Modeling Social Data, Lecture 7: Model complexity and generalization
Metabolic Model Generalization
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Transcript of Metabolic Model Generalization
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Project-teamMAGNOMEInria Bordeaux - Sud-Ouest
JOBIM 2013, July 1-4
Metabolic Model Generalization
Anna Zhukova
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Where's Wally ?
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Where are missing reactions ?
(The fi gure is produced using the Tulip graph visualization tool.)
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Where are missing reactions ?
(The fi gure is produced using the Tulip graph visualization tool.)
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Where are missing reactions ?
(The fi gure is produced using the Tulip graph visualization tool.)
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Where are missing reactions ?
MODEL1111190000
Loira et al., 2012
Metabolic Network of Y. lipolytica
(peroxisome)
(53 - 6) reactions
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Where are missing reactions ?
(The fi gure is produced using the Tulip graph visualization tool.)
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3-hydroxyacyl dehydrase ! Not that easy ?
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Model inference and refinement
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Let's generalize !
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Let's generalize : ubiquitous species !
(The fi gure is produced using the Tulip graph visualization tool.)
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Let's generalize !
(The fi gure is produced using the Tulip graph visualization tool.)
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Let's generalize : hydroxy fatty acyl-CoA !
(The fi gure is produced using the Tulip graph visualization tool.)
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Let's generalize !
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Let's generalize : dehydroacyl-CoA !
(The fi gure is produced using the Tulip graph visualization tool.)
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Let's generalize !
(The fi gure is produced using the Tulip graph visualization tool.)
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Let's generalize : 3-hydroxyacyl dehydratase !
(The fi gure is produced using the Tulip graph visualization tool.)
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Let's generalize !
(The fi gure is produced using the Tulip graph visualization tool.)
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Let's factor !
(The fi gure is produced using the Tulip graph visualization tool.)
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Let's improve the layout a bit...
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So, where's Wally (aka 3-hydroxyacyl-CoA dehydratase) ?
(The fi gure is produced using the Tulip graph visualization tool.)
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Some technical details...
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Some technical details...
M = (S, Sub, R) – model
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Some technical details...
M = (S, Sub, R) – model
S = {s1, ..., s
n} – species set
/including /
Sub – ubiquitous species set
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Some technical details...
M = (S, Sub, R) – model
S = {s1, ..., s
n} – species set
/including /
Sub – ubiquitous species set
R = {r1, ..., r
n} – reaction set
r = (S(react), S(prod)) – reaction/all the species are distinct (*)/
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Some technical details...
M = (S, Sub, R) – model
S = {s1, ..., s
n} – species set
/including /
Sub – ubiquitous species set
R = {r1, ..., r
n} – reaction set
r = (S(react), S(prod)) – reaction/all the species are distinct (*)/
![Page 27: Metabolic Model Generalization](https://reader033.fdocuments.net/reader033/viewer/2022052601/559626611a28ab905a8b45a2/html5/thumbnails/27.jpg)
Some technical details...
M = (S, Sub, R) – model
S = {s1, ..., s
n} – species set
/including /
Sub – ubiquitous species set
R = {r1, ..., r
n} – reaction set
r = (S(react), S(prod)) – reaction/all the species are distinct (*)/
stoichiometry = 2
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Some technical details...
Choose equivalence operation ~ :[s]~ = {s
i | s
i ~ s} – generalized species
[s(ub)]~ = {s(ub)} – (trivial) generalized ub. sp.
M = (S, Sub, R) – model
S = {s1, ..., s
n} – species set
/including /
Sub – ubiquitous species set
R = {r1, ..., r
n} – reaction set
r = (S(react), S(prod)) – reaction/all the species are distinct (*)/
![Page 29: Metabolic Model Generalization](https://reader033.fdocuments.net/reader033/viewer/2022052601/559626611a28ab905a8b45a2/html5/thumbnails/29.jpg)
Some technical details...
Choose equivalence operation ~ :[s]~ = {s
i | s
i ~ s} – generalized species
[s(ub)]~ = {s(ub)} – (trivial) generalized ub. sp.[r]~ = (S([react]), S([prod])) =
/all the generalized species are distinct (*)/
= {ri | r
i ~ r} – generalized reaction
M = (S, Sub, R) – model
S = {s1, ..., s
n} – species set
/including /
Sub – ubiquitous species set
R = {r1, ..., r
n} – reaction set
r = (S(react), S(prod)) – reaction/all the species are distinct (*)/
![Page 30: Metabolic Model Generalization](https://reader033.fdocuments.net/reader033/viewer/2022052601/559626611a28ab905a8b45a2/html5/thumbnails/30.jpg)
Some technical details...
