Table I. Orientational entropy, –ln faa, in kB units for each residue pair (a,a); a (a) is shown in each row (column), r is for all types of residues, and the parameters used are l = l = k = 6, Ocutoff = 1792, = 0.2, and ccutoff = 0.025.
	C	M	F	I	L	V	W	Y	A	G	T	S	Q	N	E	D	H	R	K	P	r
C	3.97	4.06	4.52	4.31	4.54	4.33	3.62	4.33	4.38	4.74	4.40	4.43	4.02	4.25	3.96	4.00	3.96	4.26	4.01	4.50	5.12
M	4.07	4.47	4.69	4.44	4.58	4.45	4.23	4.64	4.50	4.88	4.48	4.57	4.24	4.42	4.15	4.16	4.21	4.35	4.04	4.78	4.97
F	4.51	4.71	4.92	4.73	4.88	4.68	4.55	4.86	4.84	5.09	4.82	4.83	4.51	4.82	4.60	4.60	4.60	4.67	4.50	4.90	5.16
I	4.31	4.45	4.72	4.38	4.52	4.34	4.42	4.66	4.36	4.91	4.47	4.57	4.27	4.47	4.13	4.27	4.34	4.44	4.10	4.82	4.77
L	4.53	4.57	4.88	4.52	4.68	4.55	4.60	4.78	4.43	5.01	4.62	4.64	4.35	4.65	4.20	4.41	4.68	4.56	4.28	5.06	4.86
V	4.31	4.46	4.69	4.33	4.55	4.21	4.53	4.65	4.33	4.90	4.44	4.55	4.43	4.60	4.22	4.28	4.43	4.48	4.16	4.80	4.78
W	3.59	4.23	4.53	4.43	4.59	4.53	3.87	4.46	4.78	4.79	4.46	4.51	4.06	4.27	4.29	4.40	4.09	4.28	4.01	4.56	5.21
Y	4.34	4.61	4.85	4.63	4.74	4.62	4.44	4.87	4.85	5.11	4.78	4.80	4.46	4.86	4.76	4.91	4.71	4.66	4.38	4.88	5.23
A	4.34	4.50	4.85	4.33	4.42	4.29	4.76	4.85	3.76	4.88	4.46	4.45	4.37	4.52	4.10	4.05	4.60	4.53	4.20	4.96	4.78
G	4.70	4.88	5.12	4.89	4.98	4.88	4.84	5.13	4.88	5.47	5.12	5.31	5.00	5.30	4.90	4.95	5.06	5.22	4.97	5.35	5.61
T	4.37	4.46	4.82	4.44	4.62	4.44	4.44	4.80	4.46	5.13	4.23	4.54	4.19	4.63	3.95	4.16	4.52	4.62	4.16	4.91	4.95
S	4.42	4.56	4.87	4.56	4.62	4.54	4.50	4.82	4.41	5.30	4.54	4.67	4.42	4.78	4.24	4.33	4.59	4.76	4.48	4.98	5.09
Q	4.02	4.20	4.51	4.21	4.31	4.38	4.07	4.47	4.36	5.02	4.19	4.39	4.15	4.39	3.84	4.03	4.32	4.27	3.91	4.72	4.86
N	4.23	4.41	4.84	4.48	4.61	4.58	4.30	4.85	4.52	5.28	4.65	4.77	4.39	4.84	4.28	4.45	4.59	4.71	4.36	4.97	5.22
E	3.96	4.12	4.59	4.12	4.19	4.18	4.29	4.81	4.10	4.93	3.95	4.22	3.81	4.29	3.72	3.83	4.58	4.39	4.06	4.54	4.71
D	3.96	4.14	4.61	4.24	4.38	4.28	4.42	4.95	4.06	4.95	4.14	4.32	4.03	4.44	3.83	4.13	4.71	4.85	4.46	4.67	4.95
H	3.98	4.20	4.58	4.33	4.66	4.43	4.09	4.73	4.60	5.07	4.51	4.53	4.30	4.60	4.58	4.71	4.40	4.44	4.18	4.63	5.27
R	4.26	4.36	4.68	4.42	4.55	4.46	4.31	4.72	4.54	5.25	4.63	4.75	4.27	4.73	4.37	4.87	4.47	4.66	4.05	4.88	5.08
K	3.97	4.06	4.51	4.09	4.26	4.15	3.99	4.42	4.22	5.00	4.19	4.49	3.94	4.38	4.06	4.48	4.18	4.07	3.85	4.53	4.81
P	4.47	4.76	4.94	4.80	5.06	4.79	4.59	4.91	4.97	5.35	4.89	4.96	4.76	5.00	4.58	4.66	4.68	4.89	4.54	5.19	5.48
r	5.11	4.97	5.15	4.77	4.86	4.77	5.21	5.24	4.78	5.61	4.96	5.09	4.88	5.23	4.72	4.96	5.26	5.08	4.81	5.48	5.18

