Genome-scale metabolic models describe the relationships between thousands of reactions and biochemical molecules, and are used to improve our understanding of organism’s metabolism. They found applications in pharmaceutical, chemical and bioremediation industries. The complexity of metabolic models hampers many tasks that are important during the process of model inference, such as model comparison, analysis, curation and refinement by human experts. The abundance of details in large-scale networks can mask errors and important organism-specific adaptations. It is therefore important to find the right levels of abstraction that are comfortable for human experts. These abstract levels should highlight the essential model structure and the divergences from it, such as alternative paths or missing reactions, while hiding inessential details. To address this issue, we defined a knowledge-based generalization that allows for production of higher-level abstract views of metabolic network models. We developed a theoretical method that groups similar metabolites and reactions based on the network structure and the knowledge extracted from metabolite ontologies, and then compresses the network based on this grouping. We implemented our method as a python library, that is available for download from metamogen.gforge.inria.fr. To validate our method we applied it to 1 286 metabolic models from the Path2Model project, and showed that it helps to detect organism-, and domain-specific adaptations, as well as to compare models. Based on discussions with users about their ways of navigation in metabolic networks, we defined a 3-level representation of metabolic networks: the full-model level, the generalized level, the compartment level. We combined our model generalization method with the zooming user interface (ZUI) paradigm and developed Mimoza, a user-centric tool for zoomable navigation and knowledge-based exploration of metabolic networks that produces this 3-level representation. Mimoza is available both as an on-line tool and for download at mimoza.bordeaux.inria.fr.

1. Knowledge-based generalization for metabolic
models
G´en´eralisation de mod`eles m´etaboliques par connaissances
Anna Zhukova 1,2 David J. Sherman 2
1Laboratoire de m´etabolisme ´energ´etique cellulaire IBGC - CNRS
1 rue Camille Saint-Sa¨ens, 33077 Bordeaux cedex France
2Inria / CNRS / University of Bordeaux
joint project-team MAGNOME
351, cours de la Lib´eration, 33405 Talence cedex France
February 12, 2015
Anna Zhukova (MAGNOME) Knowledge-based generalization February 12, 2015 1 / 45

2. Metabolic modeling
Metabolic models are mathematical descriptions of biochemical
reactions between molecules in a cell.
Metabolic models are used for:
recording knowledge
simulation
inference of other models
understanding how genotype influences phenotype
metabolic engineering
food and beverages
pharmaceuticals
biofuels
disease analysis: novel drug targets
Anna Zhukova (MAGNOME) Knowledge-based generalization February 12, 2015 2 / 45

3. Size of metabolic models
pathway-scale - up to hundreds of reactions
genome-scale - thousands of reactions
bacterium E. coli [Smallbone, 2013] – 2 168 reactions
yeast S. cerevisiae [Aung et al., 2013] – 2 352 reactions
human [Thiele et al., 2013] – 7 440 reactions
Anna Zhukova (MAGNOME) Knowledge-based generalization February 12, 2015 3 / 45

4. Precision vs Readability
Anna Zhukova (MAGNOME) Knowledge-based generalization February 12, 2015 4 / 45

5. Precision vs Readability: our solution
Anna Zhukova (MAGNOME) Knowledge-based generalization February 12, 2015 5 / 45

6. Introduction
Outline
1 Introduction
2 Generalization method [Zhukova and Sherman, J Comput Biol 2014]
3 Validation [Zhukova and Sherman, J Bioinf Comput Biol 2014]
4 Mimoza: web-based navigation
[Zhukova and Sherman, BMC Syst Bio (forthcoming)]
5 Conclusions and Perspectives
Anna Zhukova (MAGNOME) Knowledge-based generalization February 12, 2015 6 / 45

7. Introduction
Modeling workflow
Model/pathway/reaction
repositories:
[Li et al., 2010]
[Kanehisa et al., 2012]
[Alc´antara et al., 2012]
Anna Zhukova (MAGNOME) Knowledge-based generalization February 12, 2015 7 / 45

8. Introduction
Modeling workflow
Standards:
[Hucka et al., 2003]
[Lloyd et al., 2004]
[Le Nov`ere et al., 2009]
Anna Zhukova (MAGNOME) Knowledge-based generalization February 12, 2015 7 / 45

9. Introduction
Modeling workflow
Inference Tools:
PathwayTools
[Karp et al., 2002]
SuBliMinaL
[Swainston et al., 2011]
CoReCo
[Pitk¨anen et al., 2014]
Anna Zhukova (MAGNOME) Knowledge-based generalization February 12, 2015 7 / 45

10. Introduction
Modeling workflow
Errors/Peculiarities:
Anna Zhukova (MAGNOME) Knowledge-based generalization February 12, 2015 7 / 45

11. Introduction
Modeling workflow
Ontologies:
[Courtot et al., 2011]
[Ashburner et al., 2000]
[de Matos et al., 2010]
Anna Zhukova (MAGNOME) Knowledge-based generalization February 12, 2015 7 / 45

12. Introduction
Modeling workflow
Simulation:
COPASI
[Hoops et al., 2006]
FAME
[Boele et al., 2012]
COBRApy
[Ebrahim et al., 2013]
Anna Zhukova (MAGNOME) Knowledge-based generalization February 12, 2015 7 / 45

13. Introduction
Genome-scale models are complicated
Anna Zhukova (MAGNOME) Knowledge-based generalization February 12, 2015 8 / 45

14. Introduction
Genome-scale models are complicated
Anna Zhukova (MAGNOME) Knowledge-based generalization February 12, 2015 8 / 45

