features(analysis:...

Features Analysis: Backrub Ensemble Bond Angles

Matthew O’Meara

RosettaCon 2012

backbone, but side-chains were allowed to changerotameric conformations during the simulations.The results for each protein are evaluated by thecorrelation coefficient (r) between experimental(S2exp) and calculated (S2calc) side-chain orderparameters, and the root-mean-squared deviation(rmsd) between them. Additionally, we measuredhow often we correctly model the qualitativerigidity or flexibility of a side-chain dihedral angle.

The results from Model 1 (Fig. 2) and the work ofothers5,21,24 provide a useful distinction between“rigid” and “flexible” side-chain dihedrals, as theyindicate that methyl groups with order parametersabove 0.7–0.8 are likely to sample a single rotamericwell, and methyl groups with order parametersbelow this threshold are likely to switch betweenmultiple rotameric states. When sampling within thenative rotamer well on a fixed backbone, 95% of

0.8

0.0

0.2

0.4

0.6

1.0

S2

Model 1 C!

Model 1* C!

Model 3 C!

Experimental C

!

Model 1 C"

Model 1* C"

Model 3 C"

Experimental C

"

Fig. 2. Side-chain motionswithin the native rotamer well donot sample the conformational flex-ibility observed in methyl relaxa-tion experiments. The box plotsrepresent the distributions of orderparameters for C! and C" methylgroups from different models andfrom the experimental measure-ments. White boxes: native rotamermotions on a fixed backbone(Model 1) or on an ensemble ofbackbones (generated using Back-rub Monte Carlo simulations thatkept the side-chains in their nativerotamer well, Model 1*). Gray

boxes: results from Model 3 simulations, using an ensemble of backbone conformations and allowing multiple rotamericstates. Black boxes: experimental relaxation measurements. The boxes represent the middle 25–75% of the values; thehorizontal bar inside the box is the median value; the “whiskers” extending out of the box cover !1.5 times the range ofthe box (or up to the furthest data point); dashes outside of the whiskers represent outliers.

Model 1Motions in the native rotamer

well on a fixed backbone

Find the native rotamer for

each residue from the X-ray

structure

Add nearby conformers

around each base rotamer

Sample side chains with Monte Carlo

Model 2Motions in

multiplerotamer wells

on a fixedbackbone

Find base rotamers for each residue

from PDB statistics

Model 3Motions in

multiple rotamer wells on a

flexiblebackbone

Generate 10 backbones

with Backrub simulations

C

N Ca

Ca

O

H

Mobile Atoms

Rotation Axis

CN

Ca

O

H

CN

Ca

O

H Mobile Atoms

Rotation Axis

Ca

(c)

(a) (b)

Fig. 1. Computational strategy and motional models. (a) Flowchart of the methods used for the three models ofmotion. Schematic of dipeptide (b) and tripeptide (c) Backrub conformational changes used to model backbone changes inModel 3. The Backrub motion consists of a rigid body rotation of all atoms between two 2 C# atoms, about the axisconnecting the C# atoms. This rotation is followed by optimization of bond angles involving the endpoint C# atoms (seeMaterials and Methods).

760 A Simple Model of Backbone Flexibility

Friedland JMB 2008

5

Supplemental Figures

A

0 2 4 6 8 10

0.0

0.1

0.2

0.3

0.4

Acceptance Ratio vs. Max Bond Angle Deviation

Maximum Deviation from Ideal Bond Angle (°)

Accepta

nce R

atio

B

0 10 20 30 40

0.0

0.2

0.4

0.6

0.8

Acceptance Ratio vs. Anglular Displacement

Anglular Displacement (°)

Accepta

nce R

atio

2 Residues

3 Residues

4 Residues

5 Residues

6 Residues

7 Residues

8 Residues

9 Residues

10 Residues

11 Residues

12 Residues

C

2 4 6 8 10 12

020

40

60

80

! Interval Length vs. Backrub Segment Length

Number of Residues

Mean !

