Lei-Han Tang

Department of Physics, Hong Kong Baptist University

CAS-MPG Partner Institute for Computational Biology, Shanghai 18-19 July, 2008Quantitative System Biology 2008

Organization and simplification ofOrganization and simplification ofmetabolic networksmetabolic networks

Metabolic modeling

Network simplification

Small compound regulation from BRENDA

Summary and future work

Collaborators

Prof. Terry Hwa

UCSD

Shi Xiaqing

NJU

Supported by

The RGC of the HKSAR

TonyHui

YangZhu

WangChao

CaiChunhui

Pan-JunKim

JamesH. Lee

Redoxagents

Nutrient(carbon,energy)

Otherchemical

ingredients

Biomass (aa,nt, fatty acids,etc.) energy

waste

Metabolism: a naïve physicist’s view

Synthetic efficiency: Cnutrient = Cbiomass + Cwaste

The basic theoretical issue

Chemical soup Organized behavior

regulation

Evolution: Design of circuits and fine-tuning of kinetic constants?

pyr

,pyr ',pyr '

producing rxn consuming rxn

i i i i

dCm v m v

dt= !" "

[ ][ ][ ]

,

,

cat i i i

i

m i i

k E Sv

K S=

+

Enzyme controlled kinetic equations(Michaelis-Menton):

State-of-the-art in quantitative modeling:

the flux-balance analysisconsider Steady State Flow (e.g. exponential growth in chemostat)

flux through th reactioniv i=

Network state specified by flux vector 1 2( , , , )N

v v v=v K

ADP + Phosphoenolpyruvate <=> ATP + Pyruvate Example: E2.7.1.40: pvkv

pyr

,pyr ',pyr '

producing rxn consuming rxn

0i i i i

dCm v m v

dt= ! =" "

Mass conservation:

Optimality hypothesis: Biological systems (especially microbes) operate at a fluxstate that maximizes biomass production.

N. D. Price, J. L. Reed, B. O. Palsson,Nature Reviews Microbiology 2, 886-897(2004)

Solutionspace

v1

v3

v2

Example: glucose as the carbon source, aerobic growth

282 out of1149reactionswithnonzero flux

reactioncompound

Palsson’s in silico models:Advantage: Quantitative and

organism specific

Disadvantage: Too complex to bedrawn on a piece ofpaper

More serious: Not an adequate basisfor engineering(understanding howoptimal sol’n isachieved

Proposal:

Construct coarse-grained yet quantitative models byseparating carbon flow (which defines pathways) from othercommodities (which makes Palsson’s model quantitative).

Glucose+ NH4

waste

Relativeproportion

FBA:

Blackbox

optimizer

Simplification of network topology

NetSim: Specific objectives

1. Highlight carbon flow for easy comparison with relevantexperimental flux measurements (clearly marked main roads,small streets, roundabouts, market place, etc.)

2. A quantitative understanding of the horizontal couplingbetween pathways (physico-chemical constraints such asenergy/redox balance)

3. Incorporation of regulatory interactions with a clear understandingof their physiological role (traffic control and related issues)

4. A framework to integrate protein abundance, enzyme activity, andflux measurements for dynamic simulation

Amino acid biosynthesis

Precursormolecules

Energy

Synthetic efficiencycontrolled by energy

and redox power

Horizontal+ vertical

mesh

waste

Metabolic network

reactioncompound

Degree distribution

Reiko Tanaka and John Doyle, q-bio: 0410009

Currency compoundsNitrogenous: NH4, NO, NO2, NO3, etc.

Phosphates: PO4, diphosphate, etc.

Sulfate/sulfite: SO3, SO4, etc.

Metal ions: Fe, Na, K, etc.

Water, hydrogen, oxygen

CarriersATP/ADP/AMP, GTP/GDP,CTP/CMP

nad/nadh, nadp/nadph, fad/fadh

q8/q8h2, mql8/mqn8, 2dmmq8/2dmmql8

akg/glu/gln

acCoA/CoA, sucCoA/CoA, pep/pyr

Coenzymes/cofactorsACP, THF, udcpp, etc.

