Elucidating the Roadmap of Metabolism by Pathway Analysis

Stefan Schuster

Friedrich Schiller University Jena

Dept. of Bioinformatics

Topics of this talk:

Introduction

• Metabolism is bridge between genotype and phenotype

• Networks of metabolic reactions are complex due to their size and the presence of bimolecular reactions

• Many kinetic parameters unknown. Maximal velocities depend on enzyme concentrations

„Roadmap“ as a metaphor

Roads form simple graph

Metabolism ishypergraph

Technologically relevant metabolic syntheses:

• Antibiotics by fungi• Ethanol by yeast • Amino acids by bacteria• Dyes • Perfumes• etc. etc.

Theoretical Methods

• Dynamic Simulation• Stability and bifurcation analyses• Metabolic Control Analysis (MCA)• Metabolic Pathway Analysis• Metabolic Flux Analysis (MFA)• Optimization, Evolutionary Game

Theory• and others

Theoretical Methods

• Dynamic Simulation• Stability and bifurcation analyses• Metabolic Control Analysis (MCA)• Metabolic Pathway Analysis• Metabolic Flux Analysis (MFA)• Optimization, Evolutionary Game

Theory• and others

Metabolic Pathway Analysis (or Metabolic Network Analysis)

• Decomposition of the network into the smallest functional entities (metabolic pathways)

• Does not require knowledge of kinetic parameters!!

• Uses stoichiometric coefficients and reversibility/irreversibility of reactions

History of pathway analysis

• „Direct mechanisms“ in chemistry (Milner 1964, Happel & Sellers 1982)

• Clarke 1980 „extreme currents“• Seressiotis & Bailey 1986 „biochemical pathways“• Leiser & Blum 1987 „fundamental modes“• Mavrovouniotis et al. 1990 „biochemical pathways“• Fell (1990) „linearly independent basis vectors“• Schuster & Hilgetag 1994 „elementary flux modes“• Liao et al. 1996 „basic reaction modes“• Schilling, Letscher and Palsson 2000 „extreme

pathways“

Mathematical background

Steady-state condition NV(S) = 0

If the kinetic parameters were known, this could be solved for S.

If not, one can try to solve it for V. The equation system is

linear in V. However, usually there is a manifold of solutions.

Mathematically: kernel (null-space) of N. Spanned by basis

vectors. These are not unique.

S. Schuster et al.: J. Biol. Syst. 2 (1994) 165-182;Trends Biotechnol. 17 (1999) 53-60; 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

Related concept: Extreme pathway (C.H. Schilling, D. Letscher and B.O. Palsson, J. theor. Biol. 203 (2000) 229) - distinction between internal and exchange reactions, all internal reversible reactions are split up into forward and reverse steps

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

Mathematical background (2)

Steady-state condition NV = 0Sign restriction for irreversible fluxes: Virr 0

This represents a linear equation/inequality system.

Solution is a convex region.

All edges correspond to elementary modes.

In addition, there may be elementary modes in the interior.

Geometrical interpretation

Elementary modes correspond to generating vectors (edges) of a convex polyhedral cone (= pyramid) in flux space (if all modes are irreversible)

Rate of enzyme 1

Rate 2

Rate 3

generating vectors

Software for computing elementary modesEMPATH (in SmallTalk) - J. Woods

METATOOL (in C++) - Th. Pfeiffer, F. Moldenhauer, A. von Kamp

Included in GEPASI - P. Mendesand JARNAC - H. Sauro

part of METAFLUX (in MAPLE) - K. Mauch

part of FluxAnalyzer (in MATLAB) - S. Klamt

part of ScrumPy (in Python) - M. Poolman

On-line computation:

pHpMetatool - H. Höpfner, M. Lange

http://pgrc-03.ipk-gatersleben.de/tools/phpMetatool/index.php

Alternative algorithm in MATLAB – C. Wagner (Bern)

Biochemical Applications:1. Can sugars be produced

from lipids?

• Known in biochemistry for a long time that many bacteria and plants can produce sugars from lipids (via C2 units) while animals cannot

Glucose

AcCoA

Cit

IsoCit

OG

SucCoA

PEP

Oxac

Mal

Fum

Succ

Pyr

CO2

CO2

CO2

CO2

AcCoA is linked with glucose by a chain of reactions. However, no elementary mode realizes this conversion in the absence of the glyoxylate shunt.

