section). In other words, 38.5% occurrences were out of the likelihood for random overlaps of Alu and ARE patterns in the human genome. In the ARE class II (Table  1 , (AUUU)4A pattern), 41 were found in all 3' UTR, and 7 were detected in Alu sequences among them (17.1%). The simulation results showed the 17.1% was less than the maximum random range of 7.3%. Therefore, class II data also showed a significance between ARE patterns and Alu. In class III (Table  1 ), 94 AREs were discovered from all 3' UTR. 15 out of 94 AREs were located in Alu sequences (16.0%). 16% was also statistically significant with the given sample size. In classes IV and V, 5% and 6.1% of ARE were found in Alu, respectively. These results were still out of the random chance distribution, although they were relatively less significant than the previous classes. In class VI, only 85 out of 8,649 AREs were detected in Alu (1%), and it is an insignificant hypothesis that the class VI pattern is associated with Alu sequences. Figure 2 ARE found in Alu at each class (Table 1). The numbers of ARE found in all 3' UTR, the number of ARE found in the Alu sequence, the ratio between them, and the randomly simulated results among 1,000 times at each ARE class (Table 1). Only the maximum possible ratios of the randomly simulated range at 95% confidence interval (C.I.) were shown. X-axis is for ARE patterns in all the classes. The left Y-axis is for the number of AREs, and the right Y-axis is for the overlap ratios.
Results
The results from the method are shown in Figure  2 . In the ARE class I, marked as (AUUU)5A pattern in Table  1 , 26 AREs were found in all 21,121 mRNA 3' UTR. 38.5% of 26 AREs included in the class I, were detected in Alu sequences at 3' UTR. When we did a simulation test for the 26 AREs and 1,504 Alu sequences by 1,000 times, with a 95% confidence interval (C.I.) threshold, it was statistically significant (see the statistical analysis of the search results in the Methods section). In other words, 38.5% occurrences were out of the likelihood for random overlaps of Alu and ARE patterns in the human genome. In the ARE class II (Table  1 , (AUUU)4A pattern), 41 were found in all 3' UTR, and 7 were detected in Alu sequences among them (17.1%). The simulation results showed the 17.1% was less than the maximum random range of 7.3%. Therefore, class II data also showed a significance between ARE patterns and Alu. In class III (Table  1 ), 94 AREs were discovered from all 3' UTR. 15 out of 94 AREs were located in Alu sequences (16.0%). 16% was also statistically significant with the given sample size. In classes IV and V, 5% and 6.1% of ARE were found in Alu, respectively. These results were still out of the random chance distribution, although they were relatively less significant than the previous classes. In class VI, only 85 out of 8,649 AREs were detected in Alu (1%), and it is an insignificant hypothesis that the class VI pattern is associated with Alu sequences.Discussion The possible mechanism of how AREs originated from Alu is as follows: Alu is a special sequence that contains a poly-adenine (poly-A) region at its end. The poly-A region plays an important role in the retroposition mechanism of Alu [ 35 ]. It is known that the products of LINE (L1) transposon bind the poly-A of Alu. This enables Alu to retroposition [ 36 , 37 ]. When Alu with poly-A are inserted as above, it is in the double helix form with the complementary poly-T. Therefore, the poly-T regions produce poly-uracil (poly-U) regions in mRNA when transcribed (Figure  1 ). We hypothesized that the poly-U regions generated from the Alu are the source of AREs after either random or directed mutation. With this hypothesis, we suggest a new role for Alu was involved in the 3' UTR. It is well known that Alu affected gene expression at the 5' of genes and alternative splicing at the intron region [ 38 , 39 ]. However, no Alu role at the 3' UTR has been suggested yet. We could have applied the same test to Alu at 5' UTR region, but there were too few data sources [ 32 ].
Discussion
The possible mechanism of how AREs originated from Alu is as follows: Alu is a special sequence that contains a poly-adenine (poly-A) region at its end. The poly-A region plays an important role in the retroposition mechanism of Alu [ 35 ]. It is known that the products of LINE (L1) transposon bind the poly-A of Alu. This enables Alu to retroposition [ 36 , 37 ]. When Alu with poly-A are inserted as above, it is in the double helix form with the complementary poly-T. Therefore, the poly-T regions produce poly-uracil (poly-U) regions in mRNA when transcribed (Figure  1 ). We hypothesized that the poly-U regions generated from the Alu are the source of AREs after either random or directed mutation.With this hypothesis, we suggest a new role for Alu was involved in the 3' UTR. It is well known that Alu affected gene expression at the 5' of genes and alternative splicing at the intron region [ 38 , 39 ]. However, no Alu role at the 3' UTR has been suggested yet. We could have applied the same test to Alu at 5' UTR region, but there were too few data sources [ 32 ].Conclusion AREs are mediating sequences that affect the stabilization or degradation of biologically important genes' mRNA. However, their origin in evolution has not been clear. This report presents a hypothesis and statistical evidence that Alu was one of the sources of ARE generation or origin. A possible mechanism of ARE generation from Alu via retroposition and regular pattern mutation is suggested.
