Machine learning and protein structure

1
Machine learning and protein structure

• Describing structural principles underlying fold
  space
• Core element prediction
• Folding pathways

2
Describing structural principles

• Several hundred protein folds already known
• Proteins distributed unevenly amongst different
  folds
• Many proteins adopt one of a limited number of
  fold types (superfolds)
• Most folds are adopted by only a small number of
  proteins
• Understanding this requires knowledge of protein
  structure principles in the wider context of
  folding, function and evolution
• Number of protein structures expected to increase
  with structural genomics projects
• The total number of folds in biota is predicted
  to be between 1000 and 10000.
• Automated methods of analysis needed
• Can machine learning strategies be used to learn
  and describe the structural principles
  underpinning fold space?

3
Protein structure classification

• Several classification schemes currently
• SCOP (manual)
• CATH (semi-automatic)
• FSSP (automatic)
• Largely similar in assignment but significantly
  different
• Classification alone does not explain why some
  folds are more prevalent than others
• Need to understand how folds differ in terms of
  fundamental structural properties
• Folds are usually described in terms of spatial
  and topological arrangements of secondary
  structure elements
• SCOP includes detailed (manual) descriptions of
  folds

4
SCOP

• All-b class
• Immunoglobulin-like beta-sandwich (13)
  sandwich 7 strands in 2 sheets greek-key some
  members of the fold have additional strands
• Common fold of diphtheria toxin/transcription
  factors/cytochrome f (7) sandwich 9 strands
  in 2 sheet greek-key subclass of
  immunoglobin-like fold
• Prealbumin-like (4) sandwich 7 strands in 2
  sheets, greek-key variations some members have
  additional 1-2 strands to common fold
• alpha-Amylase inhibitor tendamistat (1)
  sandwich 6 strands in 2 sheets
• Cupredoxins (1) sandwich 7 strands in 2
  sheets, greek-key variations some members have
  additional 1-2 strands
• C2 domain-like (4) sandwich 8 strands in 2
  sheets greek-key
• TRAF domain (1) sandwich 8 strands in 2
  sheets greek-key

5
SCOP

• ab class (preliminary)
• Sulfite oxidase, middle catalytic domain (1)
  unusual fold contains 3 layers of beta-sheet
  structure and a beta-grasp like motif
• Fumarylacetoacetate hydrolase, FAH (1)
  unusual fold contains 3 layers of beta-sheet
  structure and a SH3-like like motif
• Aromatic aminoacid monoxygenases, catalytic and
  oligomerization domains (1) unusual fold
• Substrate-binding domain of HMG-CoA reductase (1)
  unusual fold
• Conserved core of transcriptional regulatory
  protein vp16 (1) unusual fold
• Insert subdomain of RNA polymerase alpha subunit
  N-terminal domain (1) unusual fold contains
  a left-handed beta-alpha-beta unit
• Baseplate structural protein gp11 (1) unusual
  fold trimer
• Non-globular alpha_beta subunits of globular
  proteins (1)

6
Wish list

• We would like to generate expert-like rules
• Automatically
• Objectively
• That are easily interpreted
• That discriminate between folds

7
Learning Rules with Inductive Logic Programming
(ILP)

• Rules were learnt using the Progol-4.4 ILP
  system.
• Progol learns rules automatically from examples
  and background knowledge.
• Progol learns rules in such a way as to maximise
  the coverage of positive examples and minimise
  the coverage of negative examples.
• Weighted to favour shorter rules given similar
  coverage
• Examples, background knowledge and the final
  rules are represented as logic programs
• Can incorporate relational data
• Rules can be interpreted easily

8
Global v local features

• Previous ILP study could only learn local fold
  features
• Eg. Rules for the Rossmann fold
• Previous ILP rule (local) The 1st strand is
  followed by a helix, the two elements are
  separated by a coil of about one residue.The 6th
  strand is followed by a helix.
• SCOP (global) core 3 layers, a/b/a parallel
  beta-sheet of 6 strands, order 321456
• Insertions and deletions inhibit learning of
  global features difficult to identify
  structurally equivalent (core) secondary
  structure elements
• We avoid this problem by using multiple structure
  alignments

9

10
Multiple alignment ? Core elements
11
Background knowledge

• Background knowledge is defined in terms of the
  properties of, and relationships between, core
  elements

• number_helices(Lo lt D lt Hi)
• sheet(D, A, Stype)
• helix(D, B, Htype, Core)
• strand_position(A, B, N)
• adjacent(B, C)
• coil(B, C, N)
• contact(B, C)
• antiparallel(B, C)
• parallel(B, C)

• end_strand_distance(A, B, C, Dist)
• pair(B, C, Bloc, Cloc)
• helix_angle(B, C, Angle)
• has_n_strands(A, N)
• barrel(A)
• bifurcated(A)
• sheet_top_X(A, N1, N2,., NX)
• contains(B, AA, Loc)
• contains(B, AA)

12
ILP run

• Rules are constructed from an examples background
  knowledge
• Progol builds steadily more specific rules,
  optimising compression f
• f p n c where p positive examples
  covered
• n negative examples covered
• c length of rule
• fold(A,'Rossmann-fold').
• fold(A,'Rossmann-fold') - sheet(A,B,para).
• fold(A,'Rossmann-fold') - sheet(A,B,para),
  has_n_strands(B,6).
• .
• .
• fold(A,'Rossmann-fold') - sheet(A,B,para),
  helix(A,C,h,g),
• 
  helix(A,D,h,i), helix_angle(C,D,par
  a), sheet_top_6(B,3,2,1,4,5,6).

