Metabolic Model Generalization

Project-teamMAGNOMEInria Bordeaux - Sud-Ouest

JOBIM 2013, July 1-4

Metabolic Model Generalization

Anna Zhukova

Where's Wally ?

Where are missing reactions ?

(The fi gure is produced using the Tulip graph visualization tool.)

Where are missing reactions ?

(The fi gure is produced using the Tulip graph visualization tool.)

Where are missing reactions ?

(The fi gure is produced using the Tulip graph visualization tool.)

Where are missing reactions ?

MODEL1111190000 

Loira et al., 2012 

Metabolic Network of Y. lipolytica

(peroxisome)

(53 - 6) reactions

(The fi gure is produced using the Tulip graph visualization tool.)

Where are missing reactions ?

(The fi gure is produced using the Tulip graph visualization tool.)

3-hydroxyacyl dehydrase ! Not that easy ?

(The fi gure is produced using the Tulip graph visualization tool.)

Model inference and refinement

Let's generalize !

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Let's generalize : ubiquitous species !

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Let's generalize !

(The fi gure is produced using the Tulip graph visualization tool.)

Let's generalize : hydroxy fatty acyl-CoA !

(The fi gure is produced using the Tulip graph visualization tool.)

Let's generalize !

(The fi gure is produced using the Tulip graph visualization tool.)

Let's generalize : dehydroacyl-CoA !

(The fi gure is produced using the Tulip graph visualization tool.)

Let's generalize !

(The fi gure is produced using the Tulip graph visualization tool.)

Let's generalize : 3-hydroxyacyl dehydratase !

(The fi gure is produced using the Tulip graph visualization tool.)

Let's generalize !

(The fi gure is produced using the Tulip graph visualization tool.)

Let's factor !

(The fi gure is produced using the Tulip graph visualization tool.)

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.)

Some technical details...

Some technical details...

M = (S, Sub, R) – model

Some technical details...

M = (S, Sub, R) – model

S = {s1, ..., s

n} – species set

/including /

Sub – ubiquitous species set

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 (*)/

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 (*)/

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

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 (*)/

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 (*)/

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 (*)/

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 (*)/

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 (*)/

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 (*)/

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 (*)/

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 (*)/

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/~.  

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/~.  

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/~.  

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/~.  

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/~.  

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/~.  

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/~.  

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/~.  

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/~.  

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/~.  

53 → 15

Acknowledgements

Magnome Team, Inria Bordeaux, France

David James ShermanPascal DurrensFlorian LajusWitold DyrkaRazanne Issa

Acknowledgements

Magnome Team, Inria Bordeaux, France

David James ShermanPascal DurrensFlorian LajusWitold DyrkaRazanne Issa

Center for Genome Regulation and CIRIC-InriaSantiago, Chile

Nicolás Loira

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

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

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

Thank you!