introduction to constraint-based modeling in...

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Introduction to constraint-based modelingin metabolism

Katja TummlerHumboldt Universitat zu Berlin, Theoretische Biophysik

SyMBioSys Course, 2017/02/22

February 16, 2017

Outline Introduction Theory FBA Methods Exercise

Outline

1 IntroductionWhy CBM?What can CBMs do?

2 TheoryNetwork ReconstructionMathematical Framework

3 FBA MethodsNetwork AnalysisFlux(re)distributionsRegulatory and Dynamic FBAData Integration

4 ExerciseThe COBRA toolboxExercise


Why CBM?


Why CBM?

Genome-wide high-throughput data allow the reconstructionof the whole metabolic network of an organism

1000s of reactions and metabolites→ highly complex system

Constraint Based Models provide a simple andcomputationally cheap method for the analysis of the wholenetwork


What can CBMs do?

Flux distributionsWhich metabolic pathways are active?Which metabolic pathways are able to produce a certain product?

Drug targetsWhich reactions are possible/efficient targets for new drugs?

Metabolic engineeringWhich genetic alterations would result in a higher product yield?

Data integrationWhat can I learn from experimentally measured proteinconcentrations and expression patterns about the cellularmetabolism?

· · ·


What can CBMs do?


Genom-wide metabolic networksReconstruction and Model Building of iNJ661 from M. tb H37Rv

iNJ661 Reconstruction

iNJ661 Model

Manual Curation Steps

Evidence for gene

Identify catalytic protein complex/subunits

Reaction definition: primary metabolite conversion

Reaction definition: secondary metabolites/cofactors

Metabolites: formula and charge determination

Reaction definition: catalytic mechanism

Reaction definition: compartmentation

Confirm reaction mass conservation

Confirm reaction charge conservation

Manual Curation Resources

Primary Literature

TextbooksInternet Resource Databases: Tuberculist, KEGG, SEED

Debugging

Identify gaps and carry out directed manual curationEliminate `free energy’ loops

Convert to ModelDefine system boundaries and uptake constraintsTest anabolic and catabolic capabilities

TuberculistKEGG

The SEED

Genome Annotation (TIGR)


Genom-wide metabolic networks


Biomass reaction

Biomass is constituted of a subset of the metabolites in themodel (precursors / building blocks)

Growth ”consumes” these metabolites with a certainstoichiometric ratio corresponding to the cellular composition

Lipids RNA/DNA

Mycolic acidsAmino acids

Carbohydrates others..

Composition differs from organism to organism and not allcompounds are easy to measure.


Biomass reaction

Biomass is constituted of a subset of the metabolites in themodel (precursors / building blocks)

Growth ”consumes” these metabolites with a certainstoichiometric ratio corresponding to the cellular composition

Composition differs from organism to organism and not allcompounds are easy to measure.


Stoichiometric Matrix

All information on the topology of the reconstructed network canbe stored in a single matrix S.


Stoichiometric Matrix


From topology to flux distributions

Flux Balance Analysis allows the calculation of fluxdistributions in the reconstructed network

Central assumption of FBA: The system runs in steady state.

→ Compound concentrations and metabolic fluxes do not change→ Sum of all fluxes producing one metabolite is equal to the sum

of the consuming fluxes of the metabolite


From topology to flux distributions

Flux Balance Analysis allows the calculation of fluxdistributions in the reconstructed network

Central assumption of FBA: The system runs in steady state.

→ Compound concentrations and metabolic fluxes do not change→ Sum of all fluxes producing one metabolite is equal to the sum

of the consuming fluxes of the metabolite

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HE

X1

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I

PFK

FBP

FBA

TPI

EX

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–1

–1

–1

–1 –1

–1

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–1 –1

–1

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h

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f6p

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h

HEX1

PGI

FBP PFK

FBA

vGLCt1 − vHEX1 = 0

vPGI − vPFK + vFBP = 0

...

S · v = 0

→ linear system of equations


Topology & constraints define the feasible flux space

Based on S, the steady state assumption and specific constraints onthe fluxes, feasible flux distributions v can be calculated.

