(A) Clusters of concordantly evolving sites. Graph vertices represent sites, and edges represent concordantly evolving pairs (Appendix 1—table 7). The graph consists of 13 connected components, 8 of …
Sites of the five clusters that comprise multiple coevolving pairs of sites are shown as spheres, with color coding matching Figure 1A. (A) Closed conformation of the S-protein trimer (pdb: 7JJJ). (B…
Leading and trailing mutations are represented by blue (site 501) or red (site 1118) right-pointing and left-pointing triangles respectively; diamond-shaped signs indicate mutations that are both …
Here, mutations on terminal branches, which are excluded from the analysis, are shown in light blue, red or violet; mutations on internal branches that are followed by mutations on terminal …
Branches carrying substitutions at site 501 are shown in blue; at site 677, in red; at both sites, in violet. There is less violet color than expected. Some clades without mutations at either site …
Leading and trailing mutations are represented by blue (site 484), red (site 655) or violet (mutations at both sites on the same branch) right-pointing and left-pointing triangles respectively; …
Here, mutations on terminal branches, which are excluded from the analysis, are shown in light blue, red or violet; mutations on internal branches that are followed by mutations on terminal …
Black dots indicate numbers of site pairs having corresponded p-values in the simulated data, boxes with whiskers indicate distributions of numbers of site pairs having corresponded p-values among …
See legend for the Appendix 1—figure 1.
09.2021 (I), and to the newer PANGOLIN 4.1.3, used in the default mode (II). Α is shown in red color, Β in blue, Γ in green, and Δ in orange. There are more red (α) branches outside the main α clade …
The following characteristics are shown: coordinates on the S-protein sequence, nominal p-values, the value of the epistatic statistics, the total number of consecutive mutation pairs for the two …
site 1 | site 2 | cluster | p-value | epistatic statistics | #consec.pairs of mutations | #mutations in consec. pairs at site 1 | #mutations in consec. pairs at site 2 | #mutations at site 1 | #mutations at site2 | physical distance, Å |
---|---|---|---|---|---|---|---|---|---|---|
13 | 152 | <2e-5 | 2.864 | 5 | 5 | 4 | 5 | 16 | - | |
20 | 417 | 4 | 2.2e-4 | 1.348 | 4 | 3 | 2 | 8 | 7 | 47.83 |
26 | 190 | 4 | 1.8e-4 | 1.029 | 4 | 4 | 3 | 12 | 3 | 18.4 |
63 | 213 | 3 | 4e-5 | 0.681 | 1 | 1 | 1 | 2 | 3 | 13.51 |
69 | 70 | 3 | <2e-5 | 1.125 | 2 | 2 | 2 | 5 | 4 | 1.3 |
70 | 144 | 3 | <2e-5 | 1.301 | 3 | 3 | 3 | 4 | 5 | 14.03 |
76 | 490 | 2.6e-4 | 0.22 | 1 | 1 | 1 | 3 | 3 | 45.18 | |
189 | 360 | 2 | 1.6e-4 | 0.544 | 2 | 1 | 2 | 3 | 3 | 29.89 |
190 | 417 | 4 | 0.0001 | 1.272 | 3 | 2 | 2 | 3 | 7 | 39.93 |
259 | 261 | 3 | <2e-5 | 1.35 | 1.5 | 2 | 1 | 4 | 2 | 3.81 |
356 | 360 | 2 | <2e-5 | 1.283 | 2.5 | 2 | 3 | 2 | 3 | 10.12 |
359 | 360 | 2 | <2e-5 | 0.976 | 1.5 | 1 | 2 | 2 | 3 | 1.34 |
439 | 441 | 1 | <2e-5 | 2.097 | 4 | 3 | 4 | 9 | 8 | 3.5 |
440 | 441 | 1 | 1.4e-4 | 1.505 | 3 | 3 | 3 | 12 | 8 | 1.33 |
440 | 442 | 1 | <2e-5 | 2.476 | 3 | 2 | 3 | 12 | 6 | 3.92 |
440 | 444 | 1 | <2e-5 | 2.515 | 3.5 | 2 | 5 | 12 | 7 | 5.6 |
441 | 442 | 1 | <2e-5 | 2.244 | 4 | 4 | 4 | 8 | 6 | 1.33 |
441 | 443 | 1 | 2e-5 | 1.281 | 5 | 4 | 2 | 8 | 2 | 3.23 |
441 | 444 | 1 | <2e-5 | 3.492 | 5.5 | 4 | 4 | 8 | 7 | 2.6 |
442 | 443 | 1 | 6e-5 | 1.301 | 4 | 4 | 2 | 6 | 2 | 1.32 |
442 | 444 | 1 | <2e-5 | 3.013 | 6 | 4 | 4 | 6 | 7 | 4.05 |
443 | 444 | 1 | 8e-5 | 1.043 | 2 | 2 | 2 | 2 | 7 | 1.32 |
501 | 1118 | 5 | 1.4e-4 | 2.737 | 16 | 13 | 12 | 40 | 22 | 131.71 |
681 | 716 | 5 | <2e-5 | 3.905 | 16.5 | 12 | 16 | 59 | 21 | - |
716 | 982 | 5 | 2e-5 | 2.001 | 15 | 9 | 11 | 21 | 15 | 81.66 |
716 | 1118 | 5 | 4e-5 | 2.382 | 13 | 8 | 12 | 21 | 22 | 22.29 |
859 | 950 | <2e-5 | 2.219 | 5.5 | 4 | 5 | 11 | 9 | 15.17 | |
982 | 1118 | 5 | 1.4e-4 | 1.637 | 15 | 11 | 8 | 15 | 22 | 94.63 |
The following characteristics are shown: coordinates on the S-protein sequence, nominal p-values, the value of the epistatic statistic, the total number of consecutive mutation pairs for the two …
site 1 | site 2 | p-value | epistat. | #consec. pairs of mutations | #mut. in consec. pairs in site1 | #mut. in consec. pairs in site2 | #mut. in site1 | #mut. in site2 | FDRUShER tree | physical distance,Å |
---|---|---|---|---|---|---|---|---|---|---|
69 | 614 | 3e-3 | 0.07 | 5 | 1 | 5 | 5 | 14 | 0.231 | 46.75 |
222 | 501 | 3.1e-3 | 0.01 | 1 | 1 | 1 | 11 | 40 | 0.058 | 55.44 |
440 | 681 | 3.1e-3 | 0.01 | 1 | 1 | 1 | 12 | 59 | 0.055 | - |
501 | 675 | 1.2e-3 | 0.02 | 1 | 1 | 1 | 40 | 24 | 0.06 | 84.98 |
501 | 677 | 4.8e-4 | 0.05 | 3 | 2 | 3 | 40 | 39 | 0 | 88.20 |
570 | 614 | 2.4e-3 | 0.16 | 7 | 1 | 7 | 16 | 14 | 0.895 | 19.30 |
614 | 653 | 4e-5 | 0.03 | 4 | 1 | 4 | 14 | 5 | 0.025 | 15.47 |
614 | 982 | 3.2e-4 | 0.12 | 7 | 1 | 7 | 14 | 15 | 0.891 | 27.87 |
681 | 1176 | 3.9e-3 | 0.01 | 1 | 1 | 1 | 59 | 11 | 0.385 | - |
Number of pairs, detected under p-value threshold 10-4, and estimated FDR for this threshold are shown.