15. Introduction
Self-similarities
Anna Zhukova (MAGNOME) Knowledge-based generalization February 12, 2015 9 / 45

16. Introduction
Self-similarities
Anna Zhukova (MAGNOME) Knowledge-based generalization February 12, 2015 9 / 45

17. Introduction
Self-similarities
3-oxo-fatty acyl-CoAs: different lengths of carbon chains
Anna Zhukova (MAGNOME) Knowledge-based generalization February 12, 2015 9 / 45

18. Introduction
Self-similarities
hydroxy fatty acyl-CoAs: different lengths of carbon chains
Anna Zhukova (MAGNOME) Knowledge-based generalization February 12, 2015 9 / 45

19. Introduction
Self-similarities
oxidation: hydroxy FA-CoA + NAD ↔ 3-oxo-FA-CoA + H+
+ NADH
Anna Zhukova (MAGNOME) Knowledge-based generalization February 12, 2015 9 / 45

20. Introduction
Objective
exploit self-similarities
semantically robust
meaningful for biologists
produce abstract views
essential model structure
highlight the particularities
expose potential errors
Anna Zhukova (MAGNOME) Knowledge-based generalization February 12, 2015 10 / 45

21. Generalization method
Outline
1 Introduction
2 Generalization method [Zhukova and Sherman, J Comput Biol 2014]
3 Validation [Zhukova and Sherman, J Bioinf Comput Biol 2014]
4 Mimoza: web-based navigation
[Zhukova and Sherman, BMC Syst Bio (forthcoming)]
5 Conclusions and Perspectives
Anna Zhukova (MAGNOME) Knowledge-based generalization February 12, 2015 11 / 45

22. Generalization method
Formal definition: Model
Model: N = M, R
Metabolite set: M = {m1, . . . , mn}
Reaction set: R = {r1, . . . , rk }
reaction: R r = M(react)
, M(prod)
Anna Zhukova (MAGNOME) Knowledge-based generalization February 12, 2015 12 / 45

23. Generalization method
Formal definition: Model
Model: N = M, R - bipartite graph,
Metabolite set: M = {m1, . . . , mn} - M-nodes,
Reaction set: R = {r1, . . . , rk } - R-nodes,
reaction: R r = M(react)
, M(prod)
- edges bw M- and R-nodes
Anna Zhukova (MAGNOME) Knowledge-based generalization February 12, 2015 12 / 45

24. Generalization method
Formal definition: Model
Model: N = M, R - bipartite graph,
Metabolite set: M = {m1, . . . , mn} - M-nodes,
Ubiq. m. set: M ⊃ Mub
- duplicated M-nodes,
Reaction set: R = {r1, . . . , rk } - R-nodes,
reaction: R r = M(react)
, M(prod)
- edges bw M- and R-nodes
Anna Zhukova (MAGNOME) Knowledge-based generalization February 12, 2015 12 / 45

25. Generalization method
Formal definition: Model
Model: N = M, R - bipartite graph,
Metabolite set: M = {m1, . . . , mn} - M-nodes,
Ubiq. m. set: M ⊃ Mub
- duplicated M-nodes,
Reaction set: R = {r1, . . . , rk } - R-nodes,
reaction: R r = M(react)
, M(prod)
- edges bw M- and R-nodes
/all the met. are distinct/ /no parallel edges/.
Anna Zhukova (MAGNOME) Knowledge-based generalization February 12, 2015 12 / 45

26. Generalization method
Formal definition: Model
Model: N = M, R - bipartite graph,
Metabolite set: M = {m1, . . . , mn} - M-nodes,
Ubiq. m. set: M ⊃ Mub
- duplicated M-nodes,
Reaction set: R = {r1, . . . , rk } - R-nodes,
reaction: R r = M(react)
, M(prod)
- edges bw M- and R-nodes
/all the met. are distinct/ /no parallel edges/.
Anna Zhukova (MAGNOME) Knowledge-based generalization February 12, 2015 12 / 45

27. Generalization method
Formal definition: Model
Model: N = M, R - bipartite graph,
Metabolite set: M = {m1, . . . , mn} - M-nodes,
Ubiq. m. set: M ⊃ Mub
- duplicated M-nodes,
Reaction set: R = {r1, . . . , rk } - R-nodes,
reaction: R r = M(react)
, M(prod)
- edges bw M- and R-nodes
/all the met. are distinct/ /no parallel edges/.
Anna Zhukova (MAGNOME) Knowledge-based generalization February 12, 2015 12 / 45

28. Generalization method
Formal definition: Generalization
Choose equivalence operation ∼:
[m]∼
= { ˜m ∈ M| ˜m ∼ m} - generalized metabolite
[m(ub)
]
∼
= {m(ub)
} - (trivial) gen. ub. m.,
[r]
∼
= M([react])
, M([prod])
= {˜r|˜r ∼ r} - generalized reaction
Anna Zhukova (MAGNOME) Knowledge-based generalization February 12, 2015 13 / 45

29. Generalization method
Formal definition: Generalization
Choose equivalence operation ∼:
[m]∼
= { ˜m ∈ M| ˜m ∼ m} - generalized metabolite
[m(ub)
]
∼
= {m(ub)
} - (trivial) gen. ub. m.,
[r]
∼
= M([react])
, M([prod])
= {˜r|˜r ∼ r} - generalized reaction
Stoichiomenty preserving restriction (1): All the generalized metabolites
participating in a reaction are distinct. (In- and out-degrees of R-nodes are
conserved.)
Anna Zhukova (MAGNOME) Knowledge-based generalization February 12, 2015 13 / 45

