Introduction to constraint-based modeling in metabolism

Transcription

1 atp 3pg 13dpg adp nadp 6pgc co2 nadp ru5p-d o2 o2 nadp nad nadp nad 2o fum mal-l icit nadp nadp co2 akg nad pyr coa co2 accoa nad 2o pep co2 pi oaa 2pg 2o g6p f6p 2o fdp pi succ glx succ atp amp adp gln-l q8 q82 g3p s7p e4p f6p adp atp glu-l glu-l pyr xu5p-d coa atp pi succoa adp atp adp g3p atp n4 gln-l adp pi coa nad co2 nad coa for atp adp co2 akg dap 2o r5p accoa 2o coa pi actp coa nad co2 nad nadp nadp 6pgl 2o n4 2o pi nad nad nad nad atp 2o amp pi glc-d adp nadp nadp fum pep pyr 2o nad pi nad nadp2o nadp n4 pi 2o 2o cit coa nadp co2 nadp nad nad q8 mal-l acald acon-c pep pyr nad 2o nad coa fru nad nad eto q82 PGK GND O2t THD2 FUM ICDHyr PDH PPC ENO PGI FBP EX_suc ICL ADK1 EX_gln TALA PYK GLUt2r EX_pyr(e) RPE EX_(e) SUCOAS PFK EX_glu TKT2 GLNS NADTRHD AKGDH PFL EX_o2(e PPCK AKGt2r FBA TPI CYTBD RPI MALS PTAr GLNabc ME1 G6PDH2r GLUN ATPM LDH_D MDH TKT1 EX_ak PPS EX_glc(e) PGM GLUSy FUMt2_2 GLCpts SUCCt3 PGL GAPD EX_fum(e) SUCCt2_2 GLUDy ATPS4r CS PYRt2r ME2 ACALD ACONTa ACONTb ALCD2x FRD7 FRUpts2 EX_fru(e) MALt2_2 EX_mal-L(e) NADH16 SUCDi Introduction to constraint-based modeling in metabolism Katja Tummler Humboldt Universität zu Berlin, Teoretisce Biopysik SyMBioSys Course, 217/2/22 February 16, 217

2 Outline 1 Introduction Wy CBM? Wat can CBMs do? 2 Teory Network Reconstruction Matematical Framework 3 FBA Metods Network Analysis Flux(re)distributions Regulatory and Dynamic FBA Data Integration 4 Exercise Te COBRA toolbox Exercise

3 Wy CBM?

4 Wy CBM? Genome-wide ig-trougput data allow te reconstruction of te wole metabolic network of an organism 1s of reactions and metabolites igly complex system Constraint Based Models provide a simple and computationally ceap metod for te analysis of te wole network

5 Wat can CBMs do? Flux distributions Wic metabolic patways are active? Wic metabolic patways are able to produce a certain product? Drug targets Wic reactions are possible/efficient targets for new drugs? Metabolic engineering Wic genetic alterations would result in a iger product yield? Data integration Wat can I learn from experimentally measured protein concentrations and expression patterns about te cellular metabolism?

6 Wat can CBMs do?

7 Genom-wide metabolic networks Reconstruction and Model Building of inj661 from M. tb H37Rv Genome Annotation (TIGR) inj661 Reconstruction Tuberculist KEGG Te SEED Manual Curation Steps Evidence for gene Identify catalytic protein complex/subunits Reaction definition: catalytic mecanism Reaction definition: primary metabolite conversion Reaction definition: secondary metabolites/cofactors Reaction definition: compartmentation Metabolites: formula and carge determination Confirm reaction mass conservation Confirm reaction carge conservation Manual Curation Resources Primary Literature Internet Resource Databases: Tuberculist, KEGG, SEED Textbooks Debugging Identify gaps and carry out directed manual curation Eliminate `free energy loops Convert to Model Define system boundaries and uptake constraints Test anabolic and catabolic capabilities inj661 Model

