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. 2003 Sep 20;4:43. doi: 10.1186/1471-2105-4-43

Relationship of SARS-CoV to other pathogenic RNA viruses explored by tetranucleotide usage profiling

Yee Leng Yap 1,✉, Xue Wu Zhang 1, Antoine Danchin 2
PMCID: PMC222961  PMID: 14499005

Abstract

Background

The exact origin of the cause of the Severe Acute Respiratory Syndrome (SARS) is still an open question. The genomic sequence relationship of SARS-CoV with 30 different single-stranded RNA (ssRNA) viruses of various families was studied using two non-standard approaches. Both approaches began with the vectorial profiling of the tetra-nucleotide usage pattern V for each virus. In approach one, a distance measure of a vector V, based on correlation coefficient was devised to construct a relationship tree by the neighbor-joining algorithm. In approach two, a multivariate factor analysis was performed to derive the embedded tetra-nucleotide usage patterns. These patterns were subsequently used to classify the selected viruses.

Results

Both approaches yielded relationship outcomes that are consistent with the known virus classification. They also indicated that the genome of RNA viruses from the same family conform to a specific pattern of word usage. Based on the correlation of the overall tetra-nucleotide usage patterns, the Transmissible Gastroenteritis Virus (TGV) and the Feline CoronaVirus (FCoV) are closest to SARS-CoV. Surprisingly also, the RNA viruses that do not go through a DNA stage displayed a remarkable discrimination against the CpG and UpA di-nucleotide (z = -77.31, -52.48 respectively) and selection for UpG and CpA (z = 65.79,49.99 respectively). Potential factors influencing these biases are discussed.

Conclusion

The study of genomic word usage is a powerful method to classify RNA viruses. The congruence of the relationship outcomes with the known classification indicates that there exist phylogenetic signals in the tetra-nucleotide usage patterns, that is most prominent in the replicase open reading frames.

Keywords: RNA virus, convergent evolution, horizontal gene transfer, factor analysis, SARS

Background

Severe Acute Respiratory Syndrome (SARS), a newly identified infectious disease, has imperilled the health of human population in more than 30 nations. It has claimed over 812 lives and infected more than 8442 (9.61% death rate) by July 2, 2003 [1] since its outbreak in November 2002 in the province of GuangDong, People's Republic of China. By May 15, 2003, the primary etiological agent for SARS was found to fulfil Koch's postulate through experimental infection of cynomolgus macaques (Macaca fascicularis) [2]. Chronicles for the discovery of SARS CoronaVirus (SARS-CoV) can be found in articles [e.g. [3,4]] and websites [e.g. [5]].

A common question is often asked when investigating viral evolution: what hallmark, in term of genome sequence or RNA word usage, could be used to trace back the emergence of a new pathogen in humans/animals? In particular, CoronaViruses are prone to recombination [6,7] and like all other viruses they mutate at a high frequency [8]. This makes extremely hazardous to try to trace the origin of the virus. Nevertheless, this prompted us to investigate their relationships using the RNA word usage hoping to identify some RNA viruses that display similar word usage pattern. Such RNA viruses might hint about the origin of SARS-CoV. This study will contribute to our understanding of the RNA word usage of SARS-CoV and some other pathogenic RNA viruses. In the present study, we explored the relationships of 31 RNA viruses, which are known to cause diseases to their corresponding hosts with either similar symptoms or infectiousness, including SARS-CoV, based on their global tetra-nucleotide usage pattern.

Preliminary analysis of the sequence data indicated that there are 11–14 open reading frames in the SARS-CoV genome [9-11]. The overall gene order for this novel pathogen supported its placement in the family of Coronaviridae which includes the animal/human CoronaViruses. It should be emphasized that the sequence similarity shown is attributed mainly to the large RNA-dependent RNA polymerase (replication enzyme or RdRp) residing in the first two open reading frames (ORFs). These two ORFs constitute more than 65% (>20 kb) of the total genome size and these regions are more conserved in their nucleotide sequences due to their specialized role for viral RNA replication. Therefore, the possible relationship based on the sequence of the replication enzyme alone was also investigated.

Results and Discussion

Mono-nucleotide bias

Table 1 presents the breakdown of the RNA sequence into mononucleotide frequencies for the 31 viral genomes in our dataset. Except for the Rabbit Hemorrhagic disease Virus (RHV) that shows a fair usage of the four nucleotides in approximately equal number, the other RNA viruses have a biased genome composition. Bovine CoronaVirus (BCoV) and Human CoronaVirus 229E (HCoV) favor the U nucleotide (35.5% and 34.6%) at the expense of the C nucleotide (15.3% and 16.7%). Relatively strong nucleotide biases are visible in the other genomes and we will mention a few of the extremes. The highest base count is 28.4% G in the Yellow Fever Virus (YFV), 38.9% A in the Respiratory Syncytial Virus (RSV), 35.5% U in the Bovine CoronaVirus (BCoV) and 28.5% C count in the Foot-and-Mouth disease Virus (FMV). The lowest base counts are 15.8% G in the Human Respiratory syncytial Virus (HRV), 21.2% A in the Equine arteritis Virus (EV1), 20.9% U in the Igbo Ora Virus (IOV) and 13.6% C in the Bovine ephemeral Fever Virus (BFV). The A nucleotide is the most popular base among RNA viruses (ranging from 21.2% to 38.9%), and C is the most variable nucleotide (ranging from 13.6% to 33.1%).

Table 1.

RNA virus in current study.

Virus Name Type Acession Number DNA Stage Segment Acronym Size (nt) G A U C A+U%
ssRNA positive-strand viruses 1 Avian infectious bronchitis virus ss-RNA NC_001451 No 1 ABV 27608 21.7 28.9 33.2 16.2 62.1
2 Bovine coronavirus ss-RNA NC_003045 No 1 BCoV 31028 21.8 27.4 35.5 15.3 62.9
3 Equine arteritis virus ss-RNA NC_002532 No 1 EV1 12704 26.0 21.2 27.1 25.6 48.3
4 Human coronavirus 229E ss-RNA NC_002645 No 1 HCoV 27317 21.6 27.2 34.6 16.7 61.7
5 Lactate dehydrogenase-elevating virus ss-RNA NC_002534 No 1 LDV 14225 25.9 23.1 28.2 22.6 51.3
6 Murine hepatitis virus ss-RNA NC_001846 No 1 MHV 31357 23.9 26.0 32.3 17.9 58.2
7 Porcine epidemic diarrhea virus ss-RNA NC_003436 No 1 PDV 28033 22.8 24.7 33.2 19.2 58.0
8 Porcine reproductive and respiratory syndrome virus ss-RNA NC_001961 No 1 PRV 15428 26.2 21.7 25.3 26.7 47.0
9 SARS coronavirus ss-RNA NC_004718 No 1 SAR 29751 20.8 28.5 30.7 20.0 59.2
10 Feline coronavirus ss-RNA AY204704 No 1 FCoV 9979 22.6 27.9 29.2 20.3 57.2
11 Simian hemorrhagic fever virus ss-RNA NC_003092 No 1 SFV 15717 22.6 22.5 27.4 27.5 49.9
12 Transmissible gastroenteritis virus ss-RNA NC_002306 No 1 TGV 28586 20.6 29.5 32.9 17.0 62.4
13 Avian encephalomyelitis virus ss-RNA NC_003990 No 1 AEV 7055 25.7 27.0 28.3 19.0 55.3
14 Bovine viral diarrhea virus genotype 2 ss-RNA NC_002032 No 1 BDV 12255 25.2 32.7 22.3 19.8 54.9
15 Foot-and-mouth disease virus C ss-RNA NC_002554 No 1 FMV 8115 25.6 24.8 21.2 28.5 45.9
16 Igbo Ora virus ss-RNA NC_001924 No 1 IOV 11821 24.1 31.1 20.9 24.0 51.9
17 Poliovirus ss-RNA NC_002058 No 1 PV1 7440 23.0 29.7 24.0 23.3 53.7
18 Rabbit hemorrhagic disease virus ss-RNA NC_001543 No 1 RHV 7437 25.5 25.9 23.9 24.7 49.8
19 Tamana bat virus ss-RNA NC_003996 No 1 TBV 10053 21.5 33.2 28.3 16.9 61.6
20 Yellow fever virus ss-RNA NC_002031 No 1 YFV 10862 0.28 0.27 0.23 0.21 0.50
ssRNA negative-strand viruses 21 Avian paramyxovirus 6 ss-RNA NC_003043 No 1 APV 16236 0.23 0.29 0.25 0.23 0.54
22 Bovine ephemeral fever virus ss-RNA NC_002526 No 1 BFV 14900 0.20 0.38 0.28 0.14 0.66
23 Bovine respiratory syncytial virus ss-RNA NC_001989 No 1 BRV 15140 0.17 0.38 0.29 0.17 0.66
24 Canine distemper virus ss-RNA NC_001921 No 1 CDV 15690 0.22 0.31 0.26 0.21 0.57
25 Human respiratory syncytial virus ss-RNA NC_001781 No 1 HRV 15225 0.16 0.39 0.28 0.18 0.67
26 Hantaan virus ss-RNA AF345636 Yes 2 HV1 11772 0.21 0.33 0.29 0.17 0.62
27 Influenza B virus ss-RNA NC_002208 Yes 8 IBV 14452 0.22 0.36 0.24 0.18 0.60
28 Measles virus ss-RNA NC_001498 No 1 MV1 15894 0.24 0.29 0.23 0.24 0.53
29 Respiratory syncytial virus ss-RNA NC_001803 No 1 RSV 15191 0.16 0.39 0.28 0.18 0.67
30 Reston Ebola virus ss-RNA NC_004161 No 1 REV 18891 0.20 0.31 0.28 0.21 0.59
31 Tioman virus ss-RNA NC_004074 No 1 TV2 15522 0.21 0.30 0.26 0.22 0.57
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The information about 31 RNA viruses being investigated in this study. Their accession number, abbreviation, genome size, number of segments and whether they undergo DNA stage are tabulated. The breakdown of the RNA nucleic acids and A+U contents are also shown.