Choose equivalence operation ~ :[s]~ = {s
i | s
i ~ s} – generalized species
[s(ub)]~ = {s(ub)} – (trivial) generalized ub. sp.[r]~ = (S([react]), S([prod])) =
/all the generalized species are distinct (*)/
= {ri | r
i ~ r} – generalized reaction
M = (S, Sub, R) – model
S = {s1, ..., s
n} – species set
/including /
Sub – ubiquitous species set
R = {r1, ..., r
n} – reaction set
r = (S(react), S(prod)) – reaction/all the species are distinct (*)/
![Page 31: Metabolic Model Generalization](https://reader033.fdocuments.net/reader033/viewer/2022052601/559626611a28ab905a8b45a2/html5/thumbnails/31.jpg)
Some technical details...
Choose equivalence operation ~ :[s]~ = {s
i | s
i ~ s} – generalized species
[s(ub)]~ = {s(ub)} – (trivial) generalized ub. sp.[r]~ = (S([react]), S([prod])) =
/all the generalized species are distinct (*)/
= {ri | r
i ~ r} – generalized reaction
M = (S, Sub, R) – model
S = {s1, ..., s
n} – species set
/including /
Sub – ubiquitous species set
R = {r1, ..., r
n} – reaction set
r = (S(react), S(prod)) – reaction/all the species are distinct (*)/
![Page 32: Metabolic Model Generalization](https://reader033.fdocuments.net/reader033/viewer/2022052601/559626611a28ab905a8b45a2/html5/thumbnails/32.jpg)
Some technical details...
Choose equivalence operation ~ :[s]~ = {s
i | s
i ~ s} – generalized species
[s(ub)]~ = {s(ub)} – (trivial) generalized ub. sp.[r]~ = (S([react]), S([prod])) =
/all the generalized species are distinct (*)/
= {ri | r
i ~ r} – generalized reaction
M = (S, Sub, R) – model
S = {s1, ..., s
n} – species set
/including /
Sub – ubiquitous species set
R = {r1, ..., r
n} – reaction set
r = (S(react), S(prod)) – reaction/all the species are distinct (*)/
![Page 33: Metabolic Model Generalization](https://reader033.fdocuments.net/reader033/viewer/2022052601/559626611a28ab905a8b45a2/html5/thumbnails/33.jpg)
Some technical details...
Choose equivalence operation ~ :[s]~ = {s
i | s
i ~ s} – generalized species
[s(ub)]~ = {s(ub)} – (trivial) generalized ub. sp.[r]~ = (S([react]), S([prod])) =
/all the generalized species are distinct (*)/
= {ri | r
i ~ r} – generalized reaction
M = (S, Sub, R) – model
S = {s1, ..., s
n} – species set
/including /
Sub – ubiquitous species set
R = {r1, ..., r
n} – reaction set
r = (S(react), S(prod)) – reaction/all the species are distinct (*)/
![Page 34: Metabolic Model Generalization](https://reader033.fdocuments.net/reader033/viewer/2022052601/559626611a28ab905a8b45a2/html5/thumbnails/34.jpg)
Some technical details...
Choose equivalence operation ~ :[s]~ = {s
i | s
i ~ s} – quotient species
[s(ub)]~ = {s(ub)} – (trivial) quotient ub. sp.[r]~ = (S([react]), S([prod])) =
/all the quotient species are distinct (*)/
= {ri | r
i ~ r} – quotient reaction
S/~ = {[s1], ..., [s
n]} – quotient species set
R/~ = {[r1], ..., [r
n]} – quotient reaction set
M/~ = (S/~, R/~) – generalized model
M = (S, Sub, R) – model
S = {s1, ..., s
n} – species set
/including /
Sub – ubiquitous species set
R = {r1, ..., r
n} – reaction set
r = (S(react), S(prod)) – reaction/all the species are distinct (*)/
![Page 35: Metabolic Model Generalization](https://reader033.fdocuments.net/reader033/viewer/2022052601/559626611a28ab905a8b45a2/html5/thumbnails/35.jpg)
Some technical details...
Choose equivalence operation ~ :[s]~ = {s
i | s
i ~ s} – generalized species
[s(ub)]~ = {s(ub)} – (trivial) generalized ub. sp.[r]~ = (S([react]), S([prod])) =
/all the generalized species are distinct (*)/
= {ri | r
i ~ r} – generalized reaction
S/~ = {[s1], ..., [s
n]} – generalized species set
R/~ = {[r1], ..., [r
n]} – generalized reaction set
M/~ = (S/~, R/~) – generalized model
Problem: Given a model M = (S, Sub, R), find an equivalence operation ~ that obeys the stoichiometry
preserving restriction (*), and minimizes the number of generalized reactions #R/~. Among such
equivalence operations choose the one that defines the maximal number of generalized species #S/~.
