Systems Biology for the

development of microbial cell

factoriesEugénio Campos Ferreira

IBB – Institute for Biotechnology and Bioengineering

Centre of Biological Engineering, BioPSE group

Universidade do Minho

OUTLINE

Systems Biology approaches for modelling,

optimization, and control of microbial cell factories

Cellular Models for Metabolic Engineering: gene

networks

Inference of Biological Networks

From Genome-scale metabolic models

From experimental data

From literature data mining

In Silico Metabolic Engineering Platforms:

Optimization of Microbial strains – OptFlux tool

INTRODUCTIONSYSTEMS BIOLOGY

Metabolic Engineering can gain major benefits from the

systems biology approach

Systems Biology does not investigate individual cellular

components at a time, but the behaviour and relationships of

all of the elements in a particular biological system while it is

functioning

?

INTRODUCTIONCELLULAR MODELS

INFERENCE OF BIOLOGICAL NETWORKS

OPTIMIZATION TOOLS

Systems biology involves the use of computer

simulations of cellular

subsystems (such as the networks of metabolites and enzymes which

comprise metabolism, signal

transduction pathways and gene

regulatory networks) to both

analyze and visualize the

complex connections of these

cellular processes.

http://images.google.com/imgres?imgurl=http://akamaipix.crutchfield.com/ca/learningcenter/car/component/radio.jpg&imgrefurl=http://www.crutchfieldadvisor.com/ISEO-rgbtcspd/popups/car_components.html?section=radio&h=150&w=150&sz=7&hl=en&start=3&tbnid=l3WEnnlkRActiM:&tbnh=96&tbnw=96&prev=/images?q=+components+radio&svnum=10&hl=en&lr=

INTRODUCTIONMETABOLIC ENGINEERING

In order to economically produce desired compounds like

antibiotics, therapeutic proteins, food and feed ingredients,

fuels, vitamins and other chemicals from microbial cell

factories it is generally necessary to retrofit the metabolism

Metabolic engineering envisages the introduction of directed

genetic modifications leading to desirable metabolic

phenotypes, as opposed to traditionally used random

mutagenesis and screening

Cell factory Genome

Metabolism / Phenotype

INTRODUCTIONCELLULAR MODELS

INFERENCE OF BIOLOGICAL NETWORKS

OPTIMIZATION TOOLS

http://images.google.com/imgres?imgurl=http://res2.agr.ca/lethbridge/emia/images/SEMproj/Ecoli.jpg&imgrefurl=http://res2.agr.ca/lethbridge/emia/SEMproj/ecoli_e.htm&h=398&w=400&sz=60&hl=en&start=1&tbnid=3uJHHDPKy8pi_M:&tbnh=123&tbnw=124&prev=/images?q=coli&svnum=10&hl=en&lr=http://images.google.com/imgres?imgurl=http://genome.ornl.gov/microbial/syn_wh/embl/genome_fig.png&imgrefurl=http://genome.ornl.gov/microbial/syn_wh/&h=1583&w=1224&sz=77&hl=en&start=7&tbnid=G1Tzjt976BbctM:&tbnh=150&tbnw=116&prev=/images?q=genome&ndsp=18&svnum=10&hl=en&lr=&sa=N

Gene Deletion

Gene Addition

Gene Under/Overexpression

Manipulation of environmental conditions

INTRODUCTIONMETABOLIC ENGINEERING STRATEGIES

INTRODUCTIONCELLULAR MODELS

INFERENCE OF BIOLOGICAL NETWORKS

OPTIMIZATION TOOLS

In metabolic engineering problems, it is often difficult

to identify a priori which genetic manipulations will

originate a given desired phenotype

In order to rationally design production strains with

enhanced capabilities, it is essential to have:

INTRODUCTIONMETABOLIC ENGINEERING

ACCURATE

MATHEMATICAL

MODELS

ROBUST AND

FLEXIBLE

OPTIMIZATION

TOOLS

GOOD SIMULATION

METHODS

INTRODUCTIONCELLULAR MODELS

INFERENCE OF BIOLOGICAL NETWORKS

OPTIMIZATION TOOLS

INTRODUCTIONMETABOLIC ENGINEERING

Cellular Mathematical

Model

Gene / reaction

associations

Productivity in a

given metabolite

Simulation of Phenotype

Optimization

Algorithm

Genome modifications and manipulation of

environmental conditions

Objective function – productivity in a given metabolite

INTRODUCTIONCELLULAR MODELS

INFERENCE OF BIOLOGICAL NETWORKS

OPTIMIZATION TOOLS

CELLULAR MODELSLEVELS OF INFORMATION

Models should comprise different levels of information:

reactions stoichiometry

reactions kinetics

regulatory information

Metabolomev1 v3v2 v4

g6p f6p fdp gla glt

E1 E2 E3 E4

E5 P1 E6

Fluxome

Interactome

Proteome

Transcriptome

Genome

nPFK

A

s,p6f,PFK

p6f

PFKs,p6f,PFKp6f

s,adp,PFK

adp

s,atp,PFKatp

p6fatp

max

PFK

PFK

P6GPDH6GPGIPTA

p6g

K

BC1

L1

B

AKC

K

C1KC

CCvv

Cvvvdt

dC

INTRODUCTIONCELLULAR MODELS

INFERENCE OF BIOLOGICAL NETWORKS

OPTIMIZATION TOOLS

http://images.google.com/imgres?imgurl=http://www.nmr.utmb.edu/images/s100p_large.jpg&imgrefurl=http://www.nmr.utmb.edu/pubs/dggpubs.html&h=495&w=700&sz=137&hl=en&start=12&tbnid=_wWAt6NgK2j0uM:&tbnh=99&tbnw=140&prev=/images?q=protein&svnum=10&hl=en&lr=http://images.google.com/imgres?imgurl=http://www.steve.gb.com/images/science/histone_mrna.png&imgrefurl=http://www.steve.gb.com/science/translation.html&h=300&w=195&sz=5&hl=en&start=75&tbnid=h5YLwW9sgbphgM:&tbnh=116&tbnw=75&prev=/images?q=mrna&start=72&ndsp=18&svnum=10&hl=en&lr=&sa=Nhttp://images.google.com/imgres?imgurl=http://pharm1.pharmazie.uni-greifswald.de/bednarski_web/web/data/personen/Lectures/PMC/Wechselwirkungen/DNA structures.jpg&imgrefurl=http://www.uvm.edu/~lehiggin/teaching/science/SAAWK_syllabus.htm&h=676&w=995&sz=114&hl=en&start=14&tbnid=mbx2Hw2ltL5VuM:&tbnh=101&tbnw=149&prev=/images?q=dna&ndsp=18&svnum=10&hl=en&lr=&sa=Nhttp://images.google.com/imgres?imgurl=http://www.nmr.utmb.edu/images/s100p_large.jpg&imgrefurl=http://www.nmr.utmb.edu/pubs/dggpubs.html&h=495&w=700&sz=137&hl=en&start=12&tbnid=_wWAt6NgK2j0uM:&tbnh=99&tbnw=140&prev=/images?q=protein&svnum=10&hl=en&lr=http://images.google.com/imgres?imgurl=http://www.nmr.utmb.edu/images/s100p_large.jpg&imgrefurl=http://www.nmr.utmb.edu/pubs/dggpubs.html&h=495&w=700&sz=137&hl=en&start=12&tbnid=_wWAt6NgK2j0uM:&tbnh=99&tbnw=140&prev=/images?q=protein&svnum=10&hl=en&lr=http://images.google.com/imgres?imgurl=http://www.nmr.utmb.edu/images/s100p_large.jpg&imgrefurl=http://www.nmr.utmb.edu/pubs/dggpubs.html&h=495&w=700&sz=137&hl=en&start=12&tbnid=_wWAt6NgK2j0uM:&tbnh=99&tbnw=140&prev=/images?q=protein&svnum=10&hl=en&lr=http://images.google.com/imgres?imgurl=http://www.nmr.utmb.edu/images/s100p_large.jpg&imgrefurl=http://www.nmr.utmb.edu/pubs/dggpubs.html&h=495&w=700&sz=137&hl=en&start=12&tbnid=_wWAt6NgK2j0uM:&tbnh=99&tbnw=140&prev=/images?q=protein&svnum=10&hl=en&lr=http://images.google.com/imgres?imgurl=http://www.nmr.utmb.edu/images/s100p_large.jpg&imgrefurl=http://www.nmr.utmb.edu/pubs/dggpubs.html&h=495&w=700&sz=137&hl=en&start=12&tbnid=_wWAt6NgK2j0uM:&tbnh=99&tbnw=140&prev=/images?q=protein&svnum=10&hl=en&lr=http://images.google.com/imgres?imgurl=http://www.nmr.utmb.edu/images/s100p_large.jpg&imgrefurl=http://www.nmr.utmb.edu/pubs/dggpubs.html&h=495&w=700&sz=137&hl=en&start=12&tbnid=_wWAt6NgK2j0uM:&tbnh=99&tbnw=140&prev=/images?q=protein&svnum=10&hl=en&lr=