30. Generalization method
Formal definition: Generalization
Choose equivalence operation ∼:
[m]∼
= { ˜m ∈ M| ˜m ∼ m} - generalized metabolite
[m(ub)
]
∼
= {m(ub)
} - (trivial) gen. ub. m.,
[r]
∼
= M([react])
, M([prod])
= {˜r|˜r ∼ r} - generalized reaction
Stoichiomenty preserving restriction (1): All the generalized metabolites
participating in a reaction are distinct. (In- and out-degrees of R-nodes are
conserved.)
Anna Zhukova (MAGNOME) Knowledge-based generalization February 12, 2015 13 / 45

31. Generalization method
Formal definition: Generalization
Choose equivalence operation ∼:
[m]∼
= { ˜m ∈ M| ˜m ∼ m} - generalized metabolite
[m(ub)
]
∼
= {m(ub)
} - (trivial) gen. ub. m.,
[r]
∼
= M([react])
, M([prod])
= {˜r|˜r ∼ r} - generalized reaction
Stoichiomenty preserving restriction (1): All the generalized metabolites
participating in a reaction are distinct. (In- and out-degrees of R-nodes are
conserved.)
Anna Zhukova (MAGNOME) Knowledge-based generalization February 12, 2015 13 / 45

32. Generalization method
Formal definition: Generalization
Choose equivalence operation ∼:
[m]∼
= { ˜m ∈ M| ˜m ∼ m} - generalized metabolite
[m(ub)
]
∼
= {m(ub)
} - (trivial) gen. ub. m.,
[r]
∼
= M([react])
, M([prod])
= {˜r|˜r ∼ r} - generalized reaction
Stoichiomenty preserving restriction (1): All the generalized metabolites
participating in a reaction are distinct. (In- and out-degrees of R-nodes are
conserved.)
Anna Zhukova (MAGNOME) Knowledge-based generalization February 12, 2015 13 / 45

33. Generalization method
Formal definition: Generalization
Choose equivalence operation ∼:
[m]∼
= { ˜m ∈ M| ˜m ∼ m} - generalized metabolite
[m(ub)
]
∼
= {m(ub)
} - (trivial) gen. ub. m.,
[r]
∼
= M([react])
, M([prod])
= {˜r|˜r ∼ r} - generalized reaction
Stoichiomenty preserving restriction (1): All the generalized metabolites
participating in a reaction are distinct. (In- and out-degrees of R-nodes are
conserved.)
Anna Zhukova (MAGNOME) Knowledge-based generalization February 12, 2015 13 / 45

34. Generalization method
Formal definition: Generalization
Choose equivalence operation ∼:
[m]∼
= { ˜m ∈ M| ˜m ∼ m} - generalized metabolite
[m(ub)
]
∼
= {m(ub)
} - (trivial) gen. ub. m.,
[r]
∼
= M([react])
, M([prod])
= {˜r|˜r ∼ r} - generalized reaction
Stoichiomenty preserving restriction (1): All the generalized metabolites
participating in a reaction are distinct. (In- and out-degrees of R-nodes are
conserved.)
Anna Zhukova (MAGNOME) Knowledge-based generalization February 12, 2015 13 / 45

35. Generalization method
Formal definition: Generalization
Choose equivalence operation ∼:
[m]∼
= { ˜m ∈ M| ˜m ∼ m} - generalized metabolite
[m(ub)
]
∼
= {m(ub)
} - (trivial) gen. ub. m.,
[r]
∼
= M([react])
, M([prod])
= {˜r|˜r ∼ r} - generalized reaction
Stoichiomenty preserving restriction (1): All the generalized metabolites
participating in a reaction are distinct. (In- and out-degrees of R-nodes are
conserved.)
Anna Zhukova (MAGNOME) Knowledge-based generalization February 12, 2015 13 / 45

36. Generalization method
Formal definition: Generalization
Choose equivalence operation ∼:
[m]∼
= { ˜m ∈ M| ˜m ∼ m} - generalized metabolite
[m(ub)
]
∼
= {m(ub)
} - (trivial) gen. ub. m.,
[r]
∼
= M([react])
, M([prod])
= {˜r|˜r ∼ r} - generalized reaction
Metabolite diversity restriction (2): Equivalent metabolites must participate
in equivalent reactions. (Min. degrees of gen. M-nodes.)
Anna Zhukova (MAGNOME) Knowledge-based generalization February 12, 2015 13 / 45

37. Generalization method
Formal definition: Generalization
Choose equivalence operation ∼:
[m]∼
= { ˜m ∈ M| ˜m ∼ m} - generalized metabolite
[m(ub)
]
∼
= {m(ub)
} - (trivial) gen. ub. m.,
[r]
∼
= M([react])
, M([prod])
= {˜r|˜r ∼ r} - generalized reaction
Metabolite diversity restriction (2): Equivalent metabolites must participate
in equivalent reactions. (Min. degrees of gen. M-nodes.)
Anna Zhukova (MAGNOME) Knowledge-based generalization February 12, 2015 13 / 45

38. Generalization method
Formal definition: Generalization
Choose equivalence operation ∼:
[m]∼
= { ˜m ∈ M| ˜m ∼ m} - generalized metabolite
[m(ub)
]
∼
= {m(ub)
} - (trivial) gen. ub. m.,
[r]
∼
= M([react])
, M([prod])
= {˜r|˜r ∼ r} - generalized reaction
Metabolite diversity restriction (2): Equivalent metabolites must participate
in equivalent reactions. (Min. degrees of gen. M-nodes.)
Anna Zhukova (MAGNOME) Knowledge-based generalization February 12, 2015 13 / 45

39. Generalization method
Formal definition: Generalization
Choose equivalence operation ∼:
[m]∼
= { ˜m ∈ M| ˜m ∼ m} - generalized metabolite
[m(ub)
]
∼
= {m(ub)
} - (trivial) gen. ub. m.,
[r]
∼
= M([react])
, M([prod])
= {˜r|˜r ∼ r} - generalized reaction
Metabolite diversity restriction (2): Equivalent metabolites must participate
in equivalent reactions. (Min. degrees of gen. M-nodes.)
Anna Zhukova (MAGNOME) Knowledge-based generalization February 12, 2015 13 / 45