Often, there is no unique solution → under-determined system





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FBA

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FBA

TPIEX_g3pEX_dhap





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FBA

TPIEX_g3pEX_dhap

Allowablesolution space

v3

Unconstrainedsolution space

Constraints1) Sv = 02) ai < vi < bi

v2 v2

v1

v3Optmax

v1


Biological Objectives

To find a biologically meaningful flux distribution within thefeasible flux space , objective functions z describing thebiological/evolutionary ’aim’ of the organism, can be used.

Maximum biomass: max(z = vbiomass) growth

Minimum total flux: min(z =n∑

i=1|v |) min. effort

Maximum ATP yield: max(z =∑nvATP) energy

Maximum product yield: max(z = vproduct) product


Optimization

Linear programming:Optimization of a linear function over a subspace, subject to linearequality and inequality constraints

max z = c1 · v1 + c2 · v2 + · · ·+ cn · vnsubject to S · v = 0

and vi ,lb < vi < vi ,ub


Optimization




0 2 4 60

2

4

6

v1

v2v1 < 4


Optimization




0 2 4 60

2

4

6

v1

v2v1 < 4v2 < 5


Optimization




0 2 4 60

2

4

6

v1

v2v1 < 4v2 < 5

v2 + v1< 6


Optimization




0 2 4 60

2

4

6

v1

v2v1 < 4v2 < 5

v2 + v1< 6Objective functionmax(v1 + 2v2)


Is the model consistent?

Before carrying out FBAs, the network reconstruction needs to betested for consistency.

Are parts of the network unconnected? Dead-end reactions

Are reactions missing? Gaps

A

B

C

D

E

F

v5

v4

v6

v2v1

v3

v8

v9v7






A

B

C

D

E

F

v5

v4

v6

v2v1

v3

v8

v7

Blockedreaction






A

B

C

D

E

F

v5

v4

v6

v2v1

v3

v8

v7

Blockedreaction

A

B

C

D

E

F

v5

v4

v6v1

v3

v8

v9v7


Which are elemental submodels?

Elementary Flux Modes are minimal sets of enzymes that caneach generate valid steady states. (Schuster 1999)




A

B

C

D

E

F

v5

v4

v6

v2v1

v3

v8

v9v7




A

B

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E

F

v5

v4

v6

v2v1

v3

v8

v9v7

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v2v1

v3

v8

v9v7

A

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F

v5

v4

v6

v2v1

v3

v8

v9v7




A

B

C

D

E

F

v5

v4

v6

v2v1

v3

v8

v9v7

A

B

C

D

E

F

v5

v4

v6

v2v1

v3

v8

v9v7

A

B

C

D

E

F

v5

v4

v6

v2v1

v3

v8

v9v7

A Minimal Cut Set is a minimal (irreducible) set of reactions inthe network whose inactivation will definitely lead to a failure incertain network functions. (Klamt & Gilles 2003)




A

B

C

D

E

F

v5

v4

v6

v2

v1

v3

v8

v9v7

A

B

C

D

E

F

v5

v4

v6

v2

v1

v3

v8

v9v7

Biological function:Biomass production (v8)

A Minimal Cut Set is a minimal (irreducible) set of reactions inthe network whose inactivation will definitely lead to a failure incertain network functions. (Klamt & Gilles 2003)


Which genes are essential?

FBA can be used to find essential genes in the network, whoseknock-out or functional deficiency destroys the ability to grow.→ Drug Tragets

1 Set upper and lower boundary of a flux to 0

2 Optimize for biomass

3 The gene is essential, if the maximum possible flux throughthe biomass reaction = 0




Calculation:







Calculation:




Examplesingle gene deletion A

B

C

D

E

F

v5

v4

v6

v2v1

v3

v8

v9v7




Calculation:




Examplesingle gene deletiondouble gene deletion

A

B

C

D

E

F

v5

v4

v6

v2v1

v3

v8

v9v7


How defined is the optimal flux distribution

Optimal solutions of an FBA are not necessarily unique.

Flux Variability Analysis (FVA) allows to assess the variabilityin all possible flux distributions that yield the same optimumvalue of the objective function.