Inte

rval Length

(!)

D

2 4 6 8 10 12

0.0

0.1

0.2

0.3

Acceptance Ratio vs. # Rotamer Swaps

Number of Residues

Accepta

nce R

atio

No Rotamers

1 Rotamer

2 Rotamers

Supplemental Figure 1. Constraining both the bond angles and degree of rotation helps maintain relatively high acceptance ratios under many conditions. Monte Carlo acceptance statistics were gathered using a 106 step simulation of the Erbin PDZ domain (PDB 2H3L; Appleton 2006) using Amber bond angle parameters at kT = 0.6. A) For every step, the maximum deviation of the N-C$-C bond angle ($) from ideal ($ideal, composite !0 from Supplemental Table 1) was determined prior to evaluating the acceptance criterion. (For a move about residues i and j, max(|$i - $ideal|, |$j - $ideal|).) The acceptance remains relatively high (6.6%), even when there is a 10° strain in one of the bond angles. B) The acceptance ratio is highly dependent on both the magnitude of the rotational angular displacement (%) and segment size. Two residue moves, corresponding to peptide plane rotations, are significantly more flexible than larger moves. C) Simply limiting bond angles to within 10° from ideal and ignoring non-covalent forces, peptide bonds (size = 2) have significantly greater rotational freedom than other segment sizes. % interval lengths (the total length of Ibond angle & [-90°, 90°]) were calculated for all 2-12 residue segments of PDB 2H3L. D) Limiting the extent of angular displacement for longer segments allows the acceptance ratio to remain reasonably high (>23% for backbone only moves, red), regardless of the segment length.

Smith JMB 2008

“Ideal” Bond Angles

the atoms in two complete peptide units, and the data setincluded the bond lengths and bond angles for the peptide unitsuniquely identified by whether they mostly involve atoms fromresidue !1, 0, or +1 in the 3-residue segment (Figure 1). Basedon previous work (Karplus, 1996) indicating distinct geometricbehavior of Gly, Pro, the b-branched residues Ile and Val (Thrbehaves more like a general residue because of stabilizingsidechain-backbone hydrogen bonds), and residues precedingproline (pre-Pro), we carried out separate statistical analysesfor those five groups. The data set used here included 1,379Gly, 639 Pro, 511 general pre-Pro (644 before exclusion ofGly/Pro/Ile/Val), 1,822 Ile/Val, and 10,921 general residues (the16 other residue types taken together). All pre-Pro residues areexcluded from the other classes. As seen in Figure 2, these resi-dues were distributed in F,J as has been seen for many well-filtered data sets (Karplus, 1996; Kleywegt and Jones, 1996,Lovell et al., 2003). Figure 2 also provides the shorthand nomen-clature we will use for certain regions of the Ramachandran plot.

We analyzed these results to visualize and to document theF,J-dependent variations in bond lengths and angles. Ourapproach was to use kernel-regression methods to smooth thedata and to produce continuously variable functions for eachparameter (see Experimental Procedures). The figures andtables in this paper are based on the kernel-regression analysisand only include regions of the Ramachandran plot having anobservation density of at least 0.03 residues/degree2 (i.e., 3 resi-dues in a 10" 3 10" area) and a finite standard error of the mean.

Ubiquitous, Systematic, F,J-Dependent VariationsExist in Peptide GeometryBond AnglesThe data reveal that for general residues, all 15 bond angles inthe two peptides adjacent to the central residue vary systemat-ically with F and J (Figure 3 and Table 1). The most prominentobservation is that the variations do not occur only in rare outlierconformations, but they occur throughout even the most popu-lated areas of the plot for all residue types (Figure 3; see FiguresS1–S4 available online). Consistent with the lower-resolution