Model | #FP | min p-value | Maximal FDR threshold for#FP = 0 | |
---|---|---|---|---|
consider alleles | shuffle mutations in fgr. only | 2 | <1e-4 | 0,25 |
shuffle mutations both in bgr. and fgr. | 3 | <1e-4 | 0,15 | |
ignore alleles | shuffle mutations in fgr. only | 4 | <1e-4 | 0,11 |
shuffle mutations both in bgr. and fgr. | 24 | <1e-4 | 0,02 |
Number of pairs, detected under p-value threshold 10-4, and maximal threshold on estimated FDR that allows to avoid false discoveries are shown.
Model | #FP | min p-value | Maximal FDR threshold for #FP = 0 | |
---|---|---|---|---|
consider alleles | shuffle mutations in fgr. only | 2 | <1e-4 | 0,2 |
shuffle mutations both in bgr. and fgr. | 19 | <1e-4 | 0,026 | |
ignore alleles | shuffle mutations in fgr. only | 4 | <1e-4 | 0,125 |
shuffle mutations both in bgr. and fgr. | 16 | <1e-4 | 0,031 |
The evolution of the population of genotypes with twenty independently evolving pairs of epistatically interacting sites was simulated by MimicrEE2. Ten pairs of sites were evolving under recurrent …
Model | #FP | #TP | |
---|---|---|---|
consider alleles | shuffle mutations in fgr. only | 5 | 10 |
shuffle mutations both in bgr. and fgr. | 55 | 6 | |
ignore alleles | shuffle mutations in fgr. only | 22 | 8 |
shuffle mutations both in bgr. and fgr. | 250 | 7 |
The characteristics of predicted site pairs for the estimated FDR≤10% are shown: positions of sites on the primary sequence of S-protein (site1 and site2), the upper p-values (p-value), values of …
site1 | site2 | p-value | epistat | #consec. pairs of mut. | #mut. in consec. pairs in site1 | #mut. in consec. pairs in site2 | #mut. in site1 | #mut. in site2 | exp. epistat | SE |
---|---|---|---|---|---|---|---|---|---|---|
1 | 2 | <1e-4 | 12,36 | 66,5 | 52 | 65 | 2 | 96 | 3,97 | 0,87 |
3 | 4 | <1e-4 | 17,79 | 94 | 61 | 104 | 4 | 118 | 6,55 | 1,23 |
5 | 6 | <1e-4 | 13,87 | 54 | 48 | 54 | 6 | 105 | 3,27 | 0,83 |
5 | 43 | <1e-4 | 21,43 | 108,5 | 82 | 100 | 43 | 105 | 12,6 | 1,89 |
7 | 8 | <1e-4 | 11,36 | 50 | 42 | 50 | 8 | 109 | 3,22 | 0,78 |
9 | 10 | <1e-4 | 17,09 | 90 | 64 | 88 | 10 | 117 | 6,62 | 1,19 |
11 | 12 | <1e-4 | 13,46 | 53,5 | 48 | 51 | 12 | 108 | 2,54 | 0,69 |
13 | 14 | <1e-4 | 11,63 | 52,5 | 43 | 56 | 14 | 106 | 2,85 | 0,72 |
15 | 16 | <1e-4 | 11,84 | 69 | 47 | 70 | 16 | 116 | 5,88 | 1,08 |
19 | 20 | <1e-4 | 9,06 | 47 | 39 | 47 | 18 | 109 | 4,29 | 0,88 |
48 | 68 | <1e-4 | 29,11 | 171,5 | 110 | 169 | 20 | 95 | 2,6 | 0,69 |
17 | 18 | 2e-4 | 8,23 | 66 | 38 | 65 | 31 | 95 | 6,61 | 1,23 |
19 | 31 | 2e-4 | 11,58 | 78,5 | 56 | 78 | 67 | 176 | 20,72 | 2,09 |
50 | 94 | 2e-4 | 24,34 | 162,5 | 100 | 151 | 68 | 183 | 17,55 | 1,9 |
78 | 94 | 2e-4 | 28,50 | 172 | 110 | 169 | 94 | 178 | 20,5 | 2,07 |
See legend for Appendix 1—table 3.
Model | #FP | #TP | |
---|---|---|---|
consider alleles | shuffle mutations in fgr. only | 4 | 7 |
shuffle mutations both in bgr. and fgr. | 62 | 5 | |
ignore alleles | shuffle mutations in fgr. only | 4 | 9 |
shuffle mutations both in bgr. and fgr. | 7 | 5 |
See legend for Appendix 1—table 4. The ‘p-value’ column contains the lower p-values.