From the standpoint of the overall genomic composition analysis, the G+C content is an interesting property for a genome, in that the overall content often correlates with the organism pathogenicity [12]. Most of the pathogens genomes have a low G+C content, while some such as Mycobacterium tuberculosis has a relatively high G+C content. Therefore, as expected in Table 1, we noted that most of the pathogenic viruses are A+U-rich (>50%), except for Porcine reproductive and Respiratory syndrome Virus (PRV), Equine arteritis virus (EV1), Rabbit hemorrhagic disease virus (RHV), Simian hemorrhagic Fever Virus (SFV) and Foot-and-Mouth disease Virus C (FMV).

Di-nucleotide bias

The frequencies of occurrence for di-nucleotides were compared to the random RNA counterparts having the same base proportion in order to compute the z value that reflected their di-nucleotide bias (Table 2). Among the 31 virus sequences examined, the frequencies of occurrence for di-nucleotide were not randomly distributed, with only a few exceptional di-nucleotides starting with a purine residue present at the expected frequencies (ApC, ApG, GpC, |z| < 3). A remarkable deviation from the expected frequencies occurs for the di-nucleotide pairs CpG and UpA (suppression or under-representation, z < -50) as well as di-nucleotides pairs CpA and UpG (enhancement or over-representation, z > 40). These di-nucleotide biases, together with mono-nucleotide bias [13], have a direct impact on the codon usage of viruses. For example, in the codon usage for the 24 protein coding sequences in human CoronaVirus 229E (Table 3), only 2.85% of codons contain the under-represented subword CpG di-nucleotide whereas 11.26% of the codons contain the over-represented CpA di-nucleotide (the aggregate codon usage containing each di-nucleotide subword without mono- and di-nucleotide bias is close to 6.25%).

Table 2.

Di-nucleotide bias for six RNA viruses.

BCoV MHV SARS ABV HCoV PDV Average z value
across 31 viruses
Di-nucleotide N(w) E(w) z N(w) E(w) z N(w) E(w) z N(w) E(w) z N(w) E(w) z N(w) E(w) z
CG 497 1034 -103.81 798 1342 -104.39 566 1235 -121-14 486 976 -109.69 487 979 -95.94 684 1226 -102.03 -77.31
GC 1344 1037 62.19 1694 1341 62.33 1432 1236 36.12 1147 970 35.96 1164 976 37.86 1416 1228 35.05 5.74
AU 2845 3007 -26.44 2499 2614 -19.25 2234 2594 -58.91 2200 2642 -76.99 2092 2556 -81.97 1976 2296 -55.43 -15.54
UA 2818 3000 -30.10 2404 2616 -35.12 2080 2594 -87.64 2409 2641 -42.42 2033 2554 -84.51 1965 2299 -53.83 -52.48
AG 1824 1848 -4.25 1968 1941 4.77 1749 1760 -2.00 1844 1728 21.13 1416 1601 -34.78 1537 1579 -7.12 3.80
GA 1629 1849 -39.08 1745 1941 -32.74 1677 1764 -16.43 1505 1730 -39.47 1397 1598 -36.09 1358 1581 -38.05 -1.33
AC 1371 1303 12.93 1384 1458 -13.50 1978 1695 50.18 1474 1292 35.28 1558 1236 58.96 1594 1332 50.25 5.42
CA 1594 1297 56.03 1705 1453 46.19 2203 1695 87.29 1603 1290 59.90 1638 1234 74.68 1783 1327 83.96 49.99
CU 1801 1674 22.52 1874 1806 12.28 2190 1814 67.50 1661 1487 31.50 1724 1568 28.13 1953 1784 29.95 16.50
UC 1179 1674 -88.35 1296 1802 -94.30 1552 1815 -46.36 1127 1482 -65.41 1130 1568 -79.37 1410 1781 -67.80 -17.49
GU 2449 2394 9.10 2473 2402 11.92 1868 1898 -5.35 2154 1982 29.46 2240 2044 34.60 2262 2119 23.86 -7.13
UG 3101 2392 120.25 3146 2408 128.13 2663 1897 137.30 2476 1983 87.74 2898 2040 152.24 2814 2117 126.99 65.79
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The di-nucleotide bias in six RNA viruses. The z value quantifies the di-nucleotide bias as defined in equation 1. N (w) and E (w) are actual and expected frequency of occurrence for word w. The last column is the average z value across 31 RNA viruses.

Table 3.

Codon usage for Human CoronaVirus 229E (HCoV).

Amino Acid Codon Usage/% Amino Acid Codon Usage/%
Arg CGU 1.04 Ile AUU 3.34
CGC 0.41 AUC 0.74
CGA 0.17 AUA 1.35
CGG 0.13 Gly GGU 4.12
AGA 1.23 GGC 1.43
AGG 0.36 GGA 0.67
Leu UUA 1.49 GGG 0.22
UUG 2.96 Val GUU 6.00
CUU 2.48 GUC 1.23
CUC 0.46 GUA 1.09
CUA 0.65 GUG 1.90
CUG 0.63 Lys AAA 3.15
Ser UCU 2.70 AAG 2.31
UCC 0.66 Asn AAU 4.15
UCA 1.37 AAC 1.82
UCG 0.20 Gln CAA 2.04
AGU 1.86 CAG 1.17
AGC 0.71 his CAU 1.14
Thr ACU 3.23 CAC 0.46
ACC 0.76 Glu GAA 2.81
ACA 2.21 GAG 1.21
ACG 0.29 Asp GAU 3.09
Pro CCU 1.6S GAC 1.96
CCC 0.35 Tyr UAU 3.00
CCA 1.07 UAC 1.46
CCG 0.19 Cys UGU 2.26
Ala GCU 3.58 UGC 0.95
GCC 0.83 Phe UUU 4.59
GCA 1.80 UUC 1.10
GCG 0.42
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The relative usage of synonymous codons in the 24 known CDSs of Human Corona Virus 229E (HCoV).

