© 2015 H. Scott Hinton Lesson: Robustness and Phenotype Phase Plane AnalysisBIE 5500/6500Utah State University Constraint-based Metabolic Reconstructions.

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© 2015 H. Scott Hinton Lesson: Robustness and Phenotype Phase Plane AnalysisBIE 5500/6500Utah State University Constraint-based Metabolic Reconstructions & Analysis Robustness Analysis & Phenotype Phase Plane Analysis

© 2015 H. Scott Hinton Lesson: Robustness and Phenotype Phase Plane AnalysisBIE 5500/6500Utah State University Constraint-based Metabolic Reconstructions & Analysis Learning Objectives Explain the capabilities of robustness analysis Explain how shadow prices can be used in metabolic modeling Explain how reduced costs can be used in metabolic modeling Explain the capabilities of phenotype phase plane analysis

© 2015 H. Scott Hinton Lesson: Robustness and Phenotype Phase Plane AnalysisBIE 5500/6500Utah State University Constraint-based Metabolic Reconstructions & Analysis Lesson Outline Robustness Analysis Shadow Prices Reduced Costs Phenotype Phase Plane Analysis

© 2015 H. Scott Hinton Lesson: Robustness and Phenotype Phase Plane AnalysisBIE 5500/6500Utah State University Constraint-based Metabolic Reconstructions & Analysis ROBUSTNESS ANALYSIS The flux through one reaction is varied and the optimal objective value is calculated as a function of this flux. This reveals how sensitive the objective is to a particular reaction. Example: Determine the effect of varying glucose uptake on growth Clear; % Input model model=readCbModel('ecoli_textbook'); % Set oxygen uptake rate model = changeRxnBounds(model,'EX_o2(e)',-17,'l'); % Set the upper bound for glucose uptake model = changeRxnBounds(model,'EX_glc(e)',-18.5,'l'); % Set optimization objective model = changeObjective(model,'Biomass_Ecoli_core_N(w/GAM)_Nmet2'); % Use robustnessAnalysis for glucose uptake rate robustnessAnalysis(model,'EX_glc(e)',100); AerobicGlucoseBioMassRA.m

© 2015 H. Scott Hinton Lesson: Robustness and Phenotype Phase Plane AnalysisBIE 5500/6500Utah State University Constraint-based Metabolic Reconstructions & Analysis Robustness Analysis Example Impact of Increasing Glucose Growth remains at 0 hr -1 until a glucose uptake rate of about 0.48 mmol gDW -1 hr -1, because with such a small amount of glucose, the system cannot make 8.39 mmol gDW -1 hr -1 of ATP needed to meet the default lower bound of the ATP maintenance reaction (ATPM) Oxygen uptake limits growth! Excess glucose cannot be fully oxidized, so the acetate fermentation pathways is used. X X AerobicGlucoseBioMassRA.m

© 2015 H. Scott Hinton Lesson: Robustness and Phenotype Phase Plane AnalysisBIE 5500/6500Utah State University Constraint-based Metabolic Reconstructions & Analysis Robustness Analysis Example Maps (AerobicGlucoseBioMassRA.m) EX_glc(e) =-7 mmol gDW -1 hr -1 EX_glc(e) =-10 mmol gDW -1 hr -1

© 2015 H. Scott Hinton Lesson: Robustness and Phenotype Phase Plane AnalysisBIE 5500/6500Utah State University Constraint-based Metabolic Reconstructions & Analysis Robustness Analysis Example Impact of Increasing Oxygen At an oxygen uptake of about mmol gDW -1 hr -1, growth actually begins to decrease as oxygen uptake increases. This is because glucose becomes limiting at this point, and glucose that would have been used to produce biomass must instead be used to reduce excess oxygen. EX_glc(e) is set at -10 mmol gDW -1 hr -1 AerobicGlucoseBioMassRA.m X X

© 2015 H. Scott Hinton Lesson: Robustness and Phenotype Phase Plane AnalysisBIE 5500/6500Utah State University Constraint-based Metabolic Reconstructions & Analysis Robustness Analysis Example Maps Impact of Increasing Oxygen EX_o2(e) = -20EX_o2(e) = -25 AerobicGlucoseBioMassRA_Map.m