8 Genom-wide metabolic networks

9 Genom-wide metabolic networks

10 Biomass reaction Biomass is constituted of a subset of te metabolites in te model (precursors / building blocks) Carboydrates Amino acids oters.. Lipids RNA/DNA Mycolic acids

11 Biomass reaction Biomass is constituted of a subset of te metabolites in te model (precursors / building blocks) Growt consumes tese metabolites wit a certain stoiciometric ratio corresponding to te cellular composition

12 Biomass reaction Biomass is constituted of a subset of te metabolites in te model (precursors / building blocks) Growt consumes tese metabolites wit a certain stoiciometric ratio corresponding to te cellular composition Composition differs from organism to organism and not all compounds are easy to measure.

13 Stoiciometric Matrix All information on te topology of te reconstructed network can be stored in a single matrix S.

14 Stoiciometric Matrix

15 Stoiciometric Matrix

16 Stoiciometric Matrix

17 Stoiciometric Matrix

18 From topology to flux distributions Flux Balance Analysis allows te calculation of flux distributions in te reconstructed network

19 GLCt1 HEX1 PGI PFK FBP FBA TPI EX_glc From topology to flux distributions Flux Balance Analysis allows te calculation of flux distributions in te reconstructed network Central assumption of FBA: Te system runs in steady state. Compound concentrations and metabolic fluxes do not cange Sum of all fluxes producing one metabolite is equal to te sum of te consuming fluxes of te metabolite glc-d[e] pi 2o GLCt1 HEX1 g6p PGI FBP glc-d atp adp f6p atp PFK adp glc-d[e] glc-d atp H adp g6p f6p fdp pi 2o g3p = S v GLCt1 v HEX 1 = v PGI v PFK + v FBP =. S v = linear system of equations fdp dap 1 1 FBA

20 Topology & constraints define te feasible flux space Based on S, te steady state assumption and specific constraints on te fluxes, feasible flux distributions v can be calculated.

21 Topology & constraints define te feasible flux space Based on S, te steady state assumption and specific constraints on te fluxes, feasible flux distributions v can be calculated. Often, tere is no unique solution under-determined system glc-d[e] GLCt1 glc-d glc-d[e] GLCt1 glc-d glc-d[e] GLCt1 glc-d atp atp atp HEX1 HEX1 HEX1 adp adp adp g6p g6p g6p PGI f6p PGI f6p PGI f6p pi pi pi atp atp atp FBP PFK FBP PFK FBP PFK 2o adp 2o adp 2o adp fdp fdp fdp FBA FBA FBA dap EX_dap TPI g3p EX_g3p dap EX_dap TPI g3p EX_g3p dap EX_dap TPI g3p EX_g3p

22 Topology & constraints define te feasible flux space Based on S, te steady state assumption and specific constraints on te fluxes, feasible flux distributions v can be calculated. Often, tere is no unique solution under-determined system glc-d[e] GLCt1 glc-d glc-d[e] GLCt1 glc-d glc-d[e] GLCt1 glc-d atp HEX1 adp g6p PGI f6p atp HEX1 adp g6p PGI f6p atp HEX1 adp g6p PGI f6p v 3 Constraints 1) Sv = 2) a i < v i < b i v 3 Opt max pi pi pi atp atp atp FBP PFK FBP PFK FBP PFK 2o adp 2o adp 2o adp v 1 v 1 dap EX_dap fdp FBA g3p TPI EX_g3p dap EX_dap fdp FBA g3p TPI EX_g3p dap EX_dap fdp FBA g3p TPI EX_g3p Unconstrained solution space v 2 v 2 Allowable solution space

23 Biological Objectives To find a biologically meaningful flux distribution witin te feasible flux space, objective functions z describing te biological/evolutionary aim of te organism, can be used. Maximum biomass: max(z = v biomass ) growt Minimum total flux: min(z = n v ) min. effort i=1 Maximum ATP yield: max(z = v ATP ) energy n Maximum product yield: max(z = v product ) product

