Table I.
Computational Results for 20 Core Sequence Selection Problems
| MILP solution (no. of rotamer of MILP) | |||||
|---|---|---|---|---|---|
| PDB | No. of site (no. of rotamer) | LP solution (GMEC) | N = 0, X = 0 | N = 20, X = 2 | N = 20, X = 5 |
| 1aac | 20 (1860) | −125.99 (−124.56) | −122.86 (81) | (219)a | (342)a |
| 1b9o | 23 (2139) | −149.61 (−139.69) | (48)a | (243)a | (393)a |
| 1c5e | 18 (1674) | −104.11 (−103.03) | (24)a | (173)a | (297)a |
| 1c9o | 12 (1116) | −65.73 (−64.66) | (29)a | (129)a | (210)a |
| 1cc7 | 11 (1023) | −77.11 (−68.67) | −65.21 (20) | (114)a | (183)a |
| 1cex | 50 (4650) | −263.41 (−262.26) | −261.14 (69) | (504)a | (833)a |
| 1cku | 11 (1023) | (−61.86)a | (11)a | (111)a | (193)a |
| 1ctj | 17 (1581) | (−99.14)a | (17)a | (181)a | (290)a |
| 1cz9 | 28 (2604) | −149.96 (−147.22) | −142.13 (62) | (286)a | (462)a |
| 1czp | 18 (1674) | −85.83 (−84.30) | (28)a | (162)a | (281)a |
| 1d4t | 20 (1860) | −140.72 (−124.55) | −121.94 (81) | −122.14 (226) | (351)a |
| 1igd | 10 (930) | −70.21 (−66.79) | −60.20 (20) | (108)a | (170)a |
| 1pga | 10 (930) | (−67.75)a | (10)a | (110)a | (169)a |
| 1qq4 | 40 (3720) | −217.88 (−209.39) | −202.98 (66) | (412)a | (673)a |
| 1qtn | 26 (2418) | −169.08 (−162.60) | −160.92 (58) | (282)a | (447)a |
| 1ubq | 14 (1302) | −85.45 (−76.81) | −70.19 (66) | (154)a | (239)a |
| 2pth | 45 (4185) | −235.59 (−222.16) | −216.32 (110) | (471)a | (750)a |
| 3lzt | 26 (2418) | −157.49 (−142.01) | −138.24 (49) | −141.28 (270) | (443)a |
| 5p21 | 45 (4185) | −283.16 (−269.56) | −265.37 (104) | (465)a | (760)a |
| 7rsa | 15 (1395) | −90.82 (−89.45) | −86.68 (20) | −89.39 (145) | (253)a |
a
The global minimum solution of the sequence selection problem is represented by GMEC, and the LP relaxation solution or the heuristic MILP solution is the same as the GMEC solution.
N refers to the number of top rotamers at the current design site.
X refers to the number of top rotamers having the same amino-acid type at the current design site.