1. H. Scott Hinton, 2015 Lesson: Flux Variability Analysis & Parsimonious Flux Balance AnalysisBIE 5500/6500Utah State University Constraint-based Metabolic Reconstructions & Analysis -1- Flux Variability Analysis & Parsimonious Flux Balance Analysis

2. H. Scott Hinton, 2015 Lesson: Flux Variability Analysis & Parsimonious Flux Balance AnalysisBIE 5500/6500Utah State University Constraint-based Metabolic Reconstructions & Analysis -2- Learning Objectives Explain alternate optimal solutions, Explain flux variability analysis, Explain parsimonious flux balance analysis.

3. H. Scott Hinton, 2015 Lesson: Flux Variability Analysis & Parsimonious Flux Balance AnalysisBIE 5500/6500Utah State University Constraint-based Metabolic Reconstructions & Analysis -3- Lesson Outline Alternate Optimal Solutions Flux Variability Analysis Parsimonious FBA

4. H. Scott Hinton, 2015 Lesson: Flux Variability Analysis & Parsimonious Flux Balance AnalysisBIE 5500/6500Utah State University Constraint-based Metabolic Reconstructions & Analysis -4- Alternate Equivalent Optimal Solutions The flux distributions calculated by FBA are often not unique. In many cases, it is necessary for a biological system to achieve the same objective value by using alternate equivalent optimal pathways, creating phenotypically different alternate optimal solutions (silent phenotypes). Requires the Mixed Integer Linear Programming (MILP) solver For large models there can be a very large number of alternate equivalent optimal solutions. Maximize the objective function with the following constraints Same objective value for all alternate flux vectors Up to n alternate flux vectors v 1, v 2, …,v n all have the same value of Z

5. H. Scott Hinton, 2015 Lesson: Flux Variability Analysis & Parsimonious Flux Balance AnalysisBIE 5500/6500Utah State University Constraint-based Metabolic Reconstructions & Analysis -5- Identifying Alternate Equivalent Optimal Solutions A function that that is provided by the Cobra Toolbox to identify alternate equivalent optimal solutions is called enumerateOptimalSolutions(model) In Matlab workspace a new structure called “solutions” is created that contains all the alternate equivalent optimal solutions. For large models, this computation will take a long time to run. % findingOptimalSolutionsSucc.m clear; model = readCbModel('ecoli_textbook'); model = changeRxnBounds(model,'EX_o2(e)',-40,'l'); model = changeRxnBounds(model,'EX_glc(e)',0,'l'); model = changeRxnBounds(model,'EX_succ(e)',-20,'l'); model = changeObjective(model,'Biomass_Ecoli_core_N(w/GAM)_Nmet2'); % List optimal solutions solverOK = changeCobraSolver('glpk') [solutions] = enumerateOptimalSolutions(model); % findingOptimalSolutionsSucc.m clear; model = readCbModel('ecoli_textbook'); model = changeRxnBounds(model,'EX_o2(e)',-40,'l'); model = changeRxnBounds(model,'EX_glc(e)',0,'l'); model = changeRxnBounds(model,'EX_succ(e)',-20,'l'); model = changeObjective(model,'Biomass_Ecoli_core_N(w/GAM)_Nmet2'); % List optimal solutions solverOK = changeCobraSolver('glpk') [solutions] = enumerateOptimalSolutions(model);

6. H. Scott Hinton, 2015 Lesson: Flux Variability Analysis & Parsimonious Flux Balance AnalysisBIE 5500/6500Utah State University Constraint-based Metabolic Reconstructions & Analysis -6- Alternate Optimal Solutions Matlab Screenshot Alternate Optimal Solution Flux Vectors Alternate Optimal Solution Flux Vectors findingOptimalSolutionsSucc.m

7. H. Scott Hinton, 2015 Lesson: Flux Variability Analysis & Parsimonious Flux Balance AnalysisBIE 5500/6500Utah State University Constraint-based Metabolic Reconstructions & Analysis -7- Visualizing the Alternate Optimal Solution Flux Vectors % findingOptimalSolutionsSuccVisualize.m clear; model = readCbModel('ecoli_textbook'); model = changeRxnBounds(model,'EX_glc(e)',0,'l'); model = changeRxnBounds(model,'EX_o2(e)',-40,'l'); model = changeRxnBounds(model,'EX_succ(e)',-20,'l'); model = changeObjective(model,'Biomass_Ecoli_core_N(w/GAM)_Nmet2'); % List optimal solutions solverOK = changeCobraSolver('glpk'); [solutions] = enumerateOptimalSolutions(model); v = solutions.fluxes(:,3); % Select which vector wanted to be mapped (1-3) printFluxVector(model, FBAsolution.x, true) map=readCbMap('ecoli_Textbook_ExportMap'); options.lb = -10; options.ub = 10; options.zeroFluxWidth = 0.1; options.rxnDirMultiplier = 10; drawFlux(map, model, v, options); Solution #1

