CARRERA DE ESPECIALIZACION EN BIOTECNOLOGIA …biotecnologiaindustrial.fcen.uba.ar/.../2011/...Bal-2-Ing-Me-UBAt-13.pdf · Clase 4: Balance de Flujos Metabólicos 2 Prof: Guillermo

Clase 4: Balance de Flujos Metabólicos 2

Prof: Guillermo R. Castro Lab de Nanobiomateriales – CINDEFI UNLP – CONICET, La Plata

Materia de Articulación CEBI - E4b Ingeniería Metabólica

CARRERA DE ESPECIALIZACION EN BIOTECNOLOGIA

INDUSTRIAL . FCEyN-INTI

Flujo metabólico (def.)

El flujo metabólico se define como la velocidad a la que un sustrato se convierte en un producto mediante reacciones y rutas metabólicas. Sustrato –> Metabolito Intermedio –> Producto

3

Vias en E. coli

(A) This version of the overview shows all interconnections between occurren-ces of the same metabolite to communicate the complexity of the interconnections in the metabolic network.

Ouzonis, Karp, Genome Res. 10, 568 (2000)

Guillermo R. Castro

Guillermo R. Castro Page 4

La Cascada “Omica” Que puede suceder?

Que podría suceder?

Que hace que eso suceda?

Que ha sucedido y que pasara?

Estructuracion de modelos metabolicos

Metabolic Networks Quantitative Model

Omics data Molecular Biology data

Integration of heterogenous data

(BASE)

Genomics Transcriptomics Proteomics Metabolomics Fluxomics Physiomics

Page 5 Guillermo R. Castro

De genes a flujos metabolicos


Construcción de un modelo biológico


Aplicaciones de los modelos

Metabolic engineering

Model-directed discovery

Interpretation of phenotypic screens

Analysis of network properties

Studies of evolutionary processes

Ej.: iAF1260 model Lycopene L-valine L-threonine

Network analysis – how much value? What are the inputs and output? Buchnera has some high-value waste products. Missing biology?

Evolution of reduced networks Pan genomes.

Compare KO strains and/or Biolog data to model predictions - Improves model.

Informing on the biological function of metabolism. Orphan enzymes and transporters.


E. coli K12


E. coli Metabolic Model IAF1260

Metabolic Reactions

2382

Regulatory data RegulonDB

Regulatory Interactions 1773

Microarrays 907

Total Genes in the model 1400

Validation Data set 1875 growth phenotypes

Guillermo R. Castro 10

Modelo iAF1260 de E. coli K 12

A genome-scale metabolic reconstruction for Escherichia coli K-12 MG1655 that accounts for 1260 ORFs and thermodynamic information Mol Syst Biol. 2007; 3: 121.


Modelo iAF1260 de E. coli K 12



Glucosa, eje central del metabolismo


Glicólisis – fase preparatoria


Glicólisis – fase de síntesis


Glicólisis – resumen energético

La glicólisis se encuentra muy regulada en la célula y coordinada con otras rutas metabólicas que producen energía para poder suministrar ATP. Las enzimas Hexokinasa, PFK-1 y Piruvato Kinasa se encuentran reguladas alostericamente, lo que permite controlar el flujo de C a través de la vía metabólica y mantiene constante los niveles de los intermediarios de la ruta.

Detalle de los mecanismos: http://www.iubmb-nicholson.org/swf/glycolysis.swf

Un problema a ser resuelto S. cerevisae


Un problema a ser resuelto

Hauf, J., Zimmermann, F.K., Müller, S., 2000. Simultaneous genomic over expression of seven glycolytic enzymes in the yeast Saccharomyces cerevisiae. Ezyme. Microbiol. Technol. 26, 688-698.


Consumo de glucosa y prod de etanol en mutante sobreexpresada y WT

Se pueden determinar los flujos utilizando datos expresion genica

Sin embargo NO existe correlacion lineal


The PEP carboxykinase promoter region, showing the complexity of regulatory


Transcriptoma & proteoma Olivares R, Bordel S, Nielsen J. Codon usage variability determines the correlation between proteome and transcriptome fold changes. BMC Systems Biology.


