Protein Hypernetworks Johannes K oster, Eli Zamir, Sven Rahmann - - PowerPoint PPT Presentation

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Protein Hypernetworks

Johannes K¨

• ster, Eli Zamir, Sven Rahmann

August 20, 2012

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Protein Network Modelling

Interaction maps (undirected graphs)

A H G B C D E F I

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Protein Network Modelling

Interaction maps (undirected graphs)

A H G B C D E F I

Differential equations (Law of Mass Action), Bayesian Networks, ...

d[C] dt = kon[A][B] − koff[C]

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Protein Network Modelling

Interaction maps (undirected graphs)

A H G B C D E F I

Differential equations (Law of Mass Action), Bayesian Networks, ...

d[C] dt = kon[A][B] − koff[C]

accuracy scalability

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Protein Network Modelling

Interaction maps (undirected graphs)

A H G B C D E F I

Protein Hypernetworks

?

Differential equations (Law of Mass Action), Bayesian Networks, ...

d[C] dt = kon[A][B] − koff[C]

accuracy scalability

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Structure

1 Protein Hypernetworks 2 Mining Protein Hypernetworks 3 Data Aquisition

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Idea

Protein Network (P, I)

A H G B C D E F I

H I G B G A

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Idea

Protein Network (P, I)

A H G B C D E F I

• H

I G B G A

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Idea

Protein Hypernetwork (P, I, C) Protein Network (P, I)

A H G B C D E F I

• H

I G B G A

Boolean Logic Constraints C

{G, H} ⇒ {I, H} {A, B} ⇒ ¬{G, B} {G, B} ⇒ ¬{A, B}

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Mining Protein Hypernetworks

Protein Hypernetwork (P, I, C)

A H G B C D E F I H I G B G A

H G I A B G A B G

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Mining Protein Hypernetworks

Protein Hypernetwork (P, I, C)

A H G B C D E F I H I G B G A

Minimal network states (Nec, Imp) for q ∈ P ∪ I

q ∧

• c∈C

c

H G I A H A G B C C F G F H I F I D F C D D E E I A B G A B G

Satisfying model α : P ∪ I → {0, 1} by tableau algorithm Nec := {q′ ∈ P ∪ I | α(q′) = 1} Imp := {q′ ∈ P ∪ I | α(q′) = 0 due to active c ∈ C}

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Tableau Algorithm

Propositional Logic Tableau Algorithm

for a given formula f explore depth-first the tree

• f deductions from root f

each root-leaf-path without contradiction is a satisfying model AB ∧ (AB ⇒ BC) ∧ (CD ⇒ ¬DE) AB (AB ⇒ BC) (CD ⇒ ¬DE) ¬AB BC ¬CD

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Tableau Algorithm

Propositional Logic Tableau Algorithm

for a given formula f explore depth-first the tree

• f deductions from root f

each root-leaf-path without contradiction is a satisfying model

Modifications

expand disjunctions from left to right allow to pre-block subformulas to guide the algorithm to the right model AB ∧ (AB ⇒ BC) ∧ (CD ⇒ ¬DE) AB (AB ⇒ BC) (CD ⇒ ¬DE) ¬AB BC ¬CD

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Tableau Algorithm

Propositional Logic Tableau Algorithm

for a given formula f explore depth-first the tree

• f deductions from root f

each root-leaf-path without contradiction is a satisfying model

Modifications

expand disjunctions from left to right allow to pre-block subformulas to guide the algorithm to the right model AB ∧ (AB ⇒ BC) ∧ (CD ⇒ ¬DE) AB (AB ⇒ BC) (CD ⇒ ¬DE) ¬AB BC ¬CD

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Tableau Algorithm

Propositional Logic Tableau Algorithm

for a given formula f explore depth-first the tree

• f deductions from root f

each root-leaf-path without contradiction is a satisfying model

Modifications

expand disjunctions from left to right allow to pre-block subformulas to guide the algorithm to the right model AB ∧ (AB ⇒ BC) ∧ (CD ⇒ ¬DE) AB (AB ⇒ BC) (CD ⇒ ¬DE) ¬AB BC ¬CD

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Tableau Algorithm

Propositional Logic Tableau Algorithm

for a given formula f explore depth-first the tree

• f deductions from root f

each root-leaf-path without contradiction is a satisfying model

Modifications

expand disjunctions from left to right allow to pre-block subformulas to guide the algorithm to the right model AB ∧ (AB ⇒ BC) ∧ (CD ⇒ ¬DE) AB (AB ⇒ BC) (CD ⇒ ¬DE) ¬AB BC ¬CD

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Tableau Algorithm

Propositional Logic Tableau Algorithm

for a given formula f explore depth-first the tree

• f deductions from root f

each root-leaf-path without contradiction is a satisfying model

Modifications

expand disjunctions from left to right allow to pre-block subformulas to guide the algorithm to the right model AB ∧ (AB ⇒ BC) ∧ (CD ⇒ ¬DE) AB (AB ⇒ BC) (CD ⇒ ¬DE) ¬AB BC ¬CD

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Tableau Algorithm

Propositional Logic Tableau Algorithm

for a given formula f explore depth-first the tree

• f deductions from root f

each root-leaf-path without contradiction is a satisfying model

Modifications

expand disjunctions from left to right allow to pre-block subformulas to guide the algorithm to the right model AB ∧ (AB ⇒ BC) ∧ (CD ⇒ ¬DE) AB (AB ⇒ BC) (CD ⇒ ¬DE) ¬AB BC ¬CD