8. H. Scott Hinton, 2015 Lesson: Flux Variability Analysis & Parsimonious Flux Balance AnalysisBIE 5500/6500Utah State University Constraint-based Metabolic Reconstructions & Analysis -8- Alternate Optimal Solutions findingOptimalSolutionsSuccVisualize.m Solution #2Solution #3Solution #1

9. H. Scott Hinton, 2015 Lesson: Flux Variability Analysis & Parsimonious Flux Balance AnalysisBIE 5500/6500Utah State University Constraint-based Metabolic Reconstructions & Analysis -9- Changing Aerobic Conditions: Alternate Optimal Solutions 10 Alternate Optimal Flux Vectors EX_succ(e) = -20; EX_o2(e) = -5 (instead of 40); findingOptimalSolutionsSuccVisualize.m

10. H. Scott Hinton, 2015 Lesson: Flux Variability Analysis & Parsimonious Flux Balance AnalysisBIE 5500/6500Utah State University Constraint-based Metabolic Reconstructions & Analysis -10- Alternate Optimal Flux Vectors for Ethanol Production % findingOptimalSolutionsEthanol.m clear; model = readCbModel('ecoli_textbook'); model = changeRxnBounds(model,'EX_glc(e)',-10,'l'); model = changeRxnBounds(model,'EX_o2(e)',0,'l'); model = changeObjective(model,'EX_etoh(e)'); solverOK = changeCobraSolver('glpk'); % List optimal solutions [solutions] = enumerateOptimalSolutions(model); 69 Alternate Optimal Flux Vectors

11. H. Scott Hinton, 2015 Lesson: Flux Variability Analysis & Parsimonious Flux Balance AnalysisBIE 5500/6500Utah State University Constraint-based Metabolic Reconstructions & Analysis -11- Reducing Alternate Optimal Flux Vectors % findingOptimalSolutionsEthanolForced.m clear; model = readCbModel('ecoli_textbook'); model = changeRxnBounds(model,'EX_glc(e)',-10,'l'); model = changeRxnBounds(model,'EX_o2(e)',-0,'l'); model = changeRxnBounds(model,'EX_etoh(e)',15,'b'); model = changeObjective(model,'Biomass_Ecoli_core_N(w/GAM)_Nmet2'); % List optimal solutions solverOK = changeCobraSolver('glpk'); % Won't work with Gurobi [solutions] = enumerateOptimalSolutions(model); Note the reduction in alternate optimal flux vectors from 69 to 9 Force specific production of ethanol

12. H. Scott Hinton, 2015 Lesson: Flux Variability Analysis & Parsimonious Flux Balance AnalysisBIE 5500/6500Utah State University Constraint-based Metabolic Reconstructions & Analysis -12- Review Questions What are alternate optimal solutions? What is the relationship between alternate optimal solutions and a cell’s phenotype? What are silent phenotypes? How can you find the alternate optimal solutions using the Cobra Toolbox? How many alternate optimal solutions can there be for a given phenotype? How many alternate optimal solutions can there be for a carbon source? Do aerobic/anaerobic conditions impact the number alternate optimal solutions? Does the choice of objective function impact the number alternate optimal solutions?

13. H. Scott Hinton, 2015 Lesson: Flux Variability Analysis & Parsimonious Flux Balance AnalysisBIE 5500/6500Utah State University Constraint-based Metabolic Reconstructions & Analysis -13- Lesson Outline Alternate Optimal Solutions Flux Variability Analysis Parsimonious FBA

14. H. Scott Hinton, 2015 Lesson: Flux Variability Analysis & Parsimonious Flux Balance AnalysisBIE 5500/6500Utah State University Constraint-based Metabolic Reconstructions & Analysis -14- Flux Variability Analysis This method identifies the maximum and minimum possible fluxes through a particular reaction for a given maximum objective value. All reactions under test have the same objective value A method that uses FBA to identify alternate optimal pathways.

15. H. Scott Hinton, 2015 Lesson: Flux Variability Analysis & Parsimonious Flux Balance AnalysisBIE 5500/6500Utah State University Constraint-based Metabolic Reconstructions & Analysis -15- Flux Variability Analysis Example % FluxVariabilitySuccinate.m % Input model model=readCbModel('ecoli_textbook'); % Change carbon source from glucose to succinate model = changeRxnBounds(model,'EX_glc(e)',0,'l'); model = changeRxnBounds(model,'EX_succ(e)',-20,'l'); % Set optimization objective to Biomass_Ecoli_core_N(w/GAM)_Nmet2 model = changeObjective(model,'Biomass_Ecoli_core_N(w/GAM)_Nmet2'); % Perform flux variability analysis [minFlux,maxFlux]=fluxVariability(model); % Allows loops % Print flux values printFluxVector(model, [minFlux, maxFlux], true)