There are several ways to represents the chemical

conversions associated to metabolic reactions

Kinetic or mechanistic models use deterministic differential

equations relating the amount of reactants with the quantity of

products, according to a given reaction rate and other

parameters

Given an initial state, the trajectory of metabolite can be

obtained by numerical simulation

CELLULAR MODELSMETABOLIC REACTIONS

Ty3H

Ph4H

AttY

L-DOPA

Tyr

Phe

4-HPP

v1

v2

v3

...dt

d[Tyr]

t

[Tyr]

INTRODUCTIONCELLULAR MODELS

INFERENCE OF BIOLOGICAL NETWORKS

OPTIMIZATION TOOLS

0 v-v-v 321

A (pseudo)steady state

condition is usually assumed

inside the cell

Ty3H

Ph4H

AttY

L-DOPA

Tyr

Phe

4-HPP

v1

v2

v3

321 vvvdt

d[Tyr]

This procedure is repeated for all considered metabolites

and will originate the so-called stoichiometric model

CELLULAR MODELSSTOICHIOMETRIC MODELS

The result is a Linear Equations system described by

stoichiometric matrix S.

0vS

jjj αvβ

INTRODUCTIONCELLULAR MODELS

INFERENCE OF BIOLOGICAL NETWORKS

OPTIMIZATION TOOLS

1

2

3

4

5

6

0

0

0

0

...

n

v

v

v

v

v

v

v

1 2 3 4 5 6

...

-1 0 -1 0 0 0 ... 0

1 1 0 1 0 0 ... 1

0 1 0 0 1 0 ... 0

0 0 1 1 1 1 ... 1

0 0 0 0 0 1 ... 0

... ... ... ... ... ... ... ... ...

0 1 1 0 0 0 0 0

v v v v v v

A

B

C

S D

E

flux n

metabolite m

A

B

C

D E

v3

v5

v6v1

v2

v4

For an identified reaction set:

CELLULAR MODELSSTOICHIOMETRIC MODELS

INTRODUCTIONCELLULAR MODELS

INFERENCE OF BIOLOGICAL NETWORKS

OPTIMIZATION TOOLS

Stoichiometric models typically have more fluxes

than balanced metabolites.

The equation system, S • v = 0, then has more

variables than equations. This is a so-called under-

determined equation system with infinitely many

solutions:

CELLULAR MODELSSTOICHIOMETRIC MODELS

0vS

jjj αvβ

Hyper-cone containing

ALL solutions as defined

by the stoichiometry of

the organism

INTRODUCTIONCELLULAR MODELS

INFERENCE OF BIOLOGICAL NETWORKS

OPTIMIZATION TOOLS

How can we reduce the cone of solutions?

Reduction of

the solutions

space

Particular

Solution

By optimizing a given

criterion – FBA, MoMA,

ROOM…

By the introduction of

regulatory information (ex:

Gene Networks)

CELLULAR MODELSSTOICHIOMETRIC MODELS

INTRODUCTIONCELLULAR MODELS

INFERENCE OF BIOLOGICAL NETWORKS

OPTIMIZATION TOOLS

FBA: Flux Balance Analysis

ROOM: Regulatory On/Off

Minimization

MoMA: Minimization of Metabolic

Adjustment

prodT vvcz

Maximize:c = row vector containing weights

specifying what combination of

fluxes to optimize

Subject to:

0vS

jjj αvβ

Constraints from

stoichiometry

LINEAR

PROGRAMMING

PROBLEM!

CELLULAR MODELSFBA - FLUX BALANCE ANALYSIS

The idea is to find one solution to the under-determined

system

S • v = 0 by optimization of a given criterion.