13
Fold Rules

• Rules were learnt for 45 of the most popular
  folds in the SCOP database.
• Rules learnt were compared to descriptions given
  by SCOP.
• Cross-validation testing.

14
Rossmann fold
Has between 3 and 4 helices Has a-helix B at
core position "b" B contains a glycine in both
its middle and n-terminal regions. OR Has a
parallel sheet B of six strands with topology
321456 Has a-helices C and D at core positions
"g" and "i" respectively C and D are in contact
and parallel.
15
SCOP
ILP (old)
ILP (new)

• Global property (sheet topology) learnt
• Part of a conserved G-X-G-X-X-G sequence motif
  involved in nucleotide binding

16
Immunoglobulin fold
Has antiparallel sheets B and C B has 3
strands, topology 123 C has 4 strands, topology
2134.
17
sandwich 7 strands in 2 sheets greek-key some
members of the fold have additional strands Has
antiparallel sheets B and C B has 3 strands,
topology 123 C has 4 strands, topology
2134. sandwich 7 strands in 2 sheets,
greek-key variations some members have
additional 1-2 strands to common fold Has a mixed
sheet B. B has 3 strands with topology 213.
SCOP
Immunoglobulin
ILP
SCOP
Prealbumin
ILP

• Can learn rules to discriminate between folds
  with similar SCOP descriptions

18
TIM barrel
Has between 5 and 9 helices Has a parallel sheet
of 8 strands.
19

• SCOP contains parallel beta-sheet barrel, closed
  
• n8, S8 strand order 12345678 the first
  six superfamilies have similar phosphate-binding
  sites
• ILP Has between 5 and 9 helices Has a parallel
  sheet of 8 strands.
• ILP does not give as many details as SCOP
• Fails to find topology or barrel structure
• Many TIM barrels are not closed
• Not necessary to include many details as few
  alternative folds have 8 core strands in a
  parallel sheet

20
Cross-validation

• Each of the 45 folds was subject to a 5-fold
  cross-validation procedure.
• The overall accuracy was quite high (97)
  although this is, in part, due to the large
  number of negative examples used. A large number
  of negative examples were included in the
  learning procedure to limit the learning of
  spurious rules. A largest class prediction (that
  is, predicting that every example was NOT an
  example of the fold of interest) would give an
  accuracy of 95.
• The overall accuracy was found to be
  statistically significant (Pearsons ?2  58.5,
  p ltlt 0.01) where the reference state was based on
  such a largest class prediction.
• The overall precision and recall were 77 and 55
  respectively. The recall was relatively low for
  those folds with few examples, largely due to the
  difficulties in producing stable multiple
  structure alignments.
• For the 10 best represented folds examined here,
  the precision and recall were 83 and 69
  respectively.

21
Conclusions Fold rules

• Protein structure principles underpinning much of
  fold space can be automatically described using
  ILP.
• The rules are objective and discriminate between
  different fold classes.
• The rules learnt are readily interpretable to
  human protein structure experts.
• The rules learnt here describe global fold
  properties as well as local features.
• The rules learnt by ILP are, in many cases,
  comparable to expert principles given in the SCOP
  database.
• The procedure applied here to the manual SCOP
  fold classification could also be applied to any
  other protein structure classification scheme.
  Used in conjunction with a fully automatic
  structure classification (such as DALI), ILP
  could be used to derive the principles underlying
  fold space from coordinates in an automatic and
  objective fashion.
• Given the increasing emphasis on high-throughput
  experimental projects in biology, automatic
  methods of analysis such as ILP are going to
  become increasingly important in deriving
  principles from data.

22
Problems

• Difficult to learn rules for sparsely populated
  folds
• Fewer examples to learn from
• Difficult to validate rules
• Multiple structure alignments less reliable
• Can we predict core secondary structure elements
  without multiple structure alignments?

23
Core element prediction

• Can we predict structurally variable secondary
  structure elements in the absence of a reliable
  multiple structure alignment? Eg. singleton
• Machine learning can be used to learn rules for
  core and non-core elements from previously
  generated multiple structure alignments.
• Comparison of machine learning techniques.

