The document summarizes Anna Zhukova's presentation on metabolic model generalization. It discusses an algorithm to generalize metabolic models by finding an equivalence relation that minimizes the number of generalized reactions while maximizing the number of generalized species, while preserving stoichiometry. The algorithm works by first defining generalized ubiquitous and specific species, then using a greedy algorithm to solve the exact set cover problem of grouping species into generalized reactions in a way that preserves stoichiometry, and finally maximizing the number of generalized species. The presentation shows an example network being generalized from 53 to 15 reactions.

1. Metabolic Model Generalization
Anna Zhukova
Project-team
MAGNOME
Inria Bordeaux - Sud-Ouest
JOBIM 2013, July 1-4

2. Where's Wally ?

3. Where are missing reactions ?
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4. Where are missing reactions ?
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5. Where are missing reactions ?
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6. Where are missing reactions ?
MODEL1111190000
Loira et al., 2012
Metabolic Network of
Y. lipolytica
(peroxisome)
(53 - 6) reactions
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7. Where are missing reactions ?
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8. 3-hydroxyacyl dehydrase ! Not that easy ?
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9. Model inference and refinement

10. Let's generalize !
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11. Let's generalize : ubiquitous species !
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12. Let's generalize !
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13. Let's generalize : hydroxy fatty acyl-CoA !
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14. Let's generalize !
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15. Let's generalize : dehydroacyl-CoA !
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16. Let's generalize !
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17. Let's generalize : 3-hydroxyacyl dehydratase !
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18. Let's generalize !
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19. Let's factor !
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20. Let's improve the layout a bit...
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21. So, where's Wally (aka 3-hydroxyacyl-CoA
dehydratase) ?
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22. Some technical details...

23. Some technical details...
M = (S, Sub, R) –
model

24. Some technical details...
M = (S, Sub, R) –
S = {s1, ..., sn} –
model
species set
/including /
Sub –
ubiquitous species set

25. Some technical details...
M = (S, Sub, R) –
S = {s1, ..., sn} –
model
species set
/including /
Sub –
ubiquitous species set
R = {r1, ..., rn} –
reaction set
r = (S(react), S(prod)) –
reaction
/all the species are distinct (*)/

26. Some technical details...
M = (S, Sub, R) –
S = {s1, ..., sn} –
model
species set
/including /
Sub –
ubiquitous species set
R = {r1, ..., rn} –
reaction set
r = (S(react), S(prod)) –
reaction
/all the species are distinct (*)/

27. Some technical details...
M = (S, Sub, R) –
S = {s1, ..., sn} –
model
species set
/including /
Sub –
ubiquitous species set
R = {r1, ..., rn} –
reaction set
r = (S(react), S(prod)) –
reaction
/all the species are distinct (*)/
stoichiometry =
2

28. Some technical details...
M = (S, Sub, R) –
S = {s1, ..., sn} –
model
[s]~ = {si | si ~ s} –
species set
/including /
Sub –
ubiquitous species set
R = {r1, ..., rn} –
Choose equivalence operation ~ :
reaction set
r = (S(react), S(prod)) –
reaction
/all the species are distinct (*)/
generalized species
[s(ub)]~ = {s(ub)} –
(trivial) generalized ub. sp.

29. Some technical details...
M = (S, Sub, R) –
S = {s1, ..., sn} –
model
[s]~ = {si | si ~ s} –
species set
/including /
Sub –
ubiquitous species set
R = {r1, ..., rn} –
Choose equivalence operation ~ :
reaction set
r = (S(react), S(prod)) –
reaction
/all the species are distinct (*)/
generalized species
[s(ub)]~ = {s(ub)} – (trivial)
[r]~ = (S([react]), S([prod])) =
generalized ub. sp.
/all the generalized species are distinct (*)/
= {ri | ri ~ r} –
generalized reaction

