Insights from network analysis of

metabolism in four kingdoms of life

Stefan Schuster

Friedrich Schiller University Jena, Germany

Dept. of Bioinformatics

Introduction

• Several specific features of network analysis of metabolic systems:– Mass flow and steady-state assumption

makes analysis easier due to strict mathematical equations

– Besides monomolecular reactions, also many bi- and multimolecular reactions hypergraph, more complex than graph

Introduction (2)

• Examples of goals of modelling:

– Determining optimal pathways

– Predicting the effect of engineering these networks, e.g. by deleting and/or inserting enzymes

– Assessment of the impact of enzyme deficiencies

Synthetic biology• Design and construction of new biological

functions and systems not found in nature• Minimal genome / Minimal metabolism

Knocking out as many metabolic genes as possible so that all desired metabolic capabilities remain

Example:Can sugars be produced from lipids

in animals?

• Excess sugar in human diet is converted into storage lipids, mainly triglycerides

• Is reverse transformation feasible?

?

• 1 glycerol + 3 even-chain fatty acids (odd-chain fatty acids are rare)

• Glycerol glucose OK (gluconeogenesis)

• (Even-chain) fatty acids acetyl CoA (-oxidation)

• Acetyl CoA glucose?

Triglycerides

Glucose

AcCoA

Cit

IsoCit

OG

SucCoA

PEP

Oxac

Mal

Fum

Succ

Pyr

CO2

CO2

CO2

CO2

Exact reversal of glucose degradation impossible because pyruvate dehydrogenase is irreversible. Nevertheless, AcCoA is linked with glucose by a chain of reactions.

Fatty acids

Metabolism is hypergraph due to bimolecular reactions!

Schuster und Hilgetag: J. Biol. Syst. 2 (1994) 165-182Schuster et al., Nature Biotechnol. 18 (2000) 326-332.

non-elementary flux mode

elementary flux modes

An elementary mode is a minimal set of enzymes thatcan operate at steady state with all irreversible reactions used in the appropriate direction

The enzymes are weighted by the relative flux they carry.

The elementary modes are unique up to scaling.

All flux distributions in the living cell are non-negative linear combinations of elementary modes

Simple example:

P1 P2

P3

1S1 2

3

110

101

011Elementary modes:

flux1

flux2

flux3

generating vectors

Mathematical properties of elementary modes

Any vector representing an elementary mode involves at least dim(null-space of N) − 1 zero components.Example:

P1 P2

P3

1S1 2

3

10

01

11

K

dim(null-space of N) = 2 Elementary modes:

110

101

011

Schuster et al., J. Math. Biol. 2002, after results in theoretical chemistry by Milner et al.

Mathematical properties of elementary modes (2)

A flux mode V is elementary if and only if the null-space of the submatrix of N that only involves the reactions of V is of dimension one. Klamt, Gagneur und von Kamp, IEE Proc. Syst. Biol. 2005, after results in convex analysis by Fukuda et al.

P1 P2

P3

1S1 2

3

e.g. elementary mode:

110

101

011N = (1 1) dim = 1

Glucose

AcCoA

Cit

IsoCit

OG

SucCoA

PEP

Oxac

Mal

Fum

Succ

Pyr

CO2

CO2

CO2

CO2

If AcCoA, glucose, CO2 and all cofactors are considered external, there is NO elementarymode consuming AcCoA, nor any one producingglucose.

Intuitive explanation byregarding oxaloacetate or CO2.

Glucose

AcCoA

Cit

IsoCit

OG

SucCoA

PEP

Oxac

Mal

Fum

Succ

Gly

Pyr

CO2

CO2

CO2

CO2 IclMas

Green plants, fungi, many bacteria (e.g. E. coli) and – as the only clade of animals – nematodes harbour the glyoxylate shunt. Then, there is an

elementary mode representing conversion of AcCoA into glucose.

Caenorhabditiselegans

In a limited network of central metabolism, no gluconeogenesis from fatty acids

• Weinman,E.O. et al. (1957) Physiol. Rev. 37, 252–272.