Conclusion
AREs are mediating sequences that affect the stabilization or degradation of biologically important genes' mRNA. However, their origin in evolution has not been clear. This report presents a hypothesis and statistical evidence that Alu was one of the sources of ARE generation or origin. A possible mechanism of ARE generation from Alu via retroposition and regular pattern mutation is suggested.Methods Human 3' UTR sequences We used the RefSeq database from the National Center for Biotechnology Information (NCBI) for human 3' UTR sequences [ 41 ]. We extracted 3' UTR of CDS (coding sequence) from all the annotated mRNA sequences (mRNA_Prot, 2004.9.13). The number of 3' UTR was 21,121 and the average length was 996 bp. We used the Biojava package [ 42 ] to extract only 3' UTR with Genbank's feature information. The number of 3' UTR was 21,121 and the average length was 996 bp. Alu sequence and AU-rich element (ARE) pattern detection AREs were searched for in the all 3' UTR (Table  1 ). An in-house java program was used to search for these AREs. While the number of AUUUA repeats decreased, the T flank region increased to 21 bp. Each ARE was allowed within one base mismatch. This is a stricter mismatch criterion than the one of AU-rich elements database (ARED) (the ARED trained experimental ARE data allow 10% of ARE length mismatch [ 24 ]). The RepeatMasker program was used for finding Alu. It is a program for finding repeat sequences [ 25 ]. After finding Alu sequences using RepeatMasker at 3'UTR, for each Alu, we recorded the position information (RefSeq ID, start and end position) for the next step analysis. Comparison between two search results We compared the positions of 3' UTR Alu and ARE sequences. If an ARE was discovered within an Alu sequence, this ARE was regarded found in 3' UTR Alu. For example, if an Alu was found between 100–400 bp and an ARE was found between 99–129 bp, this ARE was in 3' UTR Alu in the same 3' UTR. If less than 50% of an ARE length was discovered in an Alu, we further check if there is 7 bp TSD (Target Site Duplication) between the Alu's end and the ARE's end [ 4 ]. For example, if an Alu is between 100–400 bp and an ARE between 80–110 bp, about 10 bp (33%) of the ARE belongs to the Alu. In this case, we check if there is 7 bp TSD between upstream region from 80 bp and downstream from 400 bp. Statistical analysis of the search results To validate the significance of the searches, we calculated the random chance of the ARE and Alu sequence overlap at each class (Table  1 ). Hypothesis H0: ARE occurs in human 3'UTR independently from Alu. Random sequence generation for statistical validation The average length of 3' UTR of 21,121 human sequences was 996 bp. Within the long theoretical sequence of 21,121 × 996 bp, we generated 1,504 Alu (300 bp) and ARE sequences (21–13 bp). For example, 1,504 Alu and 26 (21 bp) AREs in ARE class I (Table  1 ) were generated following a uniform distribution as a control set. 1,504 and the number of AREs for ARE classes were the actual numbers of Alu and AREs found by our method. This random sequence generation was done 1,000 times with a 95% significance threshold. Test results In the ARE class I (Table  1 ), the significance range at a 5% error range was 0.0–11.5% (Figure  2 ) for the random chance of association between ARE patterns and Alu sequences. The results in other ARE classes are also shown in Figure  2 . Our result of a 38.5% – 6.1% overlap between AREs and Alu, depending on ARE classes, was statistically significant. Therefore, hypothesis H0 was rejected.
Methods
Human 3' UTR sequences We used the RefSeq database from the National Center for Biotechnology Information (NCBI) for human 3' UTR sequences [ 41 ]. We extracted 3' UTR of CDS (coding sequence) from all the annotated mRNA sequences (mRNA_Prot, 2004.9.13). The number of 3' UTR was 21,121 and the average length was 996 bp. We used the Biojava package [ 42 ] to extract only 3' UTR with Genbank's feature information. The number of 3' UTR was 21,121 and the average length was 996 bp.
Human 3' UTR sequences
We used the RefSeq database from the National Center for Biotechnology Information (NCBI) for human 3' UTR sequences [ 41 ]. We extracted 3' UTR of CDS (coding sequence) from all the annotated mRNA sequences (mRNA_Prot, 2004.9.13). The number of 3' UTR was 21,121 and the average length was 996 bp. We used the Biojava package [ 42 ] to extract only 3' UTR with Genbank's feature information. The number of 3' UTR was 21,121 and the average length was 996 bp.Alu sequence and AU-rich element (ARE) pattern detection AREs were searched for in the all 3' UTR (Table  1 ). An in-house java program was used to search for these AREs. While the number of AUUUA repeats decreased, the T flank region increased to 21 bp. Each ARE was allowed within one base mismatch. This is a stricter mismatch criterion than the one of AU-rich elements database (ARED) (the ARED trained experimental ARE data allow 10% of ARE length mismatch [ 24 ]). The RepeatMasker program was used for finding Alu. It is a program for finding repeat sequences [ 25 ]. After finding Alu sequences using RepeatMasker at 3'UTR, for each Alu, we recorded the position information (RefSeq ID, start and end position) for the next step analysis.
Alu sequence and AU-rich element (ARE) pattern detection
AREs were searched for in the all 3' UTR (Table  1 ). An in-house java program was used to search for these AREs. While the number of AUUUA repeats decreased, the T flank region increased to 21 bp. Each ARE was allowed within one base mismatch. This is a stricter mismatch criterion than the one of AU-rich elements database (ARED) (the ARED trained experimental ARE data allow 10% of ARE length mismatch [ 24 ]). The RepeatMasker program was used for finding Alu. It is a program for finding repeat sequences [ 25 ]. After finding Alu sequences using RepeatMasker at 3'UTR, for each Alu, we recorded the position information (RefSeq ID, start and end position) for the next step analysis.Comparison between two search results We compared the positions of 3' UTR Alu and ARE sequences. If an ARE was discovered within an Alu sequence, this ARE was regarded found in 3' UTR Alu. For example, if an Alu was found between 100–400 bp and an ARE was found between 99–129 bp, this ARE was in 3' UTR Alu in the same 3' UTR. If less than 50% of an ARE length was discovered in an Alu, we further check if there is 7 bp TSD (Target Site Duplication) between the Alu's end and the ARE's end [ 4 ]. For example, if an Alu is between 100–400 bp and an ARE between 80–110 bp, about 10 bp (33%) of the ARE belongs to the Alu. In this case, we check if there is 7 bp TSD between upstream region from 80 bp and downstream from 400 bp.
Comparison between two search results
We compared the positions of 3' UTR Alu and ARE sequences. If an ARE was discovered within an Alu sequence, this ARE was regarded found in 3' UTR Alu. For example, if an Alu was found between 100–400 bp and an ARE was found between 99–129 bp, this ARE was in 3' UTR Alu in the same 3' UTR. If less than 50% of an ARE length was discovered in an Alu, we further check if there is 7 bp TSD (Target Site Duplication) between the Alu's end and the ARE's end [ 4 ]. For example, if an Alu is between 100–400 bp and an ARE between 80–110 bp, about 10 bp (33%) of the ARE belongs to the Alu. In this case, we check if there is 7 bp TSD between upstream region from 80 bp and downstream from 400 bp.Statistical analysis of the search results To validate the significance of the searches, we calculated the random chance of the ARE and Alu sequence overlap at each class (Table  1 ). Hypothesis H0: ARE occurs in human 3'UTR independently from Alu. Random sequence generation for statistical validation The average length of 3' UTR of 21,121 human sequences was 996 bp. Within the long theoretical sequence of 21,121 × 996 bp, we generated 1,504 Alu (300 bp) and ARE sequences (21–13 bp). For example, 1,504 Alu and 26 (21 bp) AREs in ARE class I (Table  1 ) were generated following a uniform distribution as a control set. 1,504 and the number of AREs for ARE classes were the actual numbers of Alu and AREs found by our method. This random sequence generation was done 1,000 times with a 95% significance threshold. Test results In the ARE class I (Table  1 ), the significance range at a 5% error range was 0.0–11.5% (Figure  2 ) for the random chance of association between ARE patterns and Alu sequences. The results in other ARE classes are also shown in Figure  2 . Our result of a 38.5% – 6.1% overlap between AREs and Alu, depending on ARE classes, was statistically significant. Therefore, hypothesis H0 was rejected.