site1 | site2 | p-value | epistat | #consec. pairs of mut. | #mut. in consec. pairs in site1 | #mut. in consec. pairs in site2 | #mut. in site1 | #mut. in site2 | exp. epistat | SE |
---|---|---|---|---|---|---|---|---|---|---|
16 | 50 | <1e-4 | 5,72 | 85,5 | 47 | 83 | 108 | 178 | 10,51 | 1,48 |
17 | 96 | 1e-4 | 7,44 | 93,5 | 54 | 90 | 109 | 192 | 12,92 | 1,70 |
23 | 24 | <1e-4 | 8,27 | 70,5 | 51 | 68 | 137 | 129 | 13,70 | 1,65 |
25 | 26 | <1e-4 | 6,13 | 73,5 | 37 | 74 | 139 | 121 | 10,84 | 1,46 |
26 | 95 | 1e-4 | 6,94 | 91,5 | 52 | 94 | 121 | 179 | 12,18 | 1,60 |
27 | 28 | <1e-4 | 5,90 | 76 | 42 | 73 | 168 | 149 | 13,90 | 1,82 |
33 | 34 | 1e-4 | 4,70 | 48,5 | 37 | 45 | 117 | 136 | 8,55 | 1,30 |
35 | 36 | <1e-4 | 5,47 | 59,5 | 39 | 55 | 150 | 127 | 10,81 | 1,51 |
37 | 38 | <1e-4 | 4,10 | 44,5 | 32 | 41 | 113 | 146 | 8,93 | 1,39 |
39 | 40 | <1e-4 | 4,97 | 61,5 | 37 | 59 | 115 | 142 | 11,11 | 1,47 |
39 | 47 | <1e-4 | 7,27 | 86,5 | 54 | 84 | 115 | 166 | 13,09 | 1,66 |
The characteristics of predicted site pairs for the estimated FDR≤10% are shown: the positions of sites on the primary sequence of S-protein (site1 and site2), the upper p-values (p-value), values …
site1 | site2 | p-value | epistat | #consec. pairs of mut. | #mut. in consec. pairs in site1 | #mut. in consec. pairs in site2 | #mut. in site1 | #mut. in site2 | FDRfor the USHER tree | pdb distance |
---|---|---|---|---|---|---|---|---|---|---|
13 | 152 | <2e-5 | 2,864 | 5 | 5 | 4 | 5 | 16 | 0,03 | |
18 | 20 | 0,00008 | 1,661 | 3,5 | 3 | 3 | 28 | 8 | 1,19 | 3,62 |
20 | 26 | <2e-5 | 1,985 | 4 | 3 | 3 | 8 | 12 | 0,36 | 15,19 |
20 | 417 | 0,00022 | 1,348 | 4 | 3 | 2 | 8 | 7 | 0,05 | 47,83 |
26 | 190 | 0,00018 | 1,029 | 4 | 4 | 3 | 12 | 3 | 0,06 | 18,40 |
63 | 64 | 0,00002 | 0,726 | 1 | 1 | 1 | 2 | 4 | 1,00 | 1,31 |
63 | 67 | 0,00008 | 0,726 | 1 | 1 | 1 | 2 | 5 | 1,00 | 9,38 |
63 | 69 | 0,00012 | 0,726 | 1 | 1 | 1 | 2 | 5 | 1,00 | 11,07 |
63 | 213 | 0,00004 | 0,681 | 1 | 1 | 1 | 2 | 3 | 0,01 | 13,51 |
64 | 67 | 0,00012 | 0,726 | 1 | 1 | 1 | 4 | 5 | 1,00 | 5,51 |
64 | 69 | 0,00014 | 0,726 | 1 | 1 | 1 | 4 | 5 | 1,00 | 7,05 |
67 | 69 | <2e-5 | 1,101 | 2 | 2 | 2 | 5 | 5 | 0,55 | 3,59 |
69 | 70 | <2e-5 | 1,125 | 2 | 2 | 2 | 5 | 4 | 0,01 | 1,30 |
70 | 144 | <2e-5 | 1,301 | 3 | 3 | 3 | 4 | 5 | 0,01 | 14,03 |
76 | 490 | 0,00026 | 0,220 | 1 | 1 | 1 | 3 | 3 | 0,05 | 45,18 |
154 | 1071 | <2e-5 | 1,767 | 4 | 2 | 3 | 5 | 5 | 0,25 | 95,13 |
155 | 157 | <2e-5 | 1,113 | 2 | 2 | 2 | 3 | 11 | 0,53 | 3,74 |
189 | 356 | 0,00006 | 0,544 | 2 | 1 | 2 | 3 | 2 | 0,32 | 31,63 |
189 | 360 | 0,00016 | 0,544 | 2 | 1 | 2 | 3 | 3 | 0,07 | 29,89 |
190 | 417 | 0,0001 | 1,272 | 3 | 2 | 2 | 3 | 7 | 0,01 | 39,93 |
213 | 261 | 0,00008 | 0,562 | 1 | 1 | 1 | 3 | 2 | 0,37 | 11,10 |
259 | 261 | <2e-5 | 1,350 | 1,5 | 2 | 1 | 4 | 2 | 0,05 | 3,81 |
262 | 272 | <2e-5 | 1,183 | 4 | 4 | 1 | 9 | 2 | 0,94 | 31,42 |
356 | 357 | 0,00006 | 0,448 | 1 | 1 | 1 | 2 | 2 | 0,69 | 1,33 |
356 | 360 | <2e-5 | 1,283 | 2,5 | 2 | 3 | 2 | 3 | 0,05 | 10,12 |
359 | 360 | <2e-5 | 0,976 | 1,5 | 1 | 2 | 2 | 3 | 0,01 | 1,34 |
439 | 441 | <2e-5 | 2,097 | 4 | 3 | 4 | 9 | 8 | 0,01 | 3,50 |
440 | 441 | 0,00014 | 1,505 | 3 | 3 | 3 | 12 | 8 | 0,01 | 1,33 |
440 | 442 | <2e-5 | 2,476 | 3 | 2 | 3 | 12 | 6 | 0,01 | 3,92 |
440 | 443 | 0,00002 | 1,284 | 4 | 3 | 2 | 12 | 2 | 0,25 | 3,86 |
440 | 444 | <2e-5 | 2,515 | 3,5 | 2 | 5 | 12 | 7 | 0,01 | 5,60 |
441 | 442 | <2e-5 | 2,244 | 4 | 4 | 4 | 8 | 6 | 0,01 | 1,33 |
441 | 443 | 0,00002 | 1,281 | 5 | 4 | 2 | 8 | 2 | 0,02 | 3,23 |
441 | 444 | <2e-5 | 3,492 | 5,5 | 4 | 4 | 8 | 7 | 0,01 | 2,60 |
442 | 443 | 0,00006 | 1,301 | 4 | 4 | 2 | 6 | 2 | 0,05 | 1,32 |
442 | 444 | <2e-5 | 3,013 | 6 | 4 | 4 | 6 | 7 | 0,01 | 4,05 |
443 | 444 | 0,00008 | 1,043 | 2 | 2 | 2 | 2 | 7 | 0,03 | 1,32 |
484 | 655 | 0,00004 | 1,716 | 8 | 6 | 5 | 34 | 12 | 0,89 | 73,58 |
501 | 1118 | 0,00014 | 2,737 | 16 | 13 | 12 | 40 | 22 | 0,09 | 131,71 |
681 | 716 | <2e-5 | 3,905 | 16,5 | 12 | 16 | 59 | 21 | 0,02 | |
716 | 982 | 0,00002 | 2,001 | 15 | 9 | 11 | 21 | 15 | 0,01 | 81,66 |
716 | 1118 | 0,00004 | 2,382 | 13 | 8 | 12 | 21 | 22 | 0,01 | 22,29 |
859 | 950 | <2e-5 | 2,219 | 5,5 | 4 | 5 | 11 | 9 | 0,01 | 15,17 |
982 | 1118 | 0,00014 | 1,637 | 15 | 11 | 8 | 15 | 22 | 0,01 | 94,63 |
1258 | 1259 | 0,00004 | 0,775 | 3 | 1 | 3 | 5 | 3 | NA |
See legend for Appendix 1—table 7. The ‘p-value’ column contains the lower p-values.
