Skip to main content

Table 5 Fit parameters for the HMM

From: Accurate statistics for local sequence alignment with position-dependent scoring by rare-event sampling

   HMM n = 0 HMM n = 1
L Q L S λ 10 4 λ 2 10 3 K λ 10 4 λ 2 10 3 K
348 150 0.2890 ± 0.85%   49.4722 ± 7.27% 0.2310 ± 9.32%   21.4600 ± 66.56%
  200 0.2894 ± 2.84%   50.0796 ± 24.47% 0.2274 ± 1.74%   20.1017 ± 13.25%
  300 0.2895 ± 2.69%   53.3472 ± 24.00% 0.2240 ± 4.86%   17.8934 ± 37.22%
  348 0.2988 ± 3.24%   72.2356 ± 30.15% 0.2234 ± 2.39%   16.8704 ± 18.79%
  360 0.2895 ± 1.79%   51.9056 ± 16.04% 0.2220 ± 2.14%   16.3757 ±16.52%
  400 0.2859 ± 3.49%   48.4496 ± 31.10% 0.2232 ± 2.40%   17.5141 ± 18.94%
  500 0.2912 ± 6.63%   54.0687 ± 61.22% 0.2182 ± 2.39%   14.7371 ± 19.10%
  600 0.2901 ± 3.38%   51.9412 ± 31.74% 0.2180 ± 2.59%   14.2439 ± 20.86%
   HMM n = 2 HMM n = 3
L Q L S λ 104 λ2 K λ 104 λ2 K
348 150 0.1968 ± 0.70% 2.9247 ± 1.37% 12.0400 ± 6.48% 0.1767 ± 0.44% 2.6797 ± 1.01% 7.4435 ± 3.72%
  200 0.1947 ± 2.12%   9.8704 ± 14.29% 0.1795 ± 0.46% 2.3586 ± 0.92% 8.5733 ± 3.87%
  300 0.1937 ± 3.60%   9.9597 ± 25.32% 0.1863 ± 0.41% 2.0008 ± 0.94% 11.7859 ± 5.63%
  348 0.1888 ± 3.19%   8.1338 ± 22.42% 0.1876 ± 0.32% 1.9328 ± 0.89% 12.1223 ± 3.83%
  360 0.1926 ± 3.17%   9.7957 ± 22.82% 0.1853 ± 0.27% 1.9530 ± 0.65% 10.8640 ± 2.65%
  400 0.1934 ± 1.05%   9.9321 ± 8.22% 0.1757 ± 1.64%   7.1756 ± 11.58%
  500 0.1919 ± 1.61%   9.3630 ± 12.32% 0.1783 ± 0.98%   7.7945 ± 7.18%
  600 0.1912 ± 1.70%   9.3303 ± 13.25% 0.1768 ± 1.01%   7.4165 ± 8.19%
   HMM n = 4 HMM n = 5
L Q L S λ 104 λ2 103K λ 104 λ2 103K
348 150 0.1732 ± 0.47% 2.2119 ± 1.14% 7.4991 ± 6.08% 0.1710 ± 0.38% 2.0698 ± 0.92% 8.1950 ± 3.70%
  200 0.1686 ± 0.28% 2.1187 ± 0.72% 6.4162 ± 3.14% 0.1657 ± 0.39% 1.8231 ± 1.14% 6.9148 ± 3.82%
  300 0.1682 ± 0.36% 1.9635 ± 0.79% 6.5436 ± 4.22% 0.1599 ± 0.37% 1.7836 ± 0.79% 5.4451 ± 3.85%
  348 0.1685 ± 0.35% 1.9408 ± 0.74% 7.3851 ± 3.34% 0.1580 ± 0.28% 1.7930 ± 0.68% 5.3049 ± 2.61%
  360 0.1678 ± 0.42% 1.9421 ± 0.92% 6.5775 ± 4.07% 0.1605 ± 0.23% 1.7481 ± 0.50% 5.7512 ± 2.89%
  400 0.1662 ± 0.18% 1.9782 ± 0.40% 6.4164 ± 2.32% 0.1587 ± 0.28% 1.7828 ± 0.73% 5.4513 ± 2.57%
  500 0.1693 ± 0.24% 1.9047 ± 0.51% 7.0735 ± 2.11% 0.1587 ± 0.16% 1.7957 ± 0.40% 5.4770 ± 2.31%
  600 0.1693 ± 0.17% 1.8994 ± 0.39% 7.1112 ± 2.06% 0.1575 ± 0.29% 1.8330 ± 0.58% 5.2125 ± 2.68%
   HMM n = 6 HMM n = 7
L Q L S λ 104 λ2 103K   104 λ2 103K
348 150 0.1663 ± 0.49% 2.1403 ± 1.04% 7.9392 ± 5.83% 0.1646 ± 0.30% 2.1396 ± 0.65% 8.7088 ± 4.21%
  200 0.1614 ± 0.25% 1.7767 ± 0.65% 6.7568 ± 2.30% 0.1574 ± 0.41% 1.7687 ± 1.17% 6.5219 ± 3.81%
