TreeModel.select_features

TreeModel.select_features(df_feat=None, strategy=None, param=None)[source]

Select a subset of features from a feature DataFrame using tree-based feature importance.

This is a post-fit step that turns the signals computed by TreeModel.fit() into a row-filtered feature DataFrame: the Monte Carlo feat_importance array (for 'top_k' and 'threshold') and the per-round is_selected_ masks (for 'frequency'). The retained features are chosen by strategy, sized by the single param knob:

  • 'top_k': keep the param features with the highest feat_importance.

  • 'threshold': keep features whose feat_importance is at least param.

  • 'frequency': keep features selected in at least a param fraction of the per-round is_selected_ masks.

Recursive feature elimination (RFE) is itself not a selection strategy here: it is the TreeModel.fit() engine (use_rfe=True) that produces the per-round is_selected_ masks the 'frequency' strategy aggregates; without it every round keeps all features.

Added in version 0.1.0.

Parameters:
  • df_feat (pd.DataFrame, shape (n_features, n_feature_info)) – Feature DataFrame with a unique identifier, scale information, statistics, and positions for each feature. Rows must be aligned one-to-one with the features used in TreeModel.fit().

  • strategy (str) – The selection strategy to apply. Valid strategies are: {‘top_k’, ‘threshold’, ‘frequency’}.

  • param (int or float) – The single selection knob, whose admissible type is fixed by strategy: a positive integer number of features for 'top_k', a minimum importance (>= 0) for 'threshold', or a fraction in (0, 1] of rounds for 'frequency'.

Returns:

df_feat – Feature DataFrame filtered to the selected features, with a reset index.

Return type:

pd.DataFrame, shape (n_selected_features, n_feature_info)

Notes

  • TreeModel.fit() must be called before using this method.

  • 'frequency' without fit(use_rfe=True) selects every feature (a trivial no-op) and triggers a RuntimeWarning.

  • A selection that retains no features (e.g. a 'threshold' above every importance) raises a ValueError rather than returning an empty DataFrame.

See also

  • TreeModel.fit() for fitting the model and the use_rfe recursive feature elimination.

  • TreeModel.eval() to compare the resulting feature selection against others.

Examples

To demonstrate the TreeModel().select_features() method, we obtain the DOM_GSEC example dataset and its feature set (see [Breimann25]), create the feature matrix, and fit a TreeModel to obtain Monte Carlo feature importance:

import aaanalysis as aa
aa.options["verbose"] = False # Disable verbosity

df_seq = aa.load_dataset(name="DOM_GSEC")
labels = df_seq["label"].to_list()
df_feat = aa.load_features(name="DOM_GSEC").head(50)

# Create feature matrix and fit the model
sf = aa.SequenceFeature()
df_parts = sf.get_df_parts(df_seq=df_seq)
X = sf.feature_matrix(features=df_feat["feature"], df_parts=df_parts)

tm = aa.TreeModel(random_state=0)
tm.fit(X, labels=labels)
<aaanalysis.explainable_ai._tree_model.TreeModel at 0x1180130e0>

The 'top_k' strategy keeps the param features with the highest feature importance:

df_top10 = tm.select_features(df_feat=df_feat, strategy="top_k", param=10)
aa.display_df(df_top10)
  feature category subcategory scale_name scale_description abs_auc abs_mean_dif mean_dif std_test std_ref p_val_mann_whitney p_val_fdr_bh positions feat_importance feat_importance_std
1 TMD_C_JMD_C-Seg...3,4)-FINA910104 Conformation α-helix (C-cap) α-helix termination Helix terminati...n et al., 1991) 0.243000 0.085064 0.085064 0.098774 0.096946 0.000000 0.000000 31,32,33,34,35 0.000000 0.000000
2 TMD_C_JMD_C-Seg...3,4)-HUTJ700102 Energy Entropy Entropy Absolute entrop...Hutchens, 1970) 0.229000 0.098224 0.098224 0.106865 0.124608 0.000000 0.000001 31,32,33,34,35 3.111200 3.109955
3 TMD_C_JMD_C-Seg...6,9)-AURR980110 Conformation α-helix α-helix (middle) Normalized posi...ora-Rose, 1998) 0.211000 0.125350 0.125350 0.160819 0.174121 0.000000 0.000005 32,33 1.788800 2.700803
4 TMD_C_JMD_C-Seg...2,3)-AURR980110 Conformation α-helix α-helix (middle) Normalized posi...ora-Rose, 1998) 0.211000 0.077355 0.077355 0.102965 0.107453 0.000000 0.000005 27,28,29,30,31,32,33 3.048800 3.623912
5 TMD_C_JMD_C-Seg...2,3)-CHOP780212 Conformation β-sheet (C-term) β-turn (1st residue) Frequency of th...-Fasman, 1978b) 0.199000 0.065983 -0.065983 0.087814 0.105835 0.000000 0.000016 27,28,29,30,31,32,33 4.106000 5.236574
6 TMD_C_JMD_C-Pat...5,8)-RADA880104 Energy Free energy (unfolding) Transfer free e...(TFE) to inside Transfer free e...olfenden, 1988) 0.197000 0.060758 0.060758 0.050818 0.095267 0.000000 0.000019 25,28 1.658800 3.421774
7 TMD-Pattern(C,4,7)-RADA880104 Energy Free energy (unfolding) Transfer free e...(TFE) to inside Transfer free e...olfenden, 1988) 0.195000 0.060096 0.060096 0.050818 0.095039 0.000000 0.000023 24,27 0.000000 0.000000
8 TMD_C_JMD_C-Seg...,11)-LIFS790102 Conformation β-strand β-strand Conformational ...n-Sander, 1979) 0.189000 0.125674 0.125674 0.183876 0.218813 0.000001 0.000039 28,29 4.729200 4.776785
9 TMD_C_JMD_C-Pat...4,8)-JANJ790102 Energy Free energy (unfolding) Transfer free e...(TFE) to inside Transfer free e...y (Janin, 1979) 0.187000 0.144354 -0.144354 0.181777 0.233103 0.000001 0.000049 33,37 2.833600 3.640617
10 TMD_C_JMD_C-Pat...4,8)-KANM800103 Conformation α-helix α-helix Average relativ...sa-Tsong, 1980) 0.176000 0.087846 0.087846 0.140464 0.157561 0.000004 0.000113 24,28 2.704000 4.076269

The 'threshold' strategy keeps features whose importance is at least param:

df_thr = tm.select_features(df_feat=df_feat, strategy="threshold", param=1.0)
aa.display_df(df_thr)
  feature category subcategory scale_name scale_description abs_auc abs_mean_dif mean_dif std_test std_ref p_val_mann_whitney p_val_fdr_bh positions feat_importance feat_importance_std
1 TMD_C_JMD_C-Seg...3,4)-KLEP840101 Energy Charge Charge Net charge (Kle...n et al., 1984) 0.244000 0.103666 0.103666 0.106692 0.110506 0.000000 0.000000 31,32,33,34,35 0.970400 1.438918
2 TMD_C_JMD_C-Seg...3,4)-FINA910104 Conformation α-helix (C-cap) α-helix termination Helix terminati...n et al., 1991) 0.243000 0.085064 0.085064 0.098774 0.096946 0.000000 0.000000 31,32,33,34,35 0.000000 0.000000
3 TMD_C_JMD_C-Seg...6,9)-LEVM760105 Shape Side chain length Side chain length Radius of gyrat... (Levitt, 1976) 0.233000 0.137044 0.137044 0.161683 0.176964 0.000000 0.000001 32,33 1.554800 2.109848
4 TMD_C_JMD_C-Seg...3,4)-HUTJ700102 Energy Entropy Entropy Absolute entrop...Hutchens, 1970) 0.229000 0.098224 0.098224 0.106865 0.124608 0.000000 0.000001 31,32,33,34,35 3.111200 3.109955
5 TMD_C_JMD_C-Seg...6,9)-RADA880106 ASA/Volume Volume Accessible surface area (ASA) Accessible surf...olfenden, 1988) 0.223000 0.095071 0.095071 0.114758 0.132829 0.000000 0.000002 32,33 0.000000 0.000000
6 TMD_C_JMD_C-Seg...2,3)-KLEP840101 Energy Charge Charge Net charge (Kle...n et al., 1984) 0.222000 0.058671 0.058671 0.064895 0.069547 0.000000 0.000001 27,28,29,30,31,32,33 0.000000 0.000000
7 TMD_C_JMD_C-Seg...4,5)-FAUJ880109 Energy Isoelectric point Number hydrogen bond donors Number of hydro...e et al., 1988) 0.215000 0.146661 0.146661 0.174609 0.188034 0.000000 0.000004 33,34,35,36 1.032400 1.510722
8 TMD_C_JMD_C-Seg...3,4)-JANJ780101 ASA/Volume Accessible surface area (ASA) ASA (folded protein) Average accessi...n et al., 1978) 0.215000 0.124317 0.124317 0.166309 0.153364 0.000000 0.000004 31,32,33,34,35 1.080400 1.296094
9 TMD_C_JMD_C-Seg...,10)-WILM950103 Polarity Hydrophobicity (interface) Hydrophobicity (interface) Hydrophobicity ...e et al., 1995) 0.212000 0.141305 -0.141305 0.168603 0.217235 0.000000 0.000005 33,34 1.747200 2.150664
10 TMD_C_JMD_C-Seg...6,9)-AURR980110 Conformation α-helix α-helix (middle) Normalized posi...ora-Rose, 1998) 0.211000 0.125350 0.125350 0.160819 0.174121 0.000000 0.000005 32,33 1.788800 2.700803
11 TMD_C_JMD_C-Seg...2,3)-AURR980110 Conformation α-helix α-helix (middle) Normalized posi...ora-Rose, 1998) 0.211000 0.077355 0.077355 0.102965 0.107453 0.000000 0.000005 27,28,29,30,31,32,33 3.048800 3.623912
12 TMD_C_JMD_C-Seg...6,9)-CHOC760103 ASA/Volume Buried Buried Proportion of r...(Chothia, 1976) 0.205000 0.125868 -0.125868 0.172165 0.188333 0.000000 0.000009 32,33 0.000000 0.000000
13 TMD_C_JMD_C-Seg...4,5)-LEVM760105 Shape Side chain length Side chain length Radius of gyrat... (Levitt, 1976) 0.204000 0.105513 0.105513 0.132849 0.145219 0.000000 0.000009 33,34,35,36 1.992000 2.929460
14 TMD_C_JMD_C-Seg...6,9)-DESM900102 Polarity Amphiphilicity (α-helix) Membrane preference Average membran...i et al., 1990) 0.200000 0.132693 -0.132693 0.184359 0.209008 0.000000 0.000015 32,33 0.000000 0.000000
15 TMD_C_JMD_C-Seg...3,4)-PRAM820102 Shape Shape and Surface Slope in Regression Slope in Regres...nnuswamy, 1982) 0.199000 0.073023 -0.073023 0.087336 0.107750 0.000000 0.000017 31,32,33,34,35 0.616000 0.847660