Horizontal links of the metabolic network

3O3Pamp[c]adp[c]5H2succ[c]fum[c]6O3Pgdp[c]gtp[c]8H2fad[c]fadh2[c]16HO3Ppyr[c]pep[c]10H2trdox[c]trdrd[c]25O6P2amp[c]atp[c]10H22dmmq8[c]2dmmql8[c]136O3Padp[c]atp[c]16H2mql8[c]mqn8[c]20H4NOakg[c]glu-L[c]17H2q8[c]q8h2[c]3H2NOasp-L[c]asn-L[c]49Hnadp[c]nadph[c]13H2NOglu-L[c]gln-L[c]71Hnad[c]nadh[c]

frequnecycargoCmpd2Cmpd1frequencycargoCmpd2Cmpd1

16o2[c]38nh4[c]75ppi[c]149pi[c]293h2o[c]497h[c]

frequencycompound

Free-standing

Carriers

CHO32hco3[c]C4H2O43fum[c]C4H4O47succ[c]CHO28for[c]C2H3O28ac[c]C3H3O316pyr[c]CO245co2[c]formulafrequencycompound

Adenosine deaminase: adn + h + h2o --> ins + nh4

Hexokinase: atp + glc-D --> adp + g6p + h

tree like community structure

Simplified network based on iJR904

Flux pattern, glucose-minimal, aerobic

Metabolic network topology can be greatly simplified whenviewed in terms of vertical links (pathways) and horizontalcouplings (currencies, carriers, etc.)

Modular structure (in the form of subnets) emerge naturallyafter course-graining.

Branch points, cycles, and entry and exit points of metabolicflow clearly visible.

Summary: Some global properties of themetabolic network

Mapping regulatoryinteractions onto thesimplified network

Enzyme Regulation

10-3 − 1 sec Allosteric/competitive regulation (fine-tuning)

Achieve dynamic balance

avoid accumulation ofunwanted/toxic compounds

Modifiesenzymeactivity

SecondsCovalent modification (phophorylation, adenylylation, etc.,switch like)

Minutes: Regulation of gene expression

Brenda Enzyme Database

Over 3,000 regulatingcompounds

223 out of 618metabolites in iJR904implicated

348 out of 726reactions regulated

1333 total regulatoryinteractions

E. coli

94metal ion243cofactor817inhibitor179activator

“scale free”

Classification of regulatory interactions

11110utp

17710ppi

19181cys-L

19190na1

21183nh4

22202fad

27189pi

322111adp

33285amp

431330nadph

431528nadp

43412pydx5p

462719nadh

481137nad

50500fe2

54540k

603921atp

TOTALheteroautoCOMPOUND

Compound regulatory hubs

Matches well with the compound listthat mediates horizontal coupling inour simplification scheme

Classification of regulatory interactions (cont’d)

603142Specificregulator

410178Globalregulator

Heterotropicregulation

Autoregulation

Three classes of regulationi) Global regulation (maintenance of pools for energy, redox

balance, nitrogen, sulfur, phosphate, etc.)

ii) Auto-regulation (maximal compound level, etc.)

iii) Heterotropic regulation (more complex roles)

Allosteric regulation by ATP

Substrate/product autoregulation Regulatory motifsSubstrateinhibition

Productinhibition

Heterotropic regulation: community structure

nucleotides

Amino acids

Inhibition only

ASPK

ASAD

HSDyDHDPS

HSKHSST

End product inhibitionInterlocking regulatory interactionsin the biosynthesis of several aminoacids from aspartate

DAPDC

Metabolic network topology can be greatly simplified whenviewed in terms of vertical links (pathways) and horizontalcouplings (currencies, carriers, etc.)

Modular structure (in the form of subnets) emerge naturally aftercourse-graining.

Allosteric regulatory interactions mirror separation of horizontal(global) and vertical (pathway) metabolic flows.

Concentration of end point compounds controlled throughfeedback inhibition.

Interlocked regulation not yet quantified.

Summary: Some global properties of themetabolic network

Understand the functional role of local regulatory motifs

Detailed kinetic modelling of subnets and comparison withisotope measurement of metabolic intermediates

Regulation of global resources: homeostasis of ATP/ADP,NAD/NADH, etc.

Regulation as a means to achieve optimization? (detailedcomparison with FBA)

Km: desired compound levels, branch point regulation

Future work

E. Levine and T. Hwa (2007) Stochastic fluctuations in metabolic pathways,PNAS 104, 9224-9229.