16. H. Scott Hinton, 2015 Lesson: Flux Variability Analysis & Parsimonious Flux Balance AnalysisBIE 5500/6500Utah State University Constraint-based Metabolic Reconstructions & Analysis -16- Flux Variability Analysis Example Output ACONTa8.137638.13764 ACONTb8.137638.13764 ACt2r-7.75e-006-0 ADK103.29e-005 AKGDH7.231197.23122 AKGt2r-3.06e-006-0 ALCD2x-4.39e-0060 ATPM8.398.39 ATPS4r57.781657.7817 Biomass_0.8401340.840134 CO2t-44.2477-44.2477 CS8.137638.13764 CYTBD66.552866.5528 D_LACt2-4.25e-006-0 ENO-3.49018-3.49017 ETOHt2r-4.39e-006-0 EX_ac(e)07.75e-006 EX_acald(e)05.07e-006 EX_akg(e)03.06e-006 EX_co2(e)44.247744.2477 EX_etoh(e)04.39e-006 EX_for(e)02.19e-005 EX_glu_L(e)02.74e-006 EX_h2o(e)30.367530.3675 EX_h(e)-23.1469-23.1469 EX_lac_D(e)04.25e-006 EX_nh4(e)-4.58109-4.58108 EX_o2(e)-33.2764-33.2764 EX_pi(e)-3.0906-3.0906 EX_pyr(e)05.07e-006 EX_succ(e)-20-20 FBA-0.835696-0.835681 FBP0.8356810.835714 FORt200.000131865 FORti00.000131865 FUM27.231227.2312 G6PDH2r04.39e-005 GAPD-2.23334-2.23333 GLNS0.2148220.214855 GLUDy-4.36626-4.36623 GLUN03.29e-005 GLUSy03.29e-005 GLUt2r-2.74718e-006-0 GND04.39e-005 H2Ot-30.3675-30.3675 ICDHyr8.137618.13764 ICL03.29e-005 LDH_D-4.2537e-0060 MALS03.29e-005 MDH13.56520.0575 ME106.4925 ME27.1737213.6663 NADH1639.321639.3216 NADTRHD06.4925 NH4t4.581084.58109 O2t33.276433.2764 PDH11.286311.2863 PGI-0.172271-0.172227 PGK2.233332.23334 PGL04.39e-005 PGM3.490173.49018 PIt2r3.09063.0906 PPC03.29e-005 PPCK3.9262510.4188 PPS03.29e-005 PTAr07.75e-006 PYK06.4925 PYRt2r-5.07172e-006-0 RPE-0.603888-0.603859 RPI-0.603903-0.603888 SUCCt2_22020 SUCCt304.39e-005 SUCDi27.2312 27.2312 SUCOAS-7.23122-7.23119 TALA-0.1503-0.150285 THD206.59e-005 TKT1-0.1503-0.150285 TKT2-0.453588-0.453574 TPI-0.835696-0.835681

17. H. Scott Hinton, 2015 Lesson: Flux Variability Analysis & Parsimonious Flux Balance AnalysisBIE 5500/6500Utah State University Constraint-based Metabolic Reconstructions & Analysis -17- Flux Variability Analysis Example FVA core.xlsx

18. H. Scott Hinton, 2015 Lesson: Flux Variability Analysis & Parsimonious Flux Balance AnalysisBIE 5500/6500Utah State University Constraint-based Metabolic Reconstructions & Analysis -18- Variable Reactions For Growth On Succinate J. D. Orth et al, "What is flux balance analysis? Supplementary tutorial" Reaction Minimum Flux (mmol gDW-1 hr-1) Maximum Flux (mmol gDW-1 hr-1) MDH13.5620.06 ME106.49 ME27.1713.67 NADTRHD06.49 PPCK3.9310.42 PYK06.49

19. H. Scott Hinton, 2015 Lesson: Flux Variability Analysis & Parsimonious Flux Balance AnalysisBIE 5500/6500Utah State University Constraint-based Metabolic Reconstructions & Analysis -19- Fluxes Identified Through Flux Variability Analysis (AerobicSuccinateBioMass.m) MDH (malate dehydrogenase) ME1 (malic enzyme (NAD)) ME2 (malic enzyme (NADP)) NADTRHD (NAD transhydrogenase) PPCK (phosphoenolpyruvate carboxykinase) PYK (pyruvate kinase) ME1 NADTRHD PYK MDH ME2 PPCK EX_succ(e)

