Organization and simplification of Organization and simplification - PDF document

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 Lei-Han Tang Department of Physics, Hong Kong Baptist University � Metabolism primer � Network simplification � Small compound regulation from BRENDA � Summary and future work Collaborators Prof. Terry Hwa Tony Hui UCSD Yang Zhu Shi Xiaqing Cai Wang Chunhui Chao NJU Pan-Jun James Supported by Kim H. Lee The RGC of the HKSAR

Data integration Renaissance and modeling Complex Systems Mathematical networks biology underpinning Metabolism Synthetic biology Engineering outlet Metabolism: a naïve physicist’s view Nutrient (carbon, Biomass (aa, nt, energy) fatty acids, etc.) energy Other chemical ingredients Redox waste agents A driven reaction-diffusion system with over a thousand metabolic intermediates and reactions ⇒ great news for statistical physics!

Primitive life (Oparin/Dyson) Modern life forms exhibit rich dynamical phenomena: � Oscillations (e.g., fermentation oscillators) � Switch-like behavior (e.g., diauxic shift) � Exponential growth/stationary phase � Adaptation (e.g. improved metabolic efficiency in directed evolution) Enzyme controlled kinetic equations � Epistasis/buffering, robustness (Michaelis-Menton): against knock-down/knock outs � Biological systems are amazingly dC ∑ ∑ = − pyr m v m v efficient in using resources from the i ,pyr i i ',pyr i ' dt environment to optimize growth producing rxn consuming rxn [ ][ ] k E S = cat i , i i v [ ] + i K S m i , i The basic theoretical issue regulation Chemical soup Organized behavior Evolution: Design of circuits and fine-tuning of kinetic constants?

Our Goal 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 State-of-the-art in quantitative modeling: the flux-balance analysis consider Steady State Flow (e.g. exponential growth in chemostat) = v flux through th reaction i i = … v ( , v v , , v ) Network state specified by flux vector 1 2 N v pvk Example: E2.7.1.40: ADP + Phosphoenolpyruvate <=> ATP + Pyruvate dC ∑ ∑ = − = pyr m v m v 0 Mass conservation: i ,pyr i i ',pyr i ' dt producing rxn consuming rxn = i = Or more generally, S v 0 S stoichiometric matrix v Constrained by i) thermodynamics (70% irreversible) i 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 organisms constructed by Palsson’s group at UCSD � Collection of organism-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 compound reaction

Relative proportion Palsson’s in silico models: Advantage: Quantitative and organism specific FBA: Black Glucose Disadvantage: Too complex to be box + NH4 drawn on a piece of paper optimizer More serious: Not an adequate waste 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). 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 of 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 Precursor for aa, nucleotide synthesis fatty acids synthesis and fuel for the TCA cycle

Amino acid biosynthesis Energy Precursor molecules Synthetic efficiency controlled by energy and redox power Horizontal + vertical mesh Metabolic network Degree distribution Reiko Tanaka and John Doyle, q-bio: 0410009 compound reaction

Horizontal links of the metabolic network Currency compounds Nitrogenous: NH4, NO, NO2, NO3, etc. Phosphates: PO4, diphosphate, etc. Free-standing Sulfate/sulfite: SO3, SO4, etc. compound frequency compound frequency formula Metal ions: Fe, Na, K, etc. h[c] 497 co2[c] 45 CO2 Water, hydrogen, oxygen h2o[c] 293 pyr[c] 16 C3H3O3 pi[c] 149 ac[c] 8 C2H3O2 Carriers ppi[c] 75 for[c] 8 CHO2 ATP/ADP/AMP, GTP/GDP,CTP/CMP nh4[c] 38 succ[c] 7 C4H4O4 o2[c] 16 fum[c] 3 C4H2O4 nad/nadh, nadp/nadph, fad/fadh hco3[c] 2 CHO3 q8/q8h2, mql8/mqn8, 2dmmq8/2dmmql8 akg/glu/gln Adenosine deaminase: adn + h + h2o --> ins + nh4 acCoA/CoA, sucCoA/CoA, pep/pyr Hexokinase: atp + glc-D --> adp + g6p + h Coenzymes/cofactors ACP, THF, udcpp, etc. Carriers Cmpd1 Cmpd2 cargo frequency Cmpd1 Cmpd2 cargo frequnecy nadh[c] nad[c] H 71 gln-L[c] glu-L[c] H2NO 13 nadph[c] nadp[c] H 49 asn-L[c] asp-L[c] H2NO 3 q8h2[c] q8[c] H2 17 glu-L[c] akg[c] H4NO 20 mqn8[c] mql8[c] H2 16 atp[c] adp[c] O3P 136 2dmmql8[c] 2dmmq8[c] H2 10 atp[c] amp[c] O6P2 25 trdrd[c] trdox[c] H2 10 pep[c] pyr[c] HO3P 16 fadh2[c] fad[c] H2 8 gtp[c] gdp[c] O3P 6 fum[c] succ[c] H2 5 adp[c] amp[c] O3P 3 Simplified network based on iJR904 � tree like � community structure

Flux pattern, glucose-minimal, aerobic Summary: Some global properties of the metabolic network � 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.

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

Brenda Enzyme Database E. coli � Over 3,000 regulating “scale free” compounds � 223 out of 618 metabolites in iJR904 implicated � 348 out of 726 reactions regulated � 1333 total regulatory interactions activator 179 inhibitor 817 cofactor 243 metal ion 94 Classification of regulatory interactions Compound regulatory hubs COMPOUND auto hetero TOTAL atp 21 39 60 k 0 54 54 Matches well with the compound list fe2 0 50 50 that mediates horizontal coupling in nad 37 11 48 our simplification scheme nadh 19 27 46 pydx5 p 2 41 43 nadp 28 15 43 nadph 30 13 43 am p 5 28 33 adp 11 21 32 pi 9 18 27 fad 2 20 22 nh4 3 18 21 na1 0 19 19 cys-L 1 18 19 ppi 10 7 17 utp 0 11 11

Classification of regulatory interactions (cont’d) Auto Heterotropic regulation regulation Global 178 410 regulator Specific 142 603 regulator 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

Inhibition only Heterotropic regulation: community structure Amino acids nucleotides Subnet: Amino acids biosynthesis and catabolism

End product inhibition Interlocking regulatory interactions ASPK in the biosynthesis of several amino acids from aspartate ASAD HSDy DHDPS DAPDC HSST HSK Subnet: amino acid biosynthesis FBA

Amino acid biosynthesis and catabolism Summary: Some global properties of the metabolic network � 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.