The document discusses methods for determining protein structure, including X-ray crystallography and nuclear magnetic resonance (NMR) spectroscopy. It provides details on how NMR can be used to assign chemical shifts to atoms in proteins in order to deduce molecular structures. The process involves identifying spin systems from NMR spectra, linking spin systems into segments along the protein backbone, and resolving ambiguities and conflicts between segments through graph algorithms and iterative approaches.

1. Jia-Ming Chang 0509
Graph Algorithms and Their Applications to Bioinformatics
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2. Determine Protein Structure
 X-ray
波長約 1 Å
 長度接近原子間的距離
 研究結晶的狀態的分子行為
 定出其晶體結構，也包含蛋白質體結構
X-ray 與結構生物學
 利用 X-ray 繞射法分析高度純化結晶的蛋白質的每個
基團和原子的空間定位。
 Nuclear magnetic resonance (NMR)
NMR 是涉及原子核吸收的過程。因為對某些原子核而
言，具有自旋和磁矩的性質。因此，若暴露於強磁場
中原子核會吸收電磁輻射，這是由磁場誘導而發生能
階分裂的結果。科學家並發現，分子環境會影響在磁
場中原子核的無線電波的吸收，利用這種特性來分析
分子的結構
AVANCE 800 AV IBMS, Sinica 2/40

3. NMR – Nuclear Spin (1/5)
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4. NMR – Nuclear Spin (2/5)
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5. NMR - Magnetic Field (3/5)
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6. NMR – Resonance (4/5)
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7. NMR – Chemical Shift (5/5)
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8. Find out Chemical Shift for Each Atom
• Backbone: Ca, Cb, C’, N, NH
HSQC, CBCANH, CBCACONH
Cα CΟN
H H
Cβ
Cγ
Cδ
H2
H2
H3
Chemical Shift Assignment (1/2)
One amino acid
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9. Chemical Shift Assignment (2/2)
H-C-
H
H-CC-
H
H
-N-C-C-N-C-C-N-C-C-N-C-C-
O
O
O
O
H H
H
H
H O
H
H-C-
H
CH3
Backbone
ppm18-23
19-24
16-20
17-23
31-34
55-60
CH3 30-35
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10. HSQC Spectra
 HSQC peaks (1 chemical shifts for an amino acid)
HH NN IntensityIntensity
8.1098.109 118.60118.60 6592003265920032
HSQC
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11. CBCA(CO)NH Spectra
 CBCA(CO)NH peaks (2 chemical shifts for one amino
acid)
HH NN CC IntensityIntensity
8.1168.116 118.25118.25 16.3716.37 7923881179238811
8.1098.109 118.60118.60 36.5236.52 6592003265920032
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12. CBCANH Spectra
 CBCANH peaks (4 chemical shifts for one amino acid)
 Ca (+), Cb (-)
HH NN CC IntensityIntensity
8.1168.116 118.25118.25 16.3716.37 7923881179238811
8.1098.109 118.60118.60 36.5236.52 -65920032-65920032
8.1178.117 118.90118.90 61.5861.58 -51223894-51223894
8.1198.119 117.25117.25 57.4257.42 109928374109928374
++
--
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13. A Dataset Example
N
H
HSQC
HNCACB
CBCA(CO)NH
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14. A Perfect Spin System Group
NN HH CC IntensityIntensity
113.293113.293 7.8977.897 56.29456.294 1.64325e+0081.64325e+008
113.293113.293 7.8977.897 27.85327.853 1.08099e+0081.08099e+008
CCaa
i-1i-1 CCbb
i-1i-1 CCaa
ii CCbb
ii
56.29
4
28.16
5
62.544 68.48
3NN HH CC IntensityIntensity
113.293113.293 7.927.92 62.54462.544 8.52851e+0078.52851e+007
113.293113.293 7.927.92 56.29456.294 4.71331e+0074.71331e+007
113.293113.293 7.927.92 68.48368.483 -8.54121e+007-8.54121e+007
113.293113.293 7.927.92 28.16528.165 -3.49346e+007-3.49346e+007
CBCA(CO)NH
CBCANH
i -1
i -1
Ca
Ca
Cb
Cb
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15. Coding
 Translate the target protein sequence
and spin systems into coding sequences
based on the following table.