20. H. Scott Hinton, 2015 Lesson: Flux Variability Analysis & Parsimonious Flux Balance AnalysisBIE 5500/6500Utah State University Constraint-based Metabolic Reconstructions & Analysis -20- Alternate Optimal Solutions #1 findingOptimalSolutionsSuccVisualize.m ACONTa8.13764 ACONTb8.13764 AKGDH7.23122 ATPM8.39 ATPS4r57.7816 Biomass0.840134 CO2t-44.2477 CS8.13764 CYTBD66.5528 ENO-3.49017 EX_co2(e)44.2477 EX_h2o(e)30.3675 EX_h(e)-23.1469 EX_nh4(e)-4.58108 EX_o2(e)-33.2764 EX_pi(e)-3.0906 EX_succ(e)-20 FBA-0.835681 FBP0.835681 FUM27.2312 GAPD-2.23333 GLNS0.214822 GLUDy-4.36626 H2Ot-30.3675 ICDHyr8.13764 MDH13.565 ME213.6662 NADH1639.3216 NADTRHD6.49242 NH4t4.58108 O2t33.2764 PDH11.2863 PGI-0.172228 PGK2.23333 PGM3.49017 PIt2r3.0906 PPCK3.92628 RPE-0.603888 RPI-0.603888 SUCCt2_220 SUCDi27.2312 SUCOAS-7.23122 TALA-0.1503 TKT1-0.1503 TKT2-0.453588 TPI-0.835681 Other FVA Reactions ME10 PYK0 FVA Upper Bound; Lower Bound. Solution #1 ME1 NADTRHD PYK MDH ME2 PPCK

21. H. Scott Hinton, 2015 Lesson: Flux Variability Analysis & Parsimonious Flux Balance AnalysisBIE 5500/6500Utah State University Constraint-based Metabolic Reconstructions & Analysis -21- Alternate Optimal Solutions #2 findingOptimalSolutionsSuccVisualize.m ACONTa8.13764 ACONTb8.13764 AKGDH7.23122 ATPM8.39 ATPS4r57.7816 Biomass0.840134 CO2t-44.2477 CS8.13764 CYTBD66.5528 ENO-3.49017 EX_co2(e)44.2477 EX_h2o(e)30.3675 EX_h(e)-23.1469 EX_nh4(e)-4.58108 EX_o2(e)-33.2764 EX_pi(e)-3.0906 EX_succ(e)-20 FBA-0.835681 FBP0.835681 FUM27.2312 GAPD-2.23333 GLNS0.214822 GLUDy-4.36626 H2Ot-30.3675 ICDHyr8.13764 MDH13.565 ME16.49242 ME27.1738 NADH1639.3216 NH4t4.58108 O2t33.2764 PDH11.2863 PGI-0.172228 PGK2.23333 PGM3.49017 PIt2r3.0906 PPCK3.92628 RPE-0.603888 RPI-0.603888 SUCCt2_220 SUCDi27.2312 SUCOAS-7.23122 TALA-0.1503 TKT1-0.1503 TKT2-0.453588 TPI-0.835681 Other FVA Reactions NADTRHD0 PYK0 FVA Upper Bound; Lower Bound. Solution #2 ME1 NADTRHD PYK MDH ME2 PPCK

22. H. Scott Hinton, 2015 Lesson: Flux Variability Analysis & Parsimonious Flux Balance AnalysisBIE 5500/6500Utah State University Constraint-based Metabolic Reconstructions & Analysis -22- Alternate Optimal Solutions #3 findingOptimalSolutionsSuccVisualize.m ACONTa8.13764 ACONTb8.13764 AKGDH7.23122 ATPM8.39 ATPS4r57.7816 Biomass0.840134 CO2t-44.2477 CS8.13764 CYTBD66.5528 ENO-3.49017 EX_co2(e)44.2477 EX_h2o(e)30.3675 EX_h(e)-23.1469 EX_nh4(e)-4.58108 EX_o2(e)-33.2764 EX_pi(e)-3.0906 EX_succ(e)-20 FBA-0.835681 FBP0.835681 FUM27.2312 GAPD-2.23333 GLNS0.214822 GLUDy-4.36626 H2Ot-30.3675 ICDHyr8.13764 MDH20.0574 ME27.1738 NADH1639.3216 NH4t4.58108 O2t33.2764 PDH11.2863 PGI-0.172228 PGK2.23333 PGM3.49017 PIt2r3.0906 PPCK10.4187 PYK6.49242 RPE-0.603888 RPI-0.603888 SUCCt2_220 SUCDi27.2312 SUCOAS-7.23122 TALA-0.1503 TKT1-0.1503 TKT2-0.453588 TPI-0.835681 Other FVA Reactions NADTRHD0 ME10 FVA Upper Bound; Lower Bound. Solution #3 ME1 NADTRHD PYK MDH ME2 PPCK

23. H. Scott Hinton, 2015 Lesson: Flux Variability Analysis & Parsimonious Flux Balance AnalysisBIE 5500/6500Utah State University Constraint-based Metabolic Reconstructions & Analysis -23- Three Alternate Optimal Solutions

