Organization and simplification of Organization and simplification - - PDF document

Lei-Han Tang Department of Physics, Hong Kong Baptist University

The 3rd KIAS Conference on Statistical Physics, Seoul, Korea, 1-4 July, 2008

Nonequilibrium Statistical Physics of Complex Systems

Organization and simplification of Organization and simplification of metabolic networks metabolic networks

Metabolism primer 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

Tony Hui Yang Zhu Wang Chao Cai Chunhui Pan-Jun Kim James

• H. Lee

Metabolism

Complex networks Systems biology Synthetic biology Renaissance

Mathematical underpinning Engineering

• utlet

Data integration and modeling

Redox agents Nutrient (carbon, energy) Other chemical ingredients Biomass (aa, nt,

fatty acids, etc.)

energy

waste

Metabolism: a naïve physicist’s view

A driven reaction-diffusion system with over a thousand metabolic intermediates and reactions ⇒ great news for statistical physics!

Primitive life (Oparin/Dyson)

pyr ,pyr ',pyr ' producing rxn consuming rxn i i i i

dC m v m v dt = −

∑ ∑

[ ][ ] [ ]

, , cat i i i i m i i

k E S v K S = +

Enzyme controlled kinetic equations (Michaelis-Menton): Modern life forms exhibit rich dynamical phenomena:

Oscillations (e.g., fermentation

• scillators)

Switch-like behavior (e.g., diauxic shift) Exponential growth/stationary phase Adaptation (e.g. improved metabolic efficiency in directed evolution) Epistasis/buffering, robustness against knock-down/knock outs Biological systems are amazingly efficient in using resources from the environment to optimize growth

The basic theoretical issue

Chemical soup Organized behavior regulation Evolution: Design of circuits and fine-tuning of kinetic constants?

A computational platform simple enough for i) Integration and interpretation of metabolic and regulatory information for specific organisms ii) Theoretical exploration of hidden principles, if any, for metabolic organization iii) Preparation for full dynamic modeling at the systems level

Our Goal

State-of-the-art in quantitative modeling:

the flux-balance analysis

consider Steady State Flow (e.g. exponential growth in chemostat) flux through th reaction

i

v i = Network state specified by flux vector

1 2

( , , , )

N

v v v = v …

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

pvk

v

pyr ,pyr ',pyr ' producing rxn consuming rxn i i i i

dC m v m v dt = − =

∑ ∑

Mass conservation: Or more generally,

= S v i

stoichiometric matrix = S

i

v

Constrained by i) thermodynamics (70% irreversible) ii) substrate availability iii) enzyme abundance and activity Optimality hypothesis: Biological systems (especially microbes) operate at a flux state that maximizes biomass production.

in silico

• rganisms

constructed by Palsson’s group at UCSD

Collection of

• rganism-specific

reactions leading to biomass production Allow for simulation of different growth conditions (nutrient uptake, O2 availability, etc.) Outcome: growth rate and flux pattern

Example: glucose as the carbon source, aerobic growth

282 out of 1149 reactions with nonzero flux

reaction compound

Palsson’s in silico models:

Advantage: Quantitative and

• rganism specific

Disadvantage: Too complex to be drawn on a piece of paper More serious: Not an adequate basis for engineering

Proposal: Construct coarse-grained yet quantitative models by separating carbon flow (which defines pathways) from other commodities (which makes Palsson’s model quantitative).

Glucose + NH4 waste

Relative proportion

FBA: Black box

• ptimizer

Simplification of network topology

NetSim: Specific objectives

• 1. Highlight carbon flow for easy comparison with relevant

experimental flux measurements (clearly marked main roads, small streets, roundabouts, market place, etc.)

• 2. A quantitative understanding of the horizontal coupling

between pathways (physico-chemical constraints such as energy/redox balance)

• 3. Incorporation of regulatory interactions with a clear understanding
• f their physiological role (traffic control and related issues)
• 4. A framework to integrate protein abundance, enzyme activity, and

flux measurements for dynamic simulation

Metabolic fates of glucose

Precursor for nucleotide synthesis Precursor for aa, fatty acids synthesis and fuel for the TCA cycle

Amino acid biosynthesis

Precursor molecules

Energy

Synthetic efficiency controlled by energy and redox power

Horizontal + vertical mesh

Metabolic network

reaction compound Degree distribution

Reiko Tanaka and John Doyle, q-bio: 0410009

Currency compounds

Nitrogenous: NH4, NO, NO2, NO3, etc. Phosphates: PO4, diphosphate, etc. Sulfate/sulfite: SO3, SO4, etc. Metal ions: Fe, Na, K, etc. Water, hydrogen, oxygen

Carriers

ATP/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/cofactors

ACP, THF, udcpp, etc.