Glucose

AcCoA

Cit

IsoCit

OG

SucCoA

PEP

Oxac

Mal

Fum

Succ

Gly

Pyr

CO2

CO2

CO2

CO2 IclMas

Elementary mode representing conversion of AcCoA into glucose.It requires the glyoxylate shunt.

The glyoxylate shunt is present in green plants

and many bacteria (e.g. E. coli).

This example shows that a description by usual graphs in the sense of graph theory is insufficient…

S. Schuster, D.A. Fell: Modelling and simulating metabolic networks. In: Bioinformatics: From Genomes to Therapies (T. Lengauer, ed.) Wiley-VCH, Weinheim, in press.

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 cycleGreen 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

2. Crassulacean Acid Metabolism (CAM)

• Variant of photosynthesis employed

by a range of plants (e.g. cacti) as

an adaptation to arid conditions

• To reduce water loss, stomata are

closed during daytime

• At nighttime, PEP + CO2

oxaloacetate malate

• At daytime, malate pyruvate (or

PEP) + CO2 carbohydrates

CAM metabolism during daytime

RBP

TP

CO 2

P i

TP

P i

PEP

P i

PEP

P i

starchP i

pyrpyr

chloroplastcytosol

mal

oxac

hexose

P i

CO 2

CO 2

P i

1

2

3

4

5

6

7

8

9

10

11

12

RBP

TP

CO 2

P i

TP

P i

PEP

Pi

PEP

P i

starchP

i

pyrpyr

chloroplastcytosol

mal

oxac

hexose

Pi

CO 2

CO 2

P i

RBP

TP

CO 2

P i

TP

Pi

PEP

Pi

PEP

P i

starchP

i

pyrpyr

chloroplastcytosol

mal

oxac

hexose

Pi

CO2

CO2

P i

A) B)

Elementary modes

Hexose synthesis via malic enzyme as occurring in Agavaceae and Dracaenaceae

Starch synthesis via malic enzyme as occurring in Cactaceae and Crassulacea

FerocactusDracaena

RBP

TP

CO 2

P i

TP

Pi

PEP

Pi

PEP

P i

starchP i

pyrpyr

chloroplastcytosol

mal

oxac

hexose

P i

CO 2

CO 2

P i

D)

RBP

TP

CO2

P i

TP

Pi

PEP

Pi

PEP

P i

starchP

i

pyrpyr

chloroplastcytosol

mal

oxac

hexose

Pi

CO2

CO2

P i

C)

Simultaneous starch and hexose synthesis via malic enzyme as occurring in:

Hexose synthesis via PEPCK as occurring in Clusia rosea and in:

Ananus comosus = pineapple

Clusia minor

RBP

TP

CO 2

P i

TP

P i

PEP

P i

PEP

P i

starchP i

pyrpyr

chloroplastcytosol

mal

oxac

hexose

P i

CO 2

CO 2

P i

F)

RBP

TP

CO 2

P i

TP

P i

PEP

P i

PEP

P i

starchP i

pyrpyr

chloroplastcytosol

mal

oxac

hexose

P i

CO 2

CO 2

P i

E)

Starch synthesis via PEPCK as occurring in Asclepadiaceae

Simultaneous starch and hexose synthesis via PEPCK as occurring in:

Caralluma hexagona Aloe vera

„Pure“ pathways

• In a review by Christopher and Holtum (1996), only cases A), B), D), and E) were given as “pure” functionalities. F) was considered as a superposition, and C) was not mentioned.

• However, F) is an elementary mode as well, although it produces two products. It does not use the triose phosphate transporter

• The systematic overview provided by elementary modes enables one to look for missing examples. Case C) is indeed realized in Clusia minor (Borland et al, 1994).

• Interestingly, (almost) pure elementary modes are realized here, although this should reduce robustness

S. Schuster, D.A. Fell: Modelling and simulating metabolic networks. In: Bioinformatics: From Genomes to Therapies (T. Lengauer, ed.) Wiley-VCH, Weinheim, in press.

3. Adenine and adenosine salvage pathways

• Human erythrocytes cannot synthesize nucleotide phosphates de novo

• They can recycle nucleotides to give nucleotide phosphates

• In particular, they can recycle adenine and adenosine, but not hypoxanthine

S. Schuster, D. Kenanov: Adenine and adenosine salvage pathways in erythrocytes and the role of S-adenosylhomocysteine hydrolase – A theoretical study using elementary flux modes. FEBS J. 272 (2005) 5278-5290.