Statistical analysis of the search results
To validate the significance of the searches, we calculated the random chance of the ARE and Alu sequence overlap at each class (Table  1 ).Hypothesis H0: ARE occurs in human 3'UTR independently from Alu.
Hypothesis
H0: ARE occurs in human 3'UTR independently from Alu.Random sequence generation for statistical validation The average length of 3' UTR of 21,121 human sequences was 996 bp. Within the long theoretical sequence of 21,121 × 996 bp, we generated 1,504 Alu (300 bp) and ARE sequences (21–13 bp). For example, 1,504 Alu and 26 (21 bp) AREs in ARE class I (Table  1 ) were generated following a uniform distribution as a control set. 1,504 and the number of AREs for ARE classes were the actual numbers of Alu and AREs found by our method. This random sequence generation was done 1,000 times with a 95% significance threshold.
Random sequence generation for statistical validation
The average length of 3' UTR of 21,121 human sequences was 996 bp. Within the long theoretical sequence of 21,121 × 996 bp, we generated 1,504 Alu (300 bp) and ARE sequences (21–13 bp). For example, 1,504 Alu and 26 (21 bp) AREs in ARE class I (Table  1 ) were generated following a uniform distribution as a control set. 1,504 and the number of AREs for ARE classes were the actual numbers of Alu and AREs found by our method. This random sequence generation was done 1,000 times with a 95% significance threshold.Test results In the ARE class I (Table  1 ), the significance range at a 5% error range was 0.0–11.5% (Figure  2 ) for the random chance of association between ARE patterns and Alu sequences. The results in other ARE classes are also shown in Figure  2 . Our result of a 38.5% – 6.1% overlap between AREs and Alu, depending on ARE classes, was statistically significant. Therefore, hypothesis H0 was rejected.
Test results
In the ARE class I (Table  1 ), the significance range at a 5% error range was 0.0–11.5% (Figure  2 ) for the random chance of association between ARE patterns and Alu sequences. The results in other ARE classes are also shown in Figure  2 . Our result of a 38.5% – 6.1% overlap between AREs and Alu, depending on ARE classes, was statistically significant. Therefore, hypothesis H0 was rejected.Authors' contributions HJA conceived of this study, carried out the tests, and drafted the manuscript. JB participated in the design of the study and drafted the manuscript. KWL and DL amended and improved the design of the study. All authors read and approved the final manuscript.
Authors' contributions
HJA conceived of this study, carried out the tests, and drafted the manuscript. JB participated in the design of the study and drafted the manuscript. KWL and DL amended and improved the design of the study. All authors read and approved the final manuscript.


Background Serial Analysis of Gene Expression (SAGE) is a functional genomic technique that quantitatively analyzes the cellular transcriptome. The analysis of SAGE libraries relies on the identification of ditags from sequencing files; however, the software used to examine SAGE libraries cannot distinguish between authentic versus false ditags ("quasi-ditags").
Background
Serial Analysis of Gene Expression (SAGE) is a functional genomic technique that quantitatively analyzes the cellular transcriptome. The analysis of SAGE libraries relies on the identification of ditags from sequencing files; however, the software used to examine SAGE libraries cannot distinguish between authentic versus false ditags ("quasi-ditags").Results We provide examples of quasi-ditags that originate from cloning and sequencing artifacts (i.e. genomic contamination or random combinations of nucleotides) that are included in SAGE libraries. We have employed a mathematical model to predict the frequency of quasi-ditags in random nucleotide sequences, and our data show that clones containing less than or equal to 2 ditags (which include chromosomal cloning artifacts) should be excluded from the analysis of SAGE catalogs.
Results
We provide examples of quasi-ditags that originate from cloning and sequencing artifacts (i.e. genomic contamination or random combinations of nucleotides) that are included in SAGE libraries. We have employed a mathematical model to predict the frequency of quasi-ditags in random nucleotide sequences, and our data show that clones containing less than or equal to 2 ditags (which include chromosomal cloning artifacts) should be excluded from the analysis of SAGE catalogs.Conclusions Cloning and sequencing artifacts contaminating SAGE libraries could be eliminated using simple pre-screening procedure to increase the reliability of the data.
Conclusions
Cloning and sequencing artifacts contaminating SAGE libraries could be eliminated using simple pre-screening procedure to increase the reliability of the data.

Background Serial Analysis of Gene Expression (SAGE) is a rapid method to study mRNA transcripts in cell populations [ 1 ]. Two major principles underline SAGE: (1) short expressed sequenced tags (ESTs) are sufficient to identify individual gene products, and (2) multiple tags can be concatenated and identified by sequence analysis [ 1 , 2 ]. With the ever-expanding sequence information available in public databases, identification of gene transcripts with SAGE tags has greatly facilitated transcriptome comparisons and gene identification [ 3 ]. SAGE data are usually analyzed with software packages like "SAGE300" or "SAGE2000". The majority of SAGE libraries use  NlaIII  or  Sau3A  ( SalAI ) as anchoring enzymes (AE) to create SAGE tags. Both of these enzymes have 4-bp palindromic recognition sequences (CATG for  NlaIII  and GATC for  Sau3A ) that flank individual ditags within concatemers. A major component of the software analysis is the identification of anchoring enzyme recognition sequences (AERS) that flank target sequences (SAGE ditags). After finding the first AE recognition sequence, the software continues reading the sequence until it finds the next one. The software then compares the distance between these recognition sequences with predicted ditag lengths (20–24 bp in the case of  NlaIII  or  Sau3A ), and ditags that are too short (<20 bp) or too long (>24 bp) are excluded. However, if the length of the AERS-flanked sequence satisfies the size criteria, it is identified as a ditag. This algorithm relies on the assumption that  all  sequences have correctly organized ditag concatemers; however, the cloning efficiency of SAGE rarely reaches 100%. In this report, we show that up to 5% of ditags from some SAGE libraries should be omitted from the final analysis. These false ditags (termed "quasi-ditags") result from genomic contaminants and apparently random combinations of nucleotides generated by cloning or sequencing errors. Using a mathematical model to simulate the frequency of quasi-ditags in DNA, we propose a method to exclude quasi-ditags from SAGE catalogs.