analysis (Karplus, 1996), :NCaC varies the most (6.5"), butfour other angles also vary by R 5". An important differencefrom the results of the earlier study is that the conformation-dependent standard deviations of the bond angles are abouthalf what was seen previously (Karplus, 1996), ranging from1.3"–1.8" (Table 1). These are also substantially smaller thanthe standard deviations of #2.5" used for the single ideal valuesdefined by Engh and Huber (1991) based on small-moleculestructures. It is notable that ultrahigh-resolution crystal struc-tures are generally refined using geometric restraints that donot match the local averages, so the narrow (small s) distribu-tions cannot be an artifact of the restraints used. Interestingly,the variations in the averages are 2–4 times the standard devia-tions (Table 1), implying that current modeling restraints wouldwork to wrongly pull angles away from their actual optimal valuesin many regions. Dramatically, the distributions at the extremescan even be completely nonoverlapping because of the smallstandard deviations (Figure 4). The standard errors of the F,J-dependent means (i.e., s/ON) for bond angles are less than0.5" in nearly all regions and typically less than 0.2" in the highlypopulated regions (Figures S5–S9)—however, errors should beconsidered when examining averages for the lowest-populatededges and other regions, such as the pre-Pro region for generalresidues. In comparison, the 2"–7" ranges seen for the expectedvalues are 10–50 times greater than their uncertainties. Thisshows that the variations are well-determined and backbonegeometry in no way obeys the single ideal value paradigm.Bond LengthsIn the 1996 study, the resolution of the data did not allow reliablevisualization of bond-length variations. Here at atomic resolu-tion, systematic F,J-dependent trends are now visible in bondlengths (Figure 5) but the variation ranges (0.01–0.02 A) areonly on par with the standard deviations (0.012–0.016 A),meaning the distributions are highly overlapping. The standarderrors of the mean are smaller (#0.002 A), so the variations inthe means seen are nevertheless significant (#10-fold larger).Given that the standard deviations are on par with the expectedcoordinate accuracy, we hypothesize that the true underlying

Figure 1. Evolution of the Ideal Values for Backbone Geometry Used in the Single-Value ParadigmA central residue (residue 0) is shown with atoms from residues !1 and +1 that contribute to its two adjacent peptide units. For each of the seven bond angles

associated with residue 0, three ideal values from earlier work are shown from oldest (top) to most recent (bottom). They are from Corey and Donohue (1950),

Engh and Huber (1991), and Engh and Huber (2001). Most refinement and modeling programs use one of the Engh and Huber sets or a slight variation on them.

Rotatable bonds defining the backbone torsion angles F and J are indicated. Figure created with Inkscape.

Structure

Conformation Dependence of Backbone Geometry

Structure 17, 1316–1325, October 14, 2009 ª2009 Elsevier Ltd All rights reserved 1317

Berkholz Structure 2009

the atoms in two complete peptide units, and the data setincluded the bond lengths and bond angles for the peptide unitsuniquely identified by whether they mostly involve atoms fromresidue !1, 0, or +1 in the 3-residue segment (Figure 1). Basedon previous work (Karplus, 1996) indicating distinct geometricbehavior of Gly, Pro, the b-branched residues Ile and Val (Thrbehaves more like a general residue because of stabilizingsidechain-backbone hydrogen bonds), and residues precedingproline (pre-Pro), we carried out separate statistical analysesfor those five groups. The data set used here included 1,379Gly, 639 Pro, 511 general pre-Pro (644 before exclusion ofGly/Pro/Ile/Val), 1,822 Ile/Val, and 10,921 general residues (the16 other residue types taken together). All pre-Pro residues areexcluded from the other classes. As seen in Figure 2, these resi-dues were distributed in F,J as has been seen for many well-filtered data sets (Karplus, 1996; Kleywegt and Jones, 1996,Lovell et al., 2003). Figure 2 also provides the shorthand nomen-clature we will use for certain regions of the Ramachandran plot.