First citation in article

Table II. Dependencies of the performance of fold recognition on the resolution of the orientational potential; dependencies on polar or Euler angles.
(a) Dependencies on polar angles
l	ccutoff	l = k = 0, = 0.2, Ocutoff =
		79 monomeric decoy sets				81 Ig decoy sets
		No. of tops				No. of tops
4	0.0	23	–2.79	–2.09	–1.41	29	–2.66	–1.88	–1.45
	0.025	22	–2.77	–2.02	–1.41	28	–2.67	–1.82	–1.45
5	0.0	31	–3.35	–2.57	–1.84	31	–2.68	–1.96	–1.46
	0.025	31	–3.37	–2.57	–1.84	30	–2.66	–1.93	–1.45
6	0.0	27	–3.23	–2.55	–1.77	34	–2.69	–2.19	–1.45
	0.025	28	–3.24	–2.58	–1.76	34	–2.68	–2.16	–1.44
7	0.0	30	–3.45	–2.60	–1.98	45	–2.93	–2.52	–1.57
	0.025	31	–3.46	–2.60	–1.98	45	–2.94	–2.53	–1.58
8	0.0	28	–3.37	–2.59	–1.91	38	–2.73	–2.24	–1.48
	0.025	27	–3.36	–2.55	–1.89	39	–2.74	–2.27	–1.49
9	0.0	25	–3.38	–2.43	–1.92	32	–2.66	–2.06	–1.54
	0.025	24	–3.36	–2.44	–1.90	33	–2.68	–2.08	–1.56
10	0.0	27	–3.32	–2.55	–1.83	37	–2.55	–2.13	–1.52
	0.025	26	–3.31	–2.49	–1.82	36	–2.52	–2.14	–1.55
11	0.0	28	–3.44	–2.67	–1.94	39	–2.68	–2.16	–1.71
	0.025	30	–3.48	–2.82	–1.92	39	–2.67	–2.18	–1.72
12	0.0	25	–3.29	–2.45	–1.78	41	–2.70	–2.29	–1.76
	0.025	24	–3.30	–2.50	–1.77	40	–2.70	–2.29	–1.77
13	0.0	30	–3.39	–2.73	–1.80	39	–2.80	–2.19	–1.83
	0.025	29	–3.38	–2.73	–1.80	40	–2.80	–2.20	–1.83
14	0.0	31	–3.42	–2.89	–1.84	46	–2.87	–2.48	–1.91
	0.025	30	–3.44	–2.82	–1.82	47	–2.89	–2.53	–1.89
(b) Dependencies on Euler angles
l k	ccutoff	l = 0, = 0.2, Ocutoff =
		79 monomeric decoy sets				81 Ig decoy sets
		No. of tops				No. of tops
4	0.0	25	–3.18	–2.68	–1.78	33	–2.63	–2.26	–1.31
	0.025	25	–3.14	–2.71	–1.75	33	–2.61	–2.31	–1.29
5	0.0	25	–3.26	–2.79	–1.77	44	–2.85	–2.55	–1.65
	0.025	26	–3.23	–2.80	–1.74	44	–2.84	–2.58	–1.61
6	0.0	26	–3.25	–2.79	–1.83	47	–3.04	–2.78	–1.84
	0.025	24	–3.20	–2.57	–1.81	45	–3.00	–2.79	–1.77
7	0.0	30	–3.31	–2.84	–1.88	52	–3.03	–2.94	–1.82
	0.025	28	–3.24	–2.70	–1.83	52	–3.02	–2.92	–1.73