• L.F. de Figueiredo, S. Schuster, C. Kaleta, D.A. Fell: Can sugars be produced from fatty acids? A test case for pathway analysis tools. Bioinformatics 25 (2009) 152-158.

Luis de Figueiredo

Engineering the glyoxylate shunt into mammals

• Dean JT, … Liao JC.: Resistance to diet-induced obesity in mice with synthetic glyoxylate shunt. Cell Metab. (2009) 9: 525-536.

Going genome-scale

• Can humans convert fatty acids into sugar on entangled routes across a larger network? Mentioned in literature on anecdotal basis

Going genome-scale

• Can humans convert fatty acids into sugar on entangled routes across a larger network? Mentioned in literature on anecdotal basis

• YES, WE CAN! (In principle)• C. Kaleta, L.F. de Figueiredo, S. Werner, R. Guthke,

M. Ristow, S. Schuster: In silico evidence for gluconeogenesis from fatty acids in humans, PLoS Comp. Biol. 7 (2011) e1002116

ChristophKaleta

Gluconeogenesis from fatty acids

• Is likely to be important– in sports physiology– in diets for weight reduction– in hibernating animals– in embryos within eggs

How can Inuit live on a practically carbohydrate-free diet?

C. Kaleta, L.F. de Figueiredo, S. SchusterAgainst the stream: Relevance of gluconeogenesis from fatty acids for natives of the arctic regionsIntern. J. Circumpol. Health 71 (2012) 18436

Glucose

AcCoA

Cit

IsoCit

OG

SucCoA

PEP

Oxac

Mal

Fum

Succ

Gly

Pyr

CO2

CO2

CO2

CO2

A successful theoretical predictionRed elementary mode: Usual TCA cycleBlue elementary mode: Catabolic pathwaypredicted in Liao et al. (1996) and Schuster et al. (1999) for E. coli.

Glucose

AcCoA

Cit

IsoCit

OG

SucCoA

PEP

Oxac

Mal

Fum

Succ

Gly

Pyr

CO2

CO2

CO2

CO2

Red elementary mode: Usual TCA cycleBlue elementary mode: Catabolic pathwaypredicted in Liao et al. (1996) and Schuster et al. (1999). Experimental hints in Wick et al.(2001). Experimental proof in:

E. Fischer and U. Sauer:A novel metabolic cycle catalyzes glucose oxidation and anaplerosis in hungry Escherichia coli,

J. Biol. Chem. 278 (2003) 46446–46451

NADP

NADPH

NADP

NADPH

NADHNAD

ADP

ATP

ADP

ATP

CO2

ATP ADP

G6P

X5P

Ru5P

R5P

S7P

GAP

GAP

6PG

GO6P

F6P FP2

F6P

DHAP

1.3BPG

3PG

2PG

PEP

E4P

Optimization: Maximizing molar yields

ATP:G6P yield = 3 ATP:G6P yield = 2

Pyr

Maximization of tryptophan:glucose yield

Model of 65 reactions in the central metabolism of E. coli.26 elementary modes. 2 modes with highest tryptophan:glucose yield: 0.451.

Glc

G6P

233

Anthr

Trp105

PEPPyr

3PGGAP

PrpP

Schuster, Dandekar, Fell,Trends Biotechnol. 17 (1999) 53

Tryptophan

Turning green: plant metabolism

• Previously undescribed pathway of efficient conversion of carbohydrate to oil in developing green plant seeds detected by EFMs (Schwender J, Goffman F, Ohlrogge JB, Shachar-Hill Y: Nature 2004, 432: 779-782).

• Involves pentose-phosphate pathway and RUBISCO enzyme and provides 20% more acetyl-CoA for fatty acid synthesis than glycolysis.