In double stranded DNA genomes the deficiency in di-nucleotide CpG is often supposed to be due to the fact that they are the targets for methyltransferase activity that leads to cytosine deamination [14,15]. It is however unlikely that the mechanism of deamination that alters the genetic contents at the DNA level would affect the viral RNA content of most RNA viruses without a DNA stage. There might exist specific cytosine RNA methylases that could be responsible for this effect [16]. However it is more consistent to propose that, unlike the mechanism of cytosine deamination in the DNA realm, the dominating process is cytosine deamination in RNA viruses, converting cytosine to uracil (C ♦ U) instead of thymine (T). As a consequence of this mechanism, di-nucleotide CpG changes to either di-nucleotide UpG or CpA in the direct/complementary strands of RNA viruses and causes the over-representation in di-nucleotide UpG and CpA (z > 19). Interestingly, there is experimental evidence in vitro that the rate of cytosine deamination is faster (>100 times) in the single stranded than in double-stranded state [17]. Apart from the under-representation in di-nucleotide CpG and over-representation in di-nucleotide CpA and UpG, the reason for the observed di-nucleotide UpA scarcity in RNA may be explained by its chemical lability [18]. The UpA dinucleotide is chemically the most unstable among the 16 dinucleotides. Furthermore, UpA appears to be a preferential target for ribonucleases [19]. This lability would create a selection pressure against di-nucleotide UpA in RNA viruses.

If we choose a critical value for z (|z| = 3.29) that only allows a chance of 1 in 1000 error for classifying a word as biased (over/under-represented), all di-nucleotides show some kind of bias in their usage pattern across 31 different viruses (Table 4, derived from the complete form of Table 2 provided as the additional file 1). The causes for these biases await further investigation.

Table 4.

Overall statistics for biased di-nucleotides and tetra-nucleotides.

Percentage of di-nucleotide that can be used to discriminate between vi ruses(|z| > 3.29) Percentage of tetra-nucleotide that can be used to discriminate between vi ruses(|z| > 3.29) Virus Percentage of biased di-nucleotide (|z| > 3.29)/% Percentage of biased tetra-nucleotide (|z| > 3.29)/%
100% 96.09% BCoV 93.8 29.7
MHV 93.8 28.1
SARS 81.3 34.4
ABV 81.3 27.3
HCoV 93.8 31.3
PDV 81.3 28.5
TGV 87.5 31.6
LDV 93.8 19.5
PRV 93.8 15.6
SFV 93.8 16.0
FCoV 75.0 11.7
EV1 87.5 14.5
TBV 75.0 21.9
AEV 93.8 11.7
PV1 87.5 11.7
YFV 93.8 29.3
BDV 87.5 17.6
RHV 93.8 9.4
FMV 87.5 12.1
IOV 75.0 9.8
HV1 62.5 12.5
RSV 87.5 18.8
HRV 87.5 19.1
BRV 93.8 19.9
TV2 81.3 15.2
REV 87.5 18.4
MV1 81.3 15.2
CDV 75.0 16.0
APV 93.8 11.7
BFV 81.3 15.2
IBV 87.5 23.4
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The percentage of biased di-nucleotides and tetra-nucleotides that shows strong biases (lzl > 3.29) in 31 RNA viruses (right). For di-nucleotides, all 16 (100%) of them show strong biases in part of or all 31 RNA viruses. For tetra-nucleotides, 246 (96%) of the tetra-nucleotides show strong biases in part of or all 31 RNA viruses.

Tetra-nucleotide bias

Inspection of the tetra-nucleotide usage pattern for RNA viruses (additional file 2) reveals considerable differences. The frequencies of occurrence for tetra-nucleotides were compared to artificial chromosomes constructed as random RNA sequences having the same nucleotide succession up to order three to compute the z values that reflect their tetra-nucleotide bias in the corresponding virus (Table 5). If we choose a critical value for z (|z| = 3.29) that only allows a chance of 1 in 1000 error for classifying a word as over/under-represented, 96% of the tetra-nucleotides show a strong bias in their usage pattern across 31 viruses (shown in Table 4, derived from the complete form of Table 5 provided as the additional file 1). This indicated strongly that tetra-nucleotides are being used in a different manner between different viruses, providing us with a tool to study the relationships between viruses based on the tetra-nucleotide bias exhibited in their genomes.

Table 5.

Tetra-nucleotide bias for three RNA viruses. The tetra-nucleotide bias in three viruses. z value quantifies the tetra-nucleotide bias, as defined in equation (1). N (w) and E (w) are actual and expected frequency of occurrence for word w.