First citation in article

Table III. Dependencies of the performance of fold recognition on the resolution of the orientational potential; interdependencies between polar and Euler angles.
(a) Dependencies on lmax and cutoff Ocutoff
l	Ocutoff	l = k = l, = 0.2, ccutoff = 0.025
		79 monomeric decoy sets				81 Ig decoy sets
		No. of tops				No. of tops
4	960	34	–3.72	–3.24	–2.18	47	–2.97	–2.81	–1.59
	1792	36	–3.77	–3.27	–2.21	47	–3.01	–2.79	–1.67
5	960	36	–3.82	–3.38	–2.27	56	–3.18	–3.02	–1.81
	1792	38	–3.87	–3.22	–2.33	55	–3.23	–2.92	–1.96
6	960	37	–3.83	–3.33	–2.32	60	–3.24	–3.23	–1.92
	1792	37	–3.88	–3.22	–2.38	59	–3.27	–3.11	–2.00
	2025	38	–3.85	–3.25	–2.36	56	–3.21	–3.05	–1.99
7	64	27	–3.53	–2.95	–1.93	30	–2.63	–2.04	–1.46
	960	36	–3.85	–3.22	–2.34	57	–3.22	–3.11	–1.93
	1792	38	–3.91	–3.31	–2.42	53	–3.20	–2.94	–2.02
	2025	37	–3.87	–3.29	–2.40	54	–3.20	–3.02	–2.04
(b) Dependencies on cutoff ccutoff
		l = k = l, = 0.2, Ocutoff = 960
l	ccutoff	79 monomeric decoy sets				81 Ig decoy sets
		No. of tops				No. of tops
5	0.0	35	–3.81	–3.33	–2.27	55	–3.17	–2.96	–1.83
	0.025	36	–3.82	–3.38	–2.27	56	–3.18	–3.02	–1.81
6	0.0	34	–3.80	–3.24	–2.32	60	–3.26	–3.25	–1.95
	0.025	37	–3.83	–3.33	–2.32	60	–3.24	–3.23	–1.92
7	0.0	34	–3.82	–3.11	–2.33	59	–3.25	–3.17	–1.96
	0.025	36	–3.85	–3.22	–2.34	57	–3.22	–3.11	–1.93
l	ccutoff	l = k = l, = 0.2, Ocutoff = 1792
5	0.0	38	–3.88	–3.30	–2.34	56	–3.23	–2.93	–1.96
	0.025	38	–3.87	–3.22	–2.33	55	–3.23	–2.92	–1.96
6	0.0	37	–3.87	–3.35	–2.40	60	–3.28	–3.14	–2.01
	0.025	37	–3.88	–3.22	–2.38	59	–3.27	–3.11	–2.00
7	0.0	39	–3.92	–3.27	–2.43	55	–3.20	–3.05	–2.05
	0.025	38	–3.91	–3.31	–2.42	53	–3.20	–2.94	–2.02
(c) Dependencies on a parameter for small sample correction,
		l = l = k = 6, ccutoff = 0.025
Ocutoff		79 monomeric decoy sets				81 Ig decoy sets
		No. of tops				No. of tops
960	0.1	35	–3.82	–3.26	–2.32	60	–3.25	–3.23	–1.93
	0.2	37	–3.83	–3.33	–2.32	60	–3.24	–3.23	–1.92
	1	34	–3.78	–3.23	–2.28	58	–3.22	–3.19	–1.89
1792	0.1	36	–3.86	–3.15	–2.39	59	–3.27	–3.11	–2.00
	0.2	37	–3.88	–3.22	–2.38	59	–3.27	–3.11	–2.00
	1	36	–3.85	–3.18	–2.34	57	–3.24	–3.05	–1.97

First citation in article

Table IV. Performance of each potential component in fold recognition.