P Rj jf f=[ P ] k [ mRNA]=

[ P ] k( )[ mRNA]µ=

[ P ] k( , j )[ mRNA]µ= P Rj j jf fα=

P Rj jf fα=


P, protein, R, mRNA

Guillermo R. Castro

[ ][ ] [ ] [ ]j s , j d , jj j j

d Pk mRNA k P P

dtµ= − −

[ ][ ] [ ] [ ]j Rj d , jj j j

j

d PmRNA k P P

dt tρ

µ= − −

j ij ii

t S τ= ∑


ks,j and kdj are the protein synthesis & degradation rate constants

the number of ribosomes united to each mRNA molecule ρRj and the elongation time of the protein tj.

Where Sij is the number of codons i in the gene j and Ʈi is the average time that will take to add the corresponding amino acid to the nascent peptide

Agrupamiento de genes por similaridad de secuencias


Analisis de varianza

2

Pj

j Rj

fx log

f= Total between within

SS SS SS= +

2

within jc cc j

SS x x

= −

∑ ∑

( )2between c cc

SS n x x= −∑


C, cluster, N, de Prot en el cluster

Resultados

Usaite.snf1

Usaite.snf4

Usaite.snf1.4

Griffin Ideker Washburn

Within/Total 0.27 0.09 0.27 0.13 0.39 0.20

Between/Total 0.73 0.91 0.73 0.87 0.61 0.80

F-test (B/W) 2.70 10.06 2.75 6.63 1.54 4.09

p-value 0.001 1E-06 4.5E-5 0.015 0.55 2E-5


Statistical description of gene-expression and flux changes

The RNA arrays provide measurements for the significance of the expression changes in every gene. We need a method to provide measurements for the significance of flux changes in every reaction.

Bordel S, Agren R, Nielsen J. Sampling the Solution Space in Genome-Scale Metabolic Networks Reveals Transcriptional Regulation in Key Enzymes. 2010. PLoS Comput. Boil. 6: e1000859


Guillermo R. Castro

Geometry of the sampling method


Comparison between the Hit and Run algorithm and the sampling of the convex basis.

The Hit and Run algorithm seems to underestimate the variance. Page 31 Guillermo R. Castro

Assignment of regulatory characteristics


Some results Deletion of HXK2


Gluc to Ethanol --- Transcritional reg (up) --- down regulation

Transcription factor enrichment (very significant for many TFs) Transition from glucose to ethanol or acetate: Gcr1, Gcr2 and Hap4.

Glucose-Ethanol 19 enzymes TR, Gcr1 in 11 of them 22 enzymes PR, Gcr1 in none of them

Wild type versus grr1∆ and hxk2 ∆ mutants: Pho2 and Bas1: Regulators of purine and histidine biosynthesis.

Wild type- grr1∆ 26 enzymes TR, Pho2 in 10 of them 73 enzymes PR, Pho2 in 6 of them

Wild type versus mig1∆ mig2∆ mutant: Gcn4 and Cbf1: response against starvation increases growth rate by stimulating amino-acid synthesis and ribosome proliferation


TR, transcriptional regulation

PR, post-TR

Guillermo R. Castro

The role of constraints

Bordel S, Nielsen J. Identification of flux control in metabolic networks using non-equilibrium thermodynamics. 2010. Metab. Eng. 13, 369-377 Page 36 Guillermo R. Castro

How does the cell “choose” its metabolic state?

Objective function +

Set of constraints

Metabolic state

?


Aerobic and oxygen limited chemostats


Anaerobic chemostat and glucose excess batch

Vemuri et. al. 2006 Batch fermentation

Page 39 Guillermo R. Castro NOX= NADPH oxidasas

Modelo dinamicos: Ecuaciones diferenciales, gran cantidad de parametros desconocidos

Modelos Cuantitativos

Modelos de estado estacionario: Ecuaciones Algebraicas lineales

( , , , ) d tdt

=y F x y p

0 = ⋅S v

El analisis de flujos debe ser restringuido a estado estacionario

40 Guillermo R. Castro

S: matriz estequiometrica

V: distribucion de flujos

3.- Restriccion :

Prediccion de la distribucion de flujos en estado estacionario:

X1

X2

X3

100 v1

v2

v3

v4

v5

v6

5( )F v=v

0 = ⋅S v

2.- Definir funcion:

Analisis de flujos


1.- Componentes del sistema: moleculas? (x=3) Flujos? (v=6)

X1

X2

X3

100 v1

v2

v3

v4

v5

v6

12

13

24

35

6

0 1 1 1 0 0 00 0 1 0 1 1 00 0 0 1 1 0 1

vv

Xv

Xv

Xvv

− − = = − − −

Analisis de flujos (cont)


1ra regla: balance de

masas = CERO

X1 = X2 + X3

Para mutantes con genes delecionados se empela un flujo de estado estacionario predecido mediante logica boleana

0S v⋅ =Method Optimization Algorithm Additional information

rFBA (regulatory FBA)

Linear Programming Regulatory network (genomics)

SR-FBA (Steady-state Regulatory-FBA)

Mixed Integer Linear Programming

Regulatory network

MOMA (Minimization Of Metabolic Adjustment)

Quadratic Programming Flux distribution of wild type (fluxomics)

ROOM (Regulatory On/Off Minimization)

Mixed Integer Linear Programming

Flux distribution of wild type

Reactions for knockout gene = 0 Other reactions =1


Mayores problemas: En mutantes en donde se delecionaron genes muchas otras expresiones de genes varian. Como integrar el transcriptoma o proteoma en analisis de flujos metabolicos?.

Propuesta: Metodo de analisis

elemental para realizar

la integracion.


Modo Elemental de analisis (EMs)

1

2 1 2

3

1 11 0

0 1

vvv

λ λ = − + −

EM1 EM2

A B 1v

3v

1λ

2λ

2vEM1

EM2

Minimiza la cantidad de enzimas en un grupo de

cascadas enzimaticas compuestas por

reacciones irreversibles en estado estacionario


X1

X2

X3

100

60

70

20

40 30

v1

v2

v3

v4

v5

v6

v7

30

Modos Elemetales (Ems)

Matrix estequiometrica

1

2

3

4

5

6

7

1

1 2

1 3

3 2

2

3

2 3

v Xv X Xv X Xv X Xv Xv Xv X X

→→→

→

→

→

→

１

２

３

４

５

ME

λ= ⋅v P

Flujos

Matriz Elemental

Coeficiente EM


1

2

3

4 1 2 3 4 5

5

6

7

1 1 1 1 01 0 0 1 00 1 1 0 00 0 1 0 11 0 1 0 00 1 0 1 00 0 0 1 1

vvvvvvv

λ λ λ λ λ

= + + + +

1

2 1

3 2

4 3

5 4

6 5

7

1 1 1 1 01 0 0 1 00 1 1 0 00 0 1 0 11 0 1 0 00 1 0 1 00 0 0 1 1

vvvvvvv

λλλλλ

=

1 1 1 1 1

100 1 1 1 1 060 1 0 0 1 040 0 1 1 0 0

( 30) (70 ) (60 ) ( 40)30 0 0 1 0 170 1 0 1 0 030 0 1 0 1 020 0 0 0 1 1

λ λ λ λ λ

= + − + − + − + −

1 2 3 4 5

Problema: el CEM is not uniquely determined.

Matriz estequiometrica Flujo Flujo＝ ME ・ CEM

λ= ⋅v P

ES NECESARIO determinar un objetivo Page 47 Guillermo R. Castro

(CEM, coef estequiometrico de la matriz)

Objetivos

Maximizacion del crecimiento: pgm Lineal

Funcion conveniente: programacion cuadratica

2

1

ne

ii

Max λ=

−∑

,1

ne

biomass biomass i ii

Max v p λ=

= ⋅∑

Maximizar la Entropia (MEP)


iλ ,substrate uptake ii isubstrateuptake

pv

ρ λ= ⋅

Principio de Entropia Maxima (MEP)

λ= ⋅v P


y se debe cumplir:

iρSe define como la probabilidad de eventos al azar

1log

n

i ii

Maximize ρ ρ=

− ∑1

1n

ii

ρ=

=∑

( ),1

1, 2,...,n

i r i ri

x v r mρ=

= =∑

Principio de Entropia Maxima (MEP)

,1

n

i r i ri

p vρ=

=∑

Shannon information entropy

Restricciones

λ= ⋅v PQ. Zhao, H. Kurata, Maximum entropy decomposition of flux distribution at steady state to elementary modes. J Biosci Bioeng, 107: 84-89, 2009


ECF integra los perfiles actividad enzimatica en

modos elementales. ECF es descripta por una ecuacion de poder.