Background
Serial Analysis of Gene Expression (SAGE) is a rapid method to study mRNA transcripts in cell populations [ 1 ]. Two major principles underline SAGE: (1) short expressed sequenced tags (ESTs) are sufficient to identify individual gene products, and (2) multiple tags can be concatenated and identified by sequence analysis [ 1 , 2 ]. With the ever-expanding sequence information available in public databases, identification of gene transcripts with SAGE tags has greatly facilitated transcriptome comparisons and gene identification [ 3 ].SAGE data are usually analyzed with software packages like "SAGE300" or "SAGE2000". The majority of SAGE libraries use  NlaIII  or  Sau3A  ( SalAI ) as anchoring enzymes (AE) to create SAGE tags. Both of these enzymes have 4-bp palindromic recognition sequences (CATG for  NlaIII  and GATC for  Sau3A ) that flank individual ditags within concatemers. A major component of the software analysis is the identification of anchoring enzyme recognition sequences (AERS) that flank target sequences (SAGE ditags). After finding the first AE recognition sequence, the software continues reading the sequence until it finds the next one. The software then compares the distance between these recognition sequences with predicted ditag lengths (20–24 bp in the case of  NlaIII  or  Sau3A ), and ditags that are too short (<20 bp) or too long (>24 bp) are excluded. However, if the length of the AERS-flanked sequence satisfies the size criteria, it is identified as a ditag. This algorithm relies on the assumption that  all  sequences have correctly organized ditag concatemers; however, the cloning efficiency of SAGE rarely reaches 100%. In this report, we show that up to 5% of ditags from some SAGE libraries should be omitted from the final analysis. These false ditags (termed "quasi-ditags") result from genomic contaminants and apparently random combinations of nucleotides generated by cloning or sequencing errors. Using a mathematical model to simulate the frequency of quasi-ditags in DNA, we propose a method to exclude quasi-ditags from SAGE catalogs.NlaIIISau3ASalAINlaIIISau3ANlaIIISau3AallResults From twelve independent SAGE libraries, we analyzed numerous clones lacking organized ditag concatemers that would be excluded by SAGE software packages, including clones lacking inserts, clones with inserts containing bacterial or rodent genomic sequences, and clones with unidentifiable sequences (Figure  1 ). Depending on the quality of the SAGE library, examples of clones in Figure  1A,1B,1C  can represent up to 50% of the total volume of clones sequenced [ 4 ], but generally range from 2–20%. A more typical example is taken from our R1 ES cell and AMH-II SAGE libraries [ 5 , 6 ], which contained 5,988 and 4,478 clones, respectively. The cloning efficiency was ~79% and ~76% (4,714 and 3,413 clones with inserts, respectively). Among these, 411 and 167 clones in the R1 ES SAGE library and 305 and 194 clones in the AMH-II library contained sequences with only 1 or 2 ditags, respectively. During our sequence analysis of the clones that had produced a least number of ditags (1–2 per clone), we identified a subset of sequences (up to 40%) that contain ditags that may be false. Importantly, some of these "ditags" matched bacterial genomic sequences (Figure  2A ), while others seemed to represent random combinations of nucleotides. Figure  2B  show an example of a clone that contains a single ditag sequence embedded within a sequence of unidentifiable origin. Because most of this sequence is not composed of concatenated ditags, this embedded ditag may therefore represent a quasi-ditag, which should be excluded from further analysis. These two examples, among others, suggest that some inserts in pZErO-1 contain sequences that just by chance mimic SAGE ditags. To predict the potential frequency of randomly occurring quasi-ditags, we employed a stochastic model system to generate random sequences. We then used both computer-generated random sequences and true genomic DNA sequences to test this possibility. Random sequences were generated and analyzed with a Visual Basic program designed to mimic SAGE software analysis of ditags. The simulated sequences varied in length from 600 to 1200 nucleotides, which corresponds to the average sequence lengths generated by automated sequence analyzers. One million random sequence strings with L = 600, 700, 800, 900, 1000, 1100, and 1200 nucleotides were generated. Table  1  shows expected frequencies of quasi-ditags according to the model (equation (5)) and the observed frequencies based on computer simulations. The line plots of the expected (model) and observed (computer simulation) quasi-ditag frequencies are almost identical (Figures  3  and  4 ). Fragmented  Saccharomyces cerevisiae  genomic DNA that lack SAGE ditag concatemers was also employed for  in vivo / in silico  model validation, and a number of quasi-ditags was detected in these (Figures  4  and  5 ). When compared to  Saccharomyces cerevisiae  genomic DNA [ 7 ], quasi-ditag frequencies were somewhat less abundant than those generated by the computer, potentially due to the presence of nucleotide repeats and unequal frequencies of individual nucleotides in the Yeast genomic sequences. These data, however, support our hypothesis that quasi-ditags can be generated randomly from potential sequencing errors or from genomic contaminants. This analysis furthermore underscores the limited extent that quasi-ditags occur: the distribution of expected number of quasi-ditags per clone is clearly bimodal, with peaks at 1 and 2 ditags ( Q 1  and  Q 2 , respectively). At the same time, the frequency of occurrence for three quasi-ditags ( Q 3 ) is extremely low (0.01% for L = 600 to 0.02% for L = 1200), such that the value of P 3  (20–24)  effectively converges to zero for the majority of the SAGE catalogs (i.e. <3000–5000 clones) (Figure  4 ). Accordingly, the clones that include ditag concatemers of higher length should lack quasi-ditags. Clones containing only one or two ditags/quasi-ditags, however, could be excluded from SAGE analyses, without adversely affecting the data set (Figure  6 ). As an example, we extracted sequences from clones that produce 1–2 total ditags from AMH-II and R1 ES cell libraries. This reduced the total number of tags by 1.06% for ES R1 and 1.94% for AMH-II, but it effectively removed all contaminating bacterial sequences and improved the data reliability. However, the total AMH-I library (2,365 clones, ~78% cloning efficiency; [ 6 ]) had a larger proportion of ditags extracted as being too long (>24 bp), as indicated by lower tag per clone ratio (average insert size of 12.2 tags/clone vs. 22.6 in AMH-II library) amid the same average sequence length, suggesting higher proportion of quasi-ditags. Analysis of the AMH-I SAGE library has revealed 353 and 52 clones that contained just 1 or 2 ditags, respectively. Exclusion of these sequences decreased the total number of tags by 5.21% (calculated after duplicate dimer exclusion), and proved critical to our subsequent quantitative SAGE comparisons [ 6 ]. Failure to remove these quasi-ditag sequences decreased the quantitative reproducibility (R values) between AMH-I and AMH-II SAGE libraries, showing that quasi-ditags can adversely affect the reliability of SAGE libraries.