M = (S, Sub, R) – model
S = {s1, ..., s
n} – species set
/including /
Sub – ubiquitous species set
R = {r1, ..., r
n} – reaction set
r = (S(react), S(prod)) – reaction/all the species are distinct (*)/
![Page 36: Metabolic Model Generalization](https://reader033.fdocuments.net/reader033/viewer/2022052601/559626611a28ab905a8b45a2/html5/thumbnails/36.jpg)
Algorithm
Problem: Given a model M = (S, Sub, R), find an equivalence operation ~ that obeys the stoichiometry
preserving restriction (*), and minimizes the number of generalized reactions #R/~. Among such
equivalence operations choose the one that defines the maximal number of generalized species #S/~.
![Page 37: Metabolic Model Generalization](https://reader033.fdocuments.net/reader033/viewer/2022052601/559626611a28ab905a8b45a2/html5/thumbnails/37.jpg)
Algorithm
1. Define ~0
• [s(ub)]~0 = {s(ub)} – (trivial) generalized ub. sp.• [s]~0 = S\S
ub – generalized specific species
s1 ~ s
2 and do not participate in any equivalent reactions, then split [s
1]~0c
Problem: Given a model M = (S, Sub, R), find an equivalence operation ~ that obeys the stoichiometry
preserving restriction (*), and minimizes the number of generalized reactions #R/~. Among such
equivalence operations choose the one that defines the maximal number of generalized species #S/~.
![Page 38: Metabolic Model Generalization](https://reader033.fdocuments.net/reader033/viewer/2022052601/559626611a28ab905a8b45a2/html5/thumbnails/38.jpg)
Algorithm
1. Define ~0
• [s(ub)]~0 = {s(ub)} – (trivial) generalized ub. sp.• [s]~0 = S\S
ub – generalized specific species
s1 ~ s
2 and do not participate in any equivalent reactions, then split [s
1]~0c
Problem: Given a model M = (S, Sub, R), find an equivalence operation ~ that obeys the stoichiometry
preserving restriction (*), and minimizes the number of generalized reactions #R/~. Among such
equivalence operations choose the one that defines the maximal number of generalized species #S/~.
![Page 39: Metabolic Model Generalization](https://reader033.fdocuments.net/reader033/viewer/2022052601/559626611a28ab905a8b45a2/html5/thumbnails/39.jpg)
Algorithm
1. Define ~0
2. Preserve stoichiometry
Problem: Given a model M = (S, Sub, R), find an equivalence operation ~ that obeys the stoichiometry
preserving restriction (*), and minimizes the number of generalized reactions #R/~. Among such
equivalence operations choose the one that defines the maximal number of generalized species #S/~.
![Page 40: Metabolic Model Generalization](https://reader033.fdocuments.net/reader033/viewer/2022052601/559626611a28ab905a8b45a2/html5/thumbnails/40.jpg)
Algorithm
1. Define ~0
2. Preserve stoichiometry
Exact Set Cover Problem(NP-complete)
Greedy algorithm
Problem: Given a model M = (S, Sub, R), find an equivalence operation ~ that obeys the stoichiometry
preserving restriction (*), and minimizes the number of generalized reactions #R/~. Among such
equivalence operations choose the one that defines the maximal number of generalized species #S/~.
![Page 41: Metabolic Model Generalization](https://reader033.fdocuments.net/reader033/viewer/2022052601/559626611a28ab905a8b45a2/html5/thumbnails/41.jpg)
Algorithm
1. Define ~0
2. Preserve stoichiometry
Exact Set Cover Problem (NP-complete)Greedy Algorithm
s1 ~ s
2 and do not participate in any equivalent reactions, then split [s
1]~0c
Exact Set Cover Problem(NP-complete)
Greedy algorithm
Problem: Given a model M = (S, Sub, R), find an equivalence operation ~ that obeys the stoichiometry
preserving restriction (*), and minimizes the number of generalized reactions #R/~. Among such
equivalence operations choose the one that defines the maximal number of generalized species #S/~.