La ecuacion describe como los cambios en un perfil de

actividad enzimatica entre la cepa salvaje y la mutada se

relaciona con los cambios de los coef. de la matriz

estequiometrica (EMCs).

Control de Flujos por Enzimas (ECF)

Kurata H, Zhao Q, Okuda R, Shimizu K. Integration of enzyme activities into metabolic flux distributions by elementary mode analysis. BMC Syst Biol. 2007;1:31.


Modelo de flujo wild-type Enzyme activity profile

Mutant / WT

X1

X2

X3

100

60

70

20

40 30

v1

v2

v3

v4

v5

v6

v7

30

Estimation of a flux distribution of a mutant

Power-Law formula


Control de Flujos por Enzimas (ECF)

ref refλ= ⋅v PModelo de Referencia

Power Law Formula

Change in enzyme activity profile

target targetλ= ⋅v PPrediction of a flux distribution of a target cell

ref targetλ λ→

refλMEP

1 2( , ,..., )na a a

ＥＣＦ Algorithmo


a1 a5 a2

,1

mtarget refi i j i

j

a βλ γ λ=

= ⋅ ∏

,,

,

( 0)1 ( 0)

j j ij i

j i

a if pif p

α≠

= =

1100100

1

2

5

11

11

aa

a

1 1 2 5( )target ref1 a a aλ γλ=

EMi

Ecuacion de Poder

EMi

Enzyme activity profile

Optimal β＝1


pykF knockout in a metabolic network

74 EMs

Glc

G6P

F6P

GAP

6PG

Ru5P

E4P

Sed7P

PEP

AcCoA

ICT

AKGMAL

OAA

Acetate

PYR

glycolysis

Pentose PhosphatePathways

TCA cycle

1, pts

2, pfkA

3, gapA

4, pykF

5, aceE6, pta

7, gltA

8, icdA

9, sucA

10, mdh

11, ppc

12, mez

18, pgi

13, zwf

15, ktkA

14, gnd

16, tktB

17, talB

19

20

21

22

24

25

29

30

27

28

23

26


pykF Piruvato kinasa

Effect of a pyruvate kinase (pykF-gene) knockout mutation on the control of gene expression and metabolic fluxes in Escherichia coli

Effecto del numero de

enzimas integradas en el

error del modelo de

Control de Flujo por

Enzimas (ECF)

5

10

15

20

25

30

0 2 4 6 8 10

Mod

el E

rror

Number of Integrated Enzymes

=> A mayor N de enzimas en el modelo => mayor

exactitud de calculo.


Exactitud de la Prediction del ECF

Gene deletion Number of enzymes used for

prediction

Prediction accuracy (control: no enzyme activity

profile is used) pykF 11 +++

ppc 8 +++

pgi 5 +

cra 6 +++

gnd 4 +

fnr 6 +++

FruR 6 +++


ECF provee una correlacion

cuantitativa entre los perfiles de

actividad enzimatica y la

distribucion de flujos

VENTAJAS del ECF


Modificacion genetica

de Flujos

Quanyu Zhao, Hiroyuki Kurata, Genetic modification of flux for flux prediction of mutants, Bioinformatics, 25: 1702-1708, 2009


Gene expression (enzyme activity) profile

Metabolic Networks /gene deletion

Distribucion de flujos Metabolicos

Metabolic flux distribution for genetic mutants

ECF MOMA/rFBA

Prediccion de la distribucion de flujos en mutantes geneticos

Page 61

MOMA mimimalizacion

de ajustes metabolicos

(FBA Analisis de

Balance de flujos)

ECF Enzyme Control

Flux

Guillermo R. Castro

Flow chart of GMF

Gene expression (enzyme activity) profile

Metabolic networks /genetic modification

Metabolic flux distribution

Metabolic flux distribution for genetic mutants

mCEF

ECF


Control effective fluxes (CEFs)

mCEF modified Control Effective

Flux

Expected advantage of GMF

• Available to gene knockout, over-expressing or under-expressing

mutants

• MOMA/rFBA are available only for gene deletion, because they use Boolean Logic.