We analyzed these results to visualize and to document theF,J-dependent variations in bond lengths and angles. Ourapproach was to use kernel-regression methods to smooth thedata and to produce continuously variable functions for eachparameter (see Experimental Procedures). The figures andtables in this paper are based on the kernel-regression analysisand only include regions of the Ramachandran plot having anobservation density of at least 0.03 residues/degree2 (i.e., 3 resi-dues in a 10" 3 10" area) and a finite standard error of the mean.

Ubiquitous, Systematic, F,J-Dependent VariationsExist in Peptide GeometryBond AnglesThe data reveal that for general residues, all 15 bond angles inthe two peptides adjacent to the central residue vary systemat-ically with F and J (Figure 3 and Table 1). The most prominentobservation is that the variations do not occur only in rare outlierconformations, but they occur throughout even the most popu-lated areas of the plot for all residue types (Figure 3; see FiguresS1–S4 available online). Consistent with the lower-resolution

analysis (Karplus, 1996), :NCaC varies the most (6.5"), butfour other angles also vary by R 5". An important differencefrom the results of the earlier study is that the conformation-dependent standard deviations of the bond angles are abouthalf what was seen previously (Karplus, 1996), ranging from1.3"–1.8" (Table 1). These are also substantially smaller thanthe standard deviations of #2.5" used for the single ideal valuesdefined by Engh and Huber (1991) based on small-moleculestructures. It is notable that ultrahigh-resolution crystal struc-tures are generally refined using geometric restraints that donot match the local averages, so the narrow (small s) distribu-tions cannot be an artifact of the restraints used. Interestingly,the variations in the averages are 2–4 times the standard devia-tions (Table 1), implying that current modeling restraints wouldwork to wrongly pull angles away from their actual optimal valuesin many regions. Dramatically, the distributions at the extremescan even be completely nonoverlapping because of the smallstandard deviations (Figure 4). The standard errors of the F,J-dependent means (i.e., s/ON) for bond angles are less than0.5" in nearly all regions and typically less than 0.2" in the highlypopulated regions (Figures S5–S9)—however, errors should beconsidered when examining averages for the lowest-populatededges and other regions, such as the pre-Pro region for generalresidues. In comparison, the 2"–7" ranges seen for the expectedvalues are 10–50 times greater than their uncertainties. Thisshows that the variations are well-determined and backbonegeometry in no way obeys the single ideal value paradigm.Bond LengthsIn the 1996 study, the resolution of the data did not allow reliablevisualization of bond-length variations. Here at atomic resolu-tion, systematic F,J-dependent trends are now visible in bondlengths (Figure 5) but the variation ranges (0.01–0.02 A) areonly on par with the standard deviations (0.012–0.016 A),meaning the distributions are highly overlapping. The standarderrors of the mean are smaller (#0.002 A), so the variations inthe means seen are nevertheless significant (#10-fold larger).Given that the standard deviations are on par with the expectedcoordinate accuracy, we hypothesize that the true underlying

Figure 1. Evolution of the Ideal Values for Backbone Geometry Used in the Single-Value ParadigmA central residue (residue 0) is shown with atoms from residues !1 and +1 that contribute to its two adjacent peptide units. For each of the seven bond angles

associated with residue 0, three ideal values from earlier work are shown from oldest (top) to most recent (bottom). They are from Corey and Donohue (1950),

Engh and Huber (1991), and Engh and Huber (2001). Most refinement and modeling programs use one of the Engh and Huber sets or a slight variation on them.

Rotatable bonds defining the backbone torsion angles F and J are indicated. Figure created with Inkscape.