Calculation:

1 Optimize for biomass (or other objective)

2 Fix biomass flux to optimum value

3 For each reaction, maximize and minimize the flux with thenew constraint → Upper and lower variability bounds





Insight into:

Alternative pathways

Loops

Rigorousness of the set of constraints

A

B

C

D

E

F

v5

v4

v6

v2v1

v3

v8

v9v7


How does the network adapt to geneticperturbations?

Evolutionary optimized system→ How does the flux distributionchange after a knock-out?




Minimization of metabolic adaptation(MOMA)→ smallest possible flux change




Minimization of metabolic adaptation(MOMA)→ smallest possible flux change

Regulatory On-/Off-Minimization(ROOM)→ smallest possible number of switches


Can I add growth dynamics (dFBA)?

Coupling of the model to an external growth model(substrate consumption and biomass production)

Periodic update of the exchange fluxes → Re-run FBA

FBA

FBA


Can I add regulation (rFBA)?

Coupling to a boolean regulatory gene expression model(Shlomi et al 2007)


Omics data integration

Further constrain the feasible flux space by large scale data

Nutrient uptake rates

Fluxomics

Transcriptomics

Proteomics

Metabolomics

Reaction enthalpies


Labeling data / nutrient uptake rates

Flux data can be directly included via constraints on reactions

Uptake & secretion rates: Boundary fluxes13C labeling: Internal fluxes

M1v2 v3

M2

S

v12 labeling depends

on flux partitioning

v3/v2

M

Slide from: http://www.uni-saarland.de/fak8/heinzle/de/teaching/Systems_Synthetic_Biology/SSB_5_Flux_labeling.pdf


Transcriptomics & proteomics

Limitations:

Protein/gene expression does not directly translate to flux

Neglects (translation,) PTMs, allosteric regulation, saturationstate, thermodynamics


Metabolomics

Metabolite levels are not di-rectly linked to fluxNo kinetic equations thatdescribe dependencies(like e.g. Michaelis-Menten)

BUT we can learn about the thermodynamic landscape ofthe network

Thermodynamic FBA (Henry et al. 2007, Beard et al. 2002)Thermodynamic realizability (Hoppe et al. 2007)...


The COBRA toolbox

MatLab based toolbox with important functions for thedevelopment and analysis of large metabolic networks

Easily extendable, editable open-source code

Many published genome scale network reconstructions available inthe COBRA-format, with network visualization

In addition, the import of SBML models is possible.


Now hosted on github

https://github.com/opencobraAlso available as cobrapy


Up and at ’em - Exercise!

References for the figures and the sedulous student

FBA Introduction:JD Orth et al (2010) What is flux balance analysis? Nat Biotechnol. 28(3):245-8.

COBRA toolbox:SA Becker et al (2007) Quantitative prediction of cellular metabolism with constraint-based models: the COBRAToolbox.Nat Protoc.2(3):727-38.

Example for genome-scale network reconstruction:N Jamshidi and BO Palsson (2007) Investigating the metabolic capabilities of Mycobacterium tuberculosis H37Rvusing the in silico strain iNJ661 and proposing alternative drug targets. BMC Syst Biol.1:26.

EMF:S Schuster et al (1999) Detection of elementary flux modes in biochemical networks: a promising tool for pathwayanalysis and metabolic engineering. Trends Biotechnol. Feb;17(2):53-60.

MCS:S Klamt, ED Gilles (2004) Minimal cut sets in biochemical reaction networks. Bioinformatics 20(2): 226-234

dFBA:X Feng et al (2012) Integrating Flux Balance Analysis into Kinetic Models to Decipher the Dynamic Metabolism ofShewanella oneidensis MR-1. PLoS Comput Biol 8(2): e1002376.X Fang et al (2009) A systems biology framework for modeling metabolic enzyme inhibition of Mycobacteriumtuberculosis. BMC Syst Biol. 2009 Sep 15;3:92

rFBA:T Shlomi et al (2007) A genome-scale computational study of the interplay between transcriptional regulation andmetabolism. Mol Syst Biol. 3: 101.

MOMA/ROOM:T Shlomi et al (2005) Regulatory on/off minimization of metabolic flux changes after genetic perturbations. PNAS102 (21) 7695-7700

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