Control Effective Flux (CEF)

Transcript ratio for the growth on glycerol versus glucose

Stelling J, et al, Nature, 2002, 420, 190-193

( 2)( 1, 2)

( 1)i

ii

cef ss s

cef sΘ =

Transcript ratio of metabolic genes

CEFs for different substrates glucose, glycerol and acetate.


GMF = mCEF+ECF

m mv = P λ⋅

( )( , )( )

ii

i

mCEF mw mmCEF w

Θ =

S (Stoichiometric matrix)

w wv = P λ⋅

P (EMs matrix) mCEF

ECF

mCEF

WT

Mutant

wiλ λ

1

nmi p

p

γ=

= ⋅ Θ∏

Experimental data Page 65 Guillermo R. Castro

mCEF is an extension of CEF (control efectivo de flujo)

(if reaction is modified)1 (if reaction is not modified)

ii

EAP ii

η

=

, ,

max,

( )1( )

j CELLOBJ i jj

iCELLOBJ j CELLOBJ

j

pmCEF w

p

ε

ε

⋅=

∑∑

( )( , )( )

ii

i

mCEF mutw mutmCEF w

Θ =

( ),

,,

CELLOBJ j jmj CELLOBJ

i j ii

p EA

pε

η

⋅=

⋅∑

( ), ,max

,

1( )

mj CELLOBJ i j i

ji m

CELLOBJ j CELLOBJj

pmCEF mut

p

ε η

ε

⋅ ⋅=

∑∑

available for Genetically modification mutants:

Up-regulation Down-regulation Deletion


En rojo: parametro que incopora el cambio en cada modifcacion de las reacciones. En azul: el costo que requiere para modificar el gen Y es usado para contrapesar los cambios de EM

Ishi

i N, e

t al.

Sc

ienc

e 31

6 :

593-

597,

2007

mCEF predicts the transcript ratio of a mutant to wild type


Comparison of GMF(CEF+ECF) with FBA and MOMA for E. coli gene deletion mutants

Characterization of GMF


• FBA

• MOMA

,min ,max

00

[ , ] 1,...,

biomass

k

i i i

Maximize v subject to S vvv v v i n

⋅ ==

∈ =

2

1

,min ,max

( )

00

[ , ] 1,...,

N

i ii

k

i i i

Minimize w x

subject to S vvv v v i n

=

−

⋅ ==

∈ =

∑

Vk is the flux of gene knockout reaction k

Vk is the flux of gene knockout reaction k


Prediction of the flux distribution of an E. coli zwf mutant by GMF, FBA, and MOMA

Zhao J, Baba T, Mori H, Shimizu K.

Appl M icrobiol Biotechnol. 2004;64(1):91-8.


Prediction of the flux distribution of an E. coli gnd mutant by CEF+ECF, FBA, and MOMA

Zhao

J, B

aba

T, M

ori H

, Shi

miz

u K.

App

l Mic

robi

ol

Bio

tech

nol.

2004

;64(

1):9

1-8.


gnd, gluconato P-DH

Prediction of the flux distribution of an E. coli ppc mutant by CEF+ECF, FBA, and MOMA

Peng

LF,

Ara

uzo-

Brav

o M

J, S

him

izu

K. F

EMS

Mic

robi

ol

Lett

ers,

200

4, 2

35(1

): 1

7-23


Ppc. PEP carboxylase

Prediction of the flux distribution of an E. coli pykF mutant by CEF+ECF, FBA, and MOMA

Sidd

ique

e KA

, Ara

uzo-

Brav

o M

J, S

him

izu

K.

App

l Mic

robi

ol B

iote

chol

200

4, 6

3(4)

:407

-417


pykF, Piruvate Kinase

Prediction of the flux distribution of an E. coli pgi mutant by CEF+ECF, FBA, and MOMA

Hua

Q, Y

ang

C, B

aba

T, M

ori H

, Shi

miz

u K.