Results
From twelve independent SAGE libraries, we analyzed numerous clones lacking organized ditag concatemers that would be excluded by SAGE software packages, including clones lacking inserts, clones with inserts containing bacterial or rodent genomic sequences, and clones with unidentifiable sequences (Figure  1 ). Depending on the quality of the SAGE library, examples of clones in Figure  1A,1B,1C  can represent up to 50% of the total volume of clones sequenced [ 4 ], but generally range from 2–20%. A more typical example is taken from our R1 ES cell and AMH-II SAGE libraries [ 5 , 6 ], which contained 5,988 and 4,478 clones, respectively. The cloning efficiency was ~79% and ~76% (4,714 and 3,413 clones with inserts, respectively). Among these, 411 and 167 clones in the R1 ES SAGE library and 305 and 194 clones in the AMH-II library contained sequences with only 1 or 2 ditags, respectively.During our sequence analysis of the clones that had produced a least number of ditags (1–2 per clone), we identified a subset of sequences (up to 40%) that contain ditags that may be false. Importantly, some of these "ditags" matched bacterial genomic sequences (Figure  2A ), while others seemed to represent random combinations of nucleotides. Figure  2B  show an example of a clone that contains a single ditag sequence embedded within a sequence of unidentifiable origin. Because most of this sequence is not composed of concatenated ditags, this embedded ditag may therefore represent a quasi-ditag, which should be excluded from further analysis. These two examples, among others, suggest that some inserts in pZErO-1 contain sequences that just by chance mimic SAGE ditags.To predict the potential frequency of randomly occurring quasi-ditags, we employed a stochastic model system to generate random sequences. We then used both computer-generated random sequences and true genomic DNA sequences to test this possibility. Random sequences were generated and analyzed with a Visual Basic program designed to mimic SAGE software analysis of ditags. The simulated sequences varied in length from 600 to 1200 nucleotides, which corresponds to the average sequence lengths generated by automated sequence analyzers. One million random sequence strings with L = 600, 700, 800, 900, 1000, 1100, and 1200 nucleotides were generated. Table  1  shows expected frequencies of quasi-ditags according to the model (equation (5)) and the observed frequencies based on computer simulations. The line plots of the expected (model) and observed (computer simulation) quasi-ditag frequencies are almost identical (Figures  3  and  4 ). Fragmented  Saccharomyces cerevisiae  genomic DNA that lack SAGE ditag concatemers was also employed for  in vivo / in silico  model validation, and a number of quasi-ditags was detected in these (Figures  4  and  5 ). When compared to  Saccharomyces cerevisiae  genomic DNA [ 7 ], quasi-ditag frequencies were somewhat less abundant than those generated by the computer, potentially due to the presence of nucleotide repeats and unequal frequencies of individual nucleotides in the Yeast genomic sequences. These data, however, support our hypothesis that quasi-ditags can be generated randomly from potential sequencing errors or from genomic contaminants. This analysis furthermore underscores the limited extent that quasi-ditags occur: the distribution of expected number of quasi-ditags per clone is clearly bimodal, with peaks at 1 and 2 ditags ( Q 1  and  Q 2 , respectively). At the same time, the frequency of occurrence for three quasi-ditags ( Q 3 ) is extremely low (0.01% for L = 600 to 0.02% for L = 1200), such that the value of P 3  (20–24)  effectively converges to zero for the majority of the SAGE catalogs (i.e. <3000–5000 clones) (Figure  4 ). Accordingly, the clones that include ditag concatemers of higher length should lack quasi-ditags.Saccharomyces cerevisiaein vivo / in silicoSaccharomyces cerevisiaeQ 1Q 2Q 3Clones containing only one or two ditags/quasi-ditags, however, could be excluded from SAGE analyses, without adversely affecting the data set (Figure  6 ). As an example, we extracted sequences from clones that produce 1–2 total ditags from AMH-II and R1 ES cell libraries. This reduced the total number of tags by 1.06% for ES R1 and 1.94% for AMH-II, but it effectively removed all contaminating bacterial sequences and improved the data reliability. However, the total AMH-I library (2,365 clones, ~78% cloning efficiency; [ 6 ]) had a larger proportion of ditags extracted as being too long (>24 bp), as indicated by lower tag per clone ratio (average insert size of 12.2 tags/clone vs. 22.6 in AMH-II library) amid the same average sequence length, suggesting higher proportion of quasi-ditags. Analysis of the AMH-I SAGE library has revealed 353 and 52 clones that contained just 1 or 2 ditags, respectively. Exclusion of these sequences decreased the total number of tags by 5.21% (calculated after duplicate dimer exclusion), and proved critical to our subsequent quantitative SAGE comparisons [ 6 ]. Failure to remove these quasi-ditag sequences decreased the quantitative reproducibility (R values) between AMH-I and AMH-II SAGE libraries, showing that quasi-ditags can adversely affect the reliability of SAGE libraries.Discussion SAGE is an important tool of modern molecular biology widely used in a number of applications. We hypothesized that actual SAGE catalogs could be contaminated by false ditags ("quasi-ditags") of various origins. Although SAGE software packages are designed to ignore sequences that lack 20–24 bp sequences flanked by two anchoring enzyme recognition sites, it does not exclude quasi-ditags originating from genomic contaminants or unknown sequences that may arise as cloning or sequencing artifacts (Figure  2 ). Negative controls (self-ligated vector) do not produce any colonies after Zeocin selection and cannot account for the appearance of background clones and quasi-ditags in Zeocin-resistant bacteria. Since some quasi-ditags, however, originate directly from  E. Coli , we suggest that one probable source for these contaminanting tags is from recombination events that occur in  E. Coli . Indeed, such a mechanism has already been documented [ 8 ] and has led to the development of Stbl2 bacteria that are mcrA - /mcrBC - hsdRMS - mrr - . Since pZErO-1 was not translated into recombination deficient bacteria (DH10B), large-scale amplifications of this plasmid within bacteria would be expected to lead to some random recombinations, and the generation of quasi-ditags (e.g. Figure  2A ). Some of the ditags derived from the clones that had produced a least number of ditags (1–2 per clone) do not match genomic sequences and thus might be originated from sequencing errors. We therefore suggested a model that provides a mathematical basis for the hypothesis that such a possibility exists. The mathematical model presented in the manuscript is an attempt to predict the frequency distribution of quasi-ditags in random sequences. The phenomenon itself is rather complex and there is no simple model that would capture it in full complexity. We, however, believe that we have selected a reasonable level of model complexity that captures the major pattern of frequency distribution. Using the computer simulation we show that random combinations of nucleotides generated could be indeed recognized by SAGE software as valid SAGE ditags. We also demonstrate that quasi-ditags may constitute a non-negligible proportion of SAGE catalogs. Our model, which simulates the frequency of quasi-ditags in DNA (equations (1–6)), suggests that single or double ditags may represent quasi-ditags; however, the results of the  in silico  experiments show that the probability of finding more than two quasi-ditags in the same sequence converges effectively to zero (Table  1  and Figure  4 ). Based on these findings, we suggest that additional steps be performed with SAGE libraries. We recommend removing clones with sequences containing ≤ 2 ditags at a pre-processing step ("clean-up"). The removal of clones containing 1 or 2 ditags can effectively remove bacterial genomic sequences and potential sequencing artifacts from SAGE libraries. The overall number of SAGE tags excluded by this additional step (authentic and quasi-ditags) is usually low, and generally does not exceed 1.0–1.8% of the total number of sequenced SAGE tags [ 5 , 6 , 9 , 10 ]; however, the frequency of potential quasi-ditags could be high (>5%) in some SAGE libraries. In AMH-I library, for example, the fraction of clones lacking appropriate ditag concatemers was >20%. In these instances, quasi-ditags significantly contribute to the final SAGE tag count, and should be removed. Chart in Figure  6  plots values for ditag distribution from both the model-based simulations (L = 800 bp) and actual clones from the SAGE libraries