24. H. Scott Hinton, 2015 Lesson: Flux Variability Analysis & Parsimonious Flux Balance AnalysisBIE 5500/6500Utah State University Constraint-based Metabolic Reconstructions & Analysis -24- Flux Variability Analysis for Ethanol Production % FluxVariabilityEthanol.m clear; clc; % Input the E.coli core model model=readCbModel('ecoli_textbook'); model = changeRxnBounds(model,'EX_glc(e)',0,'l'); model = changeRxnBounds(model,'EX_succ(e)',-20,'l'); model = changeObjective(model,'EX_etoh(e)'); % Perform flux variability analysis [minFluxL,maxFluxL]=fluxVariability(model,100,'max',model.rxns,false,false); minFlux = 1000*minFluxL; maxFlux = 1000*maxFluxL; Difference = abs(maxFlux – minFlux); FluxDifference = Difference; n = length(Difference); for i=1:n if Difference(i) < 0.0001 FluxDifference(i) = 0; end printFluxVector(model, [minFlux, maxFlux, FluxDifference]) 69 Alternate Optimal Flux Vectors When the “no loops” condition is activated the minFlux and maxFLux values need to be multiplied by 1000

25. H. Scott Hinton, 2015 Lesson: Flux Variability Analysis & Parsimonious Flux Balance AnalysisBIE 5500/6500Utah State University Constraint-based Metabolic Reconstructions & Analysis -25- FVA Chart for Ethanol Production FVA Ethanol Production.xlsx

26. H. Scott Hinton, 2015 Lesson: Flux Variability Analysis & Parsimonious Flux Balance AnalysisBIE 5500/6500Utah State University Constraint-based Metabolic Reconstructions & Analysis -26- FVA Classifications FVA can be used to classify the reactions in a metabolic network. Assuming a biomass production rate greater than 90% of the optimal growth rate; A reaction was classified as “Hard-coupled to biomass” if the flux varied exactly with biomass production. “Partially coupled to biomass” included reactions that were required to have a non-zero flux, but were more flexible in the range. Reactions were classified as “Not coupled to biomass” if they could have a zero or non-zero flux while maintaining 90% biomass. Reactions were considered “zero flux” if they could maintain a flux in other conditions, but could not in growth conditions. Lewis, N. E., K. K. Hixson, et al. (2010). "Omic data from evolved E. coli are consistent with computed optimal growth from genome-scale models-Supplementary Material." Molecular Systems Biology 6: 390.

27. H. Scott Hinton, 2015 Lesson: Flux Variability Analysis & Parsimonious Flux Balance AnalysisBIE 5500/6500Utah State University Constraint-based Metabolic Reconstructions & Analysis -27- FVA Classifications for Succinate Growth 'EX_fru(e)' 'EX_fum(e)' 'EX_glc(e)' 'EX_gln_L(e)' 'EX_mal_L(e)' 'FRD7' 'FRUpts2' 'FUMt2_2' 'GLCpts' 'GLNabc' 'MALt2_2' 'ACONTa' 'ACONTb' 'ATPS4r' 'Biomass 'CS' 'CYTBD' 'EX_co2(e)' 'EX_h2o(e)' 'FBP' 'FUM' 'GLNS' 'ICDHyr' 'MDH' 'NADH16' 'NH4t' 'O2t' 'PDH' 'PGK' 'PGM' 'PIt2r' 'SUCCt2_2' 'SUCDi' 'EX_fru(e)' 'EX_fum(e)' 'EX_glc(e)' 'EX_gln_L(e)' 'EX_mal_L(e)' 'FRD7' 'FRUpts2' 'FUMt2_2' 'GLCpts' 'GLNabc' 'MALt2_2' 'ACALD' 'ACALDt' 'ACKr' 'ACt2r' 'ADK1' 'AKGDH' 'AKGt2r' 'ALCD2x' 'CO2t' 'D_LACt2' 'ENO' 'ETOHt2r' 'EX_ac(e)' 'EX_acald(e)' 'EX_akg(e)' 'EX_etoh(e)' 'EX_for(e)' 'EX_glu_L(e)' 'EX_h(e)' 'EX_lac_D(e)' 'EX_nh4(e)' 'EX_o2(e)' 'EX_pi(e)' 'EX_pyr(e)' 'EX_succ(e)‘ 'FBA' 'FORt2' 'FORti' 'G6PDH2r' 'GAPD' 'GLUDy' 'GLUN' 'GLUSy' 'GLUt2r' 'GND' 'H2Ot' 'ICL' 'LDH_D' 'MALS' 'ME1' 'ME2' 'NADTRHD' 'PFK' 'PFL' 'PGI' 'PGL' 'PPC' 'PPCK' 'PPS' 'PTAr' 'PYK' 'PYRt2r' 'RPE' 'RPI' 'SUCCt3' 'SUCOAS ' 'TALA' 'THD2' 'TKT1' 'TKT2' 'TPI' Hard-Coupled ReactionsPartially-Coupled ReactionsNot-Coupled ReactionsZero-flux Reactions FVASuccinateClassification.m

28. H. Scott Hinton, 2015 Lesson: Flux Variability Analysis & Parsimonious Flux Balance AnalysisBIE 5500/6500Utah State University Constraint-based Metabolic Reconstructions & Analysis -28- Flux Variability Map map=readCbMap('ecoli_Textbook_ExportMap'); drawFluxVariability(map,model,minFlux,maxFlux) map=readCbMap('ecoli_Textbook_ExportMap'); drawFluxVariability(map,model,minFlux,maxFlux) FluxVariabilitySuccinate.m