30. Some technical details...
M = (S, Sub, R) –
S = {s1, ..., sn} –
model
[s]~ = {si | si ~ s} –
species set
/including /
Sub –
ubiquitous species set
R = {r1, ..., rn} –
Choose equivalence operation ~ :
reaction set
r = (S(react), S(prod)) –
reaction
/all the species are distinct (*)/
generalized species
[s(ub)]~ = {s(ub)} – (trivial)
[r]~ = (S([react]), S([prod])) =
generalized ub. sp.
/all the generalized species are distinct (*)/
= {ri | ri ~ r} –
generalized reaction

31. Some technical details...
M = (S, Sub, R) –
S = {s1, ..., sn} –
model
[s]~ = {si | si ~ s} –
species set
/including /
Sub –
ubiquitous species set
R = {r1, ..., rn} –
Choose equivalence operation ~ :
reaction set
r = (S(react), S(prod)) –
reaction
/all the species are distinct (*)/
generalized species
[s(ub)]~ = {s(ub)} – (trivial)
[r]~ = (S([react]), S([prod])) =
generalized ub. sp.
/all the generalized species are distinct (*)/
= {ri | ri ~ r} –
generalized reaction

32. Some technical details...
M = (S, Sub, R) –
S = {s1, ..., sn} –
model
[s]~ = {si | si ~ s} –
species set
/including /
Sub –
ubiquitous species set
R = {r1, ..., rn} –
Choose equivalence operation ~ :
reaction set
r = (S(react), S(prod)) –
reaction
/all the species are distinct (*)/
generalized species
[s(ub)]~ = {s(ub)} – (trivial)
[r]~ = (S([react]), S([prod])) =
generalized ub. sp.
/all the generalized species are distinct (*)/
= {ri | ri ~ r} –
generalized reaction

33. Some technical details...
M = (S, Sub, R) –
S = {s1, ..., sn} –
model
[s]~ = {si | si ~ s} –
species set
/including /
Sub –
ubiquitous species set
R = {r1, ..., rn} –
Choose equivalence operation ~ :
reaction set
r = (S(react), S(prod)) –
reaction
/all the species are distinct (*)/
generalized species
[s(ub)]~ = {s(ub)} – (trivial)
[r]~ = (S([react]), S([prod])) =
generalized ub. sp.
/all the generalized species are distinct (*)/
= {ri | ri ~ r} –
generalized reaction

34. Some technical details...
M = (S, Sub, R) –
S = {s1, ..., sn} –
model
[s]~ = {si | si ~ s} –
species set
/including /
Sub –
ubiquitous species set
R = {r1, ..., rn} –
Choose equivalence operation ~ :
reaction set
r = (S(react), S(prod)) –
reaction
/all the species are distinct (*)/
quotient species
[s(ub)]~ = {s(ub)} – (trivial)
[r]~ = (S([react]), S([prod])) =
quotient ub. sp.
/all the quotient species are distinct (*)/
= {ri | ri ~ r} –
quotient reaction
S/~ = {[s1], ..., [sn]} –
R/~ = {[r1], ..., [rn]} –
M/~ = (S/~, R/~) –
quotient species set
quotient reaction set
generalized model

35. Some technical details...
M = (S, Sub, R) –
S = {s1, ..., sn} –
Choose equivalence operation ~ :
model
[s]~ = {si | si ~ s} –
[s(ub)]~ = {s(ub)} – (trivial)
[r]~ = (S([react]), S([prod])) =
species set
/including /
Sub –
ubiquitous species set
R = {r1, ..., rn} –
reaction set
r = (S(react), S(prod)) –
reaction
/all the species are distinct (*)/
ub
generalized ub. sp.
/all the generalized species are distinct (*)/
= {ri | ri ~ r} –
generalized reaction
S/~ = {[s1], ..., [sn]} –
R/~ = {[r1], ..., [rn]} –
M/~ = (S/~, R/~) –
Problem: Given a model M = (S, S
generalized species
generalized species set
generalized reaction set
generalized model
, 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/~.

36. Algorithm
Problem: Given a model M = (S, S
ub
, 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/~.

37. Algorithm
0
1. Define ~
•
•
[s(ub)]~0 = {s(ub)} – (trivial) generalized ub. sp.
[s]~0 = SSub – generalized specific species
s1 ~ s2 and do not participate in any equivalent reactions, then split [s1]~0c
Problem: Given a model M = (S, S
ub
, 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/~.