site1 | site2 | p-value | epistat | #consec. pairs of mut. | #mut. in consec. pairs in site1 | #mut. in consec. pairs in site2 | #mut. in site1 | #mut. in site2 | IQ-TREE | pdb distance |
---|---|---|---|---|---|---|---|---|---|---|
12 | 346 | 0,00006 | 0,934 | 2 | 2 | 1 | 9 | 4 | 0 | - |
12 | 899 | 0,00004 | 0,724 | 2 | 2 | 1 | 9 | 3 | 0 | - |
13 | 152 | 0,00004 | 1,407 | 5 | 4 | 3 | 4 | 13 | 1 | - |
20 | 190 | 0,00022 | 0,885 | 3 | 2 | 3 | 8 | 4 | 0 | 22,59 |
20 | 417 | 0,00018 | 1,107 | 2 | 2 | 1 | 8 | 8 | 1 | 47,83 |
26 | 190 | 0,00026 | 0,913 | 4 | 3 | 4 | 12 | 4 | 1 | 18,40 |
26 | 655 | 0,00042 | 0,968 | 6,5 | 3 | 6 | 12 | 14 | 0 | 37,53 |
54 | 690 | 0,00044 | 0,714 | 1 | 1 | 1 | 11 | 3 | 0 | 33,65 |
62 | 251 | <2e-5 | 0,748 | 1 | 1 | 1 | 2 | 3 | 0 | 32,01 |
67 | 96 | <2e-5 | 0,599 | 1 | 1 | 1 | 3 | 7 | 0 | 7,12 |
69 | 70 | <2e-5 | 1,496 | 3 | 3 | 3 | 5 | 5 | 1 | 1,30 |
69 | 144 | 0,00002 | 0,984 | 2 | 2 | 2 | 5 | 5 | 0 | 12,57 |
70 | 144 | <2e-5 | 1,088 | 3 | 3 | 3 | 5 | 5 | 1 | 14,03 |
76 | 490 | 0,0001 | 0,275 | 1 | 1 | 1 | 2 | 3 | 1 | 45,18 |
80 | 215 | <2e-5 | 1,687 | 6,5 | 3 | 6 | 21 | 14 | 0 | 12,51 |
80 | 950 | 0,00014 | 1,091 | 3 | 2 | 2 | 21 | 7 | 0 | 56,59 |
152 | 252 | 0,00016 | 0,623 | 2 | 2 | 1 | 13 | 4 | 0 | 15,26 |
189 | 360 | 0,0003 | 0,534 | 1 | 1 | 1 | 2 | 2 | 1 | 29,89 |
189 | 772 | 0,00024 | 0,440 | 1 | 1 | 1 | 2 | 2 | 0 | 44,17 |
190 | 417 | <2e-5 | 1,134 | 2,5 | 2 | 2 | 4 | 8 | 1 | 39,93 |
215 | 1167 | 0,00042 | 0,853 | 2 | 2 | 2 | 14 | 4 | 0 | |
255 | 256 | 0,00022 | 0,758 | 2 | 2 | 2 | 8 | 7 | 0 | 1,32 |
255 | 260 | 0,00036 | 0,811 | 3 | 3 | 2 | 8 | 3 | 0 | 9,61 |
256 | 258 | 0,00012 | 0,660 | 1 | 1 | 1 | 7 | 2 | 0 | 2,81 |
256 | 260 | 0,00014 | 1,056 | 2 | 2 | 2 | 7 | 3 | 0 | 8,18 |
259 | 260 | <2e-5 | 1,536 | 2 | 2 | 2 | 3 | 3 | 0 | 1,31 |
259 | 261 | 0,00014 | 0,909 | 1 | 1 | 1 | 3 | 2 | 1 | 3,81 |
357 | 360 | <2e-5 | 1,025 | 1,5 | 1 | 2 | 2 | 2 | 0 | 7,59 |
359 | 360 | <2e-5 | 1,268 | 2 | 1 | 2 | 2 | 2 | 1 | 1,34 |
360 | 772 | 0,00018 | 0,534 | 1 | 1 | 1 | 2 | 2 | 0 | 58,61 |
439 | 440 | <2e-5 | 2,038 | 3,5 | 2 | 4 | 10 | 12 | 0 | 1,31 |
439 | 441 | <2e-5 | 2,795 | 5 | 3 | 4 | 10 | 5 | 1 | 3,50 |
439 | 444 | 0,00006 | 1,606 | 4,5 | 3 | 4 | 10 | 7 | 0 | 6,21 |
440 | 441 | <2e-5 | 2,822 | 4,5 | 4 | 2 | 12 | 5 | 1 | 1,33 |
440 | 442 | <2e-5 | 2,092 | 3 | 3 | 2 | 12 | 3 | 1 | 3,92 |
440 | 444 | <2e-5 | 2,947 | 4,5 | 4 | 3 | 12 | 7 | 1 | 5,60 |
441 | 442 | <2e-5 | 2,292 | 3 | 2 | 2 | 5 | 3 | 1 | 1,33 |
441 | 443 | 0,00002 | 1,383 | 2 | 2 | 2 | 5 | 2 | 1 | 3,23 |
441 | 444 | <2e-5 | 3,829 | 6,5 | 4 | 4 | 5 | 7 | 1 | 2,60 |
441 | 445 | 0,00018 | 1,086 | 2 | 2 | 1 | 5 | 6 | 0 | 8,51 |
442 | 443 | 0,0001 | 1,132 | 2 | 2 | 1 | 3 | 2 | 1 | 1,32 |
442 | 444 | 0 | 2,387 | 4 | 3 | 3 | 3 | 7 | 1 | 4,05 |
443 | 444 | 0,00006 | 1,031 | 4 | 1 | 4 | 2 | 7 | 1 | 1,32 |
444 | 445 | 0,0002 | 1,270 | 4 | 5 | 3 | 7 | 6 | 0 | 1,31 |
501 | 570 | 0 | 2,734 | 16 | 13 | 10 | 46 | 19 | 0 | 53,69 |
501 | 1118 | 0,00048 | 2,028 | 18 | 14 | 13 | 46 | 19 | 1 | 131,71 |
570 | 681 | 0,00018 | 2,538 | 17,5 | 15 | 14 | 19 | 62 | 0 | |
570 | 1118 | 0,00002 | 1,881 | 13,5 | 9 | 10 | 19 | 19 | 0 | 79,04 |
572 | 1181 | 0 | 0,533 | 1 | 1 | 1 | 3 | 2 | 0 | |
583 | 1237 | 0,00014 | 0,242 | 1 | 1 | 1 | 3 | 3 | 1 | |
681 | 716 | 0,00002 | 3,017 | 20 | 20 | 16 | 62 | 21 | 1 | |
681 | 1118 | 0,00032 | 2,334 | 18 | 14 | 12 | 62 | 19 | 0 | |
716 | 982 | 0 | 4,623 | 19,5 | 13 | 16 | 21 | 18 | 1 | 81,66 |
716 | 1118 | 0 | 2,872 | 17,5 | 11 | 13 | 21 | 19 | 1 | 22,29 |