24
Well populated folds
Machine learning
Rules
Sparsely populated folds
Predict core elements
25
Machine learning techniques

• C5.0 (decision-tree)
• SVM (support vector machine)
• ILP
• ILP (with additional relational information)
• Representation includes attributes such as
• Relative distance from centre of domain
• Number of contacts with other elements
• Hydrophobicity
• Length of element..
• ILP (relational) includes extra information such
  as sequential or spatial adjacency of secondary
  structure elements

26
Core prediction summary

• Class C5.0 SVM ILP ILP (relational)
• --------------------------------------------------
  ----------------
• All-a 79.20 74.80 68.40 66.80
• All-b 80.50 82.50 79.00 81.00
• a/b 80.40 74.00 65.60 58.80
• ab 80.80 85.60 79.20 78.80
• --------------------------------------------------
  ----------------
• All 80.26 79.65 73.83 72.61
• Number elements tested 1150
• Default accuracy (largest class prediction) 60

27
Conclusions - Core prediction

• Can predict core secondary structure elements in
  the absence of a reliable multiple structure
  alignment
• ILP worse than SVM and C5.0 for core prediction
• C5.0 cross-validated accuracy comparable to SVM
  but more consistent over main fold classes
• Does core prediction help ILP learn fold rules
  for sparsely populated folds?
• No.
• When can it help?

28
Folding pathways

• Recent interest in experimentally probing early
  folding events in proteins
• Phi values, calculated from mutation data, can
  indicate which parts of a (two-state) protein
  form the transition state when folding.
• One or more folding nuclei?
• What role do kinetics play in evolution?
• Are early folding sections of a protein conserved
  in sequence?
• Two schools of thought
• Yes
• No
• Do proteins with similar structures fold in a
  similar way?
• Are structurally invariant parts of a protein
  fold related to early folding?
• Correlation between folding in distantly related
  proteins has been seen
• Two globins with substantially different
  sequences shown to fold differently
• Applied core prediction to see if there is any
  correlation between core elements and early
  folding

29
Phi-values
T
??GT-U
WT
U
F
Mutant
??GF-U

• ? 0 Residue has disordered structure
  in the transition state
• ? 1 Residue has native-like structure
  in the transition state
• 0 lt ? lt 1 Indeterminate mixture of
  native/disordered or partially unfolded?

30
Comparing phi values with core elements- Why use
core prediction?

• Ideally, to compare structural invariance across
  a fold class to folding parameters one needs to
  generate a multiple structure alignment of
  unrelated proteins within that class
• Of those few proteins for which experimental
  phi-values are available, not all have more than
  1-2 protein families in the same fold class
• Folding parameters could be compared to predicted
  core-ness of secondary structure elements for
  all proteins
• Predicted core-ness of elements compared to
  average phi-values for that element

31
Phi-value test set

• Protein Elems Phis Res Coverage
• --------------------------------------------------
  ------------
• AcP 7 17 68 25
• ACBP 4 19 57 33
• CheY 10 25 90 28
• CI2 5 23 32 72
• FKBP12 6 19 41 46
• FNFn10 7 15 45 33
• SH3 5 19 23 83
• villin 5 16 51 31
• WW 2 8 10 80
• --------------------------------------------------
  -------------
• Total 51 161 417 39

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Wishful thinking?

• Can we reliably predict relatively early/late
  folding elements with confident/less-confident
  predictions of core-ness?
• We can test binary classification via
  leave-one-out cross validation.

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Cross-validation summary

• protein elements acc expect recall prec phi_cu
  t c50_cut
• --------------------------------------------------
  --------------------------------------------------
  ---
• AcP 7 71 57 67 67 0.34 88
• ACBP 4 25 50 0 0 0.34 89
• CheY 10 50 70 100 38 0.34 89
• CI2 5 100 100 0 0 0.34 88
• FKBP12 6 83 67 75 100 0.34 89
• FNFn10 7 71 57 50 100 0.34 90
• SH3 5 80 60 100 75 0.34 89
• villin 5 60 60 67 67 0.35 89
• WW 2 100 100 100 100 0.34 88
• --------------------------------------------------
  --------------------------------------------------
  ---
• Overall 51 69 53 71 65
• Statistical significance ?2 5.04 (p 0.02)

39
AcP
Experiment
Core Prediction
Earlier folding Later folding
More likely core Less likely core
40
ACBP
Experiment
Core Prediction
Earlier folding Later folding
More likely core Less likely core
41
CheY
Experiment
Core Prediction
Earlier folding Later folding
More likely core Less likely core
42
CI2
Experiment
Core Prediction
Earlier folding Later folding
More likely core Less likely core
43
FKBP12
Experiment
Core Prediction
Earlier folding Later folding
More likely core Less likely core
44
FNFn10
Experiment
Core Prediction
Earlier folding Later folding
More likely core Less likely core
45
SH3
Experiment
Core Prediction
Earlier folding Later folding
More likely core Less likely core
46
villin
Experiment
Core Prediction
Earlier folding Later folding
More likely core Less likely core
47
WW
Experiment
Core Prediction
Earlier folding Later folding
More likely core Less likely core
48
Fin

• People
• Mike Sternberg
• Stephen Muggleton
• Funding
• BBSRC