A vector containing the values of each

individual metabolic flux is obtained

INTRODUCTIONCELLULAR MODELS

INFERENCE OF BIOLOGICAL NETWORKS

OPTIMIZATION TOOLS

BUT WHAT SHOULD WE OPTIMIZE?

Studies in several organisms demonstrated that

their metabolic network has evolved for optimization

of the specific growth rate under several carbon

source limiting conditions

Thus, for simulating cellular behaviour, the most

common objective function is the maximization of

biomass production (BPCY: Biomass-Product Coupled Yield)

CELLULAR MODELSFBA - FLUX BALANCE ANALYSIS

INTRODUCTIONCELLULAR MODELS

INFERENCE OF BIOLOGICAL NETWORKS

OPTIMIZATION TOOLS

Ibarra et al (2002), Nature

CELLULAR MODELSMoMA - Minimisation of Metabolic Adjustment

The problem is the search of a flux set (x) that

has a minimal distance from the wild-type flux

vector (w) obtained with FBA.

The distance between w and x is given by the

Euclidean distance:

2

1

( , ) ( )N

i i

i

D w x w x

The minimization of that distance can be formulated as a

QP problem

For mutants and organisms grown on unusual

carbon sources the hypothesis of optimal growth is

not always real

Such strains may undergo minimal redistribution of

fluxes with respect to the wild-type strains (MoMA)

INTRODUCTIONCELLULAR MODELS

INFERENCE OF BIOLOGICAL NETWORKS

OPTIMIZATION TOOLS

Segre et al. (2002), PNAS

CELLULAR MODELSGENE NETWORKS

Gene Regulatory Networks represent regulatory elements

and their interactions

A regulatory network will direct the activation or repression

of a set of genes in response to a specific environmental

stimulus, like O2 or pH

Gene1

Gene1

Gene3Gene2

Gene1

Gene1 Gene3Gene2

Gene1

Gene1

Gene1

Gene1

TF1 TF2

Activation

Repression

INTRODUCTIONCELLULAR MODELS

INFERENCE OF BIOLOGICAL NETWORKS

OPTIMIZATION TOOLS

The simulation of a genetic network can be performed in

several ways

The simplest one is to consider Boolean Networks, where

ON/OFF gene states are assumed.

This approach:

Allows analysis at the network-level

Provides useful insights in network dynamics

A

B

C C = A AND B

0

1

0

CELLULAR MODELSGENE NETWORKS

INTRODUCTIONCELLULAR MODELS

INFERENCE OF BIOLOGICAL NETWORKS

OPTIMIZATION TOOLS

CELLULAR MODELSGENE NETWORKS

WORK IN PROGRESS:

Reconstruction of E. coli

regulatory network and integration

with stoichiometric model

CELLULAR MODELSGENE NETWORKS

WORK IN PROGRESS: Reconstruction of E. coli

regulatory network and integration with stoichiometric

model

INTRODUCTIONCELLULAR MODELS

INFERENCE OF BIOLOGICAL NETWORKS

OPTIMIZATION TOOLS

Genetic

Regulation

Metabolic

Transcriptional

Regulation

Inhibition /

Activation

CELLULAR MODELSGENE NETWORKS

WORK IN PROGRESS: Information System of

Biochemical and Regulatory Data on Escherichia coli

CELLULAR MODELSGENE NETWORKS

WORK IN PROGRESS: Information System of

Biochemical and Regulatory Data on Escherichia coli

HOW CAN WE BUILD THE MODELS IN AN

AUTOMATED WAY?

Ideally, it should be possible to extract all the knowledge

necessary to construct biological models from the

information obtained during genome sequencing

However, the knowledge extracted is still very limited…

INFERENCE OF BIOLOGICAL NETWORKS

GENOME

Presently, the

methodology of obtaining

stoichiometric models from

genome annotation is quite

developed

INTRODUCTIONCELLULAR MODELS

INFERENCE OF BIOLOGICAL NETWORKS

OPTIMIZATION TOOLS

http://images.google.com/imgres?imgurl=http://genome.ornl.gov/microbial/neur/embl/genome_fig.png&imgrefurl=http://genome.ornl.gov/microbial/neur/&h=950&w=734&sz=48&hl=en&start=10&tbnid=QUVkoeGD2BsffM:&tbnh=148&tbnw=114&prev=/images?q=genome&svnum=10&hl=en&lr=

INFERENCE OF BIOLOGICAL NETWORKSGENOME-SCALE METABOLIC MODELS

INTRODUCTIONCELLULAR MODELS

INFERENCE OF BIOLOGICAL NETWORKS

OPTIMIZATION TOOLS

Rocha et al (2007), Gene Ess Gen Scale

WORK IN PROGRESS:

Reconstruction of Metabolic

Networks of:

-H. pylori

-K. lactis

-Streptococcus faecalis

Inference of Biological Networks can also be performed,

from experimental data.

