multi-level representation of metabolic networks

Multi-level representation of metabolic networks

Anna Zhukova 1,2 David J. Sherman 2

1IBGC / University of Bordeaux1 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

August 5, 2015

Anna Zhukova Multi-level representation August 5, 2015 1 / 47

Metabolic modeling

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

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

Metabolic modeling

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

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 2015]

5 Conclusions and Perspectives

Introduction

Modeling workflow

Introduction

Genome-scale models are complicated

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/

/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.)

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 ∼;

[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 ∼;

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

Algorithm:

1 Define ∼;

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

Algorithm:

1 Define ∼;

Algorithm:

1 Define ∼;

Algorithm:

1 Define ∼;

Algorithm:

1 Define ∼;

Algorithm:

1 Define ∼;

Peroxisome of Y. lipolytica: 66→ 17 reactions

Using ChEBI for model generalization

What hinders generalization?

Missing ChEBI annotationsMissing relationships in ChEBIPseudoreactions

What hinders generalization?

Missing ChEBI annotationsMissing relationships in ChEBIPseudoreactions

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

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

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

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

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

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

One missing step

3 oxidation: 95 (74,2%)

Validation

One missing step

3 oxidation: 95 (74,2%)

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)!

decomposition into modulescompartmentsgeneralized elements

Mimoza

users’ models as an inputdesktop? online?

zooming user interface (ZUI)!decomposition into modules

compartmentsgeneralized elements

JWS online [Snoep et al., 2003]

Mimoza

users’ models as an inputdesktop? online?

zooming user interface (ZUI)!decomposition into modules

CellDesigner [Funahashi et al., 2008]

Mimoza

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

geometric zoom

semantic zoomdecomposition into modules

Mimoza

geometric zoom

semantic zoomdecomposition into modules

Mimoza

geometric zoomsemantic zoom

decomposition into modulescompartmentsgeneralized elements

Mimoza

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

Mimoza

http://mimoza.bordeaux.inria.fr/

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 createdCellular yes no no - no

Overview

Reactome yes/no yes no - yes

NaviCell no by user yes no by user

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] + libsbgnpy [Konig] – 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

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 elementsconserve the colorsgeneralized elements are largersimilar metabolites/reactions –next to each other inside thegeneralized element

Mimoza

Serialization of layout

SBML with layout extension[Gauges et al., 2013] – import/exportSBGN-ML [Le Novere et al., 2009]– export

Mimoza

Technical details

GeoJSON [geojson.org]

Leaflet [leafletjs.com]

Mimoza

Technical details

Mimoza

Technical details

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]

embed a Mimoza view in another web-pagedownload the Mimoza source code

Mimoza

Genome-scale model: yeast7 [Aung et al., 2003]

Mimoza

Motivation

Mimoza

Motivation

Conclusions and Perspectives

Outline

1 Introduction

Summary

Mimoza

Validation

Summary

Mimoza

Validation

Summary

Generalization method Mimoza

Validation

Compressing bipartite graphs with repetitions

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

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

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

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

Generalization for metabolic networks bipartite graphs:metabolite M-node grouping - ChEBI 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 modelcollective generalizations as templates:

several close speciesseveral partial models

details vs generalitymodel for a related organismgeneralized model

collective generalizations as templates:several close speciesseveral partial models

details vs generalitymodel for a related organismgeneralized modelcollective 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

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 [Morgat et al., 2015], BioPath [Reitz et al., 2004], KEGG reaction[Kanehisa et al., 2012], MetaCyC [Caspi et al., 2012]

involved metabolitesreversibilitycatalyzing enzymespathwayscross references

Rhea [Morgat et al., 2015]

manually annotatedmetabolites associated to ChEBI (compatible with ourgeneralization)

Generalization of RhEA =⇒ reaction hierarchy

3 applications of model generalization:

1 database-wide stoichiometry constraints

most specificcompatible with any modeldirect ancestors

2 reaction group-wide stoich. constraints

most generalroot ancestors

3 model-wide stoichiometry constraints

compatible with the modelintermediate ancestors

Suggesting extensions to ChEBI

Relaxed

Model generalization methodMetabolite grouping based on:

relationships in ChEBIno ChEBI annotation =⇒ no generalization

similar reactionsReaction grouping based on

keys:specific reactants/products

- numbers

generalized - ancestor ChEBI idsnot generalized - ids

ubiquitous reactants/products - ids

Constraints

Suggesting extensions to ChEBI

Relaxed Model generalization methodMetabolite grouping based on:

relationships in 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-Bordeaux

David J ShermanRogrigo AssarPascal DurrensWitold DyrkaXavier CalcasJoaquin FernandezAnne-Laure GautierNatalia GolenetskayaRazanne IssaFlorian LajusNicolas Loira

l’Institut Micalis,INRA-Grignon

Stephanie MichelyCecile NeuvegliseJean-Marc Nicaud

MABioVis,LaBRI, Bordeaux

Romain BourquiAntoine Lambert

Summary

Generalization method Mimoza

Validation

multi-level representation of metabolic networks

Science

mprod anna zhukova

validation zhukova

generalization method

webbased navigation

introduction outline

introduction objective

j comput biol

reactions yeast