24 Optimization Linear programming: Optimization of a linear function over a subspace, subject to linear equality and inequality constraints max z = c 1 v 1 + c 2 v c n v n subject to S v = and v i,lb < v i < v i,ub

25 Optimization Linear programming: Optimization of a linear function over a subspace, subject to linear equality and inequality constraints max z = c 1 v 1 + c 2 v c n v n subject to S v = and v i,lb < v i < v i,ub v 2 6 v 1 < v 1

26 Optimization Linear programming: Optimization of a linear function over a subspace, subject to linear equality and inequality constraints max z = c 1 v 1 + c 2 v c n v n subject to S v = and v i,lb < v i < v i,ub v 2 v 1 < 4 v 2 < v 1

27 Optimization Linear programming: Optimization of a linear function over a subspace, subject to linear equality and inequality constraints max z = c 1 v 1 + c 2 v c n v n subject to S v = and v i,lb < v i < v i,ub v 2 6 v 1 < v 2 < 5 v 2 + v 1 < v 1

28 Optimization Linear programming: Optimization of a linear function over a subspace, subject to linear equality and inequality constraints max z = c 1 v 1 + c 2 v c n v n subject to S v = and v i,lb < v i < v i,ub v 2 6 v 1 < v 1 v 2 < 5 v 2 + v 1 < 6 Objective function max(v 1 + 2v 2 )

29 Optimization Linear programming: Optimization of a linear function over a subspace, subject to linear equality and inequality constraints max z = c 1 v 1 + c 2 v c n v n subject to S v = and v i,lb < v i < v i,ub v 2 6 v 1 < v 1 v 2 < 5 v 2 + v 1 < 6 Objective function max(v 1 + 2v 2 )

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31 Is te model consistent? Before carrying out FBAs, te network reconstruction needs to be tested for consistency. v 5 B E v 2 v 4 v 1 A v 6 D v 8 v 3 C v 7 F v 9

32 Is te model consistent? Before carrying out FBAs, te network reconstruction needs to be tested for consistency. Are parts of te network unconnected? Dead-end reactions Blocked reaction v 5 B E v 2 v 4 v 1 A v 6 D v 8 v 3 C v 7 F v 9

33 Is te model consistent? Before carrying out FBAs, te network reconstruction needs to be tested for consistency. Are parts of te network unconnected? Dead-end reactions Are reactions missing? Gaps Blocked reaction v 5 v 5 B E B E v 2 v 2 v 4 v 4 v 1 A v 6 D v 8 v 1 A v 6 D v 8 v 3 C v 7 F v 9 v 3 C v 7 F v 9

34 Wic are elemental submodels? Elementary Flux Modes are minimal sets of enzymes tat can eac generate valid steady states. (Scuster 1999)

35 Wic are elemental submodels? Elementary Flux Modes are minimal sets of enzymes tat can eac generate valid steady states. (Scuster 1999) v 5 B E v 2 v 4 v 1 A v 6 D v 8 v 3 C v F 7 v 9

36 Wic are elemental submodels? Elementary Flux Modes are minimal sets of enzymes tat can eac generate valid steady states. (Scuster 1999) v 5 v 5 v 5 B E B E B E v 2 v 4 v 2 v 4 v 2 v 4 v 1 A v 6 D v 8 v 1 A v 6 D v 8 v 1 A v 6 D v 8 v 3 C v 7 F v 9 v 3 C v 7 F v 9 v 3 C v F 7 v 9

37 Wic are elemental submodels? Elementary Flux Modes are minimal sets of enzymes tat can eac generate valid steady states. (Scuster 1999) v 5 v 5 v 5 B E B E B E v 2 v 4 v 2 v 4 v 2 v 4 v 1 A v 6 D v 8 v 1 A v 6 D v 8 v 1 A v 6 D v 8 v 3 C v 7 F v 9 v 3 C v 7 F v 9 v 3 C v 7 F v 9 A Minimal Cut Set is a minimal (irreducible) set of reactions in te network wose inactivation will definitely lead to a failure in certain network functions. (Klamt & Gilles 23)