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Tableau Algorithm

Propositional Logic Tableau Algorithm

for a given formula f explore depth-first the tree

• f deductions from root f

each root-leaf-path without contradiction is a satisfying model

Modifications

expand disjunctions from left to right allow to pre-block subformulas to guide the algorithm to the right model AB ∧ (AB ⇒ BC) ∧ (CD ⇒ ¬DE) AB (AB ⇒ BC) (CD ⇒ ¬DE) ¬AB BC ¬CD

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Tableau Algorithm

Propositional Logic Tableau Algorithm

for a given formula f explore depth-first the tree

• f deductions from root f

each root-leaf-path without contradiction is a satisfying model

Modifications

expand disjunctions from left to right allow to pre-block subformulas to guide the algorithm to the right model AB ∧ (AB ⇒ BC) ∧ (CD ⇒ ¬DE) AB (AB ⇒ BC) (CD ⇒ ¬DE) ¬AB BC ¬CD

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Minimal Network States

Clashes

Two minimal network states (Nec, Imp) and (Nec′, Imp′) are clashing iff Nec ∩ Imp′ = ∅ or Nec′ ∩ Imp = ∅. not clashing pair → interactions simultaneously possible

A B

G H G I

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Minimal Network States

Clashes

Two minimal network states (Nec, Imp) and (Nec′, Imp′) are clashing iff Nec ∩ Imp′ = ∅ or Nec′ ∩ Imp = ∅. not clashing pair → interactions simultaneously possible

A B

G

+

H G I

=

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Minimal Network States

Clashes

Two minimal network states (Nec, Imp) and (Nec′, Imp′) are clashing iff Nec ∩ Imp′ = ∅ or Nec′ ∩ Imp = ∅. not clashing pair → interactions simultaneously possible

A B

G

+

A B

G

=

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Prediction of Protein Complexes

Network based complex prediction

◮ e.g. dense regions

A H G B C D E F I C D E F I A H G B I A H G B I C D E F I A H G I

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Prediction of Protein Complexes

Network based complex prediction

◮ e.g. dense regions

A H G B C D E F I

Maximal combinations of minimal network states

C D E F I A H G B I A H G B I C D E F I A H G I

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Prediction of Protein Complexes

Network based complex prediction

◮ e.g. dense regions

A H G B C D E F I

Maximal combinations of minimal network states

C D E F I A H G B I A H G B I

Refined complexes

◮ no violated constraints

C D E F I A H G I

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Prediction of Functional Importance

Minimal network state graph

A

AB AG AH GH HI EI FI FG BG BC CD CF DF ED EF

H G B C D E F I

Minimal network states

H G I A H A G B C C F G F H I F I D F C D D E E I A B G A B G

A

AB AG AH GH HI EI FI FG BG BC CD CF DF ED EF

H G B C D E F I

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Prediction of Functional Importance

Minimal network state graph

A

AB AG AH GH HI EI FI FG BG BC CD CF DF ED EF

H G B C D E F I

Breadth first search from each node

A

AB AG AH GH HI EI FI FG BG BC CD CF DF ED EF

H G B C D E F I

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Prediction of Functional Importance

Minimal network state graph

A

AB AG AH GH HI EI FI FG BG BC CD CF DF ED EF

H G B C D E F I

Breadth first search from each node

A

AB AG AH GH HI EI FI FG BG BC CD CF DF ED EF

H G B C D E F I

Perturbation Impact Score PIS(P,I,C)(Q↓) := |BFS(Q↓)|

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Harvesting Constraints

Text-Mining

Observation: Interaction dependencies are reported as single sentence natural language statements in literature. Tokenize full-text papers into relevant words and search for simple regular expression patterns. 71 new interaction dependencies from 59 000 human adhesome related papers. K¨

• ster, Zamir, Rahmann. 2012

... binding of Abl induces a conformational change in Cbl that allows binding

• f

Src ... p . i p a p i p d i p p p .

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Results for Complex Predicton

Network: CYGD (4579 proteins, 12576 interactions) Constraints: Competition on binding sites (Jung et al. 2010) Complexes: CYGD (55 connected complexes) Network based complex prediction: LCMA (Li et al. 2005)

458 458 random constraints 0.00 0.05 0.10 0.15 0.20 0.25

precision

458 458 random constraints 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

recall

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Results for Perturbation Impact Score

Network: CYGD (4579 proteins, 12576 interactions) Constraints: Competition on binding sites (Jung et al. 2010) Perturbations classified as lethal/sick and viable: SGD

prediction quality

20 40 60 80 100 % above threshold 49 50 51 52 53 54 55 56 57 % of true positives

• rand. constraints +- SD

no constraints constraints

TP: lethal/sick and PIS ≥ t, viable and PIS < t

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Conclusion

Protein Hypernetworks

A H G B C D E F I H I G B G A

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Conclusion

Protein Hypernetworks

A H G B C D E F I H I G B G A

more precise protein complexes perturbation effects

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Conclusion

text-mining logic inference from real measurements Protein Hypernetworks

A H G B C D E F I H I G B G A

more precise protein complexes perturbation effects

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Harvesting Constraints

Using the Quine-McCluskey-Algorithm

Given a truth table with interactions in columns and simultaneous observations in rows. Infer logic relationships using the Quine-McCluskey-Algorithm. AB BC

• bserved

1 1 1 1 1 1 1 Inferred constraints: AB ⇒ ¬BC

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Harvesting Constraints

Using the Quine-McCluskey-Algorithm

Given a truth table with interactions in columns and simultaneous observations in rows. Infer logic relationships using the Quine-McCluskey-Algorithm.

derive rows from

simultaneous interaction measurements (e.g. future variants of FCS) combination of protein complex measurements (e.g. MS) with binary protein interactions AB BC

• bserved

1 1 1 1 1 1 1 Inferred constraints: AB ⇒ ¬BC