859 | 950 | 0 | 1,596 | 4 | 3 | 4 | 9 | 7 | 1 | 15,17 |
982 | 1118 | 0 | 1,831 | 17,5 | 10 | 10 | 18 | 19 | 1 | 94,63 |
1027 | 1176 | 0,00016 | 1,206 | 5,5 | 5 | 4 | 12 | 9 | 0 |
The characteristics of predicted site pairs for the estimated FDR≤10% are shown: the positions of sites on the primary sequence of S-protein (site1 and site2), the upper p-values (p-value), values …
site1 | site2 | p-value | epistat | #consec. pairs of mut. | #mut. in consec. pairs in site1 | #mut. in consec. pairs in site2 | #mut. in site1 | #mut. in site2 | IQ-TREE | pdb distance |
---|---|---|---|---|---|---|---|---|---|---|
18 | 681 | 0,00344 | 0,102 | 5,5 | 5 | 4 | 22 | 62 | 0 | |
222 | 501 | 0,00314 | 0,019 | 1 | 1 | 1 | 12 | 46 | 1 | 55,44 |
439 | 501 | 0,00286 | 0 | 0 | 0 | 0 | 10 | 46 | 0 | 5,16 |
440 | 501 | 0,0019 | 0 | 0 | 0 | 0 | 12 | 46 | 0 | 9,47 |
440 | 681 | 0,00274 | 0,008 | 1 | 1 | 1 | 12 | 62 | 1 | |
484 | 982 | 0,0021 | 0,020 | 3 | 3 | 3 | 43 | 18 | 0 | 35,42 |
501 | 675 | 0,00136 | 0,025 | 1 | 1 | 1 | 46 | 22 | 1 | 84,98 |
501 | 677 | 0,0001 | 0,023 | 2 | 2 | 2 | 46 | 33 | 1 | 88,2 |
570 | 677 | 0,00226 | 0,011 | 1 | 1 | 1 | 19 | 33 | 0 | 44,77 |
614 | 653 | 0,00022 | 0,037 | 4 | 1 | 4 | 10 | 5 | 1 | 15,47 |
675 | 716 | 0,00568 | 0 | 0 | 0 | 0 | 22 | 21 | 0 | 38,15 |
675 | 1118 | 0,00524 | 0 | 0 | 0 | 0 | 22 | 19 | 0 | 58,84 |
677 | 681 | 0,00264 | 0,098 | 3 | 3 | 3 | 33 | 62 | 0 | |
677 | 716 | 0,00102 | 0,011 | 1 | 1 | 1 | 33 | 21 | 0 | 42,93 |
677 | 982 | 0,00152 | 0,004 | 1 | 1 | 1 | 33 | 18 | 0 | 54,37 |
677 | 1118 | 0,00066 | 0,002 | 1 | 1 | 1 | 33 | 19 | 0 | 64,36 |
Z-scores < 0 and upper p-values after Benjamini-Hochberg adjustment < 0.05 indicate clustering of nonconsecutive mutations; z-scores > 0 and lower p-values after Benjamini-Hochberg adjustment < 0.05 …
site 1 | site 2 | #nonseq. pairs | zscore | lower pvalue | upper pvalue | lower pvalue adj. | upper pvalue adj. |
---|---|---|---|---|---|---|---|
13 | 152 | 2569 | –0,724 | 0,7675 | 0,2325 | 1 | 0,5813 |
18 | 20 | 8610,5 | 1,148 | 0,1225 | 0,8775 | 0,3675 | 1 |
20 | 26 | 5719 | 2,444 | 0,0175 | 0,9825 | 0,1125 | 1 |
20 | 417 | 2533 | 1,738 | 0,04 | 0,96 | 0,2 | 1 |
26 | 190 | 3682 | 2,258 | 0,015 | 0,985 | 0,1125 | 1 |
63 | 64 | 124 | 1,736 | 0,06 | 0,94 | 0,2455 | 1 |
63 | 67 | 264 | 1,68 | 0,075 | 0,925 | 0,2596 | 1 |
63 | 69 | 239 | 2,224 | 0,025 | 0,975 | 0,1406 | 1 |
63 | 213 | 94 | 1,407 | 0,0825 | 0,9175 | 0,2652 | 1 |
64 | 67 | 1324 | 2,353 | 0,0125 | 0,9875 | 0,1125 | 1 |
64 | 69 | 1199 | 2,766 | 0,0025 | 0,9975 | 0,0281 | 1 |
67 | 69 | 2542 | 4,104 | 0 | 1 | 0,0281 | 1 |
69 | 70 | 2014 | 4,041 | 0 | 1 | 0,0281 | 1 |
70 | 144 | 627 | 2,952 | 0,0025 | 0,9975 | 0,0281 | 1 |
76 | 490 | 1748 | 0,632 | 0,25 | 0,75 | 0,5357 | 1 |
154 | 1071 | 502 | –1,357 | 0,925 | 0,075 | 1 | 0,225 |
155 | 157 | 482 | 0,671 | 0,2375 | 0,7625 | 0,5344 | 1 |
189 | 356 | 108 | –0,187 | 0,555 | 0,445 | 0,999 | 0,9536 |
189 | 360 | 58 | 0,927 | 0,17 | 0,83 | 0,4765 | 1 |
190 | 417 | 1631 | 0,099 | 0,445 | 0,555 | 0,8344 | 1 |
213 | 261 | 778 | –1,251 | 0,905 | 0,095 | 1 | 0,2672 |
259 | 261 | 736,5 | –2,384 | 0,9975 | 0,0025 | 1 | 0,0094 |
262 | 272 | 744 | 0,085 | 0,44 | 0,56 | 0,8344 | 1 |
356 | 357 | 65 | –0,797 | 0,7525 | 0,2475 | 1 | 0,5862 |
356 | 360 | 63,5 | –2,704 | 1 | 0,0025 | 1 | 0,0094 |
359 | 360 | 64,5 | –0,39 | 0,6275 | 0,3725 | 1 | 0,8381 |
439 | 441 | 1196 | –3,989 | 1 | 0,0025 | 1 | 0,0094 |
440 | 441 | 1647 | –3,55 | 1 | 0,0025 | 1 | 0,0094 |
440 | 442 | 822 | –3,23 | 1 | 0,0025 | 1 | 0,0094 |