Example (of Synthetic Biology?) from fungal metabolism

• Engineering of yeast (and E. coli) to produce polyhydroxy-butyric acid (PHB, a bioplastic)

• 20 EFMs in S. cerevisiae strain engineered to produce PHB, 7 of which produce PHB with different yields

• Adding the natively absent ATP citrate-lyase to the network, 496 EFMs. Maximum theoretical PHB-to-carbon yield thereby increased from 0.67 to 0.83.

PHB

Carlson, R., Fell, D., and Srienc, F. (2002) Biotechnol. Bioeng. 79, 121–134.

ATP ADP

F6P FP2

Futile cycles

One elementary mode: fructose-bisphosphate cycle

Futile cycles perform no net transformation except

hydrolysis of energy-rich compounds (mainly cofactors)

S. Schuster et al.,J. Math. Biol. 45 (2002) 153-181

Some futile cycles are not easy to find

S. Schuster et al.,J. Math. Biol. 45 (2002) 153-181

Some futile cycles are not easy to find

Going genome-scale

Gebauer J, Schuster S, de Figueiredo LF, Kaleta C. Detecting and investigating substrate cycles in a genome-scale human metabolic network. FEBS J. (2012) 279: 3192-202.

Results from analysis of futile cycles• Evolutionary pressure against futile cycles with a

particular high flux.• ATP consumption of the normal, aged and

Alzheimer brain models does not show statistically significant differences

CA = cytosol of astrocytesCN = cytosol of neurons

Gebauer et al.FEBS J. (2012) 279: 3192-202.

Applications of EFM analysis

• Checking which biotransformations are stoichiometrically and thermodynamically feasible

• Determining maximal and submaximal molar yields of wild-type, recombinant strains, and knock-out mutants

• Quantifying robustness to knock-out• Assessing impact of enzyme deficiencies• Detecting futile cycles• Determining minimal media• Functional genomics – gap filling

Application to signalling systems

E1 E1*

E2 E2*

E3 E3*

Target

Signal

Calculating elementary modes gives trivial result that each cyclecorresponds to one mode. Flow ofinformation is not reflected.

Enzyme cascades – only activated component is depicted

Signal

E1*

E2*

E4*

Target2Target1

E3*

Obviously, elementary signalling routes

How to define elementary signalling routes?

• Signalling systems are not always at steady state. Propagation of signals is time-dependent process.

• However: Averaged over longer time spans, also signalling systems must fulfill steady-state condition because system must regenerate.

Signal amplification

• Mass flow not linked with information flow.• However: Signal amplification requires that

each activated enzyme must catalyse at least one further activation.

• Minimum condition: Each activated enzyme catalyses exactly one further activation.

• Thus, operational stoichiometric coupling of cascade levels.

• E1* + E2 E1 + E2*

The elementary routes thus calculated exactly give the signalling routes

Signal

E1*

E2*

E4*

Target2Target1

E3*

J. Behre and S. Schuster,J. Comp. Biol. 16 (2009) 829-844

Conclusions• Elementary modes are an appropriate

concept to describe biochemical pathways; manifold biochemical and biotechnological applications.

• Two tendencies in modelling: large-scale vs. medium-scale

• Analysis of both types of models allows interesting conclusions

Conclusions (2)

• Previously unknown pathways have been found also in medium-scale networks

• Some questions can only be answered in whole-cell models, for example: Can some product principally be synthesized from a given substrate?

Dept. of Bioinformatics group at the School of Biology and

Pharmaceutics, Jena University

Futile cycles

• “…a search for metabolic markers of aging might include efforts to determine [...] (b) enzymes that catalyze opposing reactions” (Stadtmann, Exp. Gerontol. 23, 1988, 327-347)

• „…an attractive candidate for the function of the … energy-dissipating proton cycle [in mitochondria] is to decrease the production of … reactive oxygen species (ROS). This could be important in helping to minimise oxidative damage to DNA and in slowing ageing.“ (Brand, Exp. Gerontol. 35, 2000, 811-820)