Structure

Conformation Dependence of Backbone Geometry

Structure 17, 1316–1325, October 14, 2009 ª2009 Elsevier Ltd All rights reserved 1317

= =

=

=

=

=

=


Native Data

•  Richardson Lab: Top8000 Chains – 70-‐seq-‐homology, <2A, have EDS -‐> 6,563 chains

Strip to relevant chain -‐> 1abcFH_A.pdb: for x in \ $(find top8000_chains_eds_70_rosetta_named_hydrogens -‐name "*FH_*pdb"); do base=${x##*/}; chain=${base:7:1}; cat $x | grep "^ATOM.*$" | grep "^.\{21\}${chain}.*$” > \ top8000_chains_eds_70_rosetta_named_hydrogens_single_chains/$base; done

Backrub Protocol <ROSETTASCRIPTS> <SCOREFXNS> <s weights=score12_full> <Reweight scoretype=mm_bend weight=1/> </s> </SCOREFXNS> <TASKOPERATIONS> <RestrictToRepacking name=rtrp/> <PreserveCBeta name=preserve_cb/> </TASKOPERATIONS> <MOVERS> <MetropolisHastings name=mc scorefxn=s trials=10000> <Backrub sampling_weight=.75/> <Sidechain sampling_weight=0.25 task_operations=rtrp,preserve_cb/> </MetropolisHastings> </MOVERS> <PROTOCOLS> <Add mover_name=mc/> </PROTOCOLS> </ROSETTASCRIPTS>

COMMAND LINE FLAGS: -‐ex1 –ex2 –extrachi_cutoff 0

Features Reporters <ReportToDB name=features_reporter database_name="features_backrub_120725.db3" database_mode=sqlite3 database_separate_db_per_mpi_process=1 sample_source="Backrub Ensemble”> <feature name=ScoreTypeFeatures/> <feature name=StructureScoresFeatures scorefxn=s/> <feature name=ProteinRMSDFeatures reference_name=init_struct/> <feature name=RadiusOfGyrationFeatures/> <feature name=ResidueTypesFeatures/> <feature name=ResidueFeatures/> <feature name=PdbDataFeatures/> <feature name=ResidueScoresFeatures scorefxn=s/> <feature name=PairFeatures/> <feature name=ResidueBurialFeatures/> <feature name=ResidueSecondaryStructureFeatures/> <feature name=ProteinBackboneTorsionAngleFeatures/> <feature name=ProteinResidueConformationFeatures/> <feature name=ProteinBondGeometryFeatures/> <feature name=HBondFeatures scorefxn=s/> <feature name=SaltBridgeFeatures/> </ReportToDB>

Analysis Script Template f <-‐ query_sample_sources(sample_sources, sql_query) dens <-‐ estimate_density_1d(f, id_columns, measure_column) p <-‐ ggplot(dens) + geom_line(…) + geom_vline(…) + scale_x_…(…) + scale_y_…(…) + opts(…) + theme_…() save_plots(self, plot_id, …)

bond_angles.R

sql_query <-‐ “ SELECT b_ang.ideal, b_ang.observed FROM bond_intrares_angles AS b_ang WHERE b_ang.outAtm1Num = 1 AND b_ang.cenAtmNum = 2 AND b_ang.outAtm2Num = 3;"

bond_angles.R

sql_query <-‐ “ SELECT b_ang.ideal, b_ang.observed FROM residues AS res, residue_pdb_confidence AS res_conf, bond_intrares_angles AS b_ang WHERE res_conf.struct_id = res.struct_id AND res_conf.residue_number = res.resNum AND res_conf.max_temperature < 30 AND b_ang.struct_id = res.struct_id AND b_ang.resNum = res.resNum AND b_ang.outAtm1Num = 1 AND b_ang.cenAtmNum = 2 AND b_ang.outAtm2Num = 3;"