GLCext GLCHK

ATP ADP

G6P F6PPGI

GL6P

FDP GA3P

DHAP

ALD GAPDH1,3 DPG

TPI NAD NADH

3PG

DPGM2,3DPG

DPGasePGKGLCim

ATP ADP

G6PDH

PGLaseGO6P

CO2

RU5P

NADP 2GSH

GSSGNADPH

GSHoxGSSGR

R5P

X5P

S7P

GA3P

F6P

E4P

TKI TAR5PI

Xu5PETKII

GA3P

2PG

PGMADP ATP

PEP

EN

PKADP

ATP PYR PYRextPYRtrans

LAC LACextLACtrans

LDHNADH

NAD

ADENINE

PRPPADPRT

AMP

IMP

ADO

INOAMPDA NUC

ADANUC

HYPX

PRPPHGPRT

R1P

HYPXext

R5P PRMPRPPsyn

ATP

AMP

ATP

AK

ADP ADP

AMP

ApK

PNPaseATP

ADP

Na+ Na+

Na leak

K+K+

K leak

NaK ATPase

membrane

SAM

SAMext

SAHH2

S-AdoHcy

MT

HCY

SAHH1

3'KetoRibose

Acc

HCY

PFK

GL6PDH

HXtrans

MetAcc

+

+

Question

• As salvage pathways use enzymes consuming ATP as well as enzymes producing ATP, it is not easy to see whether a net synthesis of ATP is possible.

• Invest ATP to gain ATP - Bootstrapping like Baron Münchhausen?

Goal:

• Analyse theoretically how many salvage pathways exist

• Which enzymes involves each of these and in what flux proportions (i.e. relative fluxes)

• Compute the net overall stoichiometry of ATP anabolism

• Medical impact of enzyme deficiencies

External metabolites

• Adenine or adenosine depending on which salvage is analysed

• glucose, lactate, CO2, ATP

• hypoxanthine, sodium and potassium outside the cell

Adenine as a source

• 153 elementary modes

• 4 of these produce ATP

• ATP per adenine yield: 1:1

• ATP per glucose yields: 3:10, 2:7, 1:4, 1:6

GLCext GLCHK

ATP ADP

G6P F6PPGI

GL6P

FDP GA3P

DHAP

ALD GAPDH1,3 DPG

TPI NAD NADH

3PG

DPGM2,3DPG

DPGasePGKGLCim

ATP ADP

G6PDH

PGLaseGO6P

CO2

RU5P

NADP 2GSH

GSSGNADPH

GSHoxGSSGR

R5P

X5P

S7P

GA3P

F6P

E4P

TKI TAR5PI

Xu5PETKII

GA3P

2PG

PGMADP ATP

PEP

EN

PKADP

ATP PYR PYRextPYRtrans

LAC LACextLACtrans

LDHNADH

NAD

ADENINE

PRPPADPRT

AMP

IMP

ADO

INOAMPDA NUC

ADANUC

HYPX

PRPPHGPRT

R1P

HYPXext

R5P PRMPRPPsyn

ATP

AMP

ATP

AK

ADP ADP

AMP

ApK

PNPaseATP

ADP

Na+ Na+

Na leak

K+K+

K leak

NaK ATPase

membrane

SAM

SAMext

SAHH2

S-AdoHcy

MT

HCY

SAHH1

3'KetoRibose

Acc

HCY

PFK

GL6PDH

HXtrans

MetAcc

+

+

Elementary mode with highest ATP:glucose yield (3:10)