![Page 42: Metabolic Model Generalization](https://reader033.fdocuments.net/reader033/viewer/2022052601/559626611a28ab905a8b45a2/html5/thumbnails/42.jpg)
Algorithm
1. Define ~0
2. Preserve stoichiometry
Exact Set Cover Problem (NP-complete)Greedy Algorithm
s1 ~ s
2 and do not participate in any equivalent reactions, then split [s
1]~0c
Problem: Given a model M = (S, Sub, R), find an equivalence operation ~ that obeys the stoichiometry
preserving restriction (*), and minimizes the number of generalized reactions #R/~. Among such
equivalence operations choose the one that defines the maximal number of generalized species #S/~.
![Page 43: Metabolic Model Generalization](https://reader033.fdocuments.net/reader033/viewer/2022052601/559626611a28ab905a8b45a2/html5/thumbnails/43.jpg)
Algorithm
1. Define ~0
2. Preserve stoichiometry
Exact Set Cover Problem (NP-complete)Greedy Algorithm
s1 ~ s
2 and do not participate in any equivalent reactions, then split [s
1]~0c
Exact Set Cover Problem(NP-complete)
Greedy algorithm
Problem: Given a model M = (S, Sub, R), find an equivalence operation ~ that obeys the stoichiometry
preserving restriction (*), and minimizes the number of generalized reactions #R/~. Among such
equivalence operations choose the one that defines the maximal number of generalized species #S/~.
![Page 44: Metabolic Model Generalization](https://reader033.fdocuments.net/reader033/viewer/2022052601/559626611a28ab905a8b45a2/html5/thumbnails/44.jpg)
Algorithm
1. Define ~0
2. Preserve stoichiometry
3. Maximize generalized species numberreactions, then split [s1]~0c
Problem: Given a model M = (S, Sub, R), find an equivalence operation ~ that obeys the stoichiometry
preserving restriction (*), and minimizes the number of generalized reactions #R/~. Among such
equivalence operations choose the one that defines the maximal number of generalized species #S/~.
![Page 45: Metabolic Model Generalization](https://reader033.fdocuments.net/reader033/viewer/2022052601/559626611a28ab905a8b45a2/html5/thumbnails/45.jpg)
Algorithm
1. Define ~0
2. Preserve stoichiometry
3. Maximize generalized species numberreactions, then split [s1]~0c
Problem: Given a model M = (S, Sub, R), find an equivalence operation ~ that obeys the stoichiometry
preserving restriction (*), and minimizes the number of generalized reactions #R/~. Among such
equivalence operations choose the one that defines the maximal number of generalized species #S/~.
![Page 46: Metabolic Model Generalization](https://reader033.fdocuments.net/reader033/viewer/2022052601/559626611a28ab905a8b45a2/html5/thumbnails/46.jpg)
53 → 15
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Acknowledgements
Magnome Team, Inria Bordeaux, France
David James ShermanPascal DurrensFlorian LajusWitold DyrkaRazanne Issa
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Acknowledgements
Magnome Team, Inria Bordeaux, France
David James ShermanPascal DurrensFlorian LajusWitold DyrkaRazanne Issa
Center for Genome Regulation and CIRIC-InriaSantiago, Chile
Nicolás Loira
![Page 49: Metabolic Model Generalization](https://reader033.fdocuments.net/reader033/viewer/2022052601/559626611a28ab905a8b45a2/html5/thumbnails/49.jpg)
Acknowledgements
Magnome Team, Inria Bordeaux, France
David James ShermanPascal DurrensFlorian LajusWitold DyrkaRazanne Issa
Center for Genome Regulation and CIRIC-InriaSantiago, Chile
Nicolás Loira
L'institut MicalisGrignon, France
Stéphanie MichelyJean-Marc Nicaud
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Acknowledgements
Magnome Team, Inria Bordeaux, France
David James ShermanPascal DurrensFlorian LajusWitold DyrkaRazanne Issa
Center for Genome Regulation and CIRIC-InriaSantiago, Chile
Nicolás Loira
L'institut MicalisGrignon, France
Stéphanie MichelyJean-Marc Nicaud
LaBRI Bordeaux, France
Antoine LambertRomain Bourqui
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Acknowledgements
Magnome Team, Inria Bordeaux, France
David James ShermanPascal DurrensFlorian LajusWitold DyrkaRazanne Issa
Center for Genome Regulation and CIRIC-InriaSantiago, Chile
Nicolás Loira
L'institut MicalisGrignon, France
Stéphanie MichelyJean-Marc Nicaud
LaBRI Bordeaux, France
Antoine LambertRomain Bourqui
findwally.co.ukLondon, UK
Martin HandfordWally
![Page 52: Metabolic Model Generalization](https://reader033.fdocuments.net/reader033/viewer/2022052601/559626611a28ab905a8b45a2/html5/thumbnails/52.jpg)
Thank you!