Flux and metabolomic data allow, in principle, to

estimate model parameters for kinetic deterministic

metabolic models

However, the number of experiments and

measurements to be performed is very high!

Also, the structure of the kinetic equations has to be

imposed a priori

In this field, optimal experiment design play an

important role

An alternative is to use Text Mining tools to automatically

search in the literature for biological relations

INFERENCE OF BIOLOGICAL NETWORKSINFERENCE FROM EXPERIMENTAL DATA

INTRODUCTIONCELLULAR MODELS

INFERENCE OF BIOLOGICAL NETWORKS

OPTIMIZATION TOOLS

INFERENCE OF BIOLOGICAL NETWORKS

WORK IN PROGRESS: Experimental Design for

inferring model structure and parameters from flux

data

Mathematical Expression (rate laws and ODE)

Model Structure

Structural and Numerical

identifiability analysis

Parameter identifiable?

Parameter Estimation

Stimulus Study for

Model Validation

Initial Conditions

and Parameters

Experimental

Design and

Sensitivity Analysis

Focus at the moment

Model ReductionYES

NO

Simulations and

Confidence intervals

http://biopseg.deb.uminho.pt/acveloso/default.htm

Model Reduction based on dynamic sensitivity

analysis

High-Throughput Data

Metabolism

Complexity

Stoichiometric

and/or

Dynamic

Modelling ?

From in vivo to in silico and back

INTRODUCTIONCELLULAR MODELS

INFERENCE OF BIOLOGICAL NETWORKS

OPTIMIZATION TOOLS

A complete kinetic description

Complexity of dynamic modelling

Obstacle for their effective use in

optimization and control processes

CoAiPacetylpta

CoAacp

pptaCoAacetyli

pCoAacetyl

CoAi

CoA

acpi

acp

pi

p

CoAacetyli

CoAacetyl

eqpta

coAPacetylpCoAacetyl

pptaCoAacetyliPTA

PTA

KK

CC

KK

CC

K

C

K

C

K

C

K

C

K

CCCC

KKr

re

,,,,,,,,

,,,

max

1

1

1

re1PTA= f(metabolites, enzyme, parameters, regulators,…

Model fluxes and concentrations over time

Drawbacks

• Lots of parameters

• Measured in vitro (valid in vivo?)

• Nearly impossible to get all parameters at genome scale model

Complex E. coli dynamic model describing

the carbon central metabolism with 116

parameters was used to:

Identify key parameters that have more

impacts on the global systems – Sensitivity

analysis

Study a model reduction strategy based on

univariate analysis of the Euclidean-norm to

consider the effect to all metabolites.

Motivation for model reduction

j

i

i

j

j

jjijji

jip

ptX

pX

p

p

ppXppXtS

ln

),(ln

)(2

)()()(,

- Computing sensitivity analysis

- Dynamic sensitivity analysis based on Euclidean-norm

),,()( 0XptftX ji

- Nonlinear ODE model

j

ijiji Xrv

dt

dX

n

k

p

i jijtS

nOS

1 1

2

, )(1

Strategy

dotted line = original model

Solid line = reduced model41 (35.3%) parameters were rejected

Comparison Original and reduced Model - Metabolites

dotted line = original model

Solid line = reduced model

Comparison Original and reduced Model - Fluxes

INFERENCE OF BIOLOGICAL NETWORKS

WORK IN PROGRESS: Development of tools for

automatically inferring regulatory networks from literature

data

INFERENCE OF BIOLOGICAL NETWORKS

WORK IN PROGRESS: Development of tools for

automatically inferring regulatory networks from literature

data

INFERENCE OF BIOLOGICAL NETWORKS

WORK IN PROGRESS: Development of tools for

automatically inferring regulatory networks from literature

data

Lourenço et al., J. Biomed Inform. 2009, 42(4):710-720.