  300 0.1551 ± 0.28% 1.5986 ± 0.80% 5.2551 ± 3.18% 0.1514 ± 0.26% 1.4638 ± 0.62% 5.0238 ± 4.34%
  348 0.1531 ± 0.20% 1.5993 ± 0.55% 4.9132 ± 2.71% 0.1482 ± 0.33% 1.4755 ± 0.77% 4.4535 ± 4.13%
  360 0.1536 ± 0.34% 1.6036 ± 1.02% 4.9160 ± 3.41% 0.1490 ± 0.39% 1.4479 ± 0.93% 4.6858 ± 3.28%
  400 0.1537 ± 0.27% 1.5713 ± 0.62% 4.9524 ± 3.05% 0.1494 ± 0.24% 1.4328 ± 0.70% 4.6867 ± 2.08%
  500 0.1519 ± 0.23% 1.6229 ± 0.67% 4.6812 ± 2.14% 0.1472 ± 0.29% 1.4706 ± 0.63% 4.2881 ± 2.50%
  600 0.1489 ± 0.15% 1.7148 ± 0.33% 4.2283 ± 2.16% 0.1460 ± 0.18% 1.5193 ± 0.49% 4.2679 ± 1.74%
   HMM n = 8 HMM n = 9
L Q L S λ 104 λ2 103K λ 104 λ2 103K
348 150 0.1595 ± 0.47% 2.2162 ± 1.01% 7.5355 ± 4.01% 0.1603 ± 0.23% 2.1517 ± 0.48% 8.0273 ± 2.17%
  200 0.1534 ± 0.55% 1.8019 ± 1.46% 5.9224 ± 5.25% 0.1508 ± 0.14% 1.7854 ± 0.28% 6.3535 ± 1.89%
  300 0.1473 ± 0.47% 1.3916 ± 1.24% 4.8483 ± 4.01% 0.1413 ± 0.12% 1.4118 ± 0.35% 4.2141 ± 1.43%
  348 0.1458 ± 0.32% 1.3409 ± 0.85% 4.6141 ± 3.69% 0.1398 ± 0.10% 1.3281 ± 0.33% 3.9661 ± 1.44%
  360 0.1469 ± 0.34% 1.2868 ± 0.90% 4.9271 ± 2.73% 0.1400 ± 0.16% 1.2888 ± 0.43% 4.0126 ± 1.79%
  400 0.1440 ± 0.34% 1.3591 ± 1.05% 4.0064 ± 3.48% 0.1382 ± 0.25% 1.2954 ± 0.67% 3.7257 ± 2.14%
  500 0.1433 ± 0.29% 1.3382 ± 0.85% 3.9952 ± 2.70% 0.1352 ± 0.14% 1.3472 ± 0.42% 3.1780 ± 1.68%
  600 0.1416 ± 0.33% 1.3760 ± 0.94% 3.7782 ± 3.14% 0.1359 ± 0.13% 1.3399 ± 0.38% 3.3536 ± 1.49%
   HMM n = 10 HMM n = 11
L Q L S λ 104 λ2 103K λ 104 λ2 103K
348 150 0.1552 ± 0.14% 2.2225 ± 0.30% 6.7936 ± 2.08% 0.1455 ± 0.14% 2.3813 ± 0.15% 4.9660 ± 3.82%
  200 0.1459 ± 0.22% 1.8336 ± 0.37% 5.7585 ± 3.30% 0.1417 ± 0.17% 1.8428 ± 0.35% 5.1264 ± 2.07%
  300 0.1370 ± 0.22% 1.4024 ± 0.56% 3.8087 ± 1.79% 0.1324 ± 0.27% 1.3842 ± 0.68% 3.2129 ± 2.79%
  348 0.1353 ± 0.15% 1.2962 ± 0.38% 3.5507 ± 1.68% 0.1316 ± 0.22% 1.2518 ± 0.69% 3.1546 ± 1.94%
  360 0.1343 ± 0.13% 1.2830 ± 0.36% 3.4674 ± 1.39% 0.1297 ± 0.25% 1.2737 ± 0.52% 2.9445 ± 2.81%
  400 0.1334 ± 0.16% 1.2602 ± 0.38% 3.2164 ± 1.71% 0.1302 ± 0.20% 1.2160 ± 0.56% 2.9704 ± 1.59%
  500 0.1307 ± 0.16% 1.3013 ± 0.46% 2.8331 ± 1.22% 0.1280 ± 0.30% 1.2426 ± 0.86% 2.7433 ± 2.73%
  600 0.1305 ± 0.23% 1.3097 ± 0.56% 2.8239 ± 1.82% 0.1257 ± 0.22% 1.2908 ± 0.55% 2.4921 ± 1.79%
  1. The table shows the fit parameters of the score distribution Prob(S = s| # of helices = n) for 1 ≤ n ≤ 11 for L Q = 348 and different subject lengths. For entries, where λ2 is left out, a suitable fit (with a small reduced χ2 value) to the modified Gumbel distribution Eq. (15) was not possible and only the Gumbel parameters of the high probability region are shown.