bond_angles.R sql_query <-‐ “ SELECT res.name3 AS res_type, dssp_code.label AS dssp_label, b_ang.ideal, b_ang.observed FROM residues AS res, residue_pdb_confidence AS res_conf, residue_secondary_structure AS ss, dssp_codes AS dssp_code, bond_intrares_angles AS b_ang WHERE res_conf.struct_id = res.struct_id AND res_conf.residue_number = res.resNum AND res_conf.max_temperature < 30 AND ss.struct_id = res.struct_id AND ss.resNum == res.resNum AND dssp_code.code = ss.code AND b_ang.struct_id = res.struct_id AND b_ang.resNum = res.resNum AND b_ang.outAtm1Num = 1 AND b_ang.cenAtmNum = 2 AND b_ang.outAtm2Num = 3;"

bond_angles.R backbone_geometry_bond_angle_NCaC

Layers: •  geom_line: data=dens –  x=x, y=y, color=sample_source

•  geom_vline: data=f –  x=ideal

•  geom_indicator: data=dens –  indicator=counts –  color=sample_source

Analysis Configuration { "sample_source_comparisons" : [{ "sample_sources" : [{ "database_path" : "path/features_top8000_r50086.db3", "id" : "top8000", }, { "database_path" : "path/features_top8000_backrub_r50086.db3", "id" : "top8000_backrub", }], "analysis_scripts" : [ "scripts/analysis/plots/backbone_geometry/bond_angles.R" ], "output_dir" : "build”, "output_formats" : [ "output_slide_pdf"]}]}

Features Analysis Output $~/rosetta/rosetta/rosetta_tests/features/compare_sample_sources.R -‐-‐config analysis_configurations/bond_angles.json Sample Source Comparison: Output Directory <-‐ ‘path/build/top8000_top8000_backrub' Output Formats <-‐ output_slide_pdf Sample Sources: top8000 <-‐ path/features_top8000_r50086.db3 top8000_backrub <-‐ path/features_top8000_backrub_r50086.db3 Analysis_scripts: scripts/analysis/plots/backbone_geometry/bond_angles.R Features Analysis: bond_angles loading: top8000 ... 23.33 s loading: top8000_backrub ... 22.55 s Saving Plot: path/build/top8000_top8000_backrub/bond_angles/output_slide_pdf/backbone_geometry_bond_angle_NCaC_120727.pdf ... 0.33s

N-‐Ca-‐C Backrub vs Native

•  Observations –  Non-‐helix, mean shifted tighter –  Larger standard deviation –  Recapitulate secondary structure variation –  Angle restriction at 117

•  Questions –  Does folded structures bias towards tighter angles? –  Does backrub uniformly sample secondary structure?

–  Backrub: •  More variation in

backbone_geometry_bond_angle_NCaC_120727.pdf

0.00

0.05

0.10

0.15

1,276,4931,517,935

95 100 105 110 115 120 125

Backbone N−Ca−C Bond Angle; B−Factor < 30

Bond Angle (degrees)

Feat

ure

Den

sity

sample_source top8000 top8000_backrub

117,119

117,349

top8000

top8000_backrub0.00

0.05

0.10

0.15

0.20

0.00

0.05

0.10

0.15

0.20

95 100 105 110 115 120 125

Backbone N−Ca−C Bond Angle by Residue Type; B−Factor < 30


Feat

ure

Den

sity

ASP CYS GLN GLU GLY HIS ILE LEU LYS MET PHE PRO SER THR top8000

117,119117,349

49,34678,982

54,52666,646

73,87793,119

17,40119,726

42,17356,817

69,829104,300

101,876101,991

28,31837,117

78,40889,469

123,089143,307

61,58888,122

28,10226,764

54,24063,893

59,63859,772

77,07992,155

73,85286,367

19,38822,639

46,66355,940

99,964113,460

ALA ARG ASN ASP CYS

GLN GLU GLY HIS ILE

LEU LYS MET PHE PRO

SER THR TRP TYR VAL

0.000.050.100.150.20

0.000.050.100.150.20

0.000.050.100.150.20

0.000.050.100.150.20

9510010511011512012595100105110115120125951001051101151201259510010511011512012595100105110115120125