J

Bac

teri

ol 2

003,

185

(24)

:705

3-70

67


pgi, Phosphoglucose isomerase

Prediction errors of FBA, MOMA and GMF for five mutants of E. coli

Method zwf gnd pgi ppc pykF

FBA 18.38 14.76 23.68 29.92 21.10

MOMA 18.06 14.27 29.38 19.79 25.83

GMF 6.43 9.21 18.47 18.95 20.46

Model Error = Difference in the flux distributions between WT & a mutant


Is GMF applicable to over-expressing or less-expressing mutants?

(FBA and MOMA are not applicable to these mutants.)


Up/down-regulation mutants FBP over-expressing mutant of C. glutamicum G6P dehydrogenase over-expressing mutant of C. glutamicum gnd deficient mutant of C. glutamicum G6P dehydrogenase over-expressing mutant of E. coli


Summary of GMF • mCEF is combined to ECF for the accurate

prediction of flux distribution of mutants. • GMF is applied to the mutants where an

enzyme is over-expressed, less-expressed. It has an advantage over rFBA and MOMA.


Conclusiones

• ECF is available for the quantitative correlation between an enzyme activity profile and its associated flux distribution

• GMF is a new tool for predicting a flux distribution for genetically modified mutants.


Guillermo R. Castro 81

Clase 4: Balance de Flujos Metabólicos 2 Flujo metabólico �(def.)Vias en E. coliSlide Number 4Slide Number 5De genes a flujos metabolicos Slide Number 7Slide Number 8E. coli K12Modelo iAF1260 de E. coli K 12A genome-scale metabolic reconstruction for Escherichia coli K-12 MG1655 that accounts for 1260 ORFs and thermodynamic information�Mol Syst Biol. 2007; 3: 121. Modelo iAF1260 de E. coli K 12Glucosa, �eje central� del �metabolismoGlicólisis – fase preparatoriaGlicólisis – fase de síntesisGlicólisis – resumen energéticoUn problema a ser resuelto�S. cerevisaeUn problema� a ser resueltoSe pueden determinar los flujos utilizando datos expresion genicaSlide Number 20Transcriptoma & proteomaSlide Number 22Slide Number 23Slide Number 24Agrupamiento de genes por similaridad de secuenciasAnalisis de varianzaResultadosStatistical description of gene-expression and flux changesSlide Number 29Geometry of the sampling methodComparison between the Hit and Run algorithm and the sampling of the convex basis.Assignment of regulatory characteristicsSome resultsTranscription factor enrichment (very significant for many TFs)Slide Number 35The role of constraintsHow does the cell “choose” its metabolic state?Aerobic and oxygen limited chemostats Anaerobic chemostat and glucose excess batchSlide Number 40Slide Number 41Slide Number 42Para mutantes con genes delecionados se empela un flujo de estado estacionario predecido mediante logica boleanaSlide Number 44Slide Number 45Slide Number 46Slide Number 47Slide Number 48Slide Number 49Slide Number 50Slide Number 51Slide Number 52Slide Number 53Slide Number 54Slide Number 55Slide Number 56Slide Number 57Exactitud de la Prediction del ECFSlide Number 59Modificacion genetica �de FlujosSlide Number 61Flow chart of GMFExpected advantage of GMFControl Effective Flux (CEF)Slide Number 65Slide Number 66Slide Number 67Slide Number 68Slide Number 69Prediction of the flux distribution of an E. coli zwf mutant by GMF, FBA, and MOMAPrediction of the flux distribution of an E. coli gnd mutant by CEF+ECF, FBA, and MOMAPrediction of the flux distribution of an E. coli ppc mutant by CEF+ECF, FBA, and MOMAPrediction of the flux distribution of an E. coli pykF mutant by CEF+ECF, FBA, and MOMAPrediction of the flux distribution of an E. coli pgi mutant by CEF+ECF, FBA, and MOMASlide Number 75Slide Number 76Up/down-regulation mutantsSummary of GMFConclusionesSlide Number 80Slide Number 81

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CARRERA DE ESPECIALIZACION EN BIOTECNOLOGIA …biotecnologiaindustrial.fcen.uba.ar/.../2011/...Bal-2-Ing-Me-UBAt-13.pdf · Clase 4: Balance de Flujos Metabólicos 2 Prof: Guillermo