© 2015 H. Scott Hinton Lesson: Robustness and Phenotype Phase Plane AnalysisBIE 5500/6500Utah State University Constraint-based Metabolic Reconstructions & Analysis Maximum Anaerobic Ethanol Production AnaerobicEthanolRA.m % AnaerobicEthanolRA.m clear; % Input the E.coli core model model=readCbModel('ecoli_textbook'); % Set uptake rates model = changeRxnBounds(model,'EX_glc(e)',-10,‘b'); model = changeRxnBounds(model,'EX_o2(e)',-0,'b'); % Set optimization objective to Biomass_Ecoli_core_N(w/GAM)_Nmet2 model = changeObjective(model,'Biomass_Ecoli_core_N(w/GAM)_Nmet2'); % Using robustnessAnalysis, plot the objective function as a function % of the ethanol secretion rate [controlFlux, objFlux] = robustnessAnalysis(model,'EX_etoh(e)',100); Maximum Growth Rate (8.283, ) Maximum Ethanol Production Fix Glucose and Oxygen Uptake Rates

© 2015 H. Scott Hinton Lesson: Robustness and Phenotype Phase Plane AnalysisBIE 5500/6500Utah State University Constraint-based Metabolic Reconstructions & Analysis Ethanol Production Phenotypes AnaerobicEthanolRA.m & AnaerobicEthanolRA_Maps.m % Draw a map of the different production phenotypes clear; model=readCbModel('ecoli_textbook'); model = changeRxnBounds(model,'EX_glc(e)',-10,'b'); model = changeRxnBounds(model,'EX_o2(e)',-0,'b'); model = changeRxnBounds(model,'EX_etoh(e)',4.242,'b'); % Low %model = changeRxnBounds(model,'EX_etoh(e)',12.53,'b'); % Medium %model = changeRxnBounds(model,'EX_etoh(e)',18.38,'b'); % High model = changeObjective(model,'Biomass_Ecoli_core_N(w/GAM)_Nmet2'); FBAsolution = optimizeCbModel(model,'max',0,0) map=readCbMap('ecoli_Textbook_ExportMap'); options.zeroFluxWidth = 0.1; options.rxnDirMultiplier = 10; drawFlux(map, model, FBAsolution.x, options); printFluxVector(model, FBAsolution.x, true) Low Production (4.242, ) High Production (18.38, ) Medium Production (12.53, )

© 2015 H. Scott Hinton Lesson: Robustness and Phenotype Phase Plane AnalysisBIE 5500/6500Utah State University Constraint-based Metabolic Reconstructions & Analysis Ethanol Production Phenotype Maps AnaerobicEthanolRA_Maps.m Low Production Medium Production High Production

© 2015 H. Scott Hinton Lesson: Robustness and Phenotype Phase Plane AnalysisBIE 5500/6500Utah State University Constraint-based Metabolic Reconstructions & Analysis Lesson Outline Robustness Analysis Shadow Prices Reduced Costs Phenotype Phase Plane Analysis

© 2015 H. Scott Hinton Lesson: Robustness and Phenotype Phase Plane AnalysisBIE 5500/6500Utah State University Constraint-based Metabolic Reconstructions & Analysis Shadow Prices: Metabolites Shadow prices, π i, are the derivative of the objective function, Z, with respect to the flux, b i, of a metabolite. The shadow prices define the incremental change in the objective function if a constraining flux is incrementally changed. The sensitivity of an FBA solution is indicated by shadow prices. They indicate how much the addition of a given metabolite will increase or decrease the objective. In the COBRA Toolbox, shadow prices can be calculated by optimizeCbModel. The vector of y shadow prices is solution.y (glpk solver) ShadowPricesExampleO2.m EX_glc(e) = -10