Atreya, H.S., K.V.R. Chary, and G. Govil, Automated NMR assignments of proteins for high
throughput structure determination: TATAPRO II. Current Science, 2002. 83(11): p. 1372-1376.
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16. Backbone Assignment
 Goal
Assign chemical shifts to N, NH, Ca (and
Cb) along the protein backbone.
 General approaches
Generate spin systems
○ A spin system: an amino acid with known
chemical shifts on its N, NH, Ca (and Cb).
Link spin systems
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17. 17 /40
Backbone Assignment
DGRIGEIKGRKTLATPAVRRLAMENNIKLS

18. 18 /40
Blind Men’s Elephant
 We cannot directly “see” the positions of
these atoms (the 3D structure)
 But we can measure a set of parameters
(with constraints) on these atoms,
which can help us infer their coordinates
Each experiment can only determine
a subset of parameters (with noises)
To combine the parameters of different
experiments we need to stitch them together

19. A Peculiar Parking Lot (valet parking)
Information you have: The make of your car, the car parked in
front of you (approximately). Together with others, try to identify
as many cars as possible (maximizing the overall satisfaction).
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20. Ambiguities
 All 4 point experiments are mixed
together
 All 2 point experiments are mixed
together
 Each spin system can be mapped to
several amino acids in the protein
sequence
 False positives, false negatives
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21. Multiple Candidates
 One spin system maybe assign to many places
of a protein sequence.
 Spin system(SS)
 Protein Sequence:
AKFERQHMDSSTSRNLTKDR
NN HH CCaa
i-1i-1 CCbb
i-1i-1 CCaa
ii CCbb
ii
119.7119.7 8.848.84 58.458.4 32.732.7 56.356.3 40.840.8
SS SS SS SSPossible place
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22. False Positives and False Negatives
 False positives
Noise with high intensity
Produce fake spin systems
 False negatives
Peaks with low intensity
Missing peaks
 In real wet-lab data, nearly 50% are
noises (false positive).
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23. False Positive & False Negative
Perfect
False Negative
False Positive
N
H
HSQC
HNCACB
CBCA(CO)NH
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24. Ambiguous Spin System
NN HH CC IntensityIntensity
106.9106.9 8.878.87 54.9254.92 423879423879
106.9106.9 8.878.87 40.3540.35 524522524522
NN HH CC IntensityIntensity
106.91106.91 8.858.85 59.759.7 235673235673
106.92106.92 8.868.86 54.9354.93 346234346234
106.91106.91 8.868.86 61.561.5 432432432432
106.91106.91 8.858.85 40.3140.31 -335759-335759
106.92106.92 8.868.86 30.530.5 -483759-483759
NN HH CCaa
i-1i-1 CCbb
i-1i-1 CCaa
ii CCbb
ii
106.1106.1 8.858.85 54.9354.93 40.3140.31 59.759.7 30.530.5
106.1106.1 8.858.85 61.561.5 40.3140.31 59.759.7 30.530.5
Two possible spin systems
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25. Spin System Group
 Nearest Neighboring (TATAPRO, RIBRA, GASA)
N
H
HSQC
HNCACB
CBCA(CO)NH
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26. Spin System Linking
 Goal
Link spin system as long as possible.
 Constraints
Each spin system is uniquely assigned to a
position of the target protein sequence.
Two spin systems are linked only if the
chemical shift differences of their intra- and
inter- residues are less than the predefined
thresholds.
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27. Previous Approaches
 Constrained bipartite matching problem*
Can’t deal with ambiguous link
Legal matching Illegal matching under constraints
*Xu Y, Xu D, Kim D, Olman V, Razumovskaya J, Jiang T. Automated assignment of backbone NMR peaks using constrained
bipartite matching. Computing in Science & Engineering 2002;4(1):50-62.
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28. Naatural Language Processing
─ Noises or Ambiguity ?