Cellular

Model

Stoichiometry

Regulation

Gene / reaction

associations

Productivity in a

given metabolite

Simulation of Phenotype

(FBA, MoMA, ROOM...)

Optimization

Algorithm

Manipulation of gene deletions / additions and

environmental conditions

Objective function – productivity in a given

metabolite

OPTIMIZATION TOOLSOPTIMIZATION PROBLEM

INTRODUCTIONCELLULAR MODELS

INFERENCE OF BIOLOGICAL NETWORKS

OPTIMIZATION TOOLS

FBA: Flux Balance Analysis

ROOM: Regulatory On/Off

Minimization

MoMA: Minimization of Metabolic

Adjustment

The only reported algorithms are:

OptKnock (Burgard et al., Biotech Bioeng

2003)

Based on MILP

Only applicable to relatively small

stoichiometric models

OptGene (Patil et al., BMC Bioinf 2005) &

OptFlux (Rocha et al., BMC Bioinf 2008)

Evolutionary Algorithms

Applicable to different types of (large-

scale) models

Additional algorithms being applied:

Local Search

Simulated Annealing

OPTIMIZATION TOOLSOPTIMIZATION PROBLEM

INTRODUCTIONCELLULAR MODELS

INFERENCE OF BIOLOGICAL NETWORKS

OPTIMIZATION TOOLS

OPTIMIZATION TOOLS

OptFlux is an open-source, user-friendly and modular

software aimed at being the reference computational tool

for metabolic engineering applications. It allows the use of

stoichiometric metabolic models for simulation and

optimization purposes. www.optflux.org

WORK IN PROGRESS: OptFlux – a software for the

Optimization of microbial strains

OPTIMIZATION TOOLSOptFlux - Conceptual overview

Strain

Optimization

Evolutionary algorithms

Simulated Annealing

Local optimization

Objective

function:

Maximize the

production of a

given metabolite

Phenotype

Simulation

FBA, MoMA, ROOM

Boolean net simulation

…

Determine the

set of fluxes (in

steady state)

Model

Stoichiometric

Regulatory

…

Environmental

Conditions

Genetic conditions

(e.g. knockouts)Override Model

Original Model

OPTIMIZATION TOOLS

www.optflux.org

WORK IN PROGRESS: OptFlux – a software for the

Optimization of microbial strains

(…)

FBA

ROOM

MOMA

Steady State Models-stoichiometric-regulatory

EnvironmentalConditions

Gene/ reactionknockouts

Models and

conditions

Simulation

methods

LinearProgramming

GLPK

MILP

Quadratic Programming

Optimization

problems

Solvers

SCIP

QPGen

Problem

FormulationProblem

Solving

MPS

(…)

(…) (…)

Formats

OPTIMIZATION TOOLSOPTFLUX

www.optflux.org

OPTIMIZATION TOOLSOPTIMIZATION PROBLEM

BPCY: Biomass-Product Coupled Yield

VS: Variable size

Acknowledgments - BioPSE group

Faculty:Eugénio Ferreira

Isabel RochaMiguel Rocha

Rui MendesAna Veloso

Anália Lourenço

Post-Docs:Zita Soons

PhD students:Sónia Carneiro

Rafael CostaJosé Pedro PintoDaniel Machado

Óscar DiasCarla Portela

Daniela Correia

Other researchers:Paulo Maia

Pedro Evangelista Rafael CarreiraSimão SoaresJosé P. FariaPaulo VilaçaRui Pereira

IBB – Institute for Biotechnology and Bioengineering

Centre of Biological Engineering

Universidade do Minho

http://biopseg.deb.uminho.pt

http://biopseg.deb.uminho.pt/

INTRODUCTIONCOLLABORATIONS

Network of Excellence – EURECCA

Coordination ActionDTU - DenmarkUVigo - Spain

IU - USA

MIT - USAUCI - USA

Regulatory Model

Inference using Text

Mining Tools

Experimental Design

Dynamical ModellingData Mining Tools for

Model Inference

Algorithms for

Optimization of Microbial

strains

Development of an unified

Software Platform

European Union

SYSINBIO CA

OptFlux

Dupont - USA

Optimization of Microbial

Strains

Chalmers - Sweden

U. Auckland - New

Zealand

Fluxomics and

Metabolomics

Sony . Japan

Visualization of metabolic

networks

USPaulo

Reconstruction of

Metabolic Network

of K. lactis