40. Generalization method
Formal definition: Generalization
Choose equivalence operation ∼:
[m]∼
= { ˜m ∈ M| ˜m ∼ m} - generalized metabolite
[m(ub)
]
∼
= {m(ub)
} - (trivial) gen. ub. m.,
[r]
∼
= M([react])
, M([prod])
= {˜r|˜r ∼ r} - generalized reaction
Stoichiomenty preserving restriction (1): All the generalized metabolites
participating in a reaction are distinct. (In- and out-degrees of R-nodes are
conserved.)
Metabolite diversity restriction (2): Equivalent metabolites must participate
in equivalent reactions. (Min. degrees of gen. M-nodes.)
Anna Zhukova (MAGNOME) Knowledge-based generalization February 12, 2015 13 / 45

41. Generalization method
Formal definition: Model generalization problem
Problem: Given a metabolic model N = M ⊃ M(ub), R find an
equivalence operation ∼ that obeys the stoichiometry preserving
restriction (1) and the metabolite diversity restriction (2), and minimizes
the number of reaction equivalence classes R/ ∼.
N/ ∼ = M/ ∼, R/ ∼ - generalized model,
M/ ∼ = {[m1]∼, . . . , [m˜n]∼} - generalized metabolite set,
R/ ∼ = {[r1]∼, . . . , [r˜k ]∼} - generalized reaction set.
Anna Zhukova (MAGNOME) Knowledge-based generalization February 12, 2015 14 / 45

42. Generalization method
Model generalization algorithm
Algorithm:
1 Define ˚∼;
2 Satisfy restriction (1);
3 Satisfy restriction (2);
Anna Zhukova (MAGNOME) Knowledge-based generalization February 12, 2015 15 / 45

43. Generalization method
Model generalization algorithm
Algorithm:
1 Define ˚∼;
[m(ub)
]˚∼
= {m(ub)
} - gen. ub. m.,
[m]
˚∼
= MM(ub)
- gen. met.
Anna Zhukova (MAGNOME) Knowledge-based generalization February 12, 2015 15 / 45

44. Generalization method
Model generalization algorithm
Algorithm:
1 Define ˚∼;
[m(ub)
]˚∼
= {m(ub)
} - gen. ub. m.,
[m]
˚∼
= MM(ub)
- gen. met.
Anna Zhukova (MAGNOME) Knowledge-based generalization February 12, 2015 15 / 45

45. Generalization method
Model generalization algorithm
Algorithm:
1 Define ˚∼;
2 Satisfy restriction (1);
Anna Zhukova (MAGNOME) Knowledge-based generalization February 12, 2015 15 / 45

46. Generalization method
Model generalization algorithm
Algorithm:
1 Define ˚∼;
2 Satisfy restriction (1);
Metabolite ontology – partial order of M-nodes
[de Matos et al., 2010]
Anna Zhukova (MAGNOME) Knowledge-based generalization February 12, 2015 15 / 45

47. Generalization method
Model generalization algorithm
Algorithm:
1 Define ˚∼;
2 Satisfy restriction (1);
Metabolite ontology – partial order of M-nodes
Exact set cover (NP-complete [Goldreich, 2008])
Greedy alg. – best polyn. time approx. [Feige, 1998]
Anna Zhukova (MAGNOME) Knowledge-based generalization February 12, 2015 15 / 45

48. Generalization method
Model generalization algorithm
Algorithm:
1 Define ˚∼;
2 Satisfy restriction (1);
Metabolite ontology – partial order of M-nodes
Exact set cover (NP-complete [Goldreich, 2008])
Greedy alg. – best polyn. time approx. [Feige, 1998]
Anna Zhukova (MAGNOME) Knowledge-based generalization February 12, 2015 15 / 45

49. Generalization method
Model generalization algorithm
Algorithm:
1 Define ˚∼;
2 Satisfy restriction (1);
3 Satisfy restriction (2);
Anna Zhukova (MAGNOME) Knowledge-based generalization February 12, 2015 15 / 45

50. Generalization method
Model generalization algorithm
Algorithm:
1 Define ˚∼;
2 Satisfy restriction (1);
3 Satisfy restriction (2);
Anna Zhukova (MAGNOME) Knowledge-based generalization February 12, 2015 15 / 45

51. Generalization method
Model generalization algorithm
Algorithm:
1 Define ˚∼;
2 Satisfy restriction (1);
3 Satisfy restriction (2);
Anna Zhukova (MAGNOME) Knowledge-based generalization February 12, 2015 15 / 45

52. Generalization method
Model generalization algorithm
Algorithm:
1 Define ˚∼;
2 Satisfy restriction (1);
3 Satisfy restriction (2);
Anna Zhukova (MAGNOME) Knowledge-based generalization February 12, 2015 15 / 45

53. Generalization method
Model generalization algorithm
Algorithm:
1 Define ˚∼;
2 Satisfy restriction (1);
3 Satisfy restriction (2);
Anna Zhukova (MAGNOME) Knowledge-based generalization February 12, 2015 15 / 45

54. Generalization method
Model generalization algorithm: Example
Peroxisome of Y. lipolytica: 66 → 17 reactions
Anna Zhukova (MAGNOME) Knowledge-based generalization February 12, 2015 16 / 45

55. Generalization method
Model generalization library
download from
metamogen.gforge.inria.fr
input: SBML model
output: 2 SBML models:
1 initial model + groups extension:
group of ub. metabolites
groups of equiv. metabolites
groups of equiv. reactions
2 generalized model
implemented in Python
Anna Zhukova (MAGNOME) Knowledge-based generalization February 12, 2015 17 / 45

