Knowledge-based generalization for metabolic models

Knowledge-based generalization for metabolicmodels

Generalisation de modeles metaboliques par connaissances

Anna Zhukova 1,2 David J. Sherman 2

1Laboratoire de metabolisme energetique cellulaire IBGC - CNRS1 rue Camille Saint-Saens, 33077 Bordeaux cedex France

2Inria / CNRS / University of Bordeauxjoint project-team MAGNOME

351, cours de la Liberation, 33405 Talence cedex France

February 12, 2015

Anna Zhukova (MAGNOME) Knowledge-based generalization February 12, 2015 1 / 45

Metabolic modeling

Metabolic models are mathematical descriptions of biochemicalreactions between molecules in a cell.

Metabolic models are used for:recording knowledgesimulationinference of other models

understanding how genotype influences phenotypemetabolic engineering

food and beveragespharmaceuticalsbiofuels

disease analysis: novel drug targets


Size of metabolic models

pathway-scale - up to hundreds of reactionsgenome-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


Precision vs Readability


Precision vs Readability: our solution


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


Introduction

Modeling workflow

Model/pathway/reactionrepositories:

[Li et al., 2010]

[Kanehisa et al., 2012]

[Alcantara et al., 2012]


Introduction

Modeling workflow

Standards:

[Hucka et al., 2003]

[Lloyd et al., 2004]

[Le Novere et al., 2009]


Introduction

Modeling workflow

Inference Tools:

PathwayTools[Karp et al., 2002]

SuBliMinaL[Swainston et al., 2011]

CoReCo[Pitkanen et al., 2014]


Introduction

Modeling workflow

Errors/Peculiarities:


Introduction

Modeling workflow

Ontologies:

[Courtot et al., 2011]

[Ashburner et al., 2000]

[de Matos et al., 2010]


Introduction

Modeling workflow

Simulation:

COPASI[Hoops et al., 2006]

FAME[Boele et al., 2012]

COBRApy[Ebrahim et al., 2013]


Introduction

Genome-scale models are complicated


Introduction

Self-similarities


Introduction

Self-similarities

3-oxo-fatty acyl-CoAs: different lengths of carbon chains


Introduction

Self-similarities

hydroxy fatty acyl-CoAs: different lengths of carbon chains


Introduction

Self-similarities

oxidation: hydroxy FA-CoA + NAD↔ 3-oxo-FA-CoA + H+ + NADH


Introduction

Objective

exploit self-similaritiessemantically robustmeaningful for biologists

produce abstract viewsessential model structurehighlight the particularitiesexpose potential errors


Generalization method

Outline

1 Introduction







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 3 r = 〈M(react),M(prod)〉

- edges bw M- and R-nodes/all the met. are distinct/

/no parallel edges/.




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 3 r = 〈M(react),M(prod)〉 - edges bw M- and R-nodes

/all the met. are distinct/






Metabolite set: M = {m1, . . . ,mn} - M-nodes,Ubiq. m. set: M ⊃ Mub - duplicated M-nodes,


/all the met. are distinct/






Metabolite set: M = {m1, . . . ,mn} - M-nodes,Ubiq. m. set: M ⊃ Mub - duplicated M-nodes,


/all the met. are distinct/ /no parallel edges/.



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 metabolitesparticipating in a reaction are distinct. (In- and out-degrees of R-nodes areconserved.)








Metabolite diversity restriction (2): Equivalent metabolites must participatein equivalent reactions. (Min. degrees of gen. M-nodes.)








Stoichiomenty preserving restriction (1): All the generalized metabolitesparticipating in a reaction are distinct. (In- and out-degrees of R-nodes areconserved.)

Metabolite diversity restriction (2): Equivalent metabolites must participatein equivalent reactions. (Min. degrees of gen. M-nodes.)



Formal definition: Model generalization problem

Problem: Given a metabolic model N = 〈M ⊃ M(ub),R〉 find anequivalence operation ∼ that obeys the stoichiometry preservingrestriction (1) and the metabolite diversity restriction (2), and minimizesthe number of reaction equivalence classes ]R/ ∼.

N/ ∼ = 〈M/ ∼,R/ ∼〉 - generalized model,M/ ∼ = {[m1]∼, . . . , [mn]∼} - generalized metabolite set,R/ ∼ = {[r1]∼, . . . , [rk ]∼} - generalized reaction set.



Model generalization algorithm

Algorithm:

1 Define ∼;

2 Satisfy restriction (1);





Algorithm:

1 Define ∼;

[m(ub)]∼ = {m(ub)} - gen. ub. m.,

[m]∼ = M\M(ub) - gen. met.






