Chapter 7: Metabolic Networks 7.1 Introduction Prof. Yechiam Yemini (YY) Computer Science epartment Columbia University Introduction Metabolic flux analysis Applications Overview 2 1
Introduction 3 Metabolism: Key Cellular Function Anabolism: synthesize molecules from simpler ones (e.g., amino-acids) Catabolism: breakdown molecules into simpler ones (e.g., glycolysis) Cell organizes metabolic reactions into a network Product of one reaction is the input of other reactions Metabolic network interacts with other networks Regulation: e.g., control production of enzymes Signaling: e.g., adapt to availability of metabolites Signal transduction EGF Gene regulatory network CK E2F PFK Metabolic pathway F6P F1,6P Glycolysis 4 2
Organization: From Signaling To Metabolism 5 Metabolic Pathway (Glycolysis) Glucose + 2 AP + 2 Pi + 2 NA+ 2 Pyruvate + 2 ATP + 2 NAH + 2 H + + 2 H 2 O 6 3
Network Structure Protein Carbohydrate Lipids Amino Glucose Glycerol Fatty acids acids glycolysis CO 2 + H 2 O 3-carbon intermed. TCA cycle (dehydrogenation) electron transport β oxidation 2-carbon intermed. 7 Network Organization 8 4
Metabolic network atabases Roche @ ExPASy 9 Introduction To Reaction Kinetics k Unimolecular reaction: A B d[ B] d [ A] d[ A] v = = v = = k[ A] dt dt dt Bimolecular reaction: k A + B P + Q d[ P] d[ Q] d[ A] d[ B] v = = or v = = dt dt dt dt d[ A] v = = k[ A][ B] dt 10 5
Enzyme Kinetics The unimolecular reaction flux is linearily dependent on [A]. A P d[ A] v = = k[ A] dt v But if this reaction is catalyzed by an enzyme, the flux shows saturation behavior. Why? [A] v A Enzyme P [A] 11 Michaelis-Menten Kinetics Enzyme reaction creates a substrate comples k 1 k 2 E + S ES E + P K -2 d[ ES] Steady state assumption: [ES] remains constant = dt Under this assumption: The reaction kinetics is: E + S k 1 ES k 2 E + P K -1 The forward and reverse fluxes are equal: v f = v d v f = k 1 [ E][ S] v d = k 1 [ ES] + k2[ ES] = ( k 1 + k2 )[ ES] The enzyme concentration is: [ E t ] = [ ES] + [ E] v f = k1[ E][ S] = k1( [ Et ] [ ES][ ) S] 0 By solving these equations for the flux one gets: v k [ E t ][ S ] [ S ] + K m = 2 Km = ( k + 1 k2)/ k 1 12 6
Michaelis-Menten Formula Enzyme accelerates flux when [S] is small Enzyme bounds flux at Vmax Km and Vmax are the control parameters S E P v v v [ S] [ S] + Km = max v max K m [S] 13 Metabolic Flux Analysis [Based on R. Pinter s, B. Palsson & others] 14 7
Metabolic Networks Reactions: A B Pathways: A B C Networks: A B C E 15 Metabolic Network efinitions (I) Reaction Intermediate A B C E Substrate Product Active reaction Inactive reaction 16 8
Metabolic Network efinitions (II) Exchange flux A B C E System Boundary Internal flux Flux The production or consumption of mass per unit area per unit time. 17 Bioinformatics of Metabolic Networks Metabolic network databases Genome-scale Metabolic network reconstruction Metabolic network analyses Whole cell simulation 18 9
Metabolic network atabases With links to ENZYME 19 Metabolic network atabases KEGG (Kyoto encyclopedia of genes and genomes): Metabolic Pathways 20 10
Genome-scale Metabolic Network Reconstruction 21 The S. Cerevisiae Metabolic Network 1175 metabolic reactions 584 metabolites Assignment of 708 metabolic ORFs but 184 metabolites unconnected 22 11
The Stoichiometric Matrix Changes in metabolite X i = (inflow outflow) d[ X i] v 1 v 2 v 3 v 4 = Sijv A B C j dt j v 6 S ij is the stoichiometric coefficient of the reactant X i in the reaction j with the flux v j. S ij is negative if X i is an output of the reaction j (outflow), S ij is positive if X i is an input of reaction j (inflow) 23 Metabolic Flux Analysis (MFA) Metabolic system is assumed to be in steady state The time scale for concentration changes >> reaction kinetics d[ Xi ] = 0 dt Steady state flux distributions are described by the null space K of the stoichiometric matrix S. Flux conservation law ~ Kirchoff s current law v S v = 0 2 v 3 A B C v 1 v 4 v 6 24 12
An Example b 1 v 1 v 2 v 6 A B C E b 4 v 3 v 4 25 The Structure of Pathways Consider a basis of the null space of S. Each flux vector is a linear combination of basis vectors Each basis vector represents a pathway There are multiple bases of the null space Are these pathways biologically meaningful? Need to constrain pathways to render them meaningful b 1 v 1 v 2 v 6 A B C E b 4 v 3 v 4 26 13