38 Wic are elemental submodels? Elementary Flux Modes are minimal sets of enzymes tat can eac generate valid steady states. (Scuster 1999) v 5 v 5 Biological function: Biomass production (v 8 ) v 1 A v 2 v 6 B E v 4 D v 8 v 1 A v 2 v 6 B E v 4 D v 8 v 3 C v 7 F v 9 v 3 C v 7 F v 9 A Minimal Cut Set is a minimal (irreducible) set of reactions in te network wose inactivation will definitely lead to a failure in certain network functions. (Klamt & Gilles 23)

39 Wic are elemental submodels? Elementary Flux Modes are minimal sets of enzymes tat can eac generate valid steady states. (Scuster 1999) v 5 v 5 Biological function: Biomass production (v 8 ) v 1 A v 2 v 6 B E v 4 D v 8 v 1 A v 2 v 6 B E v 4 D v 8 v 3 C v 7 F v 9 v 3 C v 7 F v 9 A Minimal Cut Set is a minimal (irreducible) set of reactions in te network wose inactivation will definitely lead to a failure in certain network functions. (Klamt & Gilles 23)

40 Wic genes are essential? FBA can be used to find essential genes in te network, wose knock-out or functional deficiency destroys te ability to grow. Drug Tragets

41 Wic genes are essential? FBA can be used to find essential genes in te network, wose knock-out or functional deficiency destroys te ability to grow. Drug Tragets Calculation: 1 Set upper and lower boundary of a flux to 2 Optimize for biomass 3 Te gene is essential, if te maximum possible flux troug te biomass reaction =

42 Wic genes are essential? FBA can be used to find essential genes in te network, wose knock-out or functional deficiency destroys te ability to grow. Drug Tragets Calculation: 1 Set upper and lower boundary of a flux to 2 Optimize for biomass 3 Te gene is essential, if te maximum possible flux troug te biomass reaction = v 5 Example single gene deletion v 1 A v 2 v 6 B E v 4 D v 8 v 3 C v 7 F v 9

43 Wic genes are essential? FBA can be used to find essential genes in te network, wose knock-out or functional deficiency destroys te ability to grow. Drug Tragets Calculation: 1 Set upper and lower boundary of a flux to 2 Optimize for biomass 3 Te gene is essential, if te maximum possible flux troug te biomass reaction = v 5 Example single gene deletion double gene deletion v 1 A v 2 v 3 v 6 B C E v 4 v 7 D F v 9 v 8

44 Wic genes are essential? FBA can be used to find essential genes in te network, wose knock-out or functional deficiency destroys te ability to grow. Drug Tragets Calculation: 1 Set upper and lower boundary of a flux to 2 Optimize for biomass 3 Te gene is essential, if te maximum possible flux troug te biomass reaction = v 5 Example single gene deletion double gene deletion v 1 A v 2 v 3 v 6 B C E v 4 v 7 D F v 9 v 8

45 How defined is te optimal flux distribution Optimal solutions of an FBA are not necessarily unique. Flux Variability Analysis (FVA) allows to assess te variability in all possible flux distributions tat yield te same optimum value of te objective function.

46 How defined is te optimal flux distribution Optimal solutions of an FBA are not necessarily unique. Flux Variability Analysis (FVA) allows to assess te variability in all possible flux distributions tat yield te same optimum value of te objective function. Calculation: 1 Optimize for biomass (or oter objective) 2 Fix biomass flux to optimum value 3 For eac reaction, maximize and minimize te flux wit te new constraint Upper and lower variability bounds

47 How defined is te optimal flux distribution Optimal solutions of an FBA are not necessarily unique. Flux Variability Analysis (FVA) allows to assess te variability in all possible flux distributions tat yield te same optimum value of te objective function. Insigt into: Alternative patways Loops Rigorousness of te set of constraints v 5 B E v 2 v 4 v 1 A v 6 D v 8 v 3 C v 7 F v 9

48 How does te network adapt to genetic perturbations? Evolutionary optimized system How does te flux distribution cange after a knock-out?