29. H. Scott Hinton, 2015 Lesson: Flux Variability Analysis & Parsimonious Flux Balance AnalysisBIE 5500/6500Utah State University Constraint-based Metabolic Reconstructions & Analysis -29- Flux Variability Map – Close-up Unidirectional/reversible forward Unidirectional/reversible reverse Unidirectional/irreversible Bidirectional/reversible = calculated flux change is bidirectional and changes directions/Stoichiometry is reversible Unidirectional/reversible forward = calculated flux change is unidirectional in direction of listed Stoichiometry/Stoichiometry is reversible Unidirectional/reversible reverse = calculated flux change is unidirectional in opposite direction of listed Stoichiometry/Stoichiometry is reversible Unidirectional/irreversible = calculated flux change is unidirectional/Stoichiometry is irreversible Bidirectional/reversible = calculated flux change is bidirectional and changes directions/Stoichiometry is reversible Unidirectional/reversible forward = calculated flux change is unidirectional in direction of listed Stoichiometry/Stoichiometry is reversible Unidirectional/reversible reverse = calculated flux change is unidirectional in opposite direction of listed Stoichiometry/Stoichiometry is reversible Unidirectional/irreversible = calculated flux change is unidirectional/Stoichiometry is irreversible (PGK: 3pg + atp 13dpg + adp) (ENO: 2pg h2o + pep) (PPC: co2 + h2o + pep --> h + oaa + pi) Bidirectional/reversible (Not Shown in Diagram)

30. H. Scott Hinton, 2015 Lesson: Flux Variability Analysis & Parsimonious Flux Balance AnalysisBIE 5500/6500Utah State University Constraint-based Metabolic Reconstructions & Analysis -30- Review Questions What is flux variability analysis? What is the relationship between the value of the objective function and the flux values calculated through flux variability analysis? How is flux variability analysis related to alternate optimal flux vectors? How can you implement flux variability analysis using the Cobra Toolbox? Does flux variability analysis identify the specific alternate optimal solutions? What is the value of knowing which reactions carry flux, which reactions carry no flux, and which reactions span a range of flux values? Explain the different FVA classifications; hard-coupled, partially-coupled, not-coupled, and no-flux reactions?

31. H. Scott Hinton, 2015 Lesson: Flux Variability Analysis & Parsimonious Flux Balance AnalysisBIE 5500/6500Utah State University Constraint-based Metabolic Reconstructions & Analysis -31- Lesson Outline Alternate Optimal Solutions Flux Variability Analysis Parsimonious FBA

32. H. Scott Hinton, 2015 Lesson: Flux Variability Analysis & Parsimonious Flux Balance AnalysisBIE 5500/6500Utah State University Constraint-based Metabolic Reconstructions & Analysis -32- Essential Reactions Essential reactions, metabolic genes necessary for in silico growth in the given media; % EssentialReactions.m clear; clc; % Input the E.coli core model model=readCbModel('ecoli_textbook'); model = changeRxnBounds(model,'EX_glc(e)',-10,'l'); model = changeRxnBounds(model,'EX_o2(e)',-30,'l'); tol = 1e-6; %Growth rate lower limit RxnRatio = singleRxnDeletion(model); RxnRatio(isnan(RxnRatio))=0; EssentialRxns = model.rxns(RxnRatio<tol) 'ACONTa' 'ACONTb' 'Biomass' 'CS' 'ENO' 'EX_glc(e)' 'EX_h(e)' 'EX_nh4(e)' 'EX_pi(e)' 'FBA' 'GAPD' 'GLCpts' 'GLNS' 'ICDHyr' 'NH4t' 'PFK' 'PGI' 'PGK' 'PGM' 'PIt2r' 'PPC' 'RPI' 'TPI' Anaerobic 'ACONTa' 'ACONTb' 'Biomass 'CS' 'ENO' 'EX_glc(e)' 'EX_h(e)' 'EX_nh4(e)' 'EX_pi(e)' 'GAPD' 'GLCpts' 'GLNS' 'ICDHyr' 'NH4t' 'PGK' 'PGM' 'PIt2r' 'RPI' Aerobic X X X X X X X X X X X X X X X X X Biomass X X X X X X * RxnRatio = Computed growth rate ratio between deletion strain and wild type

33. H. Scott Hinton, 2015 Lesson: Flux Variability Analysis & Parsimonious Flux Balance AnalysisBIE 5500/6500Utah State University Constraint-based Metabolic Reconstructions & Analysis -33- Essential Genes Essential genes, metabolic genes necessary for in silico growth in the given media; % EssentialGenes.m clear; clc; % Input the E.coli core model model=readCbModel('ecoli_textbook'); model = changeRxnBounds(model,'EX_glc(e)',-10,'l'); model = changeRxnBounds(model,'EX_o2(e)',-30,'l'); tol = 1e-6; % Growth rate lower limit grRatio = singleGeneDeletion(model); grRatio(isnan(grRatio))=0; EssentialGenes = model.genes(grRatio<tol) [results ListResults] = findRxnsFromGenes(model, EssentialGenes);