AMP

NA

NaAD NAD

Nam

NaMN

NR

NAR

NMN

PRPP

ADP-ribosylation

ADP-ribosyl-X

Pnc1

H2ONH3

Qns1ATP

gln

H2O

gluNAD_pool

NAD_ex

NAMPT [human]

NR_pool

NR_ex

Nam_pool

Nam_ex

Npt1

NAR_pool

NAR_ex

NA_pool

NA_ex

Nma1,2ATP

Nma1,2

ATP

Nrk1

ATP

ADP

Nrk1

ATP

ADP Sdt1, Isn1

Pi

Sdt1, Isn1

Pi

Pnp1 Pi

ribose-1P

Pnp1

Pi

ribose-1P

Bna6 QA

CO2

PPi

PRPP

PPi

PPi

Npy1

AMP

Urh1

H2O

ribose

Urh1

H2O

ribose

H2O

+

+

+

PRPP

PPi

PPi

PPi

Network of NAD metabolism

Elementary flux modes include all futile cycles

AMP

ribose-P

Prs1-5

ATP

AMP

NaAD NAD

NaMNPRPP

Qns1ATP

gln

H2O

gluNAD_pool

NAD_ex

Nma1,2

ATP

Bna6 QA

CO2

PPi

PPi

PPi

AMP

ribose-P

Prs1-5

ATP

AMP

NA

NaAD NAD

NaMN

Qns1ATP

gln

H2O

gluNAD_pool

NAD_ex

Npt1

NA_pool

NA_ex

Nma1,2

ATP

PPi

PRPP

PPi

PPi

ATP

ADP

AMP

ribose-P

Prs1-5

ATP

Nam

NR

NMN

NAMPTSdt1, Isn1

Pi

Pnp1 Pi

ribose-P

PRPP

PPi

ATP

ADP

AMP

NaAD NAD

NaMN

NAR

Qns1ATP

gln

H2O

gluNAD_pool

NAD_ex

NAR_pool

NAR_ex

Nma1,2

ATP

Nrk1

ATP

ADP

PPiPPi

AMP

ribose-P

Prs1-5

ATP

AMP

NA

NaAD NAD

Nam

NaMN

NR

Pnc1

H2ONH3

Qns1ATP

gln

H2O

gluNAD_pool

NAD_ex

NR_pool

NR_ex

Npt1

Nma1,2

ATP

PPi

Urh1H2Oribose

PRPP

PPi

PPi

ATP

ADP

NAD

Nam

NR

NMN

NAD_pool

NAD_ex

NAMPT

NR_pool

NR_ex

Nma1,2

ATP

Pnp1 Pi

ribose-P

PPi

PRPP

PPi

ATP

ADP

AMP

ribose-P

Prs1-5

ATP

AMP

ribose-P

Prs1-5

ATP

AMP

NA

NaAD NAD

Nam

NaMN

ADP-ribosyl transfer

ADP-ribosyl-X

Pnc1

H2ONH3

Qns1ATP

gln

H2O

glu

Npt1

Nma1,2

ATP

PPi

PRPP

PPi

PPi

ATP

ADP

NAD

Nam

NMNADP-ribosyl transfer

NAMPT

Nma1,2

ATP

PPi

PRPP

PPi

ATP

ADPADP-ribosyl-X

AMP

ribose-P

Prs1-5

ATPPRPP

L.F. de Figueiredo, T.I. Gossmann, M. Ziegler, S. Schuster: Pathway analysis of NAD+ metabolism. Biochem. J. 439 (2011) 341–348.

Simulating circadian rhythms

• Dynamics of circadian rhythms needs to be adapted to day length changes between summer and winter.

• Hypothesis: Fraction of long-range connections between cells in Suprachiasmatic nucleus adjusts phase distribution: dense long-range connections during winter lead to a narrow activity phase, while rare long-range connections during summer lead to a broad activity phase.

Summer Winter

Connections within SCN

Bodenstein, Gosak, Schuster, Marhl, Perc: PLoS Comp. Biol. 8 (2012)