(a) For the 79 monomeric decoy sets

Potentialsa

No. of top ranks

Mean

Mean

Mean

Mean

Median

Median

Mean

e

e

eo

er

es

Total No. = 79

Ze

Zrmsd

b

eo

37

–3.88

–3.22

–2.38

–2.49

–2.09

–1.65

0.33

eo

+

er

35

–3.79

–3.08

–2.32

–2.33

–2.01

–1.49

0.33

eo

+

es

53

–4.00

–3.99

–2.96

–3.13

–3.22

–2.59

0.35

eo

+

er

+

es

53

–3.98

–3.99

–2.93

–3.13

–3.16

–2.59

0.34

ec

36

–4.12

–3.20

–2.56

–2.12

–2.37

–1.63

0.33

ec

+

er

41

–3.90

–3.12

–2.23

–2.03

–2.04

–1.74

0.32

ec

+

eo

52

–4.53

–4.24

–3.18

–3.19

–2.79

–2.60

0.37

ec

+

eo

+

er

52

–4.38

–4.04

–2.95

–3.01

–2.54

–2.50

0.37

ec

+

eo

+

es

58

–4.25

–4.30

–3.51

–3.38

–3.48

–3.04

0.37

ec

+

eo

+

er

+

es

57

–4.15

–4.24

–3.35

–3.35

–3.17

–2.80

0.37

e

+

ec

36

–4.05

–3.29

–2.68

–2.32

–2.61

–1.86

0.32

e

+

ec

+

er

38

–4.18

–3.50

–2.53

–2.50

–2.49

–2.14

0.32

e

+

ec

+

eo

58

–4.79

–4.88

–4.38

–3.92

–4.08

–3.55

0.40

e

+

ec

+

eo

+

er

57

–4.73

–4.69

–4.13

–3.74

–3.76

–3.41

0.40

e

+

ec

+

eo

+

es

61

–4.63

–4.63

–4.45

–3.68

–4.11

–3.41

0.39

e

+

ec

+

eo

+

er

+

es

59

–4.49

–4.49

–4.21

–3.56

–3.86

–3.10

0.39

(b) For the 81 immunogloblin decoy sets

Potentialsa

No. of top ranks

Mean

Mean

Mean

Mean

Median

Median

Mean

e

e

eo

er

es

Total No. = 81

Ze

Zrmsd

b

eo

59

–3.27

–3.11

–2.00

–2.74

–2.03

–2.55

0.38

eo

+

er

62

–3.35

–3.23

–2.15

–2.85

–2.27

–2.61

0.36

eo

+

es

67

–3.36

–3.42

–3.14

–3.00

–3.27

–2.69

0.39

eo

+

er

+

es

68

–3.38

–3.46

–3.29

–3.03

–3.44

–2.71

0.37

ec

6

–1.55

–1.38

–0.52

–0.65

–0.51

–0.47

0.38

ec

+

er

36

–2.78

–2.29

–1.02

–1.70

–0.95

–1.15

0.29

ec

+

eo

57

–3.20

–3.09

–1.57

–2.70

–1.55

–2.53

0.44

ec

+

eo

+

er

63

–3.39

–3.35

–1.82

–2.95

–1.79

–2.67

0.40

ec

+

eo

+

es

68

–3.36

–3.50

–2.53

–3.09

–2.44

–2.69

0.43

ec

+

eo

+

er

+

es

69

–3.39

–3.52

–2.81

–3.09

–2.81

–2.71

0.40

e

+

ec

0

–0.40

–1.33

0.54

–0.46

0.44

–0.49

0.35

e

+

ec

+

er

0

–0.44

–1.29

0.35

–0.50

0.24

–0.49

0.32

e

+

ec

+

eo

19

–2.11

–2.08

–0.86

–1.26

–0.89

–0.79

0.50

e

+

ec

+

eo

+

er

44

–2.82

–2.81

–1.20

–2.22

–1.25

–2.13

0.48

e

+

ec

+

eo

+

es

55

–3.00

–3.10

–1.83

–2.63

–1.94

–2.53

0.49

e

+

ec

+

eo

+

er

+

es

61

–3.24

–3.31

–2.25

–2.82