that had sequences of the same mean length (L ≈ 800 bp). The expected maximum frequency of 1–2 quasi-ditags in the plotted model data approximated the observed frequency of clones with 1–2 total ditags detected in the pool of the actual SAGE clones. Contrary to that, the frequency of occurrence of three or more quasi-ditags predicted by the model is extremely low, demonstrating a divergence in the distribution of expected quasi-ditags and valid SAGE ditags for higher number of ditags per clone. Note that owing to the gel-purification of concatemers the majority of clones in the representative samples belong to the clusters of higher ditag numbers (AMH-II and ES R1 libraries, 13–26 total ditags; AMH-I library, 4–11 total ditags). Comparing values of observed frequencies of the actual SAGE clones that produce 1–2 total ditags with those of expected quasi-ditag frequencies for the sequences of given length might be indicative on the possible contribution of cloning and sequencing artifact-derived quasi-ditags (Figure  6 ). The possible contribution of quasi-ditags to the final tag yield in SAGE libraries cannot be accurately predicted in advance but a failure to report the cloning efficiency and the number of clones with 1 or 2 ditags precludes an evaluation of potential false tags present in SAGE catalogs. Current SAGE protocols do not ensure 100% accurate size fractioning of concatemers: some of the smallest concatemers could therefore be cloned and sequenced. We recognize that some authentic tags (representing valid, but extremely short inserts that were not extracted during gel-purification of concatemers) will be excluded by removing all clones containing only 1 or 2 ditags. Nevertheless, we suggest that any potential loss of authentic ditags in the clean-up procedure is negligible compared to the advantage of having more reliable SAGE results. SAGE protocols are extremely complex technologically and every possible mean should be employed to ensure qualitative and quantitative accuracy of catalogs on both the experimental and analytical steps. Evaluation of the cloning efficiency and precision (e.g. with RAST-PCR [ 11 ]) and sequencing accuracy are therefore essential on the stage preceding large-scale sequencing of the clones. Nonetheless, introduction of the simple pre-processing step eliminating false ditags would further improve the accuracy of the method resulting in its wider application.
Discussion
SAGE is an important tool of modern molecular biology widely used in a number of applications. We hypothesized that actual SAGE catalogs could be contaminated by false ditags ("quasi-ditags") of various origins. Although SAGE software packages are designed to ignore sequences that lack 20–24 bp sequences flanked by two anchoring enzyme recognition sites, it does not exclude quasi-ditags originating from genomic contaminants or unknown sequences that may arise as cloning or sequencing artifacts (Figure  2 ). Negative controls (self-ligated vector) do not produce any colonies after Zeocin selection and cannot account for the appearance of background clones and quasi-ditags in Zeocin-resistant bacteria. Since some quasi-ditags, however, originate directly from  E. Coli , we suggest that one probable source for these contaminanting tags is from recombination events that occur in  E. Coli . Indeed, such a mechanism has already been documented [ 8 ] and has led to the development of Stbl2 bacteria that are mcrA - /mcrBC - hsdRMS - mrr - . Since pZErO-1 was not translated into recombination deficient bacteria (DH10B), large-scale amplifications of this plasmid within bacteria would be expected to lead to some random recombinations, and the generation of quasi-ditags (e.g. Figure  2A ).E. ColiE. ColiSome of the ditags derived from the clones that had produced a least number of ditags (1–2 per clone) do not match genomic sequences and thus might be originated from sequencing errors. We therefore suggested a model that provides a mathematical basis for the hypothesis that such a possibility exists. The mathematical model presented in the manuscript is an attempt to predict the frequency distribution of quasi-ditags in random sequences. The phenomenon itself is rather complex and there is no simple model that would capture it in full complexity. We, however, believe that we have selected a reasonable level of model complexity that captures the major pattern of frequency distribution.Using the computer simulation we show that random combinations of nucleotides generated could be indeed recognized by SAGE software as valid SAGE ditags. We also demonstrate that quasi-ditags may constitute a non-negligible proportion of SAGE catalogs. Our model, which simulates the frequency of quasi-ditags in DNA (equations (1–6)), suggests that single or double ditags may represent quasi-ditags; however, the results of the  in silico  experiments show that the probability of finding more than two quasi-ditags in the same sequence converges effectively to zero (Table  1  and Figure  4 ). Based on these findings, we suggest that additional steps be performed with SAGE libraries. We recommend removing clones with sequences containing ≤ 2 ditags at a pre-processing step ("clean-up"). The removal of clones containing 1 or 2 ditags can effectively remove bacterial genomic sequences and potential sequencing artifacts from SAGE libraries. The overall number of SAGE tags excluded by this additional step (authentic and quasi-ditags) is usually low, and generally does not exceed 1.0–1.8% of the total number of sequenced SAGE tags [ 5 , 6 , 9 , 10 ]; however, the frequency of potential quasi-ditags could be high (>5%) in some SAGE libraries. In AMH-I library, for example, the fraction of clones lacking appropriate ditag concatemers was >20%. In these instances, quasi-ditags significantly contribute to the final SAGE tag count, and should be removed.in silicoChart in Figure  6  plots values for ditag distribution from both the model-based simulations (L = 800 bp) and actual clones from the SAGE libraries that had sequences of the same mean length (L ≈ 800 bp). The expected maximum frequency of 1–2 quasi-ditags in the plotted model data approximated the observed frequency of clones with 1–2 total ditags detected in the pool of the actual SAGE clones. Contrary to that, the frequency of occurrence of three or more quasi-ditags predicted by the model is extremely low, demonstrating a divergence in the distribution of expected quasi-ditags and valid SAGE ditags for higher number of ditags per clone. Note that owing to the gel-purification of concatemers the majority of clones in the representative samples belong to the clusters of higher ditag numbers (AMH-II and ES R1 libraries, 13–26 total ditags; AMH-I library, 4–11 total ditags).Comparing values of observed frequencies of the actual SAGE clones that produce 1–2 total ditags with those of expected quasi-ditag frequencies for the sequences of given length might be indicative on the possible contribution of cloning and sequencing artifact-derived quasi-ditags (Figure  6 ). The possible contribution of quasi-ditags to the final tag yield in SAGE libraries cannot be accurately predicted in advance but a failure to report the cloning efficiency and the number of clones with 1 or 2 ditags precludes an evaluation of potential false tags present in SAGE catalogs. Current SAGE protocols do not ensure 100% accurate size fractioning of concatemers: some of the smallest concatemers could therefore be cloned and sequenced. We recognize that some authentic tags (representing valid, but extremely short inserts that were not extracted during gel-purification of concatemers) will be excluded by removing all clones containing only 1 or 2 ditags. Nevertheless, we suggest that any potential loss of authentic ditags in the clean-up procedure is negligible compared to the advantage of having more reliable SAGE results.SAGE protocols are extremely complex technologically and every possible mean should be employed to ensure qualitative and quantitative accuracy of catalogs on both the experimental and analytical steps. Evaluation of the cloning efficiency and precision (e.g. with RAST-PCR [ 11 ]) and sequencing accuracy are therefore essential on the stage preceding large-scale sequencing of the clones. Nonetheless, introduction of the simple pre-processing step eliminating false ditags would further improve the accuracy of the method resulting in its wider application.Conclusions We have hypothesized that actual SAGE catalogs could be contaminated by false ditags (termed "quasi-ditags") of various origins and employed a mathematical model to predict the frequency of quasi-ditags in random nucleotide sequences. Cloning and sequencing artifacts contaminating SAGE libraries could be eliminated using simple pre-screening procedure to increase the reliability of the data.