56. Generalization method
Model generalization library
download from
metamogen.gforge.inria.fr
input: SBML model
output: 2 SBML models:
1 initial model + groups extension:
group of ub. metabolites
groups of equiv. metabolites
groups of equiv. reactions
2 generalized model
implemented in Python
Anna Zhukova (MAGNOME) Knowledge-based generalization February 12, 2015 17 / 45

57. Validation
Outline
1 Introduction
2 Generalization method [Zhukova and Sherman, J Comput Biol 2014]
3 Validation [Zhukova and Sherman, J Bioinf Comput Biol 2014]
4 Mimoza: web-based navigation
[Zhukova and Sherman, BMC Syst Bio (forthcoming)]
5 Conclusions and Perspectives
Anna Zhukova (MAGNOME) Knowledge-based generalization February 12, 2015 18 / 45

58. Validation
Validation set-up
Goal: Mathematically the generalization method is correct. But is it
useful for biologists?
Path2Models [B¨uchel et al., 2013]
KEGG [Kanehisa et al., 2012] → SBML [Hucka et al., 2003]
non-curated
1 286 metabolic networks
mapped to the NCBI taxonomy database [Sayers et al., 2009]
138 eukaryota
1 045 bacteria
103 archaea
β−oxidation of fatty acids
Anna Zhukova (MAGNOME) Knowledge-based generalization February 12, 2015 19 / 45

59. Validation
β−oxidation of fatty acids
1 dehydraton: fatty acyl-CoA (n) →
dehydroacyl-CoA
2 hydration: dehydroacyl-CoA →
hydroxyacyl-CoA
3 oxidation: hydroxyacyl-CoA →
3-ketoacyl-CoA
4 thiolysis: 3-ketoacyl-CoA →
fatty acyl-CoA (n-2) + acetyl-CoA
Anna Zhukova (MAGNOME) Knowledge-based generalization February 12, 2015 20 / 45

60. Validation
β−oxidation of fatty acids
1 dehydraton: fatty acyl-CoA (n) →
dehydroacyl-CoA
2 hydration: dehydroacyl-CoA →
hydroxyacyl-CoA
3 oxidation: hydroxyacyl-CoA →
3-ketoacyl-CoA
4 thiolysis: 3-ketoacyl-CoA →
fatty acyl-CoA (n-2) + acetyl-CoA
Anna Zhukova (MAGNOME) Knowledge-based generalization February 12, 2015 20 / 45

61. Validation
β−oxidation of fatty acids
Anna Zhukova (MAGNOME) Knowledge-based generalization February 12, 2015 20 / 45

62. Validation
Configurations
Expected Alternative paths
Broken cycles
Anna Zhukova (MAGNOME) Knowledge-based generalization February 12, 2015 21 / 45

63. Validation
Results
β-oxidation % of
cycle configuration all networks eukaryota bacteria archaea
complete cycle 10% 3% 11% 0%
one step missing 10% 25% 7% 18%
two steps missing 11% 12% 10% 24%
three steps missing 50% 57% 49% 58%
all steps missing 19% 3% 23% 0%
Anna Zhukova (MAGNOME) Knowledge-based generalization February 12, 2015 22 / 45

64. Validation
Results
β-oxidation % of
cycle configuration all networks eukaryota bacteria archaea
complete cycle 10% 3% 11% 0%
one step missing 10% 25% 7% 18%
two steps missing 11% 12% 10% 24%
three steps missing 50% 57% 49% 58%
all steps missing 19% 3% 23% 0%
Archaea:
gene candidates for degradation of fatty acids via β-oxidation
do not encode components of a fatty acid synthase complex
[Falb et al., 2008].
Anna Zhukova (MAGNOME) Knowledge-based generalization February 12, 2015 22 / 45

65. Validation
One missing step
128 (10%) gen. networks miss 1 step:
1 dehydraton: 23 (18%)
2 hydration: 8 (6,2%)
3 oxidation: 95 (74,2%)
4 thiolysis: 2 (1,6%)
Anna Zhukova (MAGNOME) Knowledge-based generalization February 12, 2015 23 / 45

66. Validation
One missing step
128 (10%) gen. networks miss 1 step:
1 dehydraton: 23 (18%)
2 hydration: 8 (6,2%)
3 oxidation: 95 (74,2%)
4 thiolysis: 2 (1,6%)
Systematic error in Path2Models?
Anna Zhukova (MAGNOME) Knowledge-based generalization February 12, 2015 23 / 45

67. Validation
One missing step
128 (10%) gen. networks miss 1 step:
1 dehydraton: 23 (18%)
2 hydration: 8 (6,2%)
3 oxidation: 95 (74,2%)
4 thiolysis: 2 (1,6%)
Systematic error in Path2Models?
Y. lipolytica (strain CLIB 122/E 150):
BMID000000136479
– no oxidation
MODEL1111190000 (curated)
[Loira et al., 2012] – complete cycle
Anna Zhukova (MAGNOME) Knowledge-based generalization February 12, 2015 23 / 45

68. Validation
Generalization is validated
Generalization is useful to:
understand, compare and classify networks,
detect general network structure,
highlight possible problems,
detect organism-specific particularities.
Anna Zhukova (MAGNOME) Knowledge-based generalization February 12, 2015 24 / 45

69. Mimoza
Outline
1 Introduction
2 Generalization method [Zhukova and Sherman, J Comput Biol 2014]
3 Validation [Zhukova and Sherman, J Bioinf Comput Biol 2014]
4 Mimoza: web-based navigation
[Zhukova and Sherman, BMC Syst Bio (forthcoming)]
5 Conclusions and Perspectives
Anna Zhukova (MAGNOME) Knowledge-based generalization February 12, 2015 25 / 45