Horizontal links of the metabolic network

3 O3P amp[c] adp[c] 5 H2 succ[c] fum[c] 6 O3P gdp[c] gtp[c] 8 H2 fad[c] fadh2[c] 16 HO3P pyr[c] pep[c] 10 H2 trdox[c] trdrd[c] 25 O6P2 amp[c] atp[c] 10 H2 2dmmq8[c] 2dmmql8[c] 136 O3P adp[c] atp[c] 16 H2 mql8[c] mqn8[c] 20 H4NO akg[c] glu-L[c] 17 H2 q8[c] q8h2[c] 3 H2NO asp-L[c] asn-L[c] 49 H nadp[c] nadph[c] 13 H2NO glu-L[c] gln-L[c] 71 H nad[c] nadh[c] frequnecy cargo Cmpd2 Cmpd1 frequency cargo Cmpd2 Cmpd1 16

• 2[c]

38 nh4[c] 75 ppi[c] 149 pi[c] 293 h2o[c] 497 h[c] frequency compound

Free-standing Carriers

CHO3 2 hco3[c] C4H2O4 3 fum[c] C4H4O4 7 succ[c] CHO2 8 for[c] C2H3O2 8 ac[c] C3H3O3 16 pyr[c] CO2 45 co2[c] formula frequency compound

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 when viewed in terms of vertical links (pathways) and horizontal couplings (currencies, carriers, etc.) Modular structure (in the form of subnets) emerge naturally after course-graining. Branch points, cycles, and entry and exit points of metabolic flow clearly visible.

Summary: Some global properties of the metabolic network

Mapping regulatory interactions onto the simplified network

Enzyme Regulation

10-3 − 1 sec Allosteric/competitive regulation (fine-tuning) Achieve dynamic balance avoid accumulation of unwanted/toxic compounds Modifies enzyme activity SecondsCovalent modification (phophorylation, adenylylation, etc., switch like) Minutes: Regulation of gene expression

Brenda Enzyme Database

Over 3,000 regulating compounds 223 out of 618 metabolites in iJR904 implicated 348 out of 726 reactions regulated 1333 total regulatory interactions

• E. coli

94 metal ion 243 cofactor 817 inhibitor 179 activator

“scale free”

Classification of regulatory interactions

11 11 utp 17 7 10 ppi 19 18 1 cys-L 19 19 na1 21 18 3 nh4 22 20 2 fad 27 18 9 pi 32 21 11 adp 33 28 5 am p 43 13 30 nadph 43 15 28 nadp 43 41 2 pydx5 p 46 27 19 nadh 48 11 37 nad 50 50 fe2 54 54 k 60 39 21 atp TOTAL hetero auto COMPOUND

Compound regulatory hubs Matches well with the compound list that mediates horizontal coupling in

• ur simplification scheme

Classification of regulatory interactions (cont’d)

603 142 Specific regulator 410 178 Global regulator Heterotropic regulation Auto regulation

Three classes of regulation

i) 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

Allosteric regulation by NH4 Substrate/product autoregulation

Regulatory motifs

Heterotropic regulation: community structure

nucleotides Amino acids

Inhibition only

Subnet: Amino acids biosynthesis and catabolism

ASPK ASAD HSDy DHDPS HSK HSST

End product inhibition

Interlocking regulatory interactions in the biosynthesis of several amino acids from aspartate

DAPDC

Subnet: amino acid biosynthesis

FBA

Amino acid biosynthesis and catabolism Metabolic network topology can be greatly simplified when viewed in terms of vertical links (pathways) and horizontal couplings (currencies, carriers, etc.) Modular structure (in the form of subnets) emerge naturally after course-graining. Allosteric regulatory interactions mirror separation of horizontal (global) and vertical (pathway) metabolic flows. Concentration of end point compounds controlled through feedback inhibition. Interlocked regulation not yet quantified.

Summary: Some global properties of the metabolic network

Understand the functional role of local regulatory motifs Detailed kinetic modelling of specific pathways and comparison with isotope measurement of metabolic intermediates Interlocked regulatory strategies for super-imposed traffic Regulation as a means to achieve optimization?

Future work

Coming Soon: Quantitative models to interface with Traffic community (multi-colored) Network community (multi-dimensional)

• E. Levine and T. Hwa (2007) Stochastic fluctuations in metabolic pathways,

PNAS 104, 9224-9229.

Thank You!

KIAS