440 | 443 | 931 | –2,124 | 0,995 | 0,005 | 1 | 0,0173 |
440 | 444 | 1591,5 | –3,511 | 1 | 0,0025 | 1 | 0,0094 |
441 | 442 | 446 | –5,063 | 1 | 0,0025 | 1 | 0,0094 |
441 | 443 | 505 | –4,26 | 1 | 0,0025 | 1 | 0,0094 |
441 | 444 | 864,5 | –5,337 | 1 | 0,0025 | 1 | 0,0094 |
442 | 443 | 251 | –3,988 | 1 | 0,0025 | 1 | 0,0094 |
442 | 444 | 429 | –4,727 | 1 | 0,0025 | 1 | 0,0094 |
443 | 444 | 491 | –3,972 | 1 | 0,0025 | 1 | 0,0094 |
484 | 655 | 18792 | 1,038 | 0,18 | 0,82 | 0,4765 | 1 |
501 | 1118 | 16121 | 1,443 | 0,07 | 0,93 | 0,2596 | 1 |
681 | 716 | 19375,5 | –0,962 | 0,8325 | 0,1675 | 1 | 0,4434 |
716 | 982 | 8267 | 0,58 | 0,3075 | 0,6925 | 0,629 | 1 |
716 | 1118 | 9986 | 1,65 | 0,05 | 0,95 | 0,225 | 1 |
859 | 950 | 3684,5 | 0,747 | 0,2075 | 0,7925 | 0,5188 | 1 |
982 | 1118 | 8103 | 0,757 | 0,2325 | 0,7675 | 0,5344 | 1 |
1258 | 1259 | 1053 | –1,435 | 0,9375 | 0,0625 | 1 | 0,2009 |
Z-scores < 0 and upper p-values after Benjamini-Hochberg adjustment < 0.05 indicate clustering of nonconsecutive mutations; z-scores > 0 and lower p-values after Benjamini-Hochberg adjustment < 0.05 …
site 1 | site 2 | #nonseq. pairs | zscore | lower pvalue | upper pvalue | lower pvalue adj. | upper pvalue adj. |
---|---|---|---|---|---|---|---|
69 | 614 | 2875 | 2,27 | 0,015 | 0,985 | 0,06 | 1 |
222 | 501 | 17114 | –0,861 | 0,795 | 0,205 | 0,995 | 0,369 |
440 | 681 | 10559 | –2,229 | 0,995 | 0,005 | 0,995 | 0,045 |
501 | 675 | 18907 | –2,39 | 0,9875 | 0,0125 | 0,995 | 0,0563 |
501 | 677 | 30478 | –1,463 | 0,925 | 0,075 | 0,995 | 0,1856 |
570 | 614 | 5813 | 1,738 | 0,0425 | 0,9575 | 0,0956 | 1 |
614 | 653 | 1856 | 2,944 | 0,0025 | 1 | 0,0225 | 1 |
614 | 982 | 4913 | 2,226 | 0,02 | 0,98 | 0,06 | 1 |
681 | 1176 | 9599 | –1,326 | 0,9175 | 0,0825 | 0,995 | 0,1856 |
Z-scores < 0 and upper p-values after Benjamini-Hochberg adjustment < 0.05 indicate clustering of nonconsecutive mutations; z-scores > 0 and lower p-values after Benjamini-Hochberg adjustment < 0.05 …
site 1 | site 2 | #nonseq. pairs | zscore | lower pvalue | upper pvalue | lower pvalue adj. | upper pvalue adj. |
---|---|---|---|---|---|---|---|
12 | 346 | 1296 | 0,461 | 0,29 | 0,71 | 1 | 0,9263 |
12 | 899 | 883 | 0,705 | 0,245 | 0,755 | 1 | 0,9551 |
13 | 152 | 3955 | –0,731 | 0,75 | 0,25 | 1 | 0,4597 |
20 | 190 | 2357 | –0,372 | 0,6525 | 0,3475 | 1 | 0,5826 |
20 | 417 | 3184 | 0,692 | 0,225 | 0,775 | 1 | 0,9551 |
26 | 190 | 3876 | 0,993 | 0,1425 | 0,8575 | 0,8835 | 0,9975 |
26 | 655 | 10663,5 | 2,486 | 0,01 | 0,99 | 0,1425 | 1 |
54 | 690 | 923 | –1,288 | 0,9175 | 0,0825 | 1 | 0,1959 |
62 | 251 | 95 | 0,51 | 0,2875 | 0,7125 | 1 | 0,9263 |
67 | 96 | 2027 | 0,462 | 0,285 | 0,715 | 1 | 0,9263 |
69 | 70 | 2241 | 2,982 | 0 | 1 | 0,0713 | 1 |
69 | 144 | 967 | 2,582 | 0,01 | 0,99 | 0,1425 | 1 |
70 | 144 | 833 | 2,303 | 0,02 | 0,98 | 0,1832 | 1 |
76 | 490 | 1801 | 0,766 | 0,2125 | 0,7875 | 1 | 0,9551 |
80 | 215 | 13261,5 | –2,369 | 0,995 | 0,005 | 1 | 0,0204 |
80 | 950 | 6321 | –1,417 | 0,9325 | 0,0675 | 1 | 0,1749 |
152 | 252 | 1142 | 0,042 | 0,4875 | 0,5125 | 1 | 0,8063 |
189 | 360 | 43 | 0,188 | 0,395 | 0,605 | 1 | 0,8621 |
189 | 772 | 109 | –0,85 | 0,785 | 0,215 | 1 | 0,4226 |
190 | 417 | 2157,5 | –0,741 | 0,7725 | 0,2275 | 1 | 0,4323 |
215 | 1167 | 2031 | –1,602 | 0,9525 | 0,0475 | 1 | 0,1425 |
255 | 256 | 2126 | –1,048 | 0,845 | 0,155 | 1 | 0,3398 |
255 | 260 | 1285 | –2,55 | 1 | 0,0025 | 1 | 0,0119 |
256 | 258 | 645 | –1,441 | 0,9375 | 0,0625 | 1 | 0,1696 |
256 | 260 | 872 | –1,368 | 0,9275 | 0,0725 | 1 | 0,1797 |