70. Mimoza
Motivation
Anna Zhukova (MAGNOME) Knowledge-based generalization February 12, 2015 26 / 45

71. Mimoza
Visualization requirements
users’ models as an input
Anna Zhukova (MAGNOME) Knowledge-based generalization February 12, 2015 27 / 45

72. Mimoza
Visualization requirements
users’ models as an input
desktop? online?
JWS online [Snoep et al., 2003]
Anna Zhukova (MAGNOME) Knowledge-based generalization February 12, 2015 27 / 45

73. Mimoza
Visualization requirements
users’ models as an input
desktop? online?
CellDesigner [Funahashi et al., 2008]
Anna Zhukova (MAGNOME) Knowledge-based generalization February 12, 2015 27 / 45

74. Mimoza
Visualization requirements
users’ models as an input
desktop? online?
zooming user interface (ZUI)!
geometric zoom
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75. Mimoza
Visualization requirements
users’ models as an input
desktop? online?
zooming user interface (ZUI)!
geometric zoom
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76. Mimoza
Visualization requirements
users’ models as an input
desktop? online?
zooming user interface (ZUI)!
geometric zoom
semantic zoom
Anna Zhukova (MAGNOME) Knowledge-based generalization February 12, 2015 27 / 45

77. Mimoza
Visualization requirements
users’ models as an input
desktop? online?
zooming user interface (ZUI)!
geometric zoom
semantic zoom
decomposition into modules
compartments
generalized elements
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78. Mimoza
Mimoza
3-level model representation:
1 full model
2 generalized view
3 compartment view
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79. Mimoza
Mimoza
3-level model representation:
1 full model
2 generalized view
3 compartment view
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80. Mimoza
Mimoza
3-level model representation:
1 full model
2 generalized view
3 compartment view
Anna Zhukova (MAGNOME) Knowledge-based generalization February 12, 2015 28 / 45

81. Mimoza
Mimoza
3-level model representation:
1 full model
2 generalized view
3 compartment view
Anna Zhukova (MAGNOME) Knowledge-based generalization February 12, 2015 28 / 45

82. Mimoza
Comparison to other tools
Tool Imposed Semantic User’s Automatic
name layout zoom model layout Modules
Genome yes no no - no
Projector
if created if created
NaviCell no by user yes no by user
Cellular yes no no - no
Overview
Reactome yes/no yes no - yes
Mimoza no yes yes yes yes
Anna Zhukova (MAGNOME) Knowledge-based generalization February 12, 2015 29 / 45

83. Mimoza
Pipeline
1 user submits a model in SBML format
2 model generalization (if needed)
3 layout of the network graph
4 rendering into a zoomable interactive map
5 the result can be browsed online or downloaded
mimoza.bordeaux.inria.fr
Anna Zhukova (MAGNOME) Knowledge-based generalization February 12, 2015 30 / 45

84. Mimoza
Implementation details
Python + libSBML [Bornstein et el., 2008] – library
Model generalization [Zhukova and Sherman, 2014] – modules
the Gene Ontology [Ashburner et al., 2000] – compartments’ nesting
Tulip library [Auber, 2004] – graph layout
Leaflet [leafletjs.com] + GeoJSON [geojson.org] – ZUI
Javascript, JQuery – on-line
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85. Mimoza
Layers layout
Generalized model layout
Full model layout – challenge of
correspondence
Anna Zhukova (MAGNOME) Knowledge-based generalization February 12, 2015 32 / 45

86. Mimoza
Layers layout
Generalized model layout
A combination of Tulip [Auber, 2004]
algorithms:
1 split into connected components
2 apply a layout algorithm
no cycles
=⇒ Hierarchical Layout
≤ 3 cycles & ≤ 100 nodes
=⇒ Circular Layout
otherwise
=⇒ Force-Directed Layout
3 combine back together with
Connected Comp. Packing
Anna Zhukova (MAGNOME) Knowledge-based generalization February 12, 2015 32 / 45

87. Mimoza
Layers layout
Generalized model layout
A combination of Tulip [Auber, 2004]
algorithms:
1 split into connected components
2 apply a layout algorithm
no cycles
=⇒ Hierarchical Layout
≤ 3 cycles & ≤ 100 nodes
=⇒ Circular Layout
otherwise
=⇒ Force-Directed Layout
3 combine back together with
Connected Comp. Packing
Anna Zhukova (MAGNOME) Knowledge-based generalization February 12, 2015 32 / 45

88. Mimoza
Layers layout
Generalized model layout
Full model layout – challenge of
correspondence
keep coordinates for
non-generalized elements
similar metabolites/reactions –
next to each other inside the
generalized element
conserve the colors
generalized elements are larger
Anna Zhukova (MAGNOME) Knowledge-based generalization February 12, 2015 32 / 45

89. Mimoza
Layers layout
Generalized model layout
Full model layout – challenge of
correspondence
Serialization of layout
SBML with layout extension
[Gauges et al., 2013] – stores node
coordinates and sizes
import/export
Anna Zhukova (MAGNOME) Knowledge-based generalization February 12, 2015 32 / 45

90. Mimoza
Technical details
GeoJSON [geojson.org]
Leaflet [leafletjs.com]
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91. Mimoza
Technical details
GeoJSON [geojson.org]
Leaflet [leafletjs.com]
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92. Mimoza
Technical details
GeoJSON [geojson.org]
Leaflet [leafletjs.com]
Anna Zhukova (MAGNOME) Knowledge-based generalization February 12, 2015 33 / 45