16 TMD_C_JMD_C-Seg...2,3)-CHOP780212 Conformation β-sheet (C-term) β-turn (1st residue) Frequency of th...-Fasman, 1978b) 0.199000 0.065983 -0.065983 0.087814 0.105835 0.000000 0.000016 27,28,29,30,31,32,33 4.106000 5.236574
17 TMD_C_JMD_C-Seg...6,9)-RICJ880113 Conformation α-helix (C-cap) α-helix (C-terminal, inside) Relative prefer...chardson, 1988) 0.198000 0.138293 0.138293 0.172194 0.198814 0.000000 0.000017 32,33 0.832400 1.383718
18 TMD_C_JMD_C-Pat...5,8)-RADA880104 Energy Free energy (unfolding) Transfer free e...(TFE) to inside Transfer free e...olfenden, 1988) 0.197000 0.060758 0.060758 0.050818 0.095267 0.000000 0.000019 25,28 1.658800 3.421774
19 JMD_N_TMD_N-Seg...1,2)-KARP850101 Structure-Activity Flexibility Flexibility (0 ...igid neighbors) Flexibility par...s-Schulz, 1985) 0.196000 0.062671 0.062671 0.083456 0.090427 0.000000 0.000023 1,2,3,4,5,6,7,8,9,10 1.574400 1.835403
20 TMD-Pattern(C,4,7)-RADA880104 Energy Free energy (unfolding) Transfer free e...(TFE) to inside Transfer free e...olfenden, 1988) 0.195000 0.060096 0.060096 0.050818 0.095039 0.000000 0.000023 24,27 0.000000 0.000000
21 TMD_C_JMD_C-Seg...4,5)-RADA880106 ASA/Volume Volume Accessible surface area (ASA) Accessible surf...olfenden, 1988) 0.193000 0.076770 0.076770 0.092804 0.114150 0.000000 0.000027 33,34,35,36 0.000000 0.000000
22 TMD_C_JMD_C-Seg...4,6)-FAUJ880109 Energy Isoelectric point Number hydrogen bond donors Number of hydro...e et al., 1988) 0.192000 0.125521 0.125521 0.188795 0.177163 0.000000 0.000027 31,32,33 0.000000 0.000000
23 TMD_C_JMD_C-Seg...,11)-LIFS790102 Conformation β-strand β-strand Conformational ...n-Sander, 1979) 0.189000 0.125674 0.125674 0.183876 0.218813 0.000001 0.000039 28,29 4.729200 4.776785
24 TMD_C_JMD_C-Seg...6,9)-TANS770106 Conformation β-turn (TM helix) β-turn in double bend Normalized freq...Scheraga, 1977) 0.189000 0.093759 0.093759 0.136715 0.137320 0.000001 0.000039 32,33 0.000000 0.000000
25 TMD_C_JMD_C-Pat...4,8)-JANJ790102 Energy Free energy (unfolding) Transfer free e...(TFE) to inside Transfer free e...y (Janin, 1979) 0.187000 0.144354 -0.144354 0.181777 0.233103 0.000001 0.000049 33,37 2.833600 3.640617
26 TMD_C_JMD_C-Seg...4,5)-CHOC760103 ASA/Volume Buried Buried Proportion of r...(Chothia, 1976) 0.185000 0.105474 -0.105474 0.157535 0.163039 0.000001 0.000059 33,34,35,36 0.000000 0.000000
27 TMD_C_JMD_C-Seg...6,9)-MITS020101 Polarity Amphiphilicity Amphiphilicity Amphiphilicity ...u et al., 2002) 0.185000 0.101798 0.101798 0.145676 0.155096 0.000001 0.000054 32,33 0.000000 0.000000
28 JMD_N_TMD_N-Pat...,10)-AURR980116 Conformation α-helix (C-cap) α-helix (C-terminal, C-cap) Normalized posi...ora-Rose, 1998) 0.184000 0.112728 -0.112728 0.166431 0.183800 0.000001 0.000061 11,15 0.857600 1.339550
29 JMD_N_TMD_N-Seg...2,4)-ZHOH040101 Structure-Activity Stability Stability The stability s...hou-Zhou, 2004) 0.183000 0.063902 -0.063902 0.090842 0.101427 0.000002 0.000068 6,7,8,9,10 0.823200 1.404583
30 TMD_C_JMD_C-Seg...4,5)-RICJ880113 Conformation α-helix (C-cap) α-helix (C-terminal, inside) Relative prefer...chardson, 1988) 0.182000 0.121315 0.121315 0.147184 0.184212 0.000002 0.000070 33,34,35,36 0.865200 1.553379