© 2015 H. Scott Hinton Lesson: Robustness and Phenotype Phase Plane AnalysisBIE 5500/6500Utah State University Constraint-based Metabolic Reconstructions & Analysis Shadow Prices Since If the objective is set to maximize cell growth rate ( Z GR ), and the shadow price ( π i ), of oxygen ( b EX_o2(e) ) is , it means that an additional flux unit of oxygen, within the EX_o2(e) uptake region of -15 and -21, will increase the growth rate by Each steady state solution (phenotype) will have different shadow prices. This example is based on EX_glc(e) = -10 (AerobicGlucoseBioMassShadowPrices.m) 1 unit of flux of b NADH EX_glc(e) = -10 ShadowPricesExampleO2.m

© 2015 H. Scott Hinton Lesson: Robustness and Phenotype Phase Plane AnalysisBIE 5500/6500Utah State University Constraint-based Metabolic Reconstructions & Analysis Shadow Prices for Growth on Glucose (ShadowPricesAerobicGrowthRateData.m) clear; model=readCbModel('ecoli_textbook'); changeCobraSolver('glpk'); % Use Matlab solver % Set the lower bounds for oxygen and glucose uptake model = changeRxnBounds(model,'EX_o2(e)',-20,‘b '); model = changeRxnBounds(model,'EX_glc(e)',-10,'l'); % Set optimization objective to Biomass_Ecoli_core_N(w/GAM)_Nmet2 model = changeObjective(model,'Biomass_Ecoli_core_N(w/GAM)_Nmet2'); % Optimize objective function FBAsolution = optimizeCbModel(model,'max'); % Must allow loops % Print flux values printFluxVector(model, FBAsolution.x, true) % Print shadow prices 'Shadow prices' printShadowPriceVector(model, FBAsolution.y, true) clear; model=readCbModel('ecoli_textbook'); changeCobraSolver('glpk'); % Use Matlab solver % Set the lower bounds for oxygen and glucose uptake model = changeRxnBounds(model,'EX_o2(e)',-20,‘b '); model = changeRxnBounds(model,'EX_glc(e)',-10,'l'); % Set optimization objective to Biomass_Ecoli_core_N(w/GAM)_Nmet2 model = changeObjective(model,'Biomass_Ecoli_core_N(w/GAM)_Nmet2'); % Optimize objective function FBAsolution = optimizeCbModel(model,'max'); % Must allow loops % Print flux values printFluxVector(model, FBAsolution.x, true) % Print shadow prices 'Shadow prices' printShadowPriceVector(model, FBAsolution.y, true) MetaboliteSP 13dpg[c] pg[c] pg[c] pgc[c] pgl[c] ac[c] acald[c] acald[e] acon-C[c] actp[c] akg[c] akg[e] amp[c]0.010 atp[c] cit[c] coa[c]0.010 dhap[c] e4p[c] etoh[c] etoh[e] f6p[c] fdp[c] for[c] for[e] fru[e] fum[c] fum[e] g3p[c] g6p[c] MetaboliteSP glc-D[e] gln-L[c] gln-L[e] glu-L[c] glu-L[e] glx[c] h[c]0.003 icit[c] lac-D[c] lac-D[e] mal-L[c] mal-L[e] nadh[c] nadph[c] o2[c] o2[e] oaa[c] pep[c] pi[c] pyr[c] pyr[e] q8h2[c]0.006 r5p[c] ru5p-D[c] s7p[c] succ[c] succ[e] succoa[c] xu5p-D[c]-0.051