Algorithm:

1 Define ∼;






Algorithm:

1 Define ∼;


Metabolite ontology – partial order of M-nodes

[de Matos et al., 2010]





Algorithm:

1 Define ∼;


Metabolite ontology – partial order of M-nodes

Exact set cover (NP-complete [Goldreich, 2008])Greedy alg. – best polyn. time approx. [Feige, 1998]





Algorithm:

1 Define ∼;





Model generalization algorithm: Example

Peroxisome of Y. lipolytica: 66→ 17 reactions



Model generalization library

download frommetamogen.gforge.inria.fr

input: SBML model

output: 2 SBML models:1 initial model + groups extension:

group of ub. metabolitesgroups of equiv. metabolitesgroups of equiv. reactions

2 generalized model

implemented in Python


metamogen.gforge.inria.fr

Validation

Outline

1 Introduction






Validation

Validation set-up

Goal: Mathematically the generalization method is correct. But is ituseful for biologists?

Path2Models [Buchel et al., 2013]

KEGG [Kanehisa et al., 2012]→ SBML [Hucka et al., 2003]non-curated

1 286 metabolic networksmapped to the NCBI taxonomy database [Sayers et al., 2009]

138 eukaryota1 045 bacteria103 archaea

β−oxidation of fatty acids


Validation


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


Validation



Validation

Configurations

Expected Alternative paths

Broken cycles


Validation

Results

β-oxidation % ofcycle 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].


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


Validation

Generalization is validated

Generalization is useful to:understand, compare and classify networks,detect general network structure,highlight possible problems,detect organism-specific particularities.


Mimoza

Outline

1 Introduction






Mimoza

Motivation


Mimoza

Visualization requirements

users’ models as an input

desktop? online?

zooming user interface (ZUI)!geometric zoom

semantic zoom

decomposition into modulescompartmentsgeneralized elements


Mimoza


users’ models as an inputdesktop? online?


semantic zoom


JWS online [Snoep et al., 2003]


Mimoza


users’ models as an inputdesktop? online?


semantic zoom


CellDesigner [Funahashi et al., 2008]


Mimoza


users’ models as an inputdesktop? online?zooming user interface (ZUI)!

geometric zoom

semantic zoomdecomposition into modules

compartmentsgeneralized elements


Mimoza


users’ models as an inputdesktop? online?zooming user interface (ZUI)!

geometric zoomsemantic zoom



Mimoza

Mimoza

3-level model representation:1 full model2 generalized view3 compartment view


Mimoza

Comparison to other tools

Tool Imposed Semantic User’s Automaticname layout zoom model layout Modules

Genome yes no no - noProjector

if created if createdNaviCell no by user yes no by user

Cellular yes no no - noOverview

Reactome yes/no yes no - yes

Mimoza no yes yes yes yes


Mimoza

Pipeline

1 user submits a model in SBML format2 model generalization (if needed)3 layout of the network graph4 rendering into a zoomable interactive map5 the result can be browsed online or downloaded

mimoza.bordeaux.inria.fr



Mimoza

Implementation details

Python + libSBML [Bornstein et el., 2008] – libraryModel generalization [Zhukova and Sherman, 2014] – modulesthe Gene Ontology [Ashburner et al., 2000] – compartments’ nestingTulip library [Auber, 2004] – graph layoutLeaflet [leafletjs.com] + GeoJSON [geojson.org] – ZUIJavascript, JQuery – on-line


Mimoza

Layers layoutGeneralized model layout

Full model layout – challenge ofcorrespondence


Mimoza

Layers layoutGeneralized model layoutA combination of Tulip [Auber, 2004]algorithms:

1 split into connected components2 apply a layout algorithm

no cycles=⇒ Hierarchical Layout≤ 3 cycles & ≤ 100 nodes=⇒ Circular Layout

otherwise=⇒ Force-Directed Layout

3 combine back together withConnected Comp. Packing


Mimoza



keep coordinates fornon-generalized elementssimilar metabolites/reactions –next to each other inside thegeneralized elementconserve the colorsgeneralized elements are larger


Mimoza



Serialization of layout

SBML with layout extension[Gauges et al., 2013] – stores nodecoordinates and sizesimport/export


Mimoza

Technical details

GeoJSON [geojson.org]

Leaflet [leafletjs.com]


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-pagedownload the Mimoza source code



Mimoza

Motivation


Conclusions and Perspectives

Outline

1 Introduction







Summary


Mimoza

Validation



Summary

Generalization method Mimoza

Validation



Compressing bipartite graphs with repetitions

Generalization for metabolic networks :metabolite grouping - metabolite ontologyreaction grouping - repetitive patterns:reactions with equiv. reactants/products