BCoV MHV SARS BCoV MHV SARS
Tetra-nucleotide N(w) E(w) z N(w) E(w) z N(w) E(w) z Tetra-nucleotide N(w) E(w) z N(w) E(w) z N(w) E(w) z
AAAA 148 206.2 -7.4 147 145.8 0.2 222 216.5 0.7 UAAA 264 226.2 4.6 187 170.9 2.2 170 183 -1.7
AAAC 110 103.7 1.1 98 91.2 1.3 154 148.1 0.9 UAAC 78 105.1 -4.8 85 122.4 -6.1 123 128 -0.8
AAAG 184 169.7 2.0 173 133.6 6.2 165 158.8 0.9 UAAG 205 171.7 4.6 193 165.3 3.9 107 134.4 -4.3
AAAU 217 220 -0.4 179 164.9 2.0 213 200.6 1.6 UAAU 322 309.9 1.3 245 259.8 -1.7 166 193.9 -3.6
AACA 133 114.1 3.2 113 112.1 0.2 215 175.7 5.4 UACA 178 163.7 2.0 122 123.4 -0.2 230 200.3 3.8
AACC 76 61.3 3.4 107 75.2 6.7 102 92.5 1.8 UACC 97 82.9 2.8 106 98.5 1.4 118 97.1 3.8
AACG 29 40.7 -3.3 35 61.8 -6.2 44 66.3 -5.0 UACG 50 54.4 -1.1 58 72.6 -3.1 46 63.3 -3.9
AACU 91 121.5 -5.0 84 106.5 -4.0 171 168.5 0.4 UACU 196 205.2 -1.2 153 168.2 -2.1 195 192.2 0.4
AAGA 172 157.9 2.0 176 136.4 6.2 184 161.8 3.2 UAGA 128 123.4 0.8 119 124.7 -0.9 102 119.6 -2.9
AAGC 137 103.8 5.9 140 103 6.6 96 112.8 -2.9 UAGC 79 98.7 -3.6 82 118.7 -6.1 71 84.8 -2.7
AAGG 133 121.3 1.9 159 122.4 6.0 140 117.3 3.8 UAGG 73 78.8 -1.2 67 121.3 -9.0 74 75.6 -0.3
AAGU 191 180.6 1.4 179 163.1 2.3 136 139.4 -0.5 UAGU 171 213 -5.2 161 190.7 -3.9 101 126.8 -4.2
AAUA 189 215.2 -3.2 148 182.1 -4.6 113 154.1 -6.0 UAUA 251 237 1.7 192 189 0.4 99 136.5 -5.8
AAUC 100 104.5 -0.8 75 93.2 -3.4 93 121.9 -4.8 UAUC 84 112.3 -4.9 86 99.9 -2.5 84 116.1 -5.4
AAUG 246 229.3 2.0 234 232.1 0.2 230 201.5 3.7 UAUG 310 271.5 4.3 278 238.1 4.7 189 190.3 -0.2
AAUU 265 265.5 -0.1 212 207.8 0.5 211 212 -0.1 UAUU 314 345 -3.0 253 248.5 0.5 190 211.8 -2.7
ACAA 144 137.1 1.1 115 114.1 0.2 269 204.1 8.3 UCAA 131 130 0.2 136 117.7 3.1 202 174.1 3.8
ACAC 84 66.4 3.9 88 75.4 2.6 168 142.2 3.9 UCAC 53 60.4 -1.7 57 67.1 -2.2 130 109.6 3.5
ACAG 118 105.7 2.2 108 104.9 0.5 151 145.1 0.9 UCAG 107 122.1 -2.5 105 106.7 -0.3 110 121.4 -1.9
ACAU 128 123.5 0.7 106 122.7 -2.7 186 172.9 1.8 UCAU 84 124.6 -6.6 88 117.8 -5.0 153 146.7 0.9
ACCA 105 76.9 5.8 116 85 6.1 161 117.7 7.3 UCCA 68 73.4 -1.1 74 80.6 -1.3 76 95.4 -3.6
ACCC 56 37.3 5.6 84 57.6 6.3 54 60.7 -1.6 UCCC 31 37.4 -1.9 45 56 -2.7 31 44.6 -3.7
ACCG 24 35.5 -3.5 52 57.4 -1.3 31 48.8 -4.6 UCCG 15 26 -3.9 37 55.1 -4.4 19 29.7 -3.5
ACCU 83 77.7 1.1 97 97.7 -0.1 139 111.2 4.8 UCCU 74 101.4 -4.9 103 102.4 0.1 80 107.1 -4.8
ACGA 32 44.5 -3.4 31 56.5 -6.2 40 64.4 -5.5 UCGA 18 41.4 -6.6 42 50.4 -2.2 43 67.5 -5.4
ACGC 29 34.1 -1.6 49 52.5 -0.9 31 54.8 -5.8 UCGC 30 34.1 -1.3 45 54 -2.2 38 56.2 -4.4
ACGG 26 31.3 -1.7 46 48.5 -0.7 26 41 -4.2 UCGG 19 29.1 -3.4 33 49.8 -4.3 16 39.9 -6.9
ACGU 47 60.5 -3.1 53 72.1 -4.1 53 72.6 -4.2 UCGU 51 74.1 -4.9 59 74.8 -3.3 73 84.4 -2.3
ACUA 141 127.9 2.1 119 121.3 -0.4 166 167.3 -0.2 UCUA 116 130.2 -2.3 115 124.5 -1.5 130 140.9 -1.7
ACUC 49 68.2 -4.2 61 68.9 -1.7 119 115 0.7 UCUC 52 67.1 -3.3 69 69.6 -0.1 82 108.4 -4.6
ACUG 144 131.5 2.0 126 141.4 -2.4 159 163.3 -0.6 UCUG 119 135.5 -2.6 117 135.5 -2.9 133 141.4 -1.3
ACUU 142 160.9 -2.7 116 132.1 -2.5 207 184.9 3.0 UCUU 195 191.8 0.4 153 142.8 1.6 219 182.6 4.9
AGAA 147 141.6 0.8 162 126.6 5.7 144 158.7 -2.1 UGAA 174 195.3 -2.8 154 176.8 -3.1 164 180.2 -2.2
AGAC 67 71.9 -1.1 87 80.6 1.3 114 117.2 -0.5 UGAC 86 101.8 -2.8 118 127.6 -1.5 153 151.9 0.2
AGAG 107 88.9 3.5 115 103.4 2.1 146 112.3 5.8 UGAG 96 127.7 -5.1 144 167 -3.2 117 136.2 -3.0
AGAU 177 170.4 0.9 158 145.2 1.9 128 141.1 -2.0 UGAU 314 311.7 0.2 243 261 -2.0 215 196.5 2.4
AGCA 113 105.8 1.3 102 112.1 -1.7 105 118.8 -2.3 UGCA 181 166.3 2.1 187 161.5 3.6 166 182 -2.2
AGCC 77 54.1 5.7 91 80.7 2.1 68 55.4 3.1 UGCC 102 81.6 4.1 144 122.4 3.6 114 81.6 6.5
AGCG 48 44.9 0.8 62 71.2 -2.0 32 46.4 -3.8 UGCG 52 65.5 -3.0 86 97.6 -2.1 58 58.5 -0.1
AGCU 126 122.6 0.6 132 132 0.0 140 146.9 -1.0 UGCU 270 218.4 6.4 254 226.8 3.3 315 224.5 11.0
AGGA 116 96.4 3.6 114 117.8 -0.6 138 99.5 7.0 UGGA 171 154.4 2.4 187 147.4 5.9 152 126 4.2
AGGC 65 61.9 0.7 114 104.6 1.7 92 80.3 2.4 UGGC 144 103.8 7.2 184 144.4 6.0 141 103.4 6.7
AGGG 55 59.1 -1.0 88 79.5 1.7 53 60.7 -1.8 UGGG 81 105 -4.3 90 118.9 -4.8 59 74.4 -3.2
AGGU 137 143.8 -1.0 128 150 -3.3 129 119.5 1.6 UGGU 307 302.3 0.5 260 236.3 2.8 200 173.5 3.7
AGUA 137 159.2 -3.2 124 155.6 -4.6 115 116.9 -0.3 UGUA 228 233.8 -0.7 202 215.5 -1.7 161 165.6 -0.6
AGUC 62 77.6 -3.2 75 93.9 -3.5 76 87.3 -2.2 UGUC 116 116.5 -0.1 159 143.6 2.3 141 129.8 1.8
AGUG 152 156.2 -0.6 187 173.8 1.8 127 120.7 1.0 UGUG 266 246.9 2.2 300 255.8 5.0 214 170.9 6.0
AGUU 222 239.6 -2.1 214 206 1.0 126 161.7 -5.1 UGUU 498 407.8 8.1 415 346.1 6.7 274 252 2.5
AUAA 228 220.7 0.9 189 188.5 0.1 129 152.4 -3.4 UUAA 322 269.8 5.8 258 235.5 2.7 195 202.8 -1.0
AUAC 124 129.2 -0.8 100 112.8 -2.2 100 132.3 -5.1 UUAC 185 173.5 1.6 158 155.6 0.3 186 179.8 0.8
AUAG 120 141.9 -3.3 120 135 -2.3 65 91.7 -5.1 UUAG 141 177.5 -5.0 131 183 -7.0 112 119.5 -1.2
AUAU 205 237.9 -3.9 151 185.9 -4.7 99 144.4 -6.9 UUAU 397 385.6 1.1 309 269.1 4.4 191 226.5 -4.3
AUCA 105 122 -2.8 77 99.2 -4.1 139 136.8 0.3 UUCA 127 155 -4.1 132 126.1 1.0 206 180 3.5
AUCC 59 62.9 -0.9 63 65.5 -0.6 54 65.9 -2.7 UUCC 66 80.1 -2.9 75 90.9 -3.0 71 87.9 -3.3
AUCG 31 46.9 -4.2 42 57.2 -3.7 31 59.6 -6.7 UUCG 33 55.3 -5.5 64 69.3 -1.2 56 71.8 -3.4
AUCU 108 129.1 -3.4 87 109.2 -3.9 108 137.1 -4.5 UUCU 193 201.6 -1.1 133 151.2 -2.7 226 189.5 4.8
AUGA 204 212.3 -1.0 203 202.8 0.0 189 198.6 -1.2 UUGA 237 239.3 -0.3 197 213.4 -2.0 189 186.8 0.3
AUGC 186 151.1 5.2 194 164.2 4.2 179 154.3 3.6 UUGC 197 174.1 3.2 188 184.4 0.5 185 162.5 3.2
AUGG 211 180.8 4.1 197 179.4 2.4 185 143.1 6.4 UUGG 213 230.6 -2.1 208 185.6 3.0 153 143.2 1.5
AUGU 296 273.3 2.5 275 269.9 0.6 218 197.4 2.7 UUGU 415 363.3 4.9 368 298 7.4 245 204.3 5.2
AUUA 239 253.9 -1.7 191 216 -3.1 190 192 -0.3 UUUA 407 345.3 6.0 303 257.1 5.2 204 204.1 0.0
AUUC 106 126.1 -3.3 100 110.2 -1.8 127 136.8 -1.5 UUUC 141 161.3 -2.9 109 146.1 -5.6 187 162.4 3.5
AUUG 245 253.5 -1.0 206 211.6 -0.7 208 176 4.4 UUUG 367 357.7 0.9 318 271.3 5.2 207 194.8 1.6