93. Mimoza
Download and distribution
as a standalone application on the Mimoza web server:
mimoza.bordeaux.inria.fr
download the result as a COMBINE Archive [Bergmann et al., 2014]
as a Galaxy [Blankenberg et al., 2010] project tool (wrapper)
embed a Mimoza view in another web-page
download the Mimoza source code
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94. Mimoza
Motivation
Anna Zhukova (MAGNOME) Knowledge-based generalization February 12, 2015 35 / 45

95. Mimoza
Motivation
Anna Zhukova (MAGNOME) Knowledge-based generalization February 12, 2015 35 / 45

96. Conclusions and Perspectives
Outline
1 Introduction
2 Generalization method [Zhukova and Sherman, J Comput Biol 2014]
3 Validation [Zhukova and Sherman, J Bioinf Comput Biol 2014]
4 Mimoza: web-based navigation
[Zhukova and Sherman, BMC Syst Bio (forthcoming)]
5 Conclusions and Perspectives
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97. Conclusions and Perspectives
Summary
Generalization method
Anna Zhukova (MAGNOME) Knowledge-based generalization February 12, 2015 37 / 45

98. Conclusions and Perspectives
Summary
Generalization method
Validation
Anna Zhukova (MAGNOME) Knowledge-based generalization February 12, 2015 37 / 45

99. Conclusions and Perspectives
Summary
Generalization method Mimoza
Validation
Anna Zhukova (MAGNOME) Knowledge-based generalization February 12, 2015 37 / 45

100. Conclusions and Perspectives
Compressing bipartite graphs with repetitions
Generalization for metabolic networks :
metabolite grouping - metabolite ontology
reaction grouping - repetitive patterns:
reactions with equiv. reactants/products
Anna Zhukova (MAGNOME) Knowledge-based generalization February 12, 2015 38 / 45

101. Conclusions and Perspectives
Compressing bipartite graphs with repetitions
Generalization for metabolic networks :
metabolite grouping - metabolite ontology
reaction grouping - repetitive patterns:
reactions with equiv. reactants/products
Generalized model :
one representative element per pattern
minimizes number of generalized reactions
preserves reaction stoichiometries
obeys metabolite diversity constraint
Anna Zhukova (MAGNOME) Knowledge-based generalization February 12, 2015 38 / 45

102. Conclusions and Perspectives
Compressing bipartite graphs with repetitions
Generalization for metabolic networks bipartite graphs:
metabolite M-node grouping - metabolite ontology partial order
reaction R-node grouping - repetitive patterns:
reactions R-nodes with equiv. reactants/products in-/out-degrees
Generalized model Compressed graph:
one representative element per pattern
minimizes number of generalized reactions R-nodes
preserves reaction stoichiometries in-/out- degrees of R-nodes
obeys metabolite diversity constraint minim. M-node degrees
Anna Zhukova (MAGNOME) Knowledge-based generalization February 12, 2015 38 / 45

103. Conclusions and Perspectives
Finding template models for model inference
Anna Zhukova (MAGNOME) Knowledge-based generalization February 12, 2015 39 / 45

104. Conclusions and Perspectives
Finding template models for model inference
Pantograph toolbox [Loira et al., 2015]
orthology
template model
details vs generality
model for a related organism
Anna Zhukova (MAGNOME) Knowledge-based generalization February 12, 2015 39 / 45

105. Conclusions and Perspectives
Finding template models for model inference
Pantograph toolbox [Loira et al., 2015]
orthology
template model
details vs generality
model for a related organism
generalized model [Issa, work in progress]
Anna Zhukova (MAGNOME) Knowledge-based generalization February 12, 2015 39 / 45

106. Conclusions and Perspectives
Finding template models for model inference
Pantograph toolbox [Loira et al., 2015]
orthology
template model
details vs generality
model for a related organism
generalized model [Issa, work in progress]
collective generalizations as templates:
several close species
several partial models
Anna Zhukova (MAGNOME) Knowledge-based generalization February 12, 2015 39 / 45

107. Conclusions and Perspectives
Finding template models for model inference
Pantograph toolbox [Loira et al., 2015] – required update
template reaction → (at most) one target reaction
Anna Zhukova (MAGNOME) Knowledge-based generalization February 12, 2015 39 / 45

108. Conclusions and Perspectives
Finding template models for model inference
Pantograph toolbox [Loira et al., 2015] – required update
template reaction → (at most) one target reaction
generalized template reaction → (up to) several similar target
reactions
reaction specification method
Anna Zhukova (MAGNOME) Knowledge-based generalization February 12, 2015 39 / 45

109. Conclusions and Perspectives
Finding template models for model inference
Pantograph toolbox [Loira et al., 2015] – required update
template reaction → (at most) one target reaction
generalized template reaction → (up to) several similar target
reactions
reaction specification method
collective generalizations with flat met. ontology - model merge
numbers of factored reactions
as weights
Anna Zhukova (MAGNOME) Knowledge-based generalization February 12, 2015 39 / 45

110. Conclusions and Perspectives
Comparing disease and healthy metabolisms
Collective generalization of disease-affected models vs healthy ones:
common, disease-specific, adaptation;
conserved part not affected by the disease.
Anna Zhukova (MAGNOME) Knowledge-based generalization February 12, 2015 40 / 45

111. Conclusions and Perspectives
Comparing disease and healthy metabolisms
Collective generalization of disease-affected models vs healthy ones:
common, disease-specific, adaptation;
conserved part not affected by the disease.
Disease-related differences between models:
non-generalized
KEGG DISEASE database [Kanehisa, 2009] (for human)
pathway maps for cancer
immune disorders
neurodegenerative diseases, etc.
Anna Zhukova (MAGNOME) Knowledge-based generalization February 12, 2015 40 / 45