© 2015 H. Scott Hinton Lesson: Robustness and Phenotype Phase Plane AnalysisBIE 5500/6500Utah State University Constraint-based Metabolic Reconstructions & Analysis Glucose Shadow Prices: Aerobic Growth Rate Example (ShadowPricesAerobicGrowthRate_glc.m) If the objective is set to maximize cell growth rate ( Z GR ), and the shadow price ( π glc-D[e] ), of glucose is when EX_o2(e) = -20, it means that an additional molecule of glucose will increase the growth rate by clear; model=readCbModel('ecoli_textbook'); model = changeRxnBounds(model,'EX_o2(e)',-20,‘b '); model = changeRxnBounds(model,'EX_glc(e)',-10,‘b '); model = changeObjective(model,'Biomass_Ecoli_core_N(w/GAM)_Nmet2'); FBAsolution = optimizeCbModel(model,'max') printFluxVector(model, FBAsolution.x, true) clear; model=readCbModel('ecoli_textbook'); model = changeRxnBounds(model,'EX_o2(e)',-20,‘b '); model = changeRxnBounds(model,'EX_glc(e)',-10,‘b '); model = changeObjective(model,'Biomass_Ecoli_core_N(w/GAM)_Nmet2'); FBAsolution = optimizeCbModel(model,'max') printFluxVector(model, FBAsolution.x, true) Biomass (EX_glc(e) = -10) Biomass (EX_glc(e) = -11)ΔBiomass Change between -10 & -11

© 2015 H. Scott Hinton Lesson: Robustness and Phenotype Phase Plane AnalysisBIE 5500/6500Utah State University Constraint-based Metabolic Reconstructions & Analysis Lesson Outline Robustness Analysis Shadow Prices Reduced Costs Phenotype Phase Plane Analysis

© 2015 H. Scott Hinton Lesson: Robustness and Phenotype Phase Plane AnalysisBIE 5500/6500Utah State University Constraint-based Metabolic Reconstructions & Analysis Reduced Costs: Reactions Reduced costs are the derivatives of the objective function ( Z ) with respect to an internal reaction ( v i ) with 0 flux. Reduced costs indicate how much each particular reaction affects the objective. The reduced costs are associated with each flux (v i ) and signify the amount by which the objective function is decreased if v i is increased. For instance, if the input flux of glucose shows a reduced cost of -x, it means that increasing that flux by one unit will increase of the objective function by x units. In the COBRA Toolbox, reduced costs can be calculated by optimizeCbModel. The vector of reduced costs is FBAsolution.w (glpk solver) 1 unit of flux EX_glc(e) = ReducedCostsExampleO2.m

© 2015 H. Scott Hinton Lesson: Robustness and Phenotype Phase Plane AnalysisBIE 5500/6500Utah State University Constraint-based Metabolic Reconstructions & Analysis Glucose Reduced Costs: Aerobic Growth Rate Example (ReducedCostsAerobicGrowthRate_glc.m) If the objective is set to maximize cell growth rate ( Z GR ), and the reduced costs ( ρ EX_glc(e) ), of glucose ( EX_glc(e) ) is , it means that an additional unit of glucose will increase the growth rate by clear; model=readCbModel('ecoli_textbook'); model = changeRxnBounds(model,'EX_o2(e)',-20,‘b '); model = changeRxnBounds(model,'EX_glc(e)',-10,‘b '); model = changeObjective(model,'Biomass_Ecoli_core_N(w/GAM)_Nmet2'); FBAsolution = optimizeCbModel(model,'max') printFluxVector(model, FBAsolution.x, true) clear; model=readCbModel('ecoli_textbook'); model = changeRxnBounds(model,'EX_o2(e)',-20,‘b '); model = changeRxnBounds(model,'EX_glc(e)',-10,‘b '); model = changeObjective(model,'Biomass_Ecoli_core_N(w/GAM)_Nmet2'); FBAsolution = optimizeCbModel(model,'max') printFluxVector(model, FBAsolution.x, true) Biomass (EX_glc(e) = -10) Biomass (EX_glc(e) = -11) Δ Biomass Change between -10 & -11

© 2015 H. Scott Hinton Lesson: Robustness and Phenotype Phase Plane AnalysisBIE 5500/6500Utah State University Constraint-based Metabolic Reconstructions & Analysis Lesson Outline Robustness Analysis Shadow Prices Reduced Costs Phenotype Phase Plane Analysis

© 2015 H. Scott Hinton Lesson: Robustness and Phenotype Phase Plane AnalysisBIE 5500/6500Utah State University Constraint-based Metabolic Reconstructions & Analysis Phenotype Phase Plane Price, N. D., J. L. Reed, et al. (2004). "Genome-scale models of microbial cells: evaluating the consequences of constraints." Nature reviews. Microbiology 2(11):