34. H. Scott Hinton, 2015 Lesson: Flux Variability Analysis & Parsimonious Flux Balance AnalysisBIE 5500/6500Utah State University Constraint-based Metabolic Reconstructions & Analysis -34- Parsimonious FBA Flux parsimony - minimize the total material flow required to achieve an objective. The underlying assumption is that, under growth pressure, there is a selection for strains that can process the growth substrate the most rapidly and efficiently while using the minimum amount of enzyme. Genes are classified into six categories: 1.essential genes, metabolic genes necessary for in silico growth in the given media; 2.pFBA optima, non-essential genes contributing to the optimal growth rate and minimum gene-associated flux; 3.enzymatically less efficient (ELE), genes requiring more flux through enzymatic steps than alternative pathways that meet the same predicted growth rate; 4.metabolically less efficient (MLE), genes requiring a growth rate reduction if used; 5.pFBA no-flux, genes that are unable to carry flux in the experimental conditions; and 6.Blocked, genes that are only associated with the reactions that cannot carry a flux under any condition (“blocked” reactions). A map showing the category of each gene can be created. Lewis, N. E., K. K. Hixson, et al. (2010). "Omic data from evolved E. coli are consistent with computed optimal growth from genome-scale models." Molecular Systems Biology 6: 390.

35. H. Scott Hinton, 2015 Lesson: Flux Variability Analysis & Parsimonious Flux Balance AnalysisBIE 5500/6500Utah State University Constraint-based Metabolic Reconstructions & Analysis -35- Parsimonious Enzyme Usage FBA Gene A, classified as MLE, represents an enzyme that uses a suboptimal co-factor to catalyze a reaction, thereby reducing the growth rate if used. Gene B, classified as pFBA no-flux, cannot carry a flux in this example since it is unable to take up or produce a necessary precursor metabolite. Genes E and F in this example require two different enzymes to catalyze the same transformation which Gene D can do alone; therefore they are classified as ELE. Gene G is essential, since its removal will stop the flux through all pathways. Genes C and D represent the most efficient (topologically and metabolically) pathway and therefore are part of the pFBA optima. Lewis, N. E., K. K. Hixson, et al. (2010). "Omic data from evolved E. coli are consistent with computed optimal growth from genome-scale models." Molecular Systems Biology 6: 390.

36. H. Scott Hinton, 2015 Lesson: Flux Variability Analysis & Parsimonious Flux Balance AnalysisBIE 5500/6500Utah State University Constraint-based Metabolic Reconstructions & Analysis -36- Parsimonious FBA Example pFBA_Ecoli_Core.m (Aerobic) Red = Essential reactions, Orange = pFBA optima reaction Yellow Yellow = ELE reactions, Green = MLE reactions, Blue = zero flux reactions, Purple = blocked reactions, Black = not classified Red = Essential reactions, Orange = pFBA optima reaction Yellow Yellow = ELE reactions, Green = MLE reactions, Blue = zero flux reactions, Purple = blocked reactions, Black = not classified Ana TCA OxP PPP Glyc Ferm % pFBA_Ecoli_Core.m clear; model=readCbModel('ecoli_textbook'); model = changeRxnBounds(model,'EX_glc(e)',-10,'l'); model = changeRxnBounds(model,'EX_o2(e)',-0 or -30,'l'); map=readCbMap('ecoli_Textbook_ExportMap'); [GeneClasses RxnClasses modelIrrevFM] = pFBA(model, 'geneoption',0, 'tol',1e-7,'map',map,'mapOutName', 'Ecore_pFBA.svg') % pFBA_Ecoli_Core.m clear; model=readCbModel('ecoli_textbook'); model = changeRxnBounds(model,'EX_glc(e)',-10,'l'); model = changeRxnBounds(model,'EX_o2(e)',-0 or -30,'l'); map=readCbMap('ecoli_Textbook_ExportMap'); [GeneClasses RxnClasses modelIrrevFM] = pFBA(model, 'geneoption',0, 'tol',1e-7,'map',map,'mapOutName', 'Ecore_pFBA.svg') Ecore_pFBA.svg

37. H. Scott Hinton, 2015 Lesson: Flux Variability Analysis & Parsimonious Flux Balance AnalysisBIE 5500/6500Utah State University Constraint-based Metabolic Reconstructions & Analysis -37- pFBA Classification pFBA_Ecoli_Core.m (Anaerobic) 1.Essential genes, metabolic reactions/genes necessary for in silico growth in the given media; 2.pFBA optima, non-essential reactions/genes contributing to the optimal growth rate and minimum gene-associated flux; 3.Enzymatically Less Efficient (ELE), reactions/genes requiring more flux through enzymatic steps than alternative pathways that meet the same predicted growth rate; 4.Metabolically Less Efficient (MLE), reactions/genes requiring a growth rate reduction if used; 5.pFBA no-flux, reactions/genes that are unable to carry flux in the experimental conditions; and 6.Blocked, reactions/genes that are only associated with the reactions that cannot carry a flux under any condition (“blocked” reactions).