 Speech recognition ： Homopone selection
台 北 市 一 位 小 孩 走 失 了
台 北 市 小 孩
台 北
適 宜 走 失
事 宜
一 位
一 味
移 位
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29. An Error-Tolerant Algorithm
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30. Phrase, Sentence Combination
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31. Spin System Positioning
55.266 38.675 44.555 0
44.417 0 55.043 30.04
44.417 0 30.665 28.72
55356 29.782 60.044 37.541
D 50 G 10 R 40 I 50|51
55.266 38.675 44.555 0 => 50 10
44.417 0 55.043 30.04 =>10 40
44.417 0 30.665 28.72 =>10 40
55356 29.782 60.044 37.541 => 40 50
 We assign spin system groups to a proteinWe assign spin system groups to a protein
sequence according to their codes.sequence according to their codes.
Spin System
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32. Link Spin System groups
Segment 3
Segment 2
Segment 1
55.266 38.675 44.555 0
44.417 0 55.043 30.04
44.417 0 30.665 28.72
55356 29.782 60.044 37.541
D G R I
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33. Iterative Concatenation
DGRI….FKJJREKL
….
Step n Segment 99
1
2
….
56
Spin Systems
1
2
2
47
1
Step1
56…
Step2 Segment 1
Segment 2
Segment 31…
Step n-1 Segment 78 Segment 79…
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34. Conflict Segments
DGRIDGRIGEIKGRKTLATPAVRRLAMENNIKLSGEIKGRKTLATPAVRRLAMENNIKLS
Segment 78
Segment 71
Segment 79
Segment 99 Segment 98
Segment 97
Two kinds of conflict segments
Overlap (e.g. segment 71, segment 99)
Use the same spin system (e.g. both segment 78 and
segment 79 contain spin system 1)
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35. Independent Set
Subset S of vertices such that no two vertices in S are connected
www.cs.rochester.edu/~stefanko/Teaching/06CS282/06-CSC282-17.ppt
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36. Independent Set
Subset S of vertices such that no two vertices in S are connected
www.cs.rochester.edu/~stefanko/Teaching/06CS282/06-CSC282-17.ppt
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37. A Graph Model for Spin System Linking
 G(V,E)
 V: a set of nodes (segments).
 E: (u, v), u, v ∈ V, u and v are conflict.
 Goal
 Assign as many non-conflict segments
as possible => find the maximum
independent set of G.
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38. An Example of G
 Seq. :Seq. : GEIKGRKTLATPAVRRLAMENNIKLSEGEIKGRKTLATPAVRRLAMENNIKLSE
Segment1: SP12->SP13->SP14
Segment2: SP9->SP13->SP20->SP4
Segment3: SP8->SP15->SP21
Segment4: SP7->SP1->SP15->SP3
Seg1 Seg3
Seg4 Seg2
Seg1
Seg3
Seg2
Seg4
SP13
SP15
Overlap
Overlap
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39. Segment weight
 The larger length of segment is, the
higher weight of segment is.
 The less frequency of segment is, the
higher of segment is.
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40. Find Maximum Weight Independent Set of G (1/2)
 Boppana, R. and M.M. Halldόrsson, Approximating Maximum Independent
Sets by Excluding Subgraphs. BIR, 1992. 32(2).
V
N(v)
Head_N(v)
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41. Find Maximum Weight Independent Set of G (2/2)
 Boppana, R. and M.M. Halldόrsson, Approximating Maximum Independent
Sets by Excluding Subgraphs. BIR, 1992. 32(2).
V
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42. An Iterative Approach
 We perform spin system generation
and linking iteratively.
 Three stages.
 Perfect spin systems
 Weak false negative spin systems
 Severe false negative spin systems
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43. Segment Extension
DGRDGRGEKGRKTLATPAVRRLAMENNIKLSGEKGRKTLATPAVRRLAMENNIKLS
MaxIndSetMaxIndSet
77 99‘ 97‘
99 97
45
23
26
31
29
32
33
24
27
28
28
77
71
78
99‘
97‘
99 97
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