Generalized model :one representative element per patternminimizes number of generalized reactionspreserves reaction stoichiometriesobeys metabolite diversity constraint



Compressing bipartite graphs with repetitions

Generalization for metabolic networks bipartite graphs:metabolite M-node grouping - metabolite ontology partial orderreaction R-node grouping - repetitive patterns:reactions R-nodes with equiv. reactants/products in-/out-degrees

Generalized model Compressed graph:one representative element per patternminimizes number of generalized reactions R-nodespreserves reaction stoichiometries in-/out- degrees of R-nodesobeys metabolite diversity constraint minim. M-node degrees



Finding template models for model inference




Pantograph toolbox [Loira et al., 2015]

orthologytemplate model

details vs generalitymodel for a related organism

generalized model [Issa, work in progress]collective generalizations as templates:

several close speciesseveral partial models






details vs generalitymodel for a related organismgeneralized model [Issa, work in progress]

collective generalizations as templates:several close speciesseveral partial models






details vs generalitymodel for a related organismgeneralized model [Issa, work in progress]collective generalizations as templates:

several close speciesseveral partial models




Pantograph toolbox [Loira et al., 2015] – required updatetemplate reaction→ (at most) one target reaction

generalized template reaction→ (up to) several similar targetreactions

reaction specification methodcollective generalizations with flat met. ontology - model merge

numbers of factored reactionsas weights




Pantograph toolbox [Loira et al., 2015] – required updatetemplate reaction→ (at most) one target reactiongeneralized template reaction→ (up to) several similar targetreactions

reaction specification method

collective generalizations with flat met. ontology - model mergenumbers of factored reactionsas weights




Pantograph toolbox [Loira et al., 2015] – required updatetemplate reaction→ (at most) one target reactiongeneralized template reaction→ (up to) several similar targetreactions

reaction specification methodcollective generalizations with flat met. ontology - model merge

numbers of factored reactionsas weights



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 cancerimmune disordersneurodegenerative diseases, etc.

generalizednot bound to a particular organismapply to a healthy metabolism: draft for a disease-affected model?



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 generalizationcollective generalizationintersection of conserved partsorganism-specific adaptations



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 generalizationintersection of conserved partsorganism-specific adaptations



Classifying reactions in reaction databases

Rhea [Alcantara, 2012], BioPath [Reitz, 2004], KEGG reaction [Kanehisa, 2012],MetaCyC [Caspi, 2012]

involved metabolitesreversibilitycatalyzing enzymespathwayscross references




Rhea [Alcantara, 2012]

manually annotatedmetabolites associated to ChEBI (compatible with ourgeneralization)




Generalization of RhEA =⇒ reaction hierarchy

3 applications of model generalization:1 database-wide stoichiometry constraints

most specific generalizationcompatible stoichiometric constraints of any modeldirect ancestors

2 reaction group-wide stoichiometry constraintsmost general generalizationroot ancestors

3 model-wide stoichiometry constraintscompatible with the modelintermediate ancestors



Suggesting extensions to metabolite ontologies

Relaxed

Model generalization methodMetabolite grouping based on:

relationships in met. ontology (ChEBI)no ChEBI annotation =⇒ no generalization

similar reactionsReaction grouping based on

fuzzy

keys:specific reactants/products

- numbers

generalized - ancestor ChEBI idsnot generalized - ids

ubiquitous reactants/products - ids

Constraints



Suggesting extensions to metabolite ontologies

Relaxed Model generalization methodMetabolite grouping based on:

relationships in met. ontology (ChEBI) – predict them if neededno ChEBI annotation =⇒ no generalization

similar reactionsReaction grouping based on fuzzy keys:

specific reactants/products - numbersgeneralized reactants - ancestor ChEBI idsnot gen. reactants - ids

ubiquitous reactants/products - ids

Constraints



Acknowledgements

MAGNOME,Inria-BordeauxDavid J ShermanRogrigo AssarPascal DurrensWitold DyrkaXavier CalcasJoaquin FernandezAnne-Laure GautierNatalia GolenetskayaRazanne IssaFlorian LajusNicolas Loira

l’Institut Micalis,INRA-GrignonStephanie MichelyCecile NeuvegliseJean-Marc Nicaud

MABioVis,LaBRI, BordeauxRomain BourquiAntoine Lambert



Summary

Generalization method Mimoza

Validation


Knowledge-based generalization for metabolic models

Science

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