49 How does te network adapt to genetic perturbations? Evolutionary optimized system How does te flux distribution cange after a knock-out? Minimization of metabolic adaptation (MOMA) smallest possible flux cange

50 How does te network adapt to genetic perturbations? Evolutionary optimized system How does te flux distribution cange after a knock-out? Minimization of metabolic adaptation (MOMA) smallest possible flux cange Regulatory On-/Off-Minimization (ROOM) smallest possible number of switces

51 Outline Introduction Teory FBA Metods Can I add growt dynamics (dfba)? Coupling of te model to an external growt model (substrate consumption and biomass production) FBA FBA Periodic update of te excange fluxes Re-run FBA Exercise

52 Can I add regulation (rfba)? Coupling to a boolean regulatory gene expression model (Slomi et al 27)

53 Omics data integration Furter constrain te feasible flux space by large scale data Nutrient uptake rates Fluxomics Transcriptomics Proteomics Metabolomics Reaction entalpies

54 Labeling data / nutrient uptake rates Flux data can be directly included via constraints on reactions Uptake & secretion rates: Boundary fluxes 13 C labeling: Internal fluxes v 1 S M 1 v 2 v 3 M 2 labeling depends on flux partitioning M 2 v 3 /v 2 Slide from: ttp://

55 Transcriptomics & proteomics Limitations: Protein/gene expression does not directly translate to flux Neglects (translation,) PTMs, allosteric regulation, saturation state, termodynamics

56 Outline Introduction Teory Metabolomics Metabolite levels are not directly linked to flux No kinetic equations tat describe dependencies (like e.g. Micaelis-Menten) FBA Metods Exercise

57 Outline Introduction Teory FBA Metods Metabolomics Metabolite levels are not directly linked to flux No kinetic equations tat describe dependencies (like e.g. Micaelis-Menten) BUT we can learn about te termodynamic landscape of te network Termodynamic FBA (Henry et al. 27, Beard et al. 22) Termodynamic realizability (Hoppe et al. 27)... Exercise

58 Te COBRA toolbox MatLab based toolbox wit important functions for te development and analysis of large metabolic networks Easily extendable, editable open-source code Many publised genome scale network reconstructions available in te COBRA-format, wit network visualization In addition, te import of SBML models is possible.

59 Now osted on gitub ttps://gitub.com/opencobra Also available as cobrapy

60 Up and at em - Exercise! References for te figures and te sedulous student FBA Introduction: JD Ort et al (21) Wat is flux balance analysis? Nat Biotecnol. 28(3): COBRA toolbox: SA Becker et al (27) Quantitative prediction of cellular metabolism wit constraint-based models: te COBRA Toolbox.Nat Protoc.2(3): Example for genome-scale network reconstruction: N Jamsidi and BO Palsson (27) Investigating te metabolic capabilities of Mycobacterium tuberculosis H37Rv using te in silico strain inj661 and proposing alternative drug targets. BMC Syst Biol.1:26. EMF: S Scuster et al (1999) Detection of elementary flux modes in biocemical networks: a promising tool for patway analysis and metabolic engineering. Trends Biotecnol. Feb;17(2):53-6. MCS: S Klamt, ED Gilles (24) Minimal cut sets in biocemical reaction networks. Bioinformatics 2(2): dfba: X Feng et al (212) Integrating Flux Balance Analysis into Kinetic Models to Deciper te Dynamic Metabolism of Sewanella oneidensis MR-1. PLoS Comput Biol 8(2): e X Fang et al (29) A systems biology framework for modeling metabolic enzyme inibition of Mycobacterium tuberculosis. BMC Syst Biol. 29 Sep 15;3:92 rfba: T Slomi et al (27) A genome-scale computational study of te interplay between transcriptional regulation and metabolism. Mol Syst Biol. 3: 11. MOMA/ROOM: T Slomi et al (25) Regulatory on/off minimization of metabolic flux canges after genetic perturbations. PNAS 12 (21)