Backbone N−Ca−C Bond Angle by Residue Type; B−Factor < 30


Feat

ure

Den

sity


854,6551,036,923

421,838481,012

FALSE

TRUE0.00

0.05

0.10

0.15

0.20

0.25

0.00

0.05

0.10

0.15

0.20

0.25

95 100 105 110 115 120 125

Backbone N−Ca−C Bond Angle a−Helix vs Other; B−Factor < 30


Feat

ure

Den

sity


15,510

18,485

top8000

top8000_backrub0.00

0.05

0.10

0.15

0.20

0.25

0.00

0.05

0.10

0.15

0.20

0.25

95 100 105 110 115 120 125

Backbone N−Ca−C Bond Angle by DSSP; B−Factor < 30


Feat

ure

Den

sity

B: b−Bridge E: b−Sheet G: 3/10 Helix H: a−Helix I: pi−Helix Irregular S: Bend T: HB Turn top8000

15,51018,485

306,691334,175

63,42078,568

421,838481,012

2,3052,806

312,782408,222

28,40636,789

125,541157,878

B: b−Bridge E: b−Sheet G: 3/10 Helix

H: a−Helix I: pi−Helix Irregular

S: Bend T: HB Turn

0.000.050.100.150.200.25

0.000.050.100.150.200.25

0.000.050.100.150.200.25

95 100 105 110 115 120 125 95 100 105 110 115 120 125



Feat

ure

Den

sity


B: b−Bridge E: b−Sheet G: 3/10 Helix H: a−Helix I: pi−Helix Irregular S: Bend T: HB Turn