38. H. Scott Hinton, 2015 Lesson: Flux Variability Analysis & Parsimonious Flux Balance AnalysisBIE 5500/6500Utah State University Constraint-based Metabolic Reconstructions & Analysis -38- Parsimonious FBA Data Ana TCA OxP PPP Glyc Ferm Ecore_pFBA.svg pFBA_Ecoli_Core.m (Anaerobic)

39. H. Scott Hinton, 2015 Lesson: Flux Variability Analysis & Parsimonious Flux Balance AnalysisBIE 5500/6500Utah State University Constraint-based Metabolic Reconstructions & Analysis -39- Parsimonious FBA Maps pFBA_Ecoli_Core.m Aerobic Ana TCA OxP PPP Glyc Ferm Anaerobic Ana TCA OxP PPP Glyc Ferm

40. H. Scott Hinton, 2015 Lesson: Flux Variability Analysis & Parsimonious Flux Balance AnalysisBIE 5500/6500Utah State University Constraint-based Metabolic Reconstructions & Analysis -40- pFBA vs. FVA Reaction Classes The pFBA genes were mapped to the FVA reaction classes. The hard-coupled and partially-coupled reactions were all associated with the essential and pFBA optima genes, and the pFBA no-flux genes were all within the FVA zero-flux reactions. FVA Zero Flux reactions were identified in the other pFBA classes since some Zero-Flux reactions are catalyzed by genes which may be active for alternative, functional reactions. Lewis, N. E., K. K. Hixson, et al. (2010). "Omic data from evolved E. coli are consistent with computed optimal growth from genome-scale models-Supplementary Material." Molecular Systems Biology 6: 390.

41. H. Scott Hinton, 2015 Lesson: Flux Variability Analysis & Parsimonious Flux Balance AnalysisBIE 5500/6500Utah State University Constraint-based Metabolic Reconstructions & Analysis -41- Review Questions Why do they call it parsimonious flux balance analysis? What are essential genes/reactions? What are pFBA optima genes/reactions? What are enzymatically less efficient (ELE) genes/reactions? What are metabolically less efficient genes/reactions? What are pFBA no-flux genes/reactions? What are blocked genes/reactions? What is the difference between pFBA optima genes/reactions, enzymatically less efficient (ELE) genes/reactions and metabolically less efficient (MLE), genes/reactions? How can you implement parsimonious flux balance analysis using the Cobra Toolbox How can parsimonious flux balance analysis be used to metabolically engineer a cell?

42. H. Scott Hinton, 2015 Lesson: Flux Variability Analysis & Parsimonious Flux Balance AnalysisBIE 5500/6500Utah State University Constraint-based Metabolic Reconstructions & Analysis -42- Lesson Outline Alternate Optimal Solutions Flux Variability Analysis Parsimonious FBA

43. H. Scott Hinton, 2015 Lesson: Flux Variability Analysis & Parsimonious Flux Balance AnalysisBIE 5500/6500Utah State University Constraint-based Metabolic Reconstructions & Analysis -43- Extra Slides

44. H. Scott Hinton, 2015 Lesson: Flux Variability Analysis & Parsimonious Flux Balance AnalysisBIE 5500/6500Utah State University Constraint-based Metabolic Reconstructions & Analysis -44- Problems 1.Calculate the number of alternate optimal flux vectors to secrete ethanol at a fixed production rate of 15 mmol/gDW-h in the situation where fructose is used as the carbon source with a maximum uptake rate of -10 mmol/gDW-h in both aerobic (maximum O 2 uptake of -30 mmol/gDW-h) and anaerobic conditions. Plot the aerobic alternate optimal flux vectors flux vectors on textbook maps, one map for each flux vector. 2.Using flux variability analysis, find the reactions for problem #1 that have the greatest impact on the production of ethanol. Also create and print out the flux variability map for both the aerobic and anaerobic cases. 3.Using flux variability analysis, write a Matlab script to find the reactions for problem #1 associated with the FVA classifications of hard-coupled, partially-coupled, not-coupled, and no-flux reactions. 4.Using parsimonious flux balance analysis find the essential, pFBA optima, enzymatically less efficient (ELE), metabolically less efficient (MLE), pFBA no-flux, and blocked reactions associated with aerobic (-30 mmol/gDW-h) and anaerobic growth on fructose (-10 mmol/gDW-h ). Which parsimonious flux balance analysis categories do the reactions with a span of flux calculated in problem #2 fit? Are any of them essential reactions?

45. H. Scott Hinton, 2015 Lesson: Flux Variability Analysis & Parsimonious Flux Balance AnalysisBIE 5500/6500Utah State University Constraint-based Metabolic Reconstructions & Analysis -45- A flowchart for the simulation and classification of genes in pFBA.