38. Algorithm
0
1. Define ~
•
•
[s(ub)]~0 = {s(ub)} – (trivial) generalized ub. sp.
[s]~0 = SSub – generalized specific species
s1 ~ s2 and do not participate in any equivalent reactions, then split [s1]~0c
Problem: Given a model M = (S, S
ub
, 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/~.

39. Algorithm
0
1. Define ~
2. Preserve stoichiometry
Problem: Given a model M = (S, S
ub
, 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/~.

40. Algorithm
0
1. Define ~
2. Preserve stoichiometry
Exact Set Cover Problem
(NP-complete)
Greedy algorithm
Problem: Given a model M = (S, S
ub
, 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/~.

41. Algorithm
0
1. Define ~
2. Preserve stoichiometry
Exact Set Cover Problem
Exact Set Cover Problem (NP-complete)
(NP-complete)
Greedy Algorithm
Greedy algorithm
s1 ~ s2 and do not participate in any equivalent reactions, then split [s1]~0c
Problem: Given a model M = (S, S
ub
, 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/~.

42. Algorithm
0
1. Define ~
2. Preserve stoichiometry
Exact Set Cover Problem (NP-complete)
Greedy Algorithm
s1 ~ s2 and do not participate in any equivalent reactions, then split [s1]~0c
Problem: Given a model M = (S, S
ub
, 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/~.

43. Algorithm
0
1. Define ~
2. Preserve stoichiometry
Exact Set Cover Problem
Exact Set Cover Problem (NP-complete)
(NP-complete)
Greedy Algorithm
Greedy algorithm
s1 ~ s2 and do not participate in any equivalent reactions, then split [s1]~0c
Problem: Given a model M = (S, S
ub
, 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/~.

44. Algorithm
0
1. Define ~
2. Preserve stoichiometry
]~0c
1
3. Maximize generalized species numberreactions, then split [s
Problem: Given a model M = (S, S
ub
, 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/~.

45. Algorithm
0
1. Define ~
2. Preserve stoichiometry
]~0c
1
3. Maximize generalized species numberreactions, then split [s
Problem: Given a model M = (S, S
ub
, 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/~.

46. 53 → 15

47. Acknowledgements
Magnome Team, Inria
Bordeaux, France
David James Sherman
Pascal Durrens
Florian Lajus
Witold Dyrka
Razanne Issa

48. Acknowledgements
Magnome Team, Inria
Bordeaux, France
David James Sherman
Pascal Durrens
Florian Lajus
Witold Dyrka
Razanne Issa
Center for Genome Regulation
and CIRIC-Inria
Santiago, Chile
Nicolás Loira

49. Acknowledgements
Magnome Team, Inria
Bordeaux, France
David James Sherman
Pascal Durrens
Florian Lajus
Witold Dyrka
Razanne Issa
Center for Genome Regulation
and CIRIC-Inria
Santiago, Chile
Nicolás Loira
L'institut Micalis
Grignon, France
Stéphanie Michely
Jean-Marc Nicaud

50. Acknowledgements
Magnome Team, Inria
Bordeaux, France
David James Sherman
Pascal Durrens
Florian Lajus
Witold Dyrka
Razanne Issa
Nicolás Loira
L'institut Micalis
Grignon, France
Stéphanie Michely
Jean-Marc Nicaud
LaBRI
Bordeaux, France
Antoine Lambert
Romain Bourqui
Center for Genome Regulation
and CIRIC-Inria
Santiago, Chile

51. Acknowledgements
Center for Genome Regulation
and CIRIC-Inria
Santiago, Chile
Magnome Team, Inria
Bordeaux, France
David James Sherman
Pascal Durrens
Florian Lajus
Witold Dyrka
Razanne Issa
Nicolás Loira
L'institut Micalis
Grignon, France
Stéphanie Michely
Jean-Marc Nicaud
LaBRI
Bordeaux, France
findwally.co.uk
London, UK
Antoine Lambert
Romain Bourqui
Martin Handford
Wally

52. Thank you!