259 | 260 | 435 | –2,326 | 0,9925 | 0,0075 | 1 | 0,0267 |
259 | 261 | 778 | –1,861 | 0,99 | 0,01 | 1 | 0,0335 |
357 | 360 | 30,5 | –1,517 | 0,95 | 0,05 | 1 | 0,1425 |
359 | 360 | 38 | –0,549 | 0,6725 | 0,3275 | 1 | 0,5657 |
360 | 772 | 39 | –0,674 | 0,7225 | 0,2775 | 1 | 0,4943 |
439 | 440 | 2456,5 | –2,577 | 0,9925 | 0,0075 | 1 | 0,0267 |
439 | 441 | 1061 | –2,935 | 1 | 0,0025 | 1 | 0,0119 |
439 | 444 | 1143,5 | –3,434 | 1 | 0,0025 | 1 | 0,0119 |
440 | 441 | 1555,5 | –2,671 | 0,995 | 0,005 | 1 | 0,0204 |
440 | 442 | 897 | –2,686 | 1 | 0,0025 | 1 | 0,0119 |
440 | 444 | 1675,5 | –2,976 | 1 | 0,0025 | 1 | 0,0119 |
441 | 442 | 387 | –4,065 | 1 | 0,0025 | 1 | 0,0119 |
441 | 443 | 440 | –3,437 | 1 | 0,0025 | 1 | 0,0119 |
441 | 444 | 721,5 | –4,488 | 1 | 0,0025 | 1 | 0,0119 |
441 | 445 | 596 | –2,144 | 0,9825 | 0,0175 | 1 | 0,0554 |
442 | 443 | 253 | –3,58 | 1 | 0,0025 | 1 | 0,0119 |
442 | 444 | 416 | –4,346 | 1 | 0,0025 | 1 | 0,0119 |
443 | 444 | 472 | –4,301 | 1 | 0,0025 | 1 | 0,0119 |
444 | 445 | 640 | –2,502 | 0,9975 | 0,0025 | 1 | 0,0119 |
501 | 570 | 21489 | 3,943 | 0 | 1 | 0,0713 | 1 |
501 | 1118 | 21300 | 1,398 | 0,08 | 0,92 | 0,57 | 1 |
570 | 681 | 26547,5 | 2,15 | 0,015 | 0,985 | 0,171 | 1 |
570 | 1118 | 13096,5 | 1,926 | 0,0225 | 0,9775 | 0,1832 | 1 |
572 | 1181 | 511 | –0,81 | 0,785 | 0,215 | 1 | 0,4226 |
583 | 1237 | 3077 | –0,998 | 0,8325 | 0,1675 | 1 | 0,3536 |
681 | 716 | 27238 | –1,029 | 0,8575 | 0,1425 | 1 | 0,3249 |
681 | 1118 | 26316 | 0,042 | 0,475 | 0,525 | 1 | 0,8063 |
716 | 982 | 10836,5 | 0,057 | 0,4625 | 0,5375 | 1 | 0,8063 |
716 | 1118 | 13434,5 | –0,024 | 0,5175 | 0,4825 | 1 | 0,7858 |
859 | 950 | 4892 | 0,429 | 0,3125 | 0,6875 | 1 | 0,9263 |
982 | 1118 | 10470,5 | 0,258 | 0,3975 | 0,6025 | 1 | 0,8621 |
1027 | 1176 | 4023,5 | 0,98 | 0,155 | 0,845 | 0,8835 | 0,9975 |
Z-scores < 0 and upper p-values after Benjamini-Hochberg adjustment < 0.05 indicate clustering of nonconsecutive mutations; z-scores > 0 and lower p-values after Benjamini-Hochberg adjustment < 0.05 …
site 1 | site 2 | #nonseq. pairs | zscore | lower pvalue | upper pvalue | lower pvalue adj. | upper pvalue adj. |
---|---|---|---|---|---|---|---|
18 | 681 | 34644,5 | –1,979 | 0,9725 | 0,0275 | 0,98 | 0,2 |
222 | 501 | 20756 | 0,222 | 0,3825 | 0,6175 | 0,68 | 1 |
439 | 501 | 7667 | –1,207 | 0,8875 | 0,1125 | 0,98 | 0,45 |
440 | 501 | 11220 | 0,422 | 0,325 | 0,675 | 0,665 | 1 |
440 | 681 | 13859 | –0,599 | 0,7375 | 0,2625 | 0,98 | 0,6629 |
484 | 982 | 21249 | 4,304 | 0,0025 | 1 | 0,0133 | 1 |
501 | 675 | 22065 | –1,868 | 0,9625 | 0,0375 | 0,98 | 0,2 |
501 | 677 | 36276 | –0,526 | 0,71 | 0,29 | 0,98 | 0,6629 |
570 | 677 | 22309 | 4,782 | 0,0025 | 1 | 0,0133 | 1 |
614 | 653 | 2273 | 1,739 | 0,05 | 0,95 | 0,16 | 1 |
675 | 716 | 13924 | –0,731 | 0,7725 | 0,2275 | 0,98 | 0,6629 |
675 | 1118 | 13452 | 0,417 | 0,3325 | 0,6675 | 0,665 | 1 |
677 | 681 | 44811 | –2,043 | 0,98 | 0,02 | 0,98 | 0,2 |
677 | 716 | 22891 | 0,604 | 0,265 | 0,735 | 0,665 | 1 |
677 | 982 | 17847 | 3,543 | 0,0025 | 1 | 0,0133 | 1 |
677 | 1118 | 22115 | 1,869 | 0,0425 | 0,9575 | 0,16 | 1 |
Site pairs were ordered by nominal p-values; for each of the two subsets, mean rank of site pairs included into that subset is provided. The difference between mean ranks (delta) obtained for the …
mean ranks for subset I(15 site pairs) | mean ranks for subset II(17005 site pairs) | delta | |
---|---|---|---|
data | 234,7 | 8517,8 | –8283,1 |
simulations | 2182,4 | 8516,1 | –6333,7 |
Number of lineage-defining sites: 6.