–2.34

–2.61

0.46

a The orientational energies used above are calculated with l = l = k = 6, Ocutoff = 1792, = 0.2, and ccutoff = 0.025.

b R is the correlation coefficient of rank order between the energies and RMSDs of decoys in a decoy set.

First citation in article

Table V. The performance of scoring functions for each family of protein decoy sets.
Decoy ID range, decoy family potentials	No. of tops /Total No.	Mean	Mean	Mean a
1-7 4state_reduced: seven decoy sets
(e + ec + eo + es)b	7/7	–6.50	–4.44	0.66
Fain et al. (2002)c	1/7	–4.45	–2.3	0.52
Toby and Elber (2000)d	3/6	–5.42	–3.14
Samudrala and Moult (1998)e	6/7	–6.06	–2.67	0.67
Onizuka et al. (2002)f	7/7	–6.50	–3.41
Dominy and Brooks (2002)g	~7/7	~–6.5	–3.4	0.55
8–11 fisa: four decoy sets
(e + ec + eo + es)b	2/4	–4.04	–2.55	0.26
Toby and Elbner (2000)d	2/3		–3.34
Onizuka et al. (2002)f	1/3		–1.38
12–16 fisa_casp3: five decoy sets
(e + ec + eo + es)b	2/5	–5.38	–3.61	0.16
Toby and Elber (2000)d	1/3		–3.94
Onizuka et al. (2002)f	1/3		–2.01
17–45 hg_structal: 29 decoy sets
(e + ec + eo + es)b	22/29	–2.76	–2.62	0.72
Dominy and Brooks (2002)g	19/29		–2.0	0.69
46–53 lattice_ssfit: eight decoy sets
(e + ec + eo + es)b	8/8	–7.60	–11.12	–0.01
Fain et al. (2002)c	8/8	–7.60	–6.84
Toby and Elber (2000)d	4/6	–6.89	–4.10
Samudrala and Moult (1998)e	8/8	–7.60	–6.46
Onizuka et al. (2002)f	6/6	–7.60	–6.22
54–63 lmds: ten decoy sets
(e + ec + eo + es)b	8/10	–4.89	–5.34	0.14
Fain et al. (2002)c	3/9	–4.55	–2.83
Toby and Elber (2000)d	4/7	–5.32	–3.27
Samudrala and Moult (1998)e	3/9	–3.04	–0.58
Onizuka et al. (2002)f	5/7	–5.00	–3.67
64–73 lmds_v2: ten decoy sets
(e + ec + eo + es)b	8/10	–3.85	–5.03	0.18
Fain et al. (2002)c	1/2	–4.81	–3.15
Samudrala and Moult (1998)e	1/2	–4.47	–3.05
74–79 semfold: six decoy sets
(e + ec + eo + es)b	4/6	–8.13	–3.86	0.08
1–61 ig_structal: 61 dcoy sets
(eo + er + es)b	49/61	–3.55	–2.96	0.36
62–81 ig_structal_hires: 20 decoy sets
(eo + er + es)b	19/20	–2.86	–4.31	0.43
a R is the correlation coefficient of rank order between the energies and RMSDs of decoys in a decoy set.
b The present model; the orientational energies were calculated with l = l = k = 6, Ocutoff = 1792, = 0.2, and ccutoff = 0.025.
c Reference 25.
d Reference 24.
e Reference 13; taken from Ref. 25.
f Reference 33; the distance-dependent angular potential named 3C326.
g Reference 18; generalized Born, Coulomb, nonpolar solvation, and van der Waals energy terms are included.

First citation in article