31 TMD-Pattern(C,3...,15)-ANDN920101 Structure-Activity Backbone-dynamics (-CH) α-CH chemical s...kbone-dynamics) alpha-CH chemic...n et al., 1992) 0.182000 0.098529 -0.098529 0.141641 0.162412 0.000002 0.000072 16,20,24,28 0.221200 0.519240
32 TMD-Pattern(C,3...,15)-LIFS790102 Conformation β-strand β-strand Conformational ...n-Sander, 1979) 0.182000 0.096246 0.096246 0.160859 0.159538 0.000002 0.000070 16,20,24,28 0.508400 0.738667
33 JMD_N_TMD_N-Seg...2,4)-CIDH920102 Polarity Hydrophobicity Hydrophobicity Normalized hydr...d et al., 1992) 0.182000 0.066394 -0.066394 0.097857 0.103426 0.000002 0.000070 6,7,8,9,10 0.000000 0.000000
34 TMD-Pattern(N,4,7)-AURR980116 Conformation α-helix (C-cap) α-helix (C-terminal, C-cap) Normalized posi...ora-Rose, 1998) 0.181000 0.118349 -0.118349 0.169282 0.185522 0.000002 0.000078 14,17 1.226400 1.510986
35 TMD_C_JMD_C-Seg...,11)-QIAN880134 Conformation Coil Coil Weights for coi...ejnowski, 1988) 0.181000 0.057287 -0.057287 0.072234 0.106512 0.000002 0.000076 28,29 1.919600 2.094497
36 TMD_C_JMD_C-Pat...,12)-ANDN920101 Structure-Activity Backbone-dynamics (-CH) α-CH chemical s...kbone-dynamics) alpha-CH chemic...n et al., 1992) 0.180000 0.096784 -0.096784 0.151260 0.170153 0.000002 0.000084 25,29,32 0.356800 0.617224
37 TMD-PeriodicPat...3,4)-VELV850101 Energy Electron-ion interaction pot. Electron-ion in...ction potential Electron-ion in...c et al., 1985) 0.180000 0.069277 -0.069277 0.094949 0.119524 0.000002 0.000082 13,16,20,23,27 1.818000 2.308293
38 TMD_C_JMD_C-Seg...2,2)-FAUJ880109 Energy Isoelectric point Number hydrogen bond donors Number of hydro...e et al., 1988) 0.180000 0.067391 0.067391 0.098544 0.113033 0.000002 0.000080 31,32,33,34,35,36,37,38,39,40 0.635200 1.205475
39 JMD_N_TMD_N-Pat...,15)-CHAM830104 Shape Side chain length n atoms in side chain (2+1) The number of a...-Charton, 1983) 0.179000 0.115042 -0.115042 0.151938 0.189623 0.000002 0.000068 6,9,12,15 0.648400 1.061142
40 JMD_N_TMD_N-Per...4,3)-QIAN880138 Conformation Coil (C-term) Coil (C-terminal) Weights for coi...ejnowski, 1988) 0.179000 0.069852 0.069852 0.103576 0.116589 0.000003 0.000093 3,6,10,13,17,20 0.385200 0.555965
41 TMD_C_JMD_C-Pat...4,8)-KANM800103 Conformation α-helix α-helix Average relativ...sa-Tsong, 1980) 0.176000 0.087846 0.087846 0.140464 0.157561 0.000004 0.000113 24,28 2.704000 4.076269
42 TMD_C_JMD_C-Pat...,12)-FAUJ880108 Energy Electron-ion interaction pot. Electrical Effect Localized Elect...e et al., 1988) 0.176000 0.064253 -0.064253 0.092619 0.113588 0.000004 0.000113 21,24,28,32 0.826400 1.303426
43 TMD-Pattern(C,4,7)-QIAN880134 Conformation Coil Coil Weights for coi...ejnowski, 1988) 0.176000 0.056675 -0.056675 0.099355 0.114698 0.000004 0.000113 24,27 0.372000 0.882270
44 TMD_C_JMD_C-Seg...4,5)-TANS770106 Conformation β-turn (TM helix) β-turn in double bend Normalized freq...Scheraga, 1977) 0.175000 0.078020 0.078020 0.113536 0.125285 0.000005 0.000129 33,34,35,36 0.000000 0.000000
45 TMD_C_JMD_C-Seg...2,3)-WILM950103 Polarity Hydrophobicity (interface) Hydrophobicity (interface) Hydrophobicity ...e et al., 1995) 0.175000 0.055597 -0.055597 0.089100 0.105827 0.000005 0.000126 27,28,29,30,31,32,33 0.664000 1.089536
46 TMD_C_JMD_C-Seg...4,5)-YUTK870103 Energy Free energy (unfolding) Free energy (unfolding) Activation Gibb...i et al., 1987) 0.174000 0.123237 -0.123237 0.192743 0.197652 0.000005 0.000134 33,34,35,36 0.000000 0.000000