GLCext GLCHK

ATP ADP

G6P F6PPGI

GL6P

FDP GA3P

DHAP

ALD GAPDH1,3 DPG

TPI NAD NADH

3PG

DPGM2,3DPG

DPGasePGKGLCim

ATP ADP

G6PDH

PGLaseGO6P

CO2

RU5P

NADP 2GSH

GSSGNADPH

GSHoxGSSGR

R5P

X5P

S7P

GA3P

F6P

E4P

TKI TAR5PI

Xu5PETKII

GA3P

2PG

PGMADP ATP

PEP

EN

PKADP

ATP PYR PYRextPYRtrans

LAC LACextLACtrans

LDHNADH

NAD

ADENINE

PRPPADPRT

AMP

IMP

ADO

INOAMPDA NUC

ADANUC

HYPX

PRPPHGPRT

R1P

HYPXext

R5P PRMPRPPsyn

ATP

AMP

ATP

AK

ADP ADP

AMP

ApK

PNPaseATP

ADP

Na+ Na+

Na leak

K+K+

K leak

NaK ATPase

membrane

SAM

SAMext

SAHH2

S-AdoHcy

MT

HCY

SAHH1

3'KetoRibose

Acc

HCY

PFK

GL6PDH

HXtrans

MetAcc

+

+

Elementary mode with lowest ATP:glucose yield (1:6)

Adenosine as a source

• 97 elementary modes• 12 of these produce ATP• ATP per adenosine yield: 1:1, 2:3, 5:8,

8:17, 2:5, 5:14, and 1:4.• ATP per glucose yields: 1:1, 5:6, 2:3, 5:9,

1:3, 1:6, and: 1:0!!• When ATP/glucose = 1:0, then all

adenosine is used as exclusive energy source

GLCext GLCHK

ATP ADP

G6P F6PPGI

GL6P

FDP GA3P

DHAP

ALD GAPDH1,3 DPG

TPI NAD NADH

3PG

DPGM2,3DPG

DPGasePGKGLCim

ATP ADP

G6PDH

PGLaseGO6P

CO2

RU5P

NADP 2GSH

GSSGNADPH

GSHoxGSSGR

R5P

X5P

S7P

GA3P

F6P

E4P

TKI TAR5PI

Xu5PETKII

GA3P

2PG

PGMADP ATP

PEP

EN

PKADP

ATP PYR PYRextPYRtrans

LAC LACextLACtrans

LDHNADH

NAD

ADENINE

PRPPADPRT

AMP

IMP

ADO

INOAMPDA NUC

ADANUC

HYPX

PRPPHGPRT

R1P

HYPXext

R5P PRMPRPPsyn

ATP

AMP

ATP

AK

ADP ADP

AMP

ApK

PNPaseATP

ADP

Na+ Na+

Na leak

K+K+

K leak

NaK ATPase

membrane

SAM

SAMext

SAHH2

S-AdoHcy

MT

HCY

SAHH1

3'KetoRibose

Acc

HCY

PFK

GL6PDH

HXtrans

MetAcc

+

+

One elementary mode using adenosine as energy and nucleotide source

2.3-Diphosphoglycerate bypass

• Neither for adenine nor adenosine salvage, any elementary mode involves the 2.3DPG bypass

• ATP balance would not be positive anymore

Molar investment ratio

moles of ATP consumed

moles of ATP produced - moles of ATP consumed

In elementary mode 1 of adenine salvage, this ratio is

18:(20-18) = 9:1.

S. Schuster, D. Kenanov: FEBS J. 272 (2005) 5278-5290.

In glycolysis: 24-2 =1

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

S. Schuster, T. Dandekar, D.A. Fell,Trends Biotechnol. 17 (1999) 53

Conclusions

• Elementary modes are an appropriate concept to describe biochemical pathways

• Information about network structure can be used to derive far-reaching conclusions about performance of metabolism

• Elementary modes reflect specific characteristics of metabolic networks such as steady-state mass flow, thermodynamic constraints and and the systemic interactions (Systems Biology)

Conclusions (2)

• It can be tested whether connected routes can function at steady state

• A complete list of potential pathways can be generated. Thereafter, experimental search for realized pathways.

• Pathway analysis is well-suited for computing maximal and submaximal molar yields

•Steffen Klamt, Jörg Stelling, Ernst Dieter Gilles (MPI Magdeburg)•Thomas Dandekar (U Würzburg)•David Fell (Brookes U Oxford)•Thomas Pfeiffer, Sebastian Bonhoeffer (ETH Zürich)•Thomas Wilhelm (IMB Jena)•Reinhart Heinrich, Thomas Höfer (HU Berlin)•Marko Marhl (U Maribor, Slovenia) •Hans Westerhoff (VU Amsterdam)• and others

•Acknowledgement to DFG and BMBF for financial support

Cooperations

Current group members

• Dr. Axel von Kamp• Dr. Ina Weiß • Dimitar Kenanov• Jörn Behre• Beate Knoke• Ralf Bortfeldt• Gunter Neumann