Flux istributions Span A Convex Cone Flux values are non-negative: v i, b i 0 If f is a flux vector, then αf is a flux vector for α>0 A flux vector can be represented as a non-negative combination of the generating vectors of the cone, f k : n F = v R v = α kfk, α k 0 k Enzymes constrain flux rates (via Michaelis-Menten) v i < v i-max Admissible flux vectors form a convex body 27 Extreme Pathways [Palsson] Extreme Pathway (EP)= a flux that cannot be obtained by combining fluxes Corresponds to extreme vectors spanning the flux cone b 1 v 1 v 2 v 6 A B C E b 4 v 3 v 4 b 1 v 1 v 2 v 6 A B C E b 4 v 3 v 4 28 14
Extreme Pathways b 1 A v 1 B v 2 C v 6 E b 4 b 1 A v 1 B v 2 C v 6 E b 4 v 4 v 3 v 4 v 3 b 1 A v 1 B v 2 C v 6 E b 4 b 1 A v 1 B v 2 C v 6 E b 4 v 4 v 3 v 4 v 3 b 1 A v 1 B v 2 C v 6 E b 4 b 1 A v 1 B v 2 C v 6 E b 4 v 4 v 3 v 4 v 3 29 Elementary Flux Modes (EFM) When the network includes reversible reactions, the extreme pathway set may not include all elementary pathways: b 1 A v 1 B v 2 C v 6 E b 4 v 4 v 3 b 1 A v 1 B v 2 C v 6 E b 4 b 1 A v 1 B v 2 C v 6 E b 4 v 4 v 3 v 4 v 3 Elementary flux modes are the set of irreducible pathways spanning the solution space. 30 15
Elementary Flux Modes vs Extreme Pathways PYR PEP OAA PYR PYR PEP OAA PEP OAA Extreme pathways Elementary flux modes 31 Another Example 32 16
Applications 33 Applications of Elementary Flux Modes Understanding the range of metabolic pathways Metabolic engineering optimizingyield. rug target identification analyze network vulnerabilities. 34 17
Biological Network Example Reaction scheme representing part of monosaccharide metabolism 35 Elementary Flux Modes of Monosaccharide Metabolism Basic glycolitic pathway egradation of G6P to pyruvate and CO 2 producing ATP, NAPH and NAH 36 18
Elementary Flux Modes of Monosaccharide Metabolism Conversion of G6P to ribose-5- phosphate and CO 2 Conversion of 5 hexoses to 6 pentoses (when need for R5P is high) pentose phosphate cycle carbons are cycled several times before ending in CO 2. Produces NAPH but not NAH and ATP 37 Flux Balance Analysis: Assessing System Performance Extreme pathways of network: 38 19
Flux Balance Analysis: Assessing System Performance Optimize flux for biosynthetic demand: b z =[C++2E] = = Solve by LP: Maximize b z subject to constraints 39 Flux Balance Analysis: Calculating Optimal Flux istributions Case 1: Only A available 0.25 0.75 0.50 A B C E 0.25 Case 2: Only A available v 6 not functional 0.17 A B C 0.17 E 0.33 Case 3: Only C available 0.25 A B C E 0.25 0.50 Objective b z =0.25 Objective b z =0.17 Objective b z =0.25 1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 p1 p2 p3 p4 p5 p6 1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 p1 p2 p3 p4 p5 p6 1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 p1 p2 p3 p4 p5 p6 40 20
Flux Balance Analysis: S. cerevisiae vs E. coli Maximum precursor and amino acid production in S. cerevisiae and E.coli, using glucose as the sole carbon source (in mole/mole glucose) Computed using LP over whole-genome reconstruction of metabolic networks. 41 etermining Functionality from Metabolic Network Structure Whole genome metabolic analysis of E.coli: 89 substances 110 reactions 43,279 elementary flux modes Glucose Acetate Glycerol Succinate Sum All 27099 598 11332 4249 43279 Growth only 73.2% 58.7% 78.6% 76.3% 74.6% ATP only 3.2% 5.0% 2.4% 2.4% 3.0% Growth+ATP 6.6% 2.0% 5.1% 4.2% 5.9% No growth/atp 17.1% 34.3% 13.9% 17.1% 16.5% Aerobic growth 73.1% 60.7% 83.6% 80.5% 76.4% Anaerobic growth 6.6% 0.0% 0.0% 0.0% 4.1% 42 21
etermining Functionality from Metabolic Network N(µ, i) Number of flux modes of a mutant i that enable growth rate µ. Ymax( i) maximal growth yield of a mutant i. N(µ, i)=0 predicts inviability of mutant (90% accuracy) 43 etermining Regulation from Metabolic Network Efficiency of an elementary mode mode s output (growth or ATP) relative to its investment Control effective fluxes for a reaction average flux through this reaction for all elementary modes, weighed by each mode s efficiency. 44 22
etermining Regulation from Metabolic Network Structure As cellular control is achieved by genetic regulation, control effective flux (CEF) should correlate with messenger RNA levels. Theoretical transcript ratios for growth on two alternative substrates: Θ(S 1,S 2 )=CEF(S 1 )/ CEF(S 2 ) in comparison with gene expression data (r 2 =0.6) 45 Concluding Notes 46 23
Summary of Results Metabolic network analysis is reduced, under steady state assumption, to simple convex analysis Flux distributions are represented as vectors forming a cone The flux cone is spanned by the stoichiometry matrix and constraints A flux is a linear combination of extreme or elementary flux modes These extreme/elementary flux mode may be selected to represent key pathways Theoretical predictions provide reasonable approximation of cell behaviors 47 24