Conclusions
We have hypothesized that actual SAGE catalogs could be contaminated by false ditags (termed "quasi-ditags") of various origins and employed a mathematical model to predict the frequency of quasi-ditags in random nucleotide sequences. Cloning and sequencing artifacts contaminating SAGE libraries could be eliminated using simple pre-screening procedure to increase the reliability of the data.Methods SAGE Serial analysis of gene expression (SAGE) was performed according to the original protocol [ 1 ] with minor modifications [ 5 , 12 ]. Human (PC3) and mouse (P19, R1, D3, EG-1, MEF) cells and tissues (adult and old heart) have been employed for construction of SAGE libraries and sequence analysis to illustrate the "clean-up" process. SAGE tags were generated with  NlaIII  and  BsmFI  restriction enzymes (New England Biolabs, Beverly, MA, USA). Sequencing was performed by Perkin-Elmer Applied Biosystems / Celera Genomics (Foster City, CA, USA) and Agencourt Bioscience Corporation (Beverly, MA, USA). Stochastic model Anchoring enzyme recognition sites (AERS) are 4 bp long. Assuming for simplicity that all 4 nucleotide bases (A, T, C, and G) have equal frequencies, a probability that a random combination of 4 nucleotides would match the AERS is 4 -4  = 1/256. In a sequence of length  L , the expected number of AERS (e.g. CATG for  NlaIII  anchoring enzyme) is  L /256. Thus, the probability of finding  k  tags CATG in a random sequence of length L is determined by the Poisson distribution: If two CATG sequences (AERS (CATG) ) are located within the sequence of length  L , then the probability that they are separated by a 20–24 bp distance ( P (20–24) ) is approximately: where 10 is the number of possible relative positions of two AERS (CATG)  that yield a quasi-ditag and 24 is the mean distance from the center of one SAGE tag to the end of the sequence that does not leave enough space for another tag to form a quasi-ditag. If >2 AERS are present in the sequence, then there is a chance that additional AERS would appear within the quasi-ditag formed by first two AERS. A probability that additional AERS will not appear within the quasi-ditag is approximately: where 30 is the average length of a nucleotide string outside of the ditag. If the total number of AERS (CATG)  equals k, then the number of possible AERS pairs is: Taken together, a probability of at least one quasi-ditag in the sequence that has exactly  k  AERS (CATG)  is: Then, a probability ( Q 1 ) to find at least one quasi-ditag in a sequence of given length  L  is: where p(k) is given by equation (1). There is also a probability that more than one quasi-ditag exists within the sequence. In some cases the same AERS (CATG)  could serve as a portion of the two neighboring quasi-ditags (...CATG-(N) 20–24 -CATG-(N) 20–24 -CATG...). In other cases, two or more quasi-ditags can be located independently in the sequence. If a sequence with  k  tags already has one quasi-ditag bounded by two tags, then other (k-2) tags may form additional quasi-ditags. The probability of existence of additional quasi-ditags on condition that one ditag is already present is approximately q(k-2). Then the total probability that any random sequence has at least two quasi-ditags is: In the same way, and so on. The probability that a random sequence has exactly n quasi-ditags is: R n  =  Q ( n ) -  Q ( n  + 1)     (9). Software and analysis A random nucleotide generator (for L = 600–1200) and analysis program that mimics "SAGE300" or "SAGE2000" software algorithms was written in Visual Basic and is available upon request. Genomic DNA sequences of  Saccharomyces cerevisiae  that lack SAGE ditag concatemers were also employed for  in vivo / in silico  model validation. Randomly selected  S. cerevisiae  chromosomes were downloaded from GenBank, fragmented to create a minimum of 300 sequences (L = 600–1200) and searched for quasi-ditags using "SAGE2000" software (available at SAGE website [ 13 ]). Frequency distribution of the number of ditags was analyzed in raw sequences from 3 randomly chosen 96-well plates from AMH-I, AMH-II and ES R1 SAGE libraries (285 sequences for each library) using the same software.
Methods
SAGE Serial analysis of gene expression (SAGE) was performed according to the original protocol [ 1 ] with minor modifications [ 5 , 12 ]. Human (PC3) and mouse (P19, R1, D3, EG-1, MEF) cells and tissues (adult and old heart) have been employed for construction of SAGE libraries and sequence analysis to illustrate the "clean-up" process. SAGE tags were generated with  NlaIII  and  BsmFI  restriction enzymes (New England Biolabs, Beverly, MA, USA). Sequencing was performed by Perkin-Elmer Applied Biosystems / Celera Genomics (Foster City, CA, USA) and Agencourt Bioscience Corporation (Beverly, MA, USA).