112. Conclusions and Perspectives
Comparing disease and healthy metabolisms
Collective generalization of disease-affected models vs healthy ones:
common, disease-specific, adaptation;
conserved part not affected by the disease.
Disease-related differences between models:
non-generalized
KEGG DISEASE database [Kanehisa, 2009] (for human)
pathway maps for cancer
immune disorders
neurodegenerative diseases, etc.
generalized
not bound to a particular organism
apply to a healthy metabolism: draft for a disease-affected model?
Anna Zhukova (MAGNOME) Knowledge-based generalization February 12, 2015 40 / 45

113. Conclusions and Perspectives
Classifying related metabolisms
Taxonomy (systematics) is the science of biological classification.
Genomic methods - based on mutations in orthologous genes
[Olsen, 1994]
Metabolic taxonomy - based on:
substrate-product relationships [Chang 2011]
metabolic pathways [Hong, 2004; Mazurie, 2008]
enzyme information [Ma, 2004]
Anna Zhukova (MAGNOME) Knowledge-based generalization February 12, 2015 41 / 45

114. Conclusions and Perspectives
Classifying related metabolisms
Taxonomy (systematics) is the science of biological classification.
Genomic methods - based on mutations in orthologous genes
[Olsen, 1994]
Metabolic taxonomy - based on:
substrate-product relationships [Chang 2011]
metabolic pathways [Hong, 2004; Mazurie, 2008]
enzyme information [Ma, 2004]
model generalization
collective generalization
intersection of conserved parts
organism-specific adaptations
Anna Zhukova (MAGNOME) Knowledge-based generalization February 12, 2015 41 / 45

115. Conclusions and Perspectives
Classifying reactions in reaction databases
Rhea [Alcantara, 2012], BioPath [Reitz, 2004], KEGG reaction [Kanehisa, 2012],
MetaCyC [Caspi, 2012]
involved metabolites
reversibility
catalyzing enzymes
pathways
cross references
Anna Zhukova (MAGNOME) Knowledge-based generalization February 12, 2015 42 / 45

116. Conclusions and Perspectives
Classifying reactions in reaction databases
Rhea [Alcantara, 2012]
manually annotated
metabolites associated to ChEBI (compatible with our
generalization)
Anna Zhukova (MAGNOME) Knowledge-based generalization February 12, 2015 42 / 45

117. Conclusions and Perspectives
Classifying reactions in reaction databases
Generalization of RhEA =⇒ reaction hierarchy
3 applications of model generalization:
1 database-wide stoichiometry constraints
most specific generalization
compatible stoichiometric constraints of any model
direct ancestors
2 reaction group-wide stoichiometry constraints
most general generalization
root ancestors
3 model-wide stoichiometry constraints
compatible with the model
intermediate ancestors
Anna Zhukova (MAGNOME) Knowledge-based generalization February 12, 2015 42 / 45

118. Conclusions and Perspectives
Classifying reactions in reaction databases
Generalization of RhEA =⇒ reaction hierarchy
3 applications of model generalization:
1 database-wide stoichiometry constraints
most specific generalization
compatible stoichiometric constraints of any model
direct ancestors
2 reaction group-wide stoichiometry constraints
most general generalization
root ancestors
3 model-wide stoichiometry constraints
compatible with the model
intermediate ancestors
Anna Zhukova (MAGNOME) Knowledge-based generalization February 12, 2015 42 / 45

119. Conclusions and Perspectives
Classifying reactions in reaction databases
Generalization of RhEA =⇒ reaction hierarchy
3 applications of model generalization:
1 database-wide stoichiometry constraints
most specific generalization
compatible stoichiometric constraints of any model
direct ancestors
2 reaction group-wide stoichiometry constraints
most general generalization
root ancestors
3 model-wide stoichiometry constraints
compatible with the model
intermediate ancestors
Anna Zhukova (MAGNOME) Knowledge-based generalization February 12, 2015 42 / 45

120. Conclusions and Perspectives
Suggesting extensions to metabolite ontologies
Model generalization method
Metabolite grouping based on:
relationships in met. ontology (ChEBI)
no ChEBI annotation =⇒ no generalization
similar reactions
Reaction grouping based on keys:
specific reactants/products
generalized - ancestor ChEBI ids
not generalized - ids
ubiquitous reactants/products - ids
Constraints
Anna Zhukova (MAGNOME) Knowledge-based generalization February 12, 2015 43 / 45

121. Conclusions and Perspectives
Suggesting extensions to metabolite ontologies
Relaxed Model generalization method
Metabolite grouping based on:
relationships in met. ontology (ChEBI) – predict them if needed
no ChEBI annotation =⇒ no generalization
similar reactions
Reaction grouping based on fuzzy keys:
specific reactants/products - numbers
generalized reactants - ancestor ChEBI ids
not gen. reactants - ids
ubiquitous reactants/products - ids
Constraints
Anna Zhukova (MAGNOME) Knowledge-based generalization February 12, 2015 43 / 45

122. Conclusions and Perspectives
Acknowledgements
MAGNOME,
Inria-Bordeaux
David J Sherman
Rogrigo Assar
Pascal Durrens
Witold Dyrka
Xavier Calcas
Joaquin Fernandez
Anne-Laure Gautier
Natalia Golenetskaya
Razanne Issa
Florian Lajus
Nicol´as Loira
l’Institut Micalis,
INRA-Grignon
St´ephanie Michely
C´ecile Neuveglise
Jean-Marc Nicaud
MABioVis,
LaBRI, Bordeaux
Romain Bourqui
Antoine Lambert
Anna Zhukova (MAGNOME) Knowledge-based generalization February 12, 2015 44 / 45

123. Conclusions and Perspectives
Summary
Generalization method Mimoza
Validation
Anna Zhukova (MAGNOME) Knowledge-based generalization February 12, 2015 45 / 45