AUUU 361 337.8 2.3 287 251.6 4.1 197 205.6 -1.1 UUUU 454 495.8 -3.4 296 325 -2.9 215 245.2 -3.5
GAAA 118 124 -1.0 104 111.4 -1.3 142 140.8 0.2 CAAA 128 133.8 -0.9 160 108.5 9.0 221 182.3 5.2
GAAC 58 64.6 -1.5 63 75.1 -2.5 89 96.9 -1.5 CAAC 83 71 2.6 93 74.9 3.8 166 128.5 6.0
GAAG 136 125.8 1.7 153 123.2 4.9 126 117.7 1.4 CAAG 108 111 -0.5 135 111.5 4.0 158 132.5 4.0
GAAU 118 140.8 -3.5 119 142.4 -3.6 90 125.7 -5.8 CAAU 144 147.5 -0.5 126 139.1 -2.0 178 170.2 1.1
GACA 82 83 -0.2 99 91 1.5 162 128.5 5.4 CACA 82 78.3 0.8 84 80.6 0.7 168 150.9 2.5
GACC 37 39.2 -0.6 61 69.1 -1.8 66 68.5 -0.5 CACC 59 44 4.1 76 59.3 3.9 98 80.1 3.6
GACG 27 33 -1.9 46 51 -1.3 33 52.9 -5.0 CACG 28 31.5 -1.1 40 46 -1.6 27 50.4 -6.0
GACU 82 86.6 -0.9 88 94.7 -1.3 101 115.3 -2.4 CACU 108 75.3 6.8 97 93.1 0.7 184 151.4 4.8
GAGA 73 77.8 -1.0 104 100.3 0.7 105 111.8 -1.2 CAGA 125 106.4 3.3 123 98.1 4.6 141 128.8 2.0
GAGC 52 60.1 -1.9 66 90.9 -4.8 83 74.9 1.7 CAGC 96 71.9 5.2 99 82.8 3.2 95 96.6 -0.3
GAGG 73 68.6 1.0 112 108.6 0.6 95 89.1 1.1 CAGG 94 84.9 1.8 106 93.4 2.4 102 93.4 1.6
GAGU 103 100.9 0.4 128 134 -0.9 108 98.6 1.7 CAGU 108 128.7 -3.3 132 127.4 0.7 98 127.2 -4.7
GAUA 149 172.1 -3.2 127 145.4 -2.8 81 111 -5.2 CAUA 88 110.8 -3.9 92 112.5 -3.5 99 118.2 -3.2
GAUC 70 86.1 -3.2 63 73 -2.1 55 75.7 -4.3 CAUC 49 56.5 -1.8 45 67.1 -4.9 100 91.9 1.5
GAUG 231 209.7 2.7 237 199.5 4.8 198 159 5.6 CAUG 110 117.8 -1.3 119 143.9 -3.8 153 138.3 2.3
GAUU 205 201.7 0.4 159 176.8 -2.4 125 128.6 -0.6 CAUU 166 149 2.5 160 159 0.1 196 173 3.2
GCAA 104 114.7 -1.8 137 123.3 2.2 133 131 0.3 CCAA 84 81.4 0.5 126 90.8 6.7 119 107.2 2.1
GCAC 70 65.3 1.1 77 74.2 0.6 99 92 1.3 CCAC 71 41.7 8.2 74 55.9 4.4 81 77.7 0.7
GCAG 131 102.4 5.1 157 113.3 7.5 80 100.5 -3.7 CCAG 67 64.5 0.6 90 80.7 1.9 95 77.5 3.6
GCAU 120 109.4 1.8 128 140.9 -2.0 112 104.2 1.4 CCAU 81 71.9 1.9 94 97.4 -0.6 97 91 1.1
GCCA 84 57.8 6.2 111 97.4 2.5 99 76.5 4.7 CCCA 46 41.6 1.2 83 62.7 4.7 56 60.1 -1.0
GCCC 34 34.5 -0.2 75 63.8 2.5 35 36.6 -0.5 CCCC 28 22.2 2.2 43 47.5 -1.2 18 28.8 -3.6
GCCG 29 29.7 -0.2 51 60.5 -2.2 21 31.7 -3.4 CCCG 17 20.4 -1.4 45 39.4 1.6 16 20.1 -1.6
GCCU 84 66.8 3.8 122 106.2 2.8 75 71.9 0.7 CCCU 58 43.9 3.8 76 78 -0.4 48 60.7 -3.0
GCGA 30 38.9 -2.6 42 57.3 -3.7 36 43.5 -2.1 CCGA 25 27.9 -1.0 45 47.1 -0.6 16 36.2 -6.0
GCGC 31 31.7 -0.2 65 57.4 1.8 38 41 -0.8 CCGC 20 21.8 -0.7 50 47 0.8 21 32.1 -3.6
GCGG 21 31.7 -3.4 43 56.8 -3.3 23 29.6 -2.2 CCGG 11 20.9 -3.9 36 44.9 -2.4 13 21.2 -3.2
GCGU 63 55.9 1.7 87 82.1 1.0 47 52.9 -1.5 CCGU 29 38.2 -2.7 54 68.1 -3.1 37 41.8 -1.3
GCUA 165 131.3 5.4 162 144.3 2.7 153 140.7 1.9 CCUA 85 77 1.7 83 96.5 -2.5 104 88.6 3.0
GCUC 58 58.8 -0.2 75 80.5 -1.1 89 98.1 -1.7 CCUC 38 40.1 -0.6 79 58.6 4.8 63 65.2 -0.5
GCUG 136 131.5 0.7 187 173.4 1.9 196 145.3 7.6 CCUG 89 80.4 1.7 118 108.1 1.7 70 89 -3.7
GCUU 167 147.3 3.0 158 162.5 -0.6 180 149.5 4.5 CCUU 86 97.4 -2.1 119 113.3 1.0 105 104.6 0.1
GGAA 86 82.1 0.8 83 103.4 -3.7 103 86 3.3 CGAA 23 42.7 -5.5 40 58.5 -4.4 37 55.5 -4.5
GGAC 51 48.4 0.7 57 67.7 -2.4 68 72.3 -0.9 CGAC 24 22.5 0.6 32 34.3 -0.7 27 46.9 -5.3
GGAG 81 66.6 3.2 109 95.9 2.4 92 70.1 4.8 CGAG 17 29.5 -4.2 42 53.5 -2.9 35 49.8 -3.8
GGAU 122 127 -0.8 139 124.7 2.3 80 83.7 -0.7 CGAU 41 63.1 -5.0 46 63.3 -4.0 36 56 -4.9
GGCA 93 70 5.0 142 99.4 7.7 108 83.7 4.8 CGCA 38 40.7 -0.8 67 63.3 0.8 46 58.2 -2.9
GGCC 34 33.7 0.1 74 74.8 -0.2 33 39.1 -1.8 CGCC 19 17.1 0.8 50 45.6 1.2 15 27.1 -4.2
GGCG 28 32.2 -1.3 57 62.9 -1.4 33 40.5 -2.1 CGCG 17 14.9 1.0 32 39.2 -2.1 21 23.4 -0.9
GGCU 95 88.7 1.2 135 117.9 2.9 115 94.9 3.8 CGCU 36 44.4 -2.3 61 73.5 -2.7 46 74.1 -5.9
GGGA 38 53 -3.7 52 65.7 -3.1 36 48.5 -3.3 CGGA 15 26.4 -4.0 35 51 -4.1 18 33.8 -4.9
GGGC 20 37.4 -5.1 64 68.8 -1.1 36 38.3 -0.7 CGGC 21 19 0.8 45 47.2 -0.6 20 29.3 -3.1
GGGG 26 41.9 -4.5 23 53.8 -7.6 20 31.4 -3.7 CGGG 10 19.9 -4.0 27 39.1 -3.5 12 17.5 -2.4
GGGU 88 95 -1.3 88 100.4 -2.2 52 63.8 -2.7 CGGU 31 50.2 -4.9 52 67.2 -3.4 28 55.5 -6.7
GGUA 147 153.8 -1.0 113 130.8 -2.8 106 102.8 0.6 CGUA 55 53.6 0.3 52 71.6 -4.2 52 60.2 -1.9
GGUC 51 70.4 -4.2 61 76.8 -3.3 40 71.3 -6.7 CGUC 16 24.9 -3.2 29 41.9 -3.6 36 41.9 -1.6
GGUG 160 161.8 -0.3 179 171.9 1.0 135 119.9 2.5 CGUG 60 64.9 -1.1 84 90.6 -1.3 69 71.3 -0.5
GGUU 205 201.3 0.5 175 181.2 -0.8 127 123.2 0.6 CGUU 59 83.2 -4.8 88 104.4 -2.9 53 81.6 -5.8
GUAA 165 174.4 -1.3 135 160.2 -3.6 101 130.5 -4.7 CUAA 154 145.5 1.3 128 140 -1.8 141 153.8 -1.9
GUAC 99 109.2 -1.8 86 110.2 -4.2 143 109 5.9 CUAC 112 88.1 4.6 95 87.5 1.5 160 140.2 3.0
GUAG 112 118.4 -1.1 104 136.9 -5.1 96 88.6 1.4 CUAG 78 86.6 -1.7 74 103.6 -5.3 75 99.2 -4.4
GUAU 191 195.4 -0.6 166 172 -0.8 94 118.6 -4.1 CUAU 163 148.3 2.2 182 150.6 4.7 177 162 2.1
GUCA 85 95.2 -1.9 105 98.5 1.2 114 113.3 0.1 CUCA 59 75 -3.4 73 82.5 -1.9 137 130.2 1.1
GUCC 30 52.2 -5.6 59 73.4 -3.1 35 52.7 -4.4 CUCC 33 41 -2.3 62 58.7 0.8 46 62.3 -3.7
GUCG 33 39.6 -1.9 35 59 -5.7 40 51.3 -2.9 CUCG 21 32 -3.5 39 46 -1.9 43 59.9 -4.0
GUCU 97 109.1 -2.1 125 120.1 0.8 104 112.9 -1.5 CUCU 84 82 0.4 110 94.8 2.8 126 136.9 -1.7
GUGA 122 162.3 -5.8 152 163.3 -1.6 131 127 0.6 CUGA 107 124.3 -2.8 108 139.4 -4.8 141 150.6 -1.4
GUGC 113 115.2 -0.4 149 148.5 0.1 130 110.9 3.3 CUGC 109 91.9 3.2 141 110.9 5.2 159 128.2 4.9
GUGG 158 146.3 1.8 180 158.8 3.1 109 101 1.4 CUGG 121 98.1 4.2 136 123.2 2.1 106 104.8 0.2
GUGU 245 218.3 3.3 269 223.8 5.5 174 129.3 7.2 CUGU 151 157.5 -0.9 164 179.7 -2.1 152 159.3 -1.1
GUUA 255 244.6 1.2 237 225.1 1.4 126 168.7 -6.0 CUUA 143 152.3 -1.4 125 150.3 -3.8 164 163.1 0.1
GUUC 104 123 -3.1 119 116.6 0.4 97 114.8 -3.0 CUUC 68 80.6 -2.5 76 81.3 -1.1 148 124.3 3.9
GUUG 280 254.7 2.9 283 248 4.0 165 169.1 -0.6 CUUG 168 147.9 3.0 154 152.9 0.2 190 154.7 5.2
GUUU 344 316.4 2.8 253 239.5 1.6 192 171 2.9 CUUU 211 212.4 -0.2 191 177.1 1.9 209 183.8 3.4
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Approach one – Sequence Relationship of Viruses based on The Correlation of Tetra-nucleotide Bias