P{delta(simulations)≤delta(data)}<0.0025.
See legend for Appendix 1—table 14.
mean ranks for subset I(15 site pairs) | mean ranks for subset II(17005 site pairs) | delta | |
---|---|---|---|
data | 530,5 | 8517,5 | –7987,1 |
simulations | 3021,4 | 8515,3 | –5494,0 |
Number of lineage-defining sites: 6.
P{delta(simulations)≤delta(data)}<0.0025.
See legend for Appendix 1—table 14.
mean ranks for subset I(15 site pairs) | mean ranks for subset II(17005 site pairs) | delta | |
---|---|---|---|
data | 3137,2 | 8515,2 | –5378,0 |
simulations | 5545,9 | 8513,1 | –2967,2 |
Number of lineage-defining sites: 6.
P{delta(simulations)≤delta(data)}=0.005.
See legend for Appendix 1—table 14.
mean ranks for subset I(55 site pairs) | mean ranks for subset II(16965 site pairs) | delta | |
---|---|---|---|
data | 543,3 | 8536,3 | –7993,0 |
simulations | 3532,3 | 8526,6 | –4994,3 |
Number of lineage-defining sites: 11.
P{delta(simulations)≤delta(data)}<0.0025.
See legend for Appendix 1—table 14.
mean ranks for subset I(91 site pairs) | mean ranks for subset II(16929 site pairs) | delta | |
---|---|---|---|
data | 5686,0 | 8525,7 | –2839,7 |
simulations | 5540,6 | 8526,5 | –2985,9 |
Number of lineage-defining sites: 14.
P{delta(simulations)≤delta(data)}=0.635.
See legend for Appendix 1—table 14.
mean ranks for subset I(15 site pairs) | mean ranks for subset II(15385 site pairs) | delta | |
---|---|---|---|
data | 316,8 | 7707,7 | –7390,9 |
simulations | 4281,3 | 7703,8 | –3422,5 |
Number of lineage-defining sites: 6.
P{delta(simulations)≤delta(data)}<0.0025.
See legend for Appendix 1—table 14.
mean ranks for subset I(15 site pairs) | mean ranks for subset II(16275 site pairs) | delta | |
---|---|---|---|
data | 4586,7 | 8148,8 | –3562,1 |
simulations | 4522,3 | 8148,8 | –3626,6 |
Number of lineage-defining sites: 6.
P{delta(simulations)≤delta(data)}=0.5628.
See legend for Appendix 1—table 14.
mean ranks for subset I(15 site pairs) | mean ranks for subset II(16638 site pairs) | delta | |
---|---|---|---|
data | 5934,7 | 8329,2 | –2394,5 |
simulations | 5975,1 | 8329,1 | –2354,0 |
Number of lineage-defining sites: 6.
P{delta(simulations)≤delta(data)}=0.4462.
See legend for Appendix 1—table 14.
mean ranks for subset I(45 site pairs) | mean ranks for subset II(16245 site pairs) | delta | |
---|---|---|---|
data | 6424,4 | 8150,3 | –1725,8 |
simulations | 5393,5 | 8153,1 | –2759,7 |
Number of lineage-defining sites: 10.
P{delta(simulations)≤delta(data)}=0.9728.
P{delta(simulations)≥delta(data)}=0.0272.
GISAID Identifier: EPI_SET_20220729hq doi:10.55876/gis8.220729hq.
0032). The number of possible FP pairs is calculated as the number of unordered combinations of sites that produce false positive pairs. For example, 20 sites in the simulation are involved in …
site types | #FP | #total possible FP | expected FP frequency | observed FP frequency |
(pos,pos) | 7 | 180 | 0,0364 | 0,0843 |
(pos,neg) | 7 | 400 | 0,0810 | 0,0843 |
(neg,neg) | 0 | 190 | 0,0385 | 0 |
(pos,neu) | 33 | 1200 | 0,2429 | 0,3976 |
(neg,neu) | 6 | 1200 | 0,2429 | 0,0723 |
(neu,neu) | 30 | 1770 | 0,3583 | 0,3614 |
Multinomial test p-value = 0.0018.
site types | #FP | #total possible FP | expected FP frequency | observed FP frequency |
(pos,pos) | 0 | 190 | 0,0385 | 0 |
(pos,neg) | 7 | 400 | 0,0810 | 0,1556 |
(neg,neg) | 4 | 180 | 0,0364 | 0,0889 |
(pos,neu) | 5 | 1200 | 0,2429 | 0,1111 |
(neg,neu) | 19 | 1200 | 0,2429 | 0,4222 |
(neu,neu) | 10 | 1770 | 0,3583 | 0,2222 |