© 2015 H. Scott Hinton Lesson: Robustness and Phenotype Phase Plane AnalysisBIE 5500/6500Utah State University Constraint-based Metabolic Reconstructions & Analysis Phenotype Phase Plane Analysis It is also possible to vary two parameters simultaneously and plot the results as a phenotypic phase plane. These plots can reveal the interactions between two reactions. Matlab Cobra function: phenotypePhasePlane(model, ‘rxn1’,’rxn2’) Phenotype Phase PlaneShadow Prices of rxn1Shadow Prices of rxn2

© 2015 H. Scott Hinton Lesson: Robustness and Phenotype Phase Plane AnalysisBIE 5500/6500Utah State University Constraint-based Metabolic Reconstructions & Analysis Phenotype Phase Plane Analysis Example AerobicGlucoseBioMassPPP.m % Input model model=readCbModel('ecoli_textbook'); % Set oxygen and glucose uptake rates model = changeRxnBounds(model,'EX_o2(e)',-20,'l'); model = changeRxnBounds(model,'EX_glc(e)',-20,'l'); % Set optimization objective model = changeObjective(model,'Biomass_Ecoli_core_N(w/GAM)_Nmet2'); % Phenotype phase plane analysis phenotypePhasePlane(model,'EX_glc(e)', 'EX_o2(e)‘);

© 2015 H. Scott Hinton Lesson: Robustness and Phenotype Phase Plane AnalysisBIE 5500/6500Utah State University Constraint-based Metabolic Reconstructions & Analysis Phenotype Phase Plane Analysis Example (II) Variables: EX_o2(e) & EX_glc(e) Phase 1 Phase 3 Phase 2 Phase 4 Phase 5 AerobicGlucoseBioMassPPP.m

© 2015 H. Scott Hinton Lesson: Robustness and Phenotype Phase Plane AnalysisBIE 5500/6500Utah State University Constraint-based Metabolic Reconstructions & Analysis Phenotype Phase Plane Analysis Example (Phase 1) >> AerobicGlucoseBioMassPhase1 FBAsolution = f: 0 x: [] stat: -1 origStat: 110 solver: 'glpk' time: >> AerobicGlucoseBioMassPhase1 FBAsolution = f: 0 x: [] stat: -1 origStat: 110 solver: 'glpk' time: No Growth No growth; not enough glucose AerobicGlucoseBioMassPhase1.m EX_glc(e)= 1 EX_o2(e)= 10 Ferm TCA PPP Glyc Ana OxP

© 2015 H. Scott Hinton Lesson: Robustness and Phenotype Phase Plane AnalysisBIE 5500/6500Utah State University Constraint-based Metabolic Reconstructions & Analysis Phenotype Phase Plane Analysis Example (Phase 2) ACONTa ACONTb AKGDH ATPM8.39 ATPS4r Biomass CO2t CS CYTBD20 ENO EX_co2(e) EX_glc(e)-3 EX_h2o(e) EX_h(e) EX_nh4(e) EX_o2(e)-10 EX_pi(e) AerobicGlucoseBioMassPhase2.m EX_glc(e) Growth is limited by excess oxygen; not enough glucose to reduce all the oxygen and produce biomass optimally FBA FUM GAPD GLCpts3 GLNS GLUDy GLUN H2Ot ICDHyr ICL MALS MDH NADH NH4t O2t10 PDH PFK EX_glc(e)= -3 EX_o2(e)= -10 PGI PGK PGM PIt2r PYK RPE RPI SUCDi SUCOAS TALA THD TKT TKT TPI Ferm TCA PPP Glyc Ana OxP