Two relationship trees were derived, one from the entire genome and the other from the replication enzyme (Figure 1). The result based on the replication enzyme sequence was included because these regions in RNA viruses are submitted to a strong selective pressure to ensure successful replication of their own RNA in the host cell. The two distance trees can be clustered distinctly into two major groups of viruses. Interestingly, this clustering validates our approach, since these clusters are consistent with biological properties of the viruses: Group #1 corresponds to all positive strand ssRNA viruses while Group #2 corresponds to negative strand ssRNA viruses. Each group must undergo different evolutionary paths which lead to their distinct pattern in tetra-nucleotide usage. The classification for the two main groups of viruses (positive/negative strand ssRNA viruses) demonstrate a level of congruence with the taxonomy of the viruses [20] and indicated that there exists a relationship signal in tetra-nucleotide usage patterns.

Figure 1.

Figure 1

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Two Relationship trees based on the correlation coefficients of tetra-nucleotide usage bias The distance tree for 31 RNA viruses based on tetra-nucleotide usage pattern for the entire genome (right) and the replication enzyme (left). The correlation distances are shown on top of each branch.

Inside both relationship trees, Avian Encephalomyelitis Virus (AEV), Lactate Dehydrogenase-elevating Virus (LDV), Porcine Reproductive and respiratory syndrome Virus (PRV), Equine arteritis Virus (EV1), Rabbit Hemorrhagic disease Virus (RHV), Yellow Fever Virus (YFV), are the outermost group of viruses, exhibiting differences in their tetra-nucleotide usage pattern. From the family of positive strand ssRNA viruses, CoronaViruses form the largest cluster. The SARS-CoV is found to be at the basal position of other CoronaVirus types and remains closest to the Transmissible Gastroenteritis Virus (TGV) and Feline CoronaVirus (FCoV). This placement is consistent with the findings from two seminal papers [9,10] where the SARS-CoV was classified in a separate group from the rest of the known CoronaViruses. In addition, both distance trees suggested that the Bovine CoronaVirus (BCoV) and the Mouse Hepatitis Virus (MHV) should be grouped together whereas the Human CoronaVirus 229E (HCoV) is the closest to the Porcine epidemic Diarrhea Virus (PDV). For the family of negative strand ssRNA viruses, there are two obvious classes that have evolved through different branches of word usage pattern. The first class covers Hantaan Virus (HV1), Reston Ebola Virus (REV), Bovine Ephemeral Fever Virus (BFV), Bovine Respiratory syncytial Virus (BRV), Respiratory Syncytial Virus (RSV) and Human Respiratory syncytial Virus (HRV). The second class covers the remaining negative strand ssRNA viruses.

Approach two – Sequence Relationship of Viruses based on The Factors of the Tetra-nucleotide Usage Pattern [21-23]

The overall tetra-nucleotide usage pattern (additional file 2) was decomposed into several eigen-vectors using a factor analysis algorithm. They are the uncorrelated components of the original usage pattern embedded within the overall tetra-nucleotide usage pattern. Three eigen-vectors, which carry 83.3% of the variance for the viral tetra-nucleotide usage patterns, were retained (Figure 2). From the three dimensional figures (Figure 3, Figure 4, Figure 5 and Figure 6) plotted against these retained eigen-vectors, the negative strand ssRNA viruses stemmed clearly out from the positive strand ssRNA viruses. This is most obvious when the axes of projection were the 1st and 3rd eigen-vectors. This indicated that both types of viruses have a complex component of tetra-nucleotide usage patterns and that these patterns changes with different family of viruses.

Figure 2.

Figure 2

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Relationship between the number of eigen-vectors retained and the percentage of the variance they represent in the entire usage patterns for 31 viruses. As each consecutive factor is defined to identify a usage pattern that is not captured by the preceding eigen-vectors, each consecutive factors are therefore independent of each other. In addition, the order for the consecutive eigen-vectors is extracted with diminishing importance.

Figure 3.

Figure 3

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3-D plot for the vectorial profiling of each virus onto the three eigen-vectors. The tetra-nucleotide usage patterns V for the replicase open reading frame in each virus have been redisplayed on the 1st, 2nd and 3rd eigen-vector axes ('o' represents positive strand ssRNA virus; x represents negative strand ssRNA virus). The two families of viruses clustered into two different regions of the plot.

Figure 4.