SAGE
Serial analysis of gene expression (SAGE) was performed according to the original protocol [ 1 ] with minor modifications [ 5 , 12 ]. Human (PC3) and mouse (P19, R1, D3, EG-1, MEF) cells and tissues (adult and old heart) have been employed for construction of SAGE libraries and sequence analysis to illustrate the "clean-up" process. SAGE tags were generated with  NlaIII  and  BsmFI  restriction enzymes (New England Biolabs, Beverly, MA, USA). Sequencing was performed by Perkin-Elmer Applied Biosystems / Celera Genomics (Foster City, CA, USA) and Agencourt Bioscience Corporation (Beverly, MA, USA).NlaIIIBsmFIStochastic model Anchoring enzyme recognition sites (AERS) are 4 bp long. Assuming for simplicity that all 4 nucleotide bases (A, T, C, and G) have equal frequencies, a probability that a random combination of 4 nucleotides would match the AERS is 4 -4  = 1/256. In a sequence of length  L , the expected number of AERS (e.g. CATG for  NlaIII  anchoring enzyme) is  L /256. Thus, the probability of finding  k  tags CATG in a random sequence of length L is determined by the Poisson distribution: If two CATG sequences (AERS (CATG) ) are located within the sequence of length  L , then the probability that they are separated by a 20–24 bp distance ( P (20–24) ) is approximately: where 10 is the number of possible relative positions of two AERS (CATG)  that yield a quasi-ditag and 24 is the mean distance from the center of one SAGE tag to the end of the sequence that does not leave enough space for another tag to form a quasi-ditag. If >2 AERS are present in the sequence, then there is a chance that additional AERS would appear within the quasi-ditag formed by first two AERS. A probability that additional AERS will not appear within the quasi-ditag is approximately: where 30 is the average length of a nucleotide string outside of the ditag. If the total number of AERS (CATG)  equals k, then the number of possible AERS pairs is: Taken together, a probability of at least one quasi-ditag in the sequence that has exactly  k  AERS (CATG)  is: Then, a probability ( Q 1 ) to find at least one quasi-ditag in a sequence of given length  L  is: where p(k) is given by equation (1). There is also a probability that more than one quasi-ditag exists within the sequence. In some cases the same AERS (CATG)  could serve as a portion of the two neighboring quasi-ditags (...CATG-(N) 20–24 -CATG-(N) 20–24 -CATG...). In other cases, two or more quasi-ditags can be located independently in the sequence. If a sequence with  k  tags already has one quasi-ditag bounded by two tags, then other (k-2) tags may form additional quasi-ditags. The probability of existence of additional quasi-ditags on condition that one ditag is already present is approximately q(k-2). Then the total probability that any random sequence has at least two quasi-ditags is: In the same way, and so on. The probability that a random sequence has exactly n quasi-ditags is: R n  =  Q ( n ) -  Q ( n  + 1)     (9).
Stochastic model
Anchoring enzyme recognition sites (AERS) are 4 bp long. Assuming for simplicity that all 4 nucleotide bases (A, T, C, and G) have equal frequencies, a probability that a random combination of 4 nucleotides would match the AERS is 4 -4  = 1/256. In a sequence of length  L , the expected number of AERS (e.g. CATG for  NlaIII  anchoring enzyme) is  L /256. Thus, the probability of finding  k  tags CATG in a random sequence of length L is determined by the Poisson distribution:LNlaIIILkIf two CATG sequences (AERS (CATG) ) are located within the sequence of length  L , then the probability that they are separated by a 20–24 bp distance ( P (20–24) ) is approximately:LPwhere 10 is the number of possible relative positions of two AERS (CATG)  that yield a quasi-ditag and 24 is the mean distance from the center of one SAGE tag to the end of the sequence that does not leave enough space for another tag to form a quasi-ditag.If >2 AERS are present in the sequence, then there is a chance that additional AERS would appear within the quasi-ditag formed by first two AERS. A probability that additional AERS will not appear within the quasi-ditag is approximately:where 30 is the average length of a nucleotide string outside of the ditag.If the total number of AERS (CATG)  equals k, then the number of possible AERS pairs is:Taken together, a probability of at least one quasi-ditag in the sequence that has exactly  k  AERS (CATG)  is:kThen, a probability ( Q 1 ) to find at least one quasi-ditag in a sequence of given length  L  is:QLwhere p(k) is given by equation (1).There is also a probability that more than one quasi-ditag exists within the sequence. In some cases the same AERS (CATG)  could serve as a portion of the two neighboring quasi-ditags (...CATG-(N) 20–24 -CATG-(N) 20–24 -CATG...). In other cases, two or more quasi-ditags can be located independently in the sequence. If a sequence with  k  tags already has one quasi-ditag bounded by two tags, then other (k-2) tags may form additional quasi-ditags. The probability of existence of additional quasi-ditags on condition that one ditag is already present is approximately q(k-2). Then the total probability that any random sequence has at least two quasi-ditags is:kIn the same way,and so on.The probability that a random sequence has exactly n quasi-ditags is:R n  =  Q ( n ) -  Q ( n  + 1)     (9).RnQnQnSoftware and analysis A random nucleotide generator (for L = 600–1200) and analysis program that mimics "SAGE300" or "SAGE2000" software algorithms was written in Visual Basic and is available upon request. Genomic DNA sequences of  Saccharomyces cerevisiae  that lack SAGE ditag concatemers were also employed for  in vivo / in silico  model validation. Randomly selected  S. cerevisiae  chromosomes were downloaded from GenBank, fragmented to create a minimum of 300 sequences (L = 600–1200) and searched for quasi-ditags using "SAGE2000" software (available at SAGE website [ 13 ]). Frequency distribution of the number of ditags was analyzed in raw sequences from 3 randomly chosen 96-well plates from AMH-I, AMH-II and ES R1 SAGE libraries (285 sequences for each library) using the same software.
Software and analysis
A random nucleotide generator (for L = 600–1200) and analysis program that mimics "SAGE300" or "SAGE2000" software algorithms was written in Visual Basic and is available upon request. Genomic DNA sequences of  Saccharomyces cerevisiae  that lack SAGE ditag concatemers were also employed for  in vivo / in silico  model validation. Randomly selected  S. cerevisiae  chromosomes were downloaded from GenBank, fragmented to create a minimum of 300 sequences (L = 600–1200) and searched for quasi-ditags using "SAGE2000" software (available at SAGE website [ 13 ]). Frequency distribution of the number of ditags was analyzed in raw sequences from 3 randomly chosen 96-well plates from AMH-I, AMH-II and ES R1 SAGE libraries (285 sequences for each library) using the same software.Saccharomyces cerevisiaein vivo / in silicoS. cerevisiaeAuthors' contributions SVA developed the hypothesis, overall plan and performed SAGE, computer simulations, and analysis of Yeast genome fragments. AAS developed and implemented the mathematical model predicting the appearance of "quasi-ditags" in random sequences of given length. Both authors have contributed to the writing and approved the final manuscript.
Authors' contributions
SVA developed the hypothesis, overall plan and performed SAGE, computer simulations, and analysis of Yeast genome fragments. AAS developed and implemented the mathematical model predicting the appearance of "quasi-ditags" in random sequences of given length. Both authors have contributed to the writing and approved the final manuscript.