0.000.050.100.150.200.25

0.000.050.100.150.200.25

0.000.050.100.150.200.25

0.000.050.100.150.200.25

0.000.050.100.150.200.25

0.000.050.100.150.200.25

0.000.050.100.150.200.25

0.000.050.100.150.200.25

0.000.050.100.150.200.25

0.000.050.100.150.200.25

0.000.050.100.150.200.25

0.000.050.100.150.200.25

0.000.050.100.150.200.25

0.000.050.100.150.200.25

0.000.050.100.150.200.25

0.000.050.100.150.200.25

0.000.050.100.150.200.25

0.000.050.100.150.200.25

0.000.050.100.150.200.25

790843

6721,023

704796

706860

276321

457625

542724

972985

435542

1,1721,435

1,3881,704

694957

352332

1,0161,170

1,0501,163

1,1421,339

314370

735897

1,3891,687

20,68420,356

10,70115,131

8,1258,815

9,86810,861

5,2565,577

7,8719,286

12,34015,696

16,18915,670

6,7477,806

31,39833,529

32,88435,261

12,00314,900

6,9326,078

17,91519,587

15,79116,850

20,70222,240

5,7626,326

15,17716,953

44,30147,420

6,1986,793

2,6674,522

3,2703,994

4,4705,508

763852

2,6293,700

4,4817,128

4,1583,997

1,6662,212

1,9372,445

5,7667,385

3,7945,532

1,3171,211

2,6893,148

5,2306,099

2,7873,200

1,1551,352

2,3482,801

2,2402,768

56,43354,402

19,61430,135

13,38514,916

20,73623,882

4,8435,216

18,05222,984

32,55345,543

15,64414,707

8,19710,033

27,13729,977

53,54959,370

24,01932,188

11,90810,724

17,35719,753

19,99621,709

19,16920,829

6,3987,236

14,42516,646

29,47032,132

128133

5186

5899

133164

3140

5067

129183

186216

6274

203213

294370

101160

3336

138164

8298

145152

4349

122162

294315

22,16623,512

10,70419,203

17,84623,992

25,27634,617

4,5995,717

8,86913,558

12,49422,120

35,93338,175

7,74811,400

12,53416,353

20,73127,973

13,86222,896

5,5576,271

10,73814,214

24,73332,864

22,65629,228

3,7704,850

9,69312,952

16,78121,885

1,7981,962

1,0031,722

1,4931,903

2,2903,039

523654

7621,125

8041,401

1,3611,570

7311,021

1,6192,162

2,4263,017

1,0601,675

541545

1,1291,466

2,1872,875

1,5762,113

458562

9501,252

2,1682,827

8,9229,348

3,9347,160

9,64512,131

10,39814,188

1,1101,349

3,4835,472

6,48611,505

27,43326,671

2,7324,029

2,4083,355

6,0518,227

6,0559,814

1,4621,567

3,2584,391

8,01010,497

5,6757,266

1,4881,894

3,2134,277

3,3214,426

ALAAR

GASN

ASPC

YSG

LNG

LUG

LYH

ISILE

LEULYS

MET

PHE

SERTH

RTR

PTYR

VAL

95 100 105 110 115 120 125 95 100 105 110 115 120 125 95 100 105 110 115 120 125 95 100 105 110 115 120 125 95 100 105 110 115 120 125 95 100 105 110 115 120 125 95 100 105 110 115 120 125 95 100 105 110 115 120 125

Backbone N−Ca−C Bond Angle by ResType and DSSP; B−Factor < 30


Feat

ure

Den

sity


0.00

0.05

0.10

0.15

1,276,4931,517,935

95 100 105 110 115 120 125



Feat

ure

Den

sity


Prior Distribution on Bond Angles?

0.1

0.2

0.3

−6 −4 −2 0 2 4

probability

0.00

0.05

0.10

0.15

1,572,0421,568,8231,567,1831,569,670

95 100 105 110 115 120 125



Feat

ure

Den

sity sample_source

top8000top8000_backrub_weaktop8000_backrub_mediumtop8000_backrub_strong

18,067

18,906

18,805

18,829

top8000

top8000_backrub_weak

top8000_backrub_medium

top8000_backrub_strong

0.000.050.100.150.200.25

0.000.050.100.150.200.25

0.000.050.100.150.200.25

0.000.050.100.150.200.25

95 100 105 110 115 120 125



Feat

ure

Den

sity

sample_sourceB: b−BridgeE: b−SheetG: 3/10 HelixH: a−HelixI: pi−HelixIrregularS: BendT: HB Turntop8000top8000_backrub_mediumtop8000_backrub_strongtop8000_backrub_weak

18,06718,90618,80518,829

346,755336,904337,560336,297

81,17982,03381,28382,587

515,123492,179490,945489,503

2,7472,9442,8622,880

407,297426,825428,947432,442

35,13837,77738,14539,183

165,736171,255168,636167,949

B: b−Bridge E: b−Sheet G: 3/10 Helix

H: a−Helix I: pi−Helix Irregular

S: Bend T: HB Turn

0.00

0.05

0.10

0.15

0.20

0.25

0.00

0.05

0.10

0.15

0.20

0.25

0.00

0.05

0.10

0.15

0.20

0.25

95 10010511011512012595 100105110115120125



Feat

ure

Den

sity sample_source

top8000top8000_backrub_weaktop8000_backrub_mediumtop8000_backrub_strong

Thanks •  Brian Kuhlman / Jack Snoeyink (advisors) •  Sam Deluca, Tim Jacobs (database support) •  Andrew Leaver-‐Fay, Steven Combs (Features Beta testers) •  Colin Smith, Frank DiMaio, Patrick Conway (Bond Angle Advice) •  Rosetta Community Community •  Friedland, Linares, Smith Kortemme, A Simple Model of Backbone

Flexibility Improves Modeling of Side-‐chain Conformational Variability, JMB 2008

•  Smith, Kortemme , Backrub-‐Like Backbone Simulation Recapitulates Natural Protein Conformational Variability and Improves Mutant Side-‐Chain Prediction, JMB 2008

•  Berkholz, Shapovalov, Dunbrack Jr., Karplus, Conformation Dependence of Backbone Geometry in Proteins, Structure 2009

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