Figure 4

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2-D plots for Figure 3 with different viewpoint specifications. The tetra-nucleotide usage patterns for the replicase open reading frame in each virus have been redisplayed on the (1st vs 2nd), (1st vs 3rd) and (2nd vs 3rd) eigen-vector axes ('o' represents positive strand ssRNA virus; 'x' represents negative strand ssRNA virus). For the top figure, the order for 'o' is [15,17,12,16,8,14,9,11,13,4,7,3,10,6,2,5,1]* (left to right), whereas 'x' is [24,27,25,28,22,26,18,23,20,19,21]* (left to right). For the middle figure, the order for 'o' is [15,17,12,16,8,14,9,11,13,4,7,3,10,6,2,5,1]* (left to right), whereas 'x' is [24,27,25,28,22,26,18,23,20,19,21]* (left to right). For the bottom figure, the order for 'o' is [15,17,12,16,8,14,9,11,13,4,7,3,10,6,2,5,1]* (left to right), whereas 'x' is [24,27,25,28,22,26,18,23,20,19,21]* (left to right). *The corresponded virus for each number follows Figure 3.

Figure 5.

Figure 5

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3-D plot for the vectorial profiling of each virus onto the three eigen-vectors. The tetra-nucleotide usage patterns table in the additional file 2 (entire genome) for each virus have been redisplayed on the 1st, 2nd and 3rd eigen-vector axes ('o' represents positive strand ssRNA virus; 'x' represents negative strand ssRNA virus). The two families of viruses clustered into three different regions of the plot.

Figure 6.

Figure 6

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2-D plots for Figure 5 with different viewpoint specifications. The tetra-nucleotide usage patterns table in the additional file 2 (entire genome) for each virus have been redisplayed on the (1st vs 2nd), (1st vs 3rd) and (2nd vs 3rd) eigen-vector axes ('o' represents positive strand ssRNA virus, 'x' represents negative strand ssRNA virus). For the top figure, the order for 'o' is [3,7,1,4,2,5,6,17,13,20,10,16,9,8,11,15,12,14,18,19]* (left to right), whereas 'x' is [26,22,30,23,24,28,31,27,25,29,21]* (left to right). For the middle figure, the order for 'o' is [3,7,1,4,2,5,6,17,13,20,10,16,9,8,11,15,12,14,18,19]* (left to right), whereas 'x' is [26,22,30,23,24,28,31,27,25,29,21]* (left to right). For the bottom figure, the order for 'o' is [3,7,1,4,2,5,6,17,13,20,10,16,9,8,11,15,12,14,18,19]* (left to right), whereas 'x' is [26,22,30,23,24,28,31,27,25,29,21]* (left to right). *The corresponded virus for each number follows Figure 5.

In the result based on replication enzyme sequence (Figure 3 and Figure 4), we observed a clear splitting between two main families of RNA viruses (positive/negative strand ssRNA virus). All viruses that belong to a specific family were clustered together closely. This pointed to an interesting hypothesis that the replication enzyme sequence between closely related RNA viruses adopt a common word usage pattern that are closely linked. In addition, it is clear that the viruses from different family groups adopt different strategy of word usage.

However in Figure 5 and Figure 6, when we project the tetra-nucleotide usage patterns (entire genome) for each virus on the 1st, 2nd and 3rd eigen-vector axes, the separation between viruses showed a different outcome when V was derived from the entire genome. The two main families of viruses were grouped into three clusters, two being allocated to the positive strand ssRNA viruses. It is particularly interesting that all viruses in the upper left corner corresponded to the viruses originating from the CoronaVirus family. Unexpectedly, the Hantaan Virus (HV1) is the only negative strand ssRNA virus to have a high loading on the eigen-vector that corresponded to the tetra-nucleotide usage pattern for the positive strand ssRNA viruses.

It is important to realize what factor analysis will provide and how this analysis is different from the previous method of relationship tree generation using correlation coefficient. For the previous method that is based on correlation coefficient of word usage patterns, it treats the vectorial profiling V for each virus as a whole entity, However, the factor analysis considered the vectorial profiling V as a superposition of many patterns which can be separated into mutually uncorrelated patterns of word usage. Each eigen-vector represents the embedded component of RNA word usage patterns communalised by a group of viruses presumably under the same selection pressures. By projecting the overall usage patterns on these eigen-vectors, it is possible to determine a group of viruses that adopt a common strategy of word usage.

Conclusion

Using the two approaches to study the tetra-nucleotide usage pattern in RNA viruses, we reached the following conclusions:

1. Based on the correlation of the overall tetra-nucleotide usage patterns, the Transmissible Gastroenteritis Virus (TGV) and the Feline CoronaVirus (FCoV) are closest to SARS-CoV.

2. Based on the three most significant eigen-vectors, the genomes of the viruses from the same family conform to a similar tetra-nucleotide usage pattern, irrespective of their genome size.

3. The study of word usage is a powerful method to classify RNA viruses. The congruence of the relationship trees with the known classification indicates that there exist phylogenetic signals in tetra-nucleotide usage patterns, and this signal is most prominent in the replicase open reading frames.

Methods

Dataset

We focused our study on the genomic sequences (their translated strand) of ssRNA viruses (Table 1), which incorporated 20 species from the family of positive strand ssRNA viruses and 11 species from the family of negative strand ssRNA viruses. We are aware of the fact that these viruses constitute completely different species, most probably unrelated to one another. They are included in a common study in order to try to have means to identify relevant features from purely statistical background properties. The coverage included the viruses that are known to cause diseases to their corresponding hosts. The acronym for each virus is shown in the table and is referred to throughout this study. All sequences corresponding to their translated strand were retrieved from GenBank, and the accession numbers and genomic size (in nucleotides) for individual virus were provided for reference. For the present study, two sets of data were generated from the complete sequence for each virus. Dataset 1 covered the entire genome and dataset 2 covered only their replicase open reading frame. The flowchart for studying the tetra-nucleotide usage pattern in 31 viruses is shown in Figure 7.

Figure 7.

Figure 7

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Flowchart for studying the tetra-nucleotide usage pattern. The FA and NJ algorithms stand for factor analysis [21-23] and neighbor joining [29] algorithm.

Computer hardware and software

Sun Fire 6800 Server with 24 CPUs (each running with a clock speed of 900 MHz) was employed throughout this study. The computation of correlation coefficient and factor analysis algorithm were implemented using Matlab Technical Programming language.

Method for counting the frequency of occurrence for RNA words

It is necessary to address the question of how we counted the number of time each tetra-nucleotide (for example 'GAGA' or any other tetra-nucleotide), appeared in a given genome. For this study, we adopted the convention of not counting overlapping words [24]. Take a sequence "UAUGAGAGAUCCGAGA' as example. With second or higher overlapping words not counted, the tetra-nucleotide 'GAGA' is counted as occurring only twice, namely in position 4–7 and 13–16. Positions 6–9 are omitted because they overlap with 'GAGA' at position 4–7.

However, when we counted tetra-nucleotide 'UGAG', position 3–6 would also be registered as position 4–6 already recorded when counting tetra-nucleotide 'GAGA'. In short, all frequency counting of tetra-nucleotide were started anew when we changed from counting the frequency of one tetra-nucleotide to another; this was to preserve the correlation of tetra-nucleotides which have overlapping subword (e.g: 'UAGA' and 'GACA'). A table showing the frequencies of tetra-nucleotides is shown in the additional file 2.

Vectorial profiling (V) of the viral RNA genome word usage pattern

The nucleotide composition has being suggested to be a specific characteristic in different virus phylogeny [25]. Because most viral genomes are short, and because we lack a prior information on the tempo and modes of evolution of RNA viruses, we proceeded as follows. We created a vector, V = [C1,C2, ... Ci, ... Ck], with each element representing the frequency for a specific RNA word of length n. The number of components (k) in V increases exponentially with word size (n) - k = 4n. In order to use V for discrimination between viruses, two criteria must be met. First, V must contain sufficient components (di-nucleotide k = 16; tri-nucleotide k = 64; tetra-nucleotide k = 256); second, the frequencies for tetra-nucleotides must show a prominent bias (over/under-representation) that is unique for a family of viruses.

