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

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Presentation transcript:

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

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.

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

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

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);

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

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

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

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

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

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

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?

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

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.

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)

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 ACONTa ACONTb ACt2r-7.75e ADK103.29e-005 AKGDH AKGt2r-3.06e ALCD2x-4.39e-0060 ATPM ATPS4r Biomass_ CO2t CS CYTBD D_LACt2-4.25e ENO ETOHt2r-4.39e EX_ac(e)07.75e-006 EX_acald(e)05.07e-006 EX_akg(e)03.06e-006 EX_co2(e) EX_etoh(e)04.39e-006 EX_for(e)02.19e-005 EX_glu_L(e)02.74e-006 EX_h2o(e) EX_h(e) EX_lac_D(e)04.25e-006 EX_nh4(e) EX_o2(e) EX_pi(e) EX_pyr(e)05.07e-006 EX_succ(e) FBA FBP FORt FORti FUM G6PDH2r04.39e-005 GAPD GLNS GLUDy GLUN03.29e-005 GLUSy03.29e-005 GLUt2r e GND04.39e-005 H2Ot ICDHyr ICL03.29e-005 LDH_D e-0060 MALS03.29e-005 MDH ME ME NADH NADTRHD NH4t O2t PDH PGI PGK PGL04.39e-005 PGM PIt2r PPC03.29e-005 PPCK PPS03.29e-005 PTAr07.75e-006 PYK PYRt2r e RPE RPI SUCCt2_22020 SUCCt304.39e-005 SUCDi SUCOAS TALA THD206.59e-005 TKT TKT TPI

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

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) MDH ME ME NADTRHD06.49 PPCK PYK06.49

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)

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 ACONTa ACONTb AKGDH ATPM8.39 ATPS4r Biomass CO2t CS CYTBD ENO EX_co2(e) EX_h2o(e) EX_h(e) EX_nh4(e) EX_o2(e) EX_pi(e) EX_succ(e)-20 FBA FBP FUM GAPD GLNS GLUDy H2Ot ICDHyr MDH ME NADH NADTRHD NH4t O2t PDH PGI PGK PGM PIt2r PPCK RPE RPI SUCCt2_220 SUCDi SUCOAS TALA TKT TKT TPI Other FVA Reactions ME10 PYK0 FVA Upper Bound; Lower Bound. Solution #1 ME1 NADTRHD PYK MDH ME2 PPCK

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 ACONTa ACONTb AKGDH ATPM8.39 ATPS4r Biomass CO2t CS CYTBD ENO EX_co2(e) EX_h2o(e) EX_h(e) EX_nh4(e) EX_o2(e) EX_pi(e) EX_succ(e)-20 FBA FBP FUM GAPD GLNS GLUDy H2Ot ICDHyr MDH ME ME NADH NH4t O2t PDH PGI PGK PGM PIt2r PPCK RPE RPI SUCCt2_220 SUCDi SUCOAS TALA TKT TKT TPI Other FVA Reactions NADTRHD0 PYK0 FVA Upper Bound; Lower Bound. Solution #2 ME1 NADTRHD PYK MDH ME2 PPCK

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 ACONTa ACONTb AKGDH ATPM8.39 ATPS4r Biomass CO2t CS CYTBD ENO EX_co2(e) EX_h2o(e) EX_h(e) EX_nh4(e) EX_o2(e) EX_pi(e) EX_succ(e)-20 FBA FBP FUM GAPD GLNS GLUDy H2Ot ICDHyr MDH ME NADH NH4t O2t PDH PGI PGK PGM PIt2r PPCK PYK RPE RPI SUCCt2_220 SUCDi SUCOAS TALA TKT TKT TPI Other FVA Reactions NADTRHD0 ME10 FVA Upper Bound; Lower Bound. Solution #3 ME1 NADTRHD PYK MDH ME2 PPCK

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

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) < 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

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

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.

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

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

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)

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?

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

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

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);

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.

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.

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

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).

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)

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

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.

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?

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

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

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?

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.