The 'frequency' strategy keeps features selected in at least param (a fraction) of the per-round masks. These masks only vary when recursive feature elimination is enabled, so fit with use_rfe=True first:

tm = aa.TreeModel(random_state=0)
tm.fit(X, labels=labels, use_rfe=True, n_feat_min=10, n_feat_max=25)
df_freq = tm.select_features(df_feat=df_feat, strategy="frequency", param=0.5)
aa.display_df(df_freq)
  feature category subcategory scale_name scale_description abs_auc abs_mean_dif mean_dif std_test std_ref p_val_mann_whitney p_val_fdr_bh positions feat_importance feat_importance_std
1 TMD_C_JMD_C-Seg...3,4)-FINA910104 Conformation α-helix (C-cap) α-helix termination Helix terminati...n et al., 1991) 0.243000 0.085064 0.085064 0.098774 0.096946 0.000000 0.000000 31,32,33,34,35 0.000000 0.000000
2 TMD_C_JMD_C-Seg...6,9)-LEVM760105 Shape Side chain length Side chain length Radius of gyrat... (Levitt, 1976) 0.233000 0.137044 0.137044 0.161683 0.176964 0.000000 0.000001 32,33 1.554800 2.109848
3 TMD_C_JMD_C-Seg...6,9)-AURR980110 Conformation α-helix α-helix (middle) Normalized posi...ora-Rose, 1998) 0.211000 0.125350 0.125350 0.160819 0.174121 0.000000 0.000005 32,33 1.788800 2.700803
4 TMD_C_JMD_C-Seg...2,3)-AURR980110 Conformation α-helix α-helix (middle) Normalized posi...ora-Rose, 1998) 0.211000 0.077355 0.077355 0.102965 0.107453 0.000000 0.000005 27,28,29,30,31,32,33 3.048800 3.623912
5 TMD_C_JMD_C-Seg...4,5)-LEVM760105 Shape Side chain length Side chain length Radius of gyrat... (Levitt, 1976) 0.204000 0.105513 0.105513 0.132849 0.145219 0.000000 0.000009 33,34,35,36 1.992000 2.929460
6 TMD_C_JMD_C-Seg...2,3)-CHOP780212 Conformation β-sheet (C-term) β-turn (1st residue) Frequency of th...-Fasman, 1978b) 0.199000 0.065983 -0.065983 0.087814 0.105835 0.000000 0.000016 27,28,29,30,31,32,33 4.106000 5.236574
7 TMD_C_JMD_C-Pat...5,8)-RADA880104 Energy Free energy (unfolding) Transfer free e...(TFE) to inside Transfer free e...olfenden, 1988) 0.197000 0.060758 0.060758 0.050818 0.095267 0.000000 0.000019 25,28 1.658800 3.421774
8 JMD_N_TMD_N-Seg...1,2)-KARP850101 Structure-Activity Flexibility Flexibility (0 ...igid neighbors) Flexibility par...s-Schulz, 1985) 0.196000 0.062671 0.062671 0.083456 0.090427 0.000000 0.000023 1,2,3,4,5,6,7,8,9,10 1.574400 1.835403
9 TMD-Pattern(C,4,7)-RADA880104 Energy Free energy (unfolding) Transfer free e...(TFE) to inside Transfer free e...olfenden, 1988) 0.195000 0.060096 0.060096 0.050818 0.095039 0.000000 0.000023 24,27 0.000000 0.000000
10 TMD_C_JMD_C-Seg...,11)-LIFS790102 Conformation β-strand β-strand Conformational ...n-Sander, 1979) 0.189000 0.125674 0.125674 0.183876 0.218813 0.000001 0.000039 28,29 4.729200 4.776785
11 TMD_C_JMD_C-Pat...4,8)-JANJ790102 Energy Free energy (unfolding) Transfer free e...(TFE) to inside Transfer free e...y (Janin, 1979) 0.187000 0.144354 -0.144354 0.181777 0.233103 0.000001 0.000049 33,37 2.833600 3.640617
12 TMD_C_JMD_C-Seg...4,5)-RICJ880113 Conformation α-helix (C-cap) α-helix (C-terminal, inside) Relative prefer...chardson, 1988) 0.182000 0.121315 0.121315 0.147184 0.184212 0.000002 0.000070 33,34,35,36 0.865200 1.553379
13 TMD_C_JMD_C-Seg...,11)-QIAN880134 Conformation Coil Coil Weights for coi...ejnowski, 1988) 0.181000 0.057287 -0.057287 0.072234 0.106512 0.000002 0.000076 28,29 1.919600 2.094497
14 TMD-PeriodicPat...3,4)-VELV850101 Energy Electron-ion interaction pot. Electron-ion in...ction potential Electron-ion in...c et al., 1985) 0.180000 0.069277 -0.069277 0.094949 0.119524 0.000002 0.000082 13,16,20,23,27 1.818000 2.308293
15 TMD_C_JMD_C-Pat...4,8)-KANM800103 Conformation α-helix α-helix Average relativ...sa-Tsong, 1980) 0.176000 0.087846 0.087846 0.140464 0.157561 0.000004 0.000113 24,28 2.704000 4.076269