For the first criteria, there are pros and cons for choosing either longer or shorter words. When the shorter words are used, they inherit the problem of inadequate representation of the viral genome because the long motifs will be neglected. But the shorter words have an advantage of saving computational time. On the other hand, when the longer words are used, they cause a problem of computer tractability due to a larger word set to explore (k = 4n). However, the larger words have an advantage of accounting for the correlation of their sub-words. In contrast the number of their occurrences falls down rapidly, preventing accurate statistical analysis. We chose tetra-nucleotides for our study because they provide 256 vector components (additional file 2) and account for correlation of sub-words up to the order three.

For the second criteria, the bias in RNA word usage was examined. The bias in word usage (of size n) is influenced by the bias of word with sizes less than n [26]. Therefore, in order to evaluate the true bias of word size m, it is required to compare the frequencies of word usage in the original sequence to that of model chromosomes that take into account the biases of word size m - 1, m - 2 ... 1. These model chromosomes were generated by obeying the Markov model of the order (m - 1)th. This can be achieved by shuffling m - 1 viral nucleotides as one whole unit so that the nucleotide successions up to order (m - 1)th were being preserved. Several statistical approaches have been proposed for quantifying word biases [27,28]. In this study, we employed the z statistics (Equation 1) for di-nucleotide and tetra-nucleotide biases [27,28]. The z value is a measure of the bias of a word, with values close to zero meaning no bias, negative values meaning under-representation and positive values meaning over-representation of the word w in the RNA text.

graphic file with name 1471-2105-4-43-i1.gif

where w is a word of size m; N(w) is observed count in actual viral RNA; E(w) and Var(w) are expected count and variance for w derived from the 100 artificial chromosomes that preserved the nucleotide succession up to order m - 1.

Approach one – sequence relationship of viruses based on the correlation of tetra-nucleotide bias

A scale-invariant parameter, the correlation coefficient r, was employed to compare between word usage patterns of viruses. The correlation coefficient r measures the degree of linear relationship between two vectors. Here, the two vectors are the tetra-nucleotide word usage pattern V corresponding to each viral genome. The magnitude of r would indicate how much of the change of pattern in the tetra-nucleotide word usage in one virus is explained by the change in another. The magnitude of r is always between -1 and +1 and the relationship between the two variables will approach perfect linearity as the magnitude of correlation coefficient approaches to extreme values (+/-1). However, perfect positive correlation (r = 1) does not mean identity of the paired Vi, but, rather, identity up to positive linearity, that is, identity between the paired standardized values. This is a crucial property of r (scale-invariant) that enables the comparison of viral genome despite their differences in genomic sizes. Positive magnitude of r indicates positive association whereas negative magnitude of r indicates negative association between two usage patterns. For this study, correlation coefficient, r, for let say virus 1 and virus 2, is defined as follow:

graphic file with name 1471-2105-4-43-i2.gif

where V1, V2 are vector representing the tetra-nucleotide usage pattern; SV1 and SV2 standard deviation of V1, V2; Inline graphic are the mean of V1, V2.

Then, the distance between the tetra-nucleotide usage patterns of two viruses is defined as follows:

Distance Dij = 1 - rij;     (3)

where Dij is the distance between the tetra-nucleotide usage patterns of virus i and virus j; rij is the correlation coefficient between the tetra-nucleotide usage patterns of virus i and virus j

Prior to the construction of a relationship tree, the pair-wise distance matrix M of size 31 by 31 was constructed (see additional file 3). Pair-wise distance between two viral genomes is measured by the value of (1 - r). Each row/column corresponds to a specific virus and an entry at the intersection of row X and column Y corresponds to the distance between virus X and virus Y. Such matrix has a diagonal entry of value 0. For the purpose of constructing a relationship tree, only the lower/upper triangular matrix of M is required. After obtaining lower/upper triangular matrix of M, the neighbor-joining method (NJ) algorithm was used to construct the relationship tree (Figure 1). The neighbor-joining method is based on minimum-distance principle. Details of the NJ algorithm are available in [29].

Approach two – sequence relationship of viruses based on the factors of the tetra-nucleotide usage pattern

The factor analysis is a statistical method that reveals simpler patterns within a complex set of tetra-nucleotide usage patterns V (additional file 2). It seeks to discover if the observed usage patterns can be explained in terms of a much smaller number of un-correlated pattern sets called factors (eigen-vectors). Suppose we take a simple case where there are 31 viruses each represented by two components (x,y) in vector V (x,y represent the frequencies of occurrence for two specific tetra-nucleotides). Then, in a scatter-plot we can think of the regression line as the original X-axis, rotated so that it approximates the regression line. This type of rotation maximize the variance of the variables (x,y) on the eigen-vector. The remaining variability around this the first eigen-vector was captured in the subsequent eigen-vectors. In this manner, consecutive eigen-vectors are extracted but with a diminishing importance. What each eigen-vector represents is the embedded RNA word usage patterns communalised by a group of viruses presumably under the same selection pressures.

We implemented the factor analysis algorithm [21-23] in Matlab Technical Programming Language and computed a set of eigen-vectors. Then, the original usage pattern V was re-mapped for each virus onto the new coordinate system based on these derived eigen-vectors. The difference between approach two and approach one is discussed in the results and discussion section.

Authors' contributions

YLY participated in the design and performed the statistical analysis.

AD participated in the design and overall coordination of this study.

XWZ participated in the design of the study.

All authors read and approved the final manuscript.

Supplementary Material

Additional File 1

The RNA word biases of different sizes in RNA viruses. These tables show the di-nucleotide, tetra-nucleotide and penta-nucleotide biases for 31 RNA viruses.

Click here for file (1.7MB, xls)
Additional File 2

Vectorial profiling of tetra-nucleotide usage pattern in seven RNA viruses. The tetra-nucleotide frequencies of occurrence in seven viral genomes. Each column represents a tetra-nucleotide usage pattern Vi for a single virus. We derived correlation coefficient (r) by comparing any two columns simultaneously. This parameter r indicates the likeness of word usage patterns in any two viruses.

Click here for file (38KB, xls)
Additional File 3

The distance matrices. Each entry in matrix M is computed using Equation 3. The correlation coefficient (r) in equation 3 is obtained by comparing any two columns in the tetra-nucleotide usage patterns table in the additional file 2 simultaneously.

Click here for file (31KB, xls)

Acknowledgments

Acknowledgements

Indispensable support was provided by the doctoral fellowship from The University of Hong Kong (HKU). We wish to thank the Hong Kong Innovation and Technology Fund for supporting work upstream of the present study, that made it possible at a time when the unexpected SARS outbreak reached Hong Kong. Finally, we wish to thank Dr Ralf Altmeyer for his critical interest for this work as he came at the head of the HKU-Pasteur Research Centre.

Contributor Information

Yee Leng Yap, Email: daniely@hkusua.hku.hk.

Xue Wu Zhang, Email: xwzhang@hkucc.hku.hk.

Antoine Danchin, Email: adanchin@pasteur.fr.

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Associated Data

This section collects any data citations, data availability statements, or supplementary materials included in this article.

Supplementary Materials

Additional File 1

The RNA word biases of different sizes in RNA viruses. These tables show the di-nucleotide, tetra-nucleotide and penta-nucleotide biases for 31 RNA viruses.

Click here for file (1.7MB, xls)
Additional File 2

Vectorial profiling of tetra-nucleotide usage pattern in seven RNA viruses. The tetra-nucleotide frequencies of occurrence in seven viral genomes. Each column represents a tetra-nucleotide usage pattern Vi for a single virus. We derived correlation coefficient (r) by comparing any two columns simultaneously. This parameter r indicates the likeness of word usage patterns in any two viruses.

Click here for file (38KB, xls)
Additional File 3

The distance matrices. Each entry in matrix M is computed using Equation 3. The correlation coefficient (r) in equation 3 is obtained by comparing any two columns in the tetra-nucleotide usage patterns table in the additional file 2 simultaneously.

Click here for file (31KB, xls)

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