© 2015 H. Scott Hinton Lesson: Robustness and Phenotype Phase Plane AnalysisBIE 5500/6500Utah State University Constraint-based Metabolic Reconstructions & Analysis Phenotype Phase Plane Analysis Example (Phase 3) ACKr ACONTa2.106 ACONTb2.106 ACt2r AKGDH ATPM8.39 ATPS4r Biomass CO2t CS2.106 CYTBD20 ENO EX_ac(e) EX_co2(e) EX_glc(e)-5 EX_h2o(e) EX_h(e) AerobicGlucoseBioMassPhase3.m EX_nh4(e) EX_o2(e)-10 EX_pi(e) FBA FUM G6PDH2r GAPD GLCpts5 GLNS GLUDy GND H2Ot ICDHyr2.106 MDH NADH NH4t O2t10 PDH PFK PGI PGK PGL PGM PIt2r PPC PTAr PYK RPE RPI SUCDi SUCOAS TALA TKT TKT TPI EX_glc(e) EX_glc(e)= -3 EX_o2(e)= -10 EX_glc(e) Ferm TCA PPP Glyc Ana OxP Not enough oxygen to fully oxidize glucose; acetate produced through fermentation EX_glc(e)= -5 EX_o2(e)= -10

© 2015 H. Scott Hinton Lesson: Robustness and Phenotype Phase Plane AnalysisBIE 5500/6500Utah State University Constraint-based Metabolic Reconstructions & Analysis Phenotype Phase Plane Analysis Example (Phase 4) ACKr ACONTa ACONTb ACt2r ATPM8.39 ATPS4r Biomass CO2t CS CYTBD20 ENO EX_ac(e) EX_co2(e) EX_for(e) EX_glc(e)-10 EX_h2o(e) EX_h(e) EX_nh4(e) AerobicGlucoseBioMassPhase4.m EX_o2(e)-10 EX_pi(e) FBA FORti G6PDH2r GAPD GLCpts10 GLNS GLUDy GND H2Ot ICDHyr NADH1620 NH4t O2t10 PDH PFK PFL PGI PGK PGL PGM PIt2r PPC PTAr PYK RPE RPI TALA TKT TKT TPI EX_glc(e) Ferm TCA PPP Glyc Ana OxP EX_glc(e)= -10 EX_o2(e)= -10 Not enough oxygen to fully oxidize glucose; acetate and formate are produced and secreted

© 2015 H. Scott Hinton Lesson: Robustness and Phenotype Phase Plane AnalysisBIE 5500/6500Utah State University Constraint-based Metabolic Reconstructions & Analysis Phenotype Phase Plane Analysis Example (Phase 5) ACALD ACKr ACONTa ACONTb ACt2r ALCD2x ATPM8.39 ATPS4r Biomass CO2t CS CYTBD20 ENO ETOHt2r EX_ac(e) EX_co2(e) EX_etoh(e) EX_for(e) AerobicGlucoseBioMassPhase5.m EX_glc(e)-19 EX_h2o(e) EX_h(e) EX_nh4(e) EX_o2(e)-10 EX_pi(e) FBA FORti GAPD GLCpts19 GLNS GLUDy H2Ot ICDHyr NADH1620 NH4t O2t10 PFK PFL PGI PGK PGM PIt2r PPC PTAr PYK RPE RPI TALA THD TKT TKT TPI EX_glc(e) Ferm TCA PPP Glyc Ana OxP EX_glc(e)= -19 EX_o2(e)= -10 Not enough oxygen to fully oxidize glucose; acetate, formate and ethanol are produced and secreted.

© 2015 H. Scott Hinton Lesson: Robustness and Phenotype Phase Plane AnalysisBIE 5500/6500Utah State University Constraint-based Metabolic Reconstructions & Analysis Phenotype Phase Plane Analysis Example (VI) Variables: EX_o2(e) & EX_glc(e) Phase 1 Phase 3 Phase 2 Phase 4 Phase 5 No growth; not enough glucose Growth is limited by excess oxygen; not enough glucose to reduce all the oxygen and produce biomass optimally Not enough oxygen to fully oxidize glucose; acetate produced through fermentation Not enough oxygen to fully oxidize glucose; acetate and formate are produced and secreted Not enough oxygen to fully oxidize glucose; acetate, formate and ethanol are produced and secreted. AerobicGlucoseBioMassPPP.m

© 2015 H. Scott Hinton Lesson: Robustness and Phenotype Phase Plane AnalysisBIE 5500/6500Utah State University Constraint-based Metabolic Reconstructions & Analysis Phenotype Phase Plane Analysis Example (VII) There is a different phenotype for each phase region Phase 1 Phase 2 Phase 3 Phase 4 Phase Oxygen Shadow Prices Phase 1 Phase 2 Phase 3 Phase 4 Phase Glucose Shadow Prices

© 2015 H. Scott Hinton Lesson: Robustness and Phenotype Phase Plane AnalysisBIE 5500/6500Utah State University Constraint-based Metabolic Reconstructions & Analysis Phenotype Phase Plane Analysis Example (VIII) (Robustness Analysis setting O 2 = -5 mmol/g DW-hr) There is a different phenotype for each phase region Given: O 2 = -5 mmol/g DW-hr Phase Boundaries Robustness Analysis Phase 1 Phase 2 Phase 3 Phase 4 Phase Glucose Shadow Prices

© 2015 H. Scott Hinton Lesson: Robustness and Phenotype Phase Plane AnalysisBIE 5500/6500Utah State University Constraint-based Metabolic Reconstructions & Analysis Phenotype Phase Plane Analysis Example (IX) (Robustness Analysis setting O 2 = -15 mmol/g DW-hr) There is a different phenotype for each phase region Given: O 2 = -15 mmol/g DW-hr Phase Boundaries Robustness Analysis Phase 1 Phase 2 Phase 3 Phase 4 Phase Glucose Shadow Prices

© 2015 H. Scott Hinton Lesson: Robustness and Phenotype Phase Plane AnalysisBIE 5500/6500Utah State University Constraint-based Metabolic Reconstructions & Analysis Phenotype Phase Plane Analysis Example (X) (Robustness Analysis setting O 2 = 10 mmol/g DW-hr) There is a different phenotype for each phase region Given: O 2 = 10 mmol/g DW-hr Phase Boundaries Robustness Analysis Phase 1 Phase 2 Phase 3 Phase 4 Phase Glucose Shadow Prices

© 2015 H. Scott Hinton Lesson: Robustness and Phenotype Phase Plane AnalysisBIE 5500/6500Utah State University Constraint-based Metabolic Reconstructions & Analysis Line of Optimality The line of optimality (LO) is defined as a line representing the optimal relation between the two metabolic fluxes used to create a phenotype phase plane. The line of optimality is determined by specifying an uptake rate of the substrate along the x-axis and then allowing any value for the flux along the y-axis. Linear Programming can then be used to calculate the optimal value of the objective as a function of the y-axis flux. Once the objective is determined, the corresponding flux value for the y-axis is used to plot the line of optimality (LO). The LO defines the optimal utilization of the metabolic pathways without limitations on the availability of the substrates. LO

© 2015 H. Scott Hinton Lesson: Robustness and Phenotype Phase Plane AnalysisBIE 5500/6500Utah State University Constraint-based Metabolic Reconstructions & Analysis Phenotype Phase Plane Analysis Example (XI) (Robustness Analysis setting Glucose = -2.5 mmol/gDW-hr) Phase 1 Phase 2 Phase 3 Phase 4 Phase There is a different phenotype for each phase region Given: Glucose = -2.5 mmol/gDW-hr Phase Boundaries Robustness Analysis LO Glucose Shadow Prices

© 2015 H. Scott Hinton Lesson: Robustness and Phenotype Phase Plane AnalysisBIE 5500/6500Utah State University Constraint-based Metabolic Reconstructions & Analysis Phenotype Phase Plane Analysis Example (XII) (Robustness Analysis setting Glucose = -5 mmol/gDW-hr) There is a different phenotype for each phase region Given: Glucose = -5 mmol/gDW-hr Phase Boundaries Robustness Analysis LO Phase 1 Phase 2 Phase 3 Phase 4 Phase LO Glucose Shadow Prices

© 2015 H. Scott Hinton Lesson: Robustness and Phenotype Phase Plane AnalysisBIE 5500/6500Utah State University Constraint-based Metabolic Reconstructions & Analysis Phenotype Phase Plane Analysis Example (XIII) Variables: EX_o2(e) & EX_glc(e) Phase 1 Phase 3 Phase 2 Phase 4 Phase 5 No growth; not enough glucose Growth is limited by excess oxygen; not enough glucose to reduce all the oxygen and produce biomass optimally Not enough oxygen to fully oxidize glucose; acetate produced through fermentation Not enough oxygen to fully oxidize glucose; acetate and formate are produced and secreted Not enough oxygen to fully oxidize glucose; acetate, formate and ethanol are produced and secreted. Line of Optimality (LO) AerobicGlucoseBioMassPPP.m

© 2015 H. Scott Hinton Lesson: Robustness and Phenotype Phase Plane AnalysisBIE 5500/6500Utah State University Constraint-based Metabolic Reconstructions & Analysis Adaptive Laboratory Evolution A phenotypic phase plane is a representation of how two fluxes in a metabolic network relate to each other and affect in silico-predicted optimal growth. Distinct planes are represented by several colors. Here, the line of optimality (LO, yellow) defines the ratio of glycerol uptake rate to oxygen uptake rate (OUR) that leads to optimal biomass production. On glycerol, wild-type E. coli initially has a phenotype that maps to a suboptimal region of the portrait. After a growing for several hundred generations on glycerol, the E. coli phenotype migrates to the line of optimality. (Conrad, T. M., N. E. Lewis, et al. (2011). "Microbial laboratory evolution in the era of genome-scale science." Molecular Systems Biology 7: 509.)

© 2015 H. Scott Hinton Lesson: Robustness and Phenotype Phase Plane AnalysisBIE 5500/6500Utah State University Constraint-based Metabolic Reconstructions & Analysis Lesson Outline Robustness Analysis Shadow Prices Reduced Costs Phenotype Phase Plane Analysis

© 2015 H. Scott Hinton Lesson: Robustness and Phenotype Phase Plane AnalysisBIE 5500/6500Utah State University Constraint-based Metabolic Reconstructions & Analysis Extra Slides

© 2015 H. Scott Hinton Lesson: Robustness and Phenotype Phase Plane AnalysisBIE 5500/6500Utah State University Constraint-based Metabolic Reconstructions & Analysis Phenotype Phase Plane Analysis Example (III) EX_glc(e) = -1 mmol/g DW-hr Phase 1 EX_glc(e) Ferm TCA PPP Glyc Ana OxP No growth; not enough glucose EX_glc(e) = -3 mmol/g DW-hr Phase 2 EX_glc(e) Ferm TCA PPP Glyc Ana OxP Growth is limited by excess oxygen; not enough glucose to reduce all the oxygen and produce biomass optimally

© 2015 H. Scott Hinton Lesson: Robustness and Phenotype Phase Plane AnalysisBIE 5500/6500Utah State University Constraint-based Metabolic Reconstructions & Analysis Phenotype Phase Plane Analysis Example (IV) Phase 3 EX_glc(e) = -5 mmol/g DW-hr EX_glc(e) Ferm TCA PPP Glyc Ana OxP Not enough oxygen to fully oxidize glucose; acetate produced through fermentation Phase 4 EX_glc(e) = -10 mmol/g DW-hr EX_glc(e) Ferm TCA PPP Glyc Ana OxP Not enough oxygen to fully oxidize glucose; acetate and formate are produced and secreted

© 2015 H. Scott Hinton Lesson: Robustness and Phenotype Phase Plane AnalysisBIE 5500/6500Utah State University Constraint-based Metabolic Reconstructions & Analysis Phenotype Phase Plane Analysis Example (V) Phase 5 EX_glc(e) = -19 mmol/g DW-hr EX_glc(e) Ferm TCA PPP Glyc Ana OxP Not enough oxygen to fully